Design of Welded Structures

BY

rner

ES F. LIMGOLN ARC WELDING FOUNDATION CLEVELAND OHIO

Published as a Seroice to Education

by

S F. LINCOLN ARC WELDING FOUN

First Printing 5,000 June 1966 Second Printing 10,000 November 1966 Third Printing 15,000 August 1967 Fourth Printing 15,000 July 1968 Fifth Printing 10,000 May 1972 Sixth Printing 10,000 February 1974 Seventh Printing 10,000 October 1975 Eighth Printing 10,000 July 1976

Special acknowledgment is herewith made to

Watson N. Nordquist

who has contributed much to the editing a d organization of the material from which this manual has been prepared

rustees of the Foundation:

E. E. Dreese, Chairman; The Ohio State University, Columbus, Ohio

T. V. Koykka, Partner, Arter and Haddcn, Cleveland, Ohio

R. C. Palmer, Vice President, Central National Bank, Cleveland, Ohio

fficerr:

Secretary-Richard S. Sabo, Cleveland, Ohio

Price:

in U.S.A. (Postage included)

Ocerseas and Quantity Prices Upon Request

FB-37

Library of Congress Catalog Card Alumbe?: 66-23123

Printed in U.S.A.

Permission to reprodnce any material contained herein will be granted upon request, providcd proper credit is given to The James F. Lincoln Arc Welding Foundation, P. 0. Box 3035, Cleveland, Ohio, 44117.

Copyright 1966 by The James F. Lincoln Arc Welding Foundation

WELDED STRUCTURAL CONNECTIONS have long been used in the coristrnction of buildings, bridges, and other strnctures. Tho first \\&led buildings were erectcd in the '20s-the greatest application being in low-level buildings of many types. The American Welding Society first puhlislxd specifications for welded bridges in 1936. Hut earl!. progress came slowly.

During that ycar, 1936, The Jalncs F. Lincoln Arc Welding Foundation was created by The Linwln Electric Company to help advance the progress in welded dcsign and construction. Through its award programs and educational activities, the Foundation providcd an exchange of experience and gave impehls to the growing application of welding.

Thus, within the last decadc and particularly the past few years, unitized welded design llas become widely accepted for high-rise buildings and bridges of nobler proportions in addition to the broad base of more modest structures.

Now, the Foundation publishes this manna1 for fi~rther guidance and cl~allenge to architects, strtrctural engineers, fabricators and contractors who will build the structures of tomorrow . . . and to the educators who will prepare young people for thest: professions. This material represents an interpretation of the best in accumulated esperiencc of all w11o have participated in prior Foundation activities. The autlior has coordinated this \vith a continuing study of current welding research conducted hoth in the United States and Eumpe, and against a background of participation on various code-writing cominittees. Much of the direct instructional information that resulted has been pretested in over 70 structural seminars attended by over 4000 engineers.

Tho prodnction of this manual has spanned several years during \&ch constant effort \vas made to eliminate errors. The author will appreciate having callcd to his attentiorr any errors that have escaped his attention and inliitcs corrr~~pcmdei~ce on subjects about which the reader may have questions. Neither the author nor the pblisher , howover, can assume responsibility for the results of designers using values and forniulas contained in the manual since so many variables affect every design.

The Jomer F. Lincoln Arc Welding Foundation

June 1966

ITS

The author and the publisher firatefully acl<nowledge the organi- zations and individuals who h a w contributed photographs or other ihstrativo material:

Allied Stcrl Corporation Nathan N. Hoffman Allison Steel Mfg. Co. HoyIc, Doran & B e q Allison Structural Steel Co. Inland Steel Company American Bridge Division, Jackson & hloreland Division,

U.S. Steel Corporation United Engineers and Conshxctors, Inc. .4merican Institute of Steel Constmction Kaiser Steel Corp. American Iron & Steel Institute Kansas City Stn~ctural Steel Co. American Welding Society Felix hl. Krans, Consulting Engineer Barb~r-Magee 8 Hoffman 1.rhigh Construction Company John F. Beasley Constmction Co. Lehigh University, Fritz Enginecsing Laboratmy Bethlehem Fabricating Co. Robert Charles Lesser, Architect Bethlehem Steel Corporation R. C. Mahon Company J. G. Bouwkamp P. H. Mvllog Co. Bnrklrardt Steel Company McGaw-Hill Book Co. The California Co. Midwest Steel & Iron Works California State Division of Highways Xelson Shld Welding Division, Canadian Wuirling Magazine Gregory Industries, Inc. J. A. Cappuccilli, .4rchitect New England Construction Magazine Columi Resellrch Council Pacific Car 8 Foundry Co. Connecticut Statc Highway Dept. Pacific lron and Steel Corporation Ihwidd io Constmction Company Phillips-Carter-Osbom, Inc. - uominion Brrdge Company, Ltd. Pittsburgh-Des Mo~nes Steei Co. Dominion Structural Steel Co., Ltd. H. Platt Company B. M. Domblatt 8 Associates, Inc. Port 01 New Yo& Authority Dreier Structural Steel Co. Product Engineering Magazine Edmundson, KochendotlEer S. Kennedy H q i i b l i ~ Sled Corporation Enginecring News-Record Joseph T. Ryerson 8 Sons, Inc. Englert Engineering Company Van Renssrlser P. Saxe, Engineer Flint Steel Corporation Schact Steel Construction, Inc. Frankel Stecl Company Steel Joist Instihrte General Electric Company, Tonnessec Gas Pipeline Co.

In~iwtrial Heating Dcpt. United States Stccl Corporation David R. Graham & Asswiates I'eimont Stnictural Steel Ca. Granco Steel Products Co. Paul Weidlinger, Consulting Engineers Harley, Ellington, Cuwin 8 Stirton, Inc. Welding Engineer Magazine I iavmdusch Co. Welding Reseavch Co~mcil Horzberg & Associates West Coast Stccl Works Hewitt-Robins, Inc. hlinom Yamasaki-Smith, Hinchman & Grylls

In certain sobjeot areas, the author hns made adaptations of work done by cailier investigators, to wit:

Friedrich Bleich S. Timoshenko "Buckling Strength of Metal Stru~tures" "Theory of Elasticity" hlcCraw-Hill Book Co., New York, N. Y1 McGraw-Hi11 Book Co., New York, N. Y. Raymond Roark S. Timoshcnko and S. Woinowsky Krieger "Formulas for Strcss and Strain" "Theory of Platcs and Shells" McGraw-IiiIl Book Co., Sew Yor11, N. Y. McCraw-Hill Book Co., New York, N. Y.

F. K. Shanley S. Timoshenko and James Gerc 'Strcn@h of Materials" "Theory of Elastic Stability" McCraw-Hill Dook Co., New York, N. Y. .McCTrawHill Book Co., New York, N. Y.

The publisher regrets any omissions from this list, and would apprwiate being advised about them so that tho records can be corrected.

G FOUNDATION

Mctcils und How to Weld Thcm. This dnal purpose texthook and reference manual cle;irly describes thc internal strnctnrc of metals and its relation to ri~eehanical end physical properties and weldnbility. The book thoroughly disc~~sses the metai1nrgic:rl aspects of welding various metals used in Indnstry. drscrihing welding processes and procedures that are applicable in each case. 400 pages, 195 illustrations. $2.00 U.S.A., postpaid.

Modern Wcldcd Strz~cttrrcs. Vol. I. h behind-the-scenes look at how 83 notcd arcliitrcts, enginwrs :md drsignars chose welded design to economically improvc the fmiction and aesthetic appeal of varied strnctures. -4dapted from outstanding papers submitted in the 1962 Awards Program for Progress in the Desigri of Arc Welded Stmcturcs sponsored by The James F. Lincoin -4re Welding Foundation. Each study relates the ilesign problem, then tells and explains the soli~tion found with arc-wclded steol. 150 pngcs, 335 illilstrations. 52.00 U.S.A., postpaid.

Modem IYoldetE Structtjrcs, Vol. 11. Welded design aspccts of 64 excit- ing projects developed by sonic of thc ~quntry's leading architects and engineers are described in this book. These men tell you in their own w-ords how they approached the dcsign problem and solved it; how they applied the latest concepts and techniques in arc-a&ed design :ind construction to improve function, add beauty, lower costs. Studies are adaptcd from the best entries in 'Ilx janies F. Lincoln Arc Welding Foundation's 1964 Awards Program for Progress in the Design of .4rc Viield~d Structures. 280 pages, 335 illustrations. $2.50 U.S.A., postpaid.

Design of Wcldmenfs. Anthoriiative combined textbook and reference manual describes in detail many desig~i techniques for creating macl3in- cry &signs in arc-\vt:ided steel. h41ieh of this material riot available elsen~here. Thcoreticnl analysis and prohlen~-solution examples explain how to &sign machiiicry comporlcnts for manufacturing economies and improvement of product performance. 464 pages, 823 illustrations, nomograpi~s and charts. $5.00 U.S.A., postpaid.

Overseas and Quuntity Prices Avoiluble Uy~on Request

The James F. Lincoln Arc Welding Foundation P. 0. Box 3035, Cleveland, Ohio, 44117

Introduction to Welded Construction 1 .1 Part One

Part Two

ANALYSIS

Analysis of Compression 3.1 Design of Compression Members 3.2 Part Three Column Bases 3.3 fdumn Splices 3 4 COLUMN-RELATED

~earing-Pin Connections 3.5 DESIGN

Designing Built-Up Columns 3.6

Part Four

Part Five

ELDED-CON N ECTI ESIGN

Part Six

DESIGN

Part Seven

JOINT DESIGN AND PRODUCTION

Part Eight

EFERENCE DESIGN FORMULAS

h m rlkrgrruns and Formulas 8.1 Yo& Membw Diagrams and formulas 8.2

n = angular acceleration (radians/sec/sec); included angle of beam cwvature (degrees); form +actor

A = perpendici~lar deflection (in.), bending (A*) or shear (As)

E = unit strain, elongation or emtraction (in./in.) c, = unit shear strain (in./in.) v = Poisson's ratio (steel = 0.3 usually); unit

shear force o = leg size of fillet weld (in.); rate of angular

motion about an axis (radians/sec) + = unit angular twist (radians/linear inch); included angle; angle of rotation

E = sum u = nonnd stress, tensile or compressive (psi);

strength (psi) ub = bending stress (psi) u? = yield strength (psi) T = shear stress (psi); shear strength ((pi) 0 =, anglc of twist (radians; I radian = 57.3 d e

gets); angle of rotation (radians); slope of tapered girder; any speckled angle

a = area of section beyond plane where stress is desired or applied (in.'); langtb of plate (in.); ncceleration or docelmation (ft/min, ft/sec); clear distance between transverse stiffeners of girder (in.)

b = width of section (in. ); distance of area's cen tcr of gravity to reference axis ( in .)

c = distance from neutral axis to extreme Fibex (in.); distance of elastic center from reference axis

d = depth of section (in. ) ; moment arm of force (in.); distance (in.); distance betwcen centers of gravily of girder flanges ( i l l . )

d, = clear distanm: between girder flanges (in.) e = eccentricity of applied load (in.); total axial

strain (in.); moment arm of force (in.); d- fective width (in.); length of Tee section. in open-web girder (in.)

f = force per linear inch of weld (lbs/in. ) ; horizontal shear force (lbs/in.); (vectorial) resultant force (lbs/in.); allowable strength of weld (lbs/in.)

f,' = mmpressiw strmrgth of concrete ( p i ) g = accelrration of gravity (386,4"/seG) h = height; height of i d ; distance oi expansion

on open-web girder (in.) k = any specified mnstnnt or amplification factor

m = mass; statical moment of transformed concrete (composite mnstmction)

n = distance of section's neutral axis from reference axis (in.); mmber of mits in scrics

p -- internal pressure (psi) q = allowable force on shcar connector r = radius (in. ); radius of gyration s == length of curved beam segment (in. ); clear

distance betwecu ends of increments of weld (in.)

t -- thickness of scrtim (in.); time (min.); time interval (sec)

u = material's tensile rnodulus of resilience (in..lb/in!)

u, .= material 's ul t imate cnergy resis tance (in.-Ib/in.*)

w = uniformly distributed load (Ibs/linear inch) x = length of moment arm (cuned beam) y == distance of area's center of gravity to neutral

axis of entir? se~.tion (in.)

A = arrm (in.'); Iota1 area of cross-section C r= stiffness factor used in moment distribution;

any specified constant E = modulus of elasticity, tension (psi); arc volt-

age (volts) E, .-- modulus of elslsticity in shear (psi) Ek =r tangential modulus of elasticity (psi) El, =r l<inetic energy E, = potential cncrgy F -- total force (Ibs); radial force (Ibs) I = moment of inertia ( h 4 ) ; welding current

(amps) J u polar momtmt of incrtia (in?); heat input

( joulcs/in. or watt-sec/in.) K -- ratio of minimum to maximum load (fatigue,;

ratio of web doptl~ to wkb thichness; distance from outer face of beam flange to web toe of fillet (in. ); thermal conductivity; any specified constant

L =. length of mcmber ( i n 01. ft. ); span between supports (iu.)

L, = effpctive length of column M = bending moment (in.-lbs)

M, -- applied bending momcnt (in.-lbs) M, = plastic moment at connection (in-lbs)

N = numbrr of service cyclcs; minimum bearing Imgth of beam on scat (in.)

P = conceiitrated load (Ibs) Q = shear centw; statical moment of cover plate

area about neutral axis of cowr-plated beam section

R = reattion (11,s); torsiu~ral resistance of member (in."; weld cooling rate ("F/scc)

S : section modulus ( i d ) = I/c T = torque or twisting momcnt ( iwlbs) ; tem-

perature ('F) U = stored energy V := vertical shear load (lbs); shear reaction;

velocity; vnlume; arc s p e ~ d (in./min) W = total load (lbs); weight (Ibs); total width

(in.) Y =- effective bearing length on base plate (in.) Z :=- plastic section modulus ( h 3 )

C.G. = cmtcr of gravity HP = horsepower

N.A. = ncut r~ l axis RPM = revolutions per minute

1. WELDING'S IMPORTANCE TO STRUCTURAL FIELD

Welding has been an important factor in our economy. The progressmade in welding equipment and elec- t rode , the advancing art and science of designing for welding, and the growth in trust and acceptance of welding havo combined to make welding a powerful implemcnt for an espanding constrnction industry.

More and more buildings and bridges are being built according to the precepts of good welded design. The economies inherent in welding are helping to offset evolutionary incrcases in the prices of materials and cost of labor. In addition, the shortend production cycles, made possible by wclding, have helped cffect a quickening in the pace of new construction.

Welded constrnction has paid off handsomely for many architects, structural engineers, contractors, and thcir client-customers. It will become increasingly important as more people acqnirc a greater depth of knowledge and experience with it.

2. RECOGNITION OF WELDING

The widespread recognition of welding as a safe mcans of making structural connections has come about only after years of diligent effort, pioneering action by the more progressive enginaers and buildcrs, and heavy documentation of research findings and successes attained.

Today, thcre just arcn't marly rncn in industry who speak disparagingly of welding. Most regnlatory agen- cies of local and federal government now acccpt welded joints which moet thr reqnirements imposed by codewriting bodies such as the American Institiitc of Steel Construction and the Arneri~in Welding Society.

With this acceptarrcr. there rcmains however a considerable task of education and simple dissemin:ition of inionnation to achieve maximum efficiency in the application of welded design. And, there is even a continning need for more thorough understanding of welding by codewriting bodies who fail to use the full streugth of welded joints.

ELDED CONSTRUCTION?

There are ninny reasons for using welded design and constrnction, hut probably the two basic ones are 1) welded design offcrs the opportnnity to i~cliieue more efficient nse of inateriais, and 2 ) thc speed of fabrication and erection can holp compress production sclied- nles, enabling the entire industry to he more sensitive and react faster to rapidly shifting market needs.

Freedom of Design

Welding pem~its the architect and structurd engineer complete freedom of design-freedorn to dcvclop and use modem economical design principles, freedom to

FIG. 1 Indicative of the design freedom offered by unitized welding design, the Yale Rare Book Library's four outside walls are each a 5-story high Vierendeel truss. Each is a network of Greek-type crosses. The structure is all welded-shop and field.

employ the most elementary or most daring concepts of form, proportion and balance to satisfy the need for greater aesthetic value. Just about anything the designer may envision can ~ i o w be given reality . . . bcca~ise of welding.

Welded constmction imposes no restrictions on tlie thinking of the designer. Already, this has resulted in wide usage of such outstanding design advancements as open-web expandc~l beams and girders, tapered beams and girders, Vierendcel trusses, cellular floor construction, orthotropic bridge decks, composite floor constrrrction, and tubular columns and trusses.

eld Metal Superior to Base Meta l

A welded joint basically is one-piece construction. All of the other methods of connecting members are mechanical lap joints. A properly welded joint is stronger than the ma t<~ ia l joined. The fused joints create a rigid structure in contrast to the nonrigid structure made with rncchanical joints. The compact- ness and calculable degree of greater rigidity permits design assumptions to be realized more accurately. Welded joints are better for fatigue loads, impact loads, and severe vibration.

Welding Saves Weight, Cuts Costs

Connecting steel plates are reduced or eliminated since they often are not required. Welded connections save steel because no dedw;tions need he made for holes in the plate: the gross section is effective in carrying loads. They offer the best method of making rigid

connections, resdting in reduced beam depth and weight.

This reduced beam depth can noticeably lower the overall height of a building. The weight uf the structure and therefore static loatling is greatly reduced. This saves column steel, walls and partitions, facia, and reduced foundation requirements.

Welded connections are well suited to the new field of plastic design, resrllting in further appreciable weight savings ovcr conventional rigid frame design.

Savings in transportation, handling time, and erection are proportional to the weight savings.

Available Standards

Arc welding, either in the shop or in the field, has been used long enough to have bcen proved tlioroughly dependable. The AWS and AISC have set up dependable standards for all phases of strnctural activity. These standards are hacked I I ~ by years of research and a c t d testing. They simplify the design of welded connections and facilitate acceptance by purchasers and inspectors.

Other Advantages

Less time is required on detailing, layout and fahrica- tion since fewer pieces are used. Punching or drilling, and reaming or countersinking are eliminated-a snh- stantid saving on large projects.

The typical welded joint produces a smooth, un- cluttered connection that can be left exposed, without detracting from the appearance of the structure. Welded

FIG. 2 The athletic unit of Ladue Jr. High School (Missouri) features an all-welded steel lamella roof frame spanning 252', expressing the strength of one-piece welded construction.

introduction t a eided Construct ion / 1.1-3

joints exhibit less corrosion and require little or 110

maintenance. The smooth wcldeil joints also make it easier to install masonry, facia and other close iitting members, often reducing tire thickness of walls or floors in buildings.

Structnrcs can be erected in rclativo silence, a definite asst,t in lxiilding in tlouiiliown art2ns, near office b~iildings or hospitals.

4. HOW GOOD I S A WELD?

Many engineers are unaware of the great reserve of strength that welds have, ;ind in many cases this is not recognized by code bodies.

Notice in Table 1 that the minimum yield strengtl~s of the ordinmy E6Oxx electrodes are about 50% higher than the corresponding values of the A7, A373 and A36 structural steels with which they would be used.

e n d Steels

Moterial Minimum I Yield Strength

AWS A5.1 &

ASTM A233

Weld

Metoi ioi welded)

ASTM S t e i s

Minimum Tensile Strength

62,000 psi 67,000 62,000 62,000 72,000

60.000 to 75,000 58,000 to 75,000

58,000 to 80,000 63.000

67,000 70.000

Many of the commercial Ef3Oxu electrodes also meet E70xs specifications. Used on the same A7, A373 and A36 steals, they have about 75% higher yield strength than the steel.

There are numerous reasons why weld metal has higher strength than the corresporiding plate. The two most important 'we:

1. Thc core wire wed in the electrode is of pre- mium steel, held to closer specifications than the plate.

2. There is complete shielding of the molten metal during welding. This, plus the scavenging and deoxidiz- ing agents and other ingredients in the electrode coating, produces ;I uniformity of crystal strncture and physical pmpertirs on a p:x with electric furnace steel.

Recamse of tllesc, propt:rly deposited welds have a tremendous rcservc of strength or factor of safety, far beyond wliat irrdnstry specifications iisually recognize. Rut cven witliout a reduced safety factor, there is a considerabic cost :idvantage.

inspection and Qual i fy

hlnch money is spcnt :ninoally by industry and goverm merit in obt;iining a i d inspecting for a specified weld q~xdity. Usually tlic weld quality specifiod is obtained, bxt too often the quality specified has little or no relation to sorvice requirements.

Welds that meet the ;rcti~al scrvice requirements, at thc least possible cost, are the result of-

1) proper design of connections and joints, 2) good welding procedure, 3 ) good weldor technique and workmanship, 2111d 1) intelligent, responsible inspection. In the follo\ving exnmpl(s (Figures 3, 4, 5 :md 6 )

test specimens exhibit undercut; ondrrsize, lack of fusion, and porosity. In spite of tlic:se adverse conditions,

REDUCTION iM PLATE SiLTioN (iN PERCCNT)

7.6 % q6% /5%

FIG. 3 Test samples prepared to show effect of undercut. Samples were pulled in tension under a stotic Iood; in al l cases foilure occurred in the plate ond not in the weld.

FIG. 4 One rule of thumb says fillet size should equal

3/q plote thickness to develop full plate strength. Using this method, a 3/8" fillet weld on fi" plate should "beat the plate". But so did 11/32" and 5/16" fillets. Not until fillet size was reduced to G'' did weld foilure occur . . . at a stress of 12,300 Ibs/lineor in., more than 5 times the AWS allowable.

1.1-4 / In t roduct ion

considered individually, the weld imclcr steady tensile load was found to be stronger than the plate. Thcsc examples are not neari it to show that the standard of w-eld quality should Be lowered. However, they are striking evidence of how easy it is to make full-strength welds, welds stronger than the plate.

Welding is the only process that prodt~ces a unitized, or one-piece, construction. The welded plate is so sound, strong, and ductile as to permit somc trsting procedures that froq~ently are impossible or impractical to perform \ritli other conr~ection methods.

The weld is so duvtile that it can bc readily bent

FIG. 5 Weld somples were mode, with varying degrees of lack of fusion, 0s reduced-section tensile specimens. Welds were mochined flush before testing, ond weld failure did no? occur until the un- penetroted throo? dimension hod reached 31% of the total ioint throat.

around a sniall radius. Figure 7. Apparently because it is possible to do so, bend tests are often reqnircd. Unfortunately, il-bend tcst results do not correlate wcll with actual service performance,

Reca~ise it is possible to examine a welded joint by radiographic inspection, some engineers feel this must be done.

Most radiographic inspection is based on responsible standards. These specifications assure the quality reqnircd, yet are realistic. Frequenly, however, local decisions arc made to require more perfect radiographic soundness than the specifications demand.

ALL W E L D S MACHINED FLUS#

-

FIG. 6 Excessive porosity (weld 1) os shown by rodiogroph did not weaken the joint. Weld 2 shows perfect. In both canes the weld wos stronger than the plofe. Specimens broke in the plate o t opproxi- mately 60,100 psi.

l n t r o d u c ~ i o n t o e lded C o ~ s t r u c t i o n / 1.1-5

H o w lmportont i s Porosity?

Normally, porosity if it should cxist is not a problem, because each void is spherical. It does not represent a notch. Even with a slight loss in section because of the void, its spherical shape allows a smooth flow of stress around the void without any measurable loss in strength.

Tests have shown that a weld can contain a large amount of porosity without materially changing the tensile or impact strength and ductility of the weld. This porosity cwuld amount in total volume to a void equal to 7% of the weld's cross-section without impair- ing the joint's performance.

The ASME Boiler and Pressure Vessel Code, Sec- tion VIIS and X, will allow porosity in a weld to the extent shown on charts incorporated into the Code. These charts consider size, distribution, and alignment of voids, versus plate thickness.

The AWS Building Code will allow a slight porosity if well dispersed in the weld. This is defined as "gas pockets and any similar generally globular type voids."

The AWS Bridge Specification allows some porosity. For porosity above Xt;" in void size, a table shows minimum clearance between voids and maximum size of void for any given plate thiclaess.

5. DESIGN FOR WELDING

A designer must know the fundamental differences bctween welding and other assembly methods if he is to detail economical welded members. If a welded girder,

FIG. 7 Weld mefol in we l l -des igned joints d e m o n s t r a t e m u c h g r e a t e r duc t i l i t y t h a n would be required in any type of structures.

for example, were constructed with multiple cover plates, the cost would be excessive. The use of only one flange plate with a reasonable number of butt welded splices, at points where the plate thickness can be reduced, is usually adequate and also gives improved fatigue resistance.

The selection of a connecting system should be made at the design level; for some types of structures, may even influence the architectural concept itself.

FIG. 8 Many contemporory structures are using exposed steel framing as part of the ortistic scheme. Welding provides the unencumbered simplicity of form essential to the modern look in architecture, typified in this showcase building.

The most efficient t~sc of steel is achieved with w l d e d design, the adva~~tages of whicl~ grow with the sizc of the structure. In fact, the full advantages of using steel in competition with other materials will only he realized whm the structure is erected as a welded design, and when fabricators and erectors use modern techniques of welding, production scheduling, and materials handling.

A welded office building in Dallas, Texas, is an example of the rxxmomies possible in structural welding. The building is 413 feet high, has 34 floors, and contains 600,000 square feet of usable floor space. The savings are impressive. The contractor states that by

FIG. 9 Welded connectior~s contributed to sofer and more economical erection of the stately 33-story Hartford Building in Son Francisco, California's tallest skyscraper. Semi-automatic welding, using self-shielding cored electrode, speeded completion of 80 beam-to-column connections per floor.

designing for welding he saved 650 tons of steel. Com- parison estimates show an additional saving of approximately $16.00 per ton in fabrication and erection. Futhermore, approxin~ately six months in construction time will be saved as a result of using a welded steel frame.

Comparative experience has proved that had this type structure involved welded connections that were simply converted from another type of connection, there still would have been savings hut substantially less than when designing specifically for welding.

6. WELDED DESIGN OF BUILDINGS

The taller that buildings grow, tho greater the role of welding. This applies to the shop fabrication of columns and other structurals, and also to the field welding associated with erection.

A majority of the more recently built skyscrapers are of welded design. These arc found in all sections of the country, including eartliquake-prone San Fran- cisco.

Expanded open-web hcams and girders-fabricated from standard rolled beams-are providing great savings in both bridge and huilding design. An open- web girder dcsigned to have the required momcnt 05 inertia will result in a weight saving as high as 50%. In mnlti-story buildings, where utility supply lincs can be nui through these beams and girders rather than suspended below, the overall building height is substantially shortened. This results in significant savings in material costs-for columns, facia, stairs, etc.

Tlra ease with which tapered beams a ~ i d girders can be fabricated from standard rolled hcams permits an endless variety of savings in building design. Tap- ered spandrel beams are often made deep enough at the column end to reduce the bending force and dim-

- inate need for column stiffeners. The spandrel beam is shop welded to the column for lowest cost and shipped to the site.

Special built-up columns can be used to obtain open, column-free interiors, to inonnt facia economically, to provide the steel-and-glass look whiclr dominates today's downtown and industrial park arch- tccture.

The new look in building design-especially research centers, office buildings, libraries a ~ i d museum --calls for a heavy use of exposed stecls, including the corrosion-resistant steels such as ASTM A242. The clean trim lines which are demand~d wit11 this use of exposed steel can be acliievcd only by welding.

Light, airy roof supporting space frames-tl~rea- ili~nensiorial truss systems-arc being shop-fabricated in sections, final assrmhled on the ground at thc, site and liftcd into plxcc. Welding facilitates the use of

Introduction to elded Construction / 1.1-7

srich drxsigns, since there is a lack of estraneom matcrial in the multiplicity of coimections as would be the ulsc with any other means of assembly.

Plastic dr:sign does not use the conventional allowable stresses, but rather the calculated ultimate load- carrying capacity of the striicturc. In the case of rigid framing, plastic design rcquires less engineering time than docs conventional elastic dcsign and, in most cases, rcsirlts in sigriificant savings in steel over the use of elastic design. Welding is the most practical method of making connections for plastic design. This is becaiise the conrrection must allow the members to reach their full plastic moments with srifficicnt strcngtli. adequate rotational ability, and proper stiflness.

ELDED C O N S T R U C T I O N O F B R I

Today bridges of every type-suspension, arch, truss, plate and hox girder, etc.-are constrncted of steel because of strength, dependability. and permalielice. Be- cause tlierc are no limitations placcd on welding, the bridge engine~m is not limited or restricted in his thinking. Due to this new freedom of design effected by welding, some rather unusual and nnique bridges have ap&)eared in recent years.

The State of Connc:dicut has favored welding design for its high:hwa)- h1idgr.s for over 20 years. T l ~ e Turnpike has 28 all-welded bridges, thc largest of which is the 24-span. 2661-foot Miam~s River Bridge: at Greenwich. The esperierrce of thc States of Connecticut. New York, Texas, California and Kansas has clearly show11 that substantial savings are possible in properly designed welded bridges.

Bridge girders of variable depth enhancta the! appcaronce of the strlicture, while placing the metal where needed ;~nd takiug i t away wherc shallower section dcpth is pcrn~issibk-thereby saving toris of steel.

.!I '300' 1m1g weldcd hridge spanning tlrc tr;lcks of the Erie Railroad or1 the: Ncw I'ork ThrnwaY had to be shaped to meet sitc rrquirerncnts. Tilt. Thrti\va); at this point is on both n vrrtical grxd(~ wid a 11orizont;rl curve, r n i r i g srrperr1~:v;ition. It is rstirr~ated that morr-Bexiblr: \vcldrd design also dew-loped ;t 50% savings in thc weight of steel.

In both building arid trridgo construction, tire developmc~nt of wcldcd sh tw coiincctors and sp~,cial- izccl welding equipmmt for attactiiog such coiincctors has ;iccclcr;ited tlrc use of compositr floor constroction -ud~ere th? concrete m~cl stwl act to get lit:^ wit11 a strength greater tkitirr either compont:nt. resulting in large savings.

Orthotn>pic bridgr, design, long accepted in Eli- rope:, is coming into pnminencc i l l Amrrica as a major approach to reduction of bridge costs. This coucmpt calls

FIG. 10 Large bridge sections are shop-fobricoted, shipped to the site, and lifted into position. This lowers erection costs ond compresses the project tirnetoble.

for tlrt, romplctc deck to act as a nnit. Olihotropic dcsign could not he rxecr~ted without welding.

8. W E L D E D C O N S T R U C T 1 0 STRUCTURES

\V&iing h;is f;wilit;itcd thr. design and construction of :t grrat mriety of strnctirres with the mntrmporary look. liven \v;itcr to\vcrs hiivc takm oir o bcauty that comple- nients adjncrrrt ar(.hitccturt,.

Stadiums for big-lc;igt~c sports clubs and for Eig- xunc collcgrs arta lmiring Ilcavily on wc~lding. Among tllcsc ar<, Shca Stndi~~m, l n n i r t h ' s w w liomc for the h g c l s , and othms. A v 1 ~ y iinirliic~ fcnturc of tllc modern stadium I-esultir~g from wddcd stwl dcsign is the C t i l l ~ i l t T ~ ~ < d roof whi~11 rlsmoVCS cO~ll1n11s as O ~ S ~ T U C - tio~is to slx3ctator vision mid plrastire.

Towers, space 11wdi~~s. h g c ridio t~ l~scop( . s , radar antcrmns, OK-sllorc drilling rigs, ore ~rriloadc~rs, and many other structurc~s are 11rir1g designed for welded constructio~~.

8 / Int roduct ion

9. REVOLUTION IN SHOP FABRlCATlON & ERECTION

Today's structure goes up quickly diie to welding. The trcnd is to build the structure on a sob-assembly basis, doing as much work as possible ui~der ideal shop conditions wbrre mass-production techniqries can be fully employed.

Tilt, progress made in I-ecent ycars in auton~atic and semi-automatic welding cqrripmrmt and in positionors and manipulators has made shop iahricotion of spccial girders, knees, and built-up colirlnns extremely attrac- tive. In many cases, tlw ingeirio~is disignt>r can make tremendous savings tl~roogh tlic design of special stnictirral members, This irrcludes members lraving complex cross-sectional coriGguration and hybrid mcmbers that are a mix of steels iraving different analyses.

Modern strnctui-nl fabricating shops have fixtures for assembling plates into colum~rs anti girders, manipulators for welding aotom:itically, ;md positioners for supporting ~nernhers so that att:icIring plates may bc welded in thc flat position.

Welding developments in the past few- ycars h a w greatly incrcased welding speeds, while assuring high quality welds. In sribmerged-arc welding the use of multiple arcs, will1 two and three, welding heads has

trmn~endor~sly increased welding sp~eds . Contintioris wire processes for semi-meclranized welding for both shop am1 field applications have substantially increasd prodoctivity.

Mtich progress has been made in automatic manip- r~lators, enabling the welding head to be p i t into proper aligninel~t with the joint of the membcr in a matter of scconds. This alignment is automatically maintainctl along the length of the joir~t during wclding. Thtrse manipulators represent :I major cost rcductioii pssi ldi ty. As the size of the struclurc increases, tlrc total arc time on a n.eldcd job becomcs a decreasingly smaller percentag<z oi the total fabricating time. Thus savings in handling tinre and increasing nramfact~iring cycle dficieilcy are thc major potc~ltinls for cost re- d uclion.

Semi-automatic field welding is spceding up ercction and lowering costs. Snbmrrged-arc has long hem ut id in the field for Rat welding. Recently the use of self-shirlding cored electrode wire, automatically fed, has greatly extended tht: speed and uniforrn quality ir~liere~it with semi-automatic welding. This process is rapidly winning gentmil ii~ceptance. It is not affected by rather scvere wiird and other adverse climatic conditions. I3otlr siibmcrgcd-arc and certain cored electrode pr-ocessczs arc cousidered low hydrogen.

WELDING METHOD ARC SPEED IN. /MIN.

STICK ELECTRODE ( E 7 0 2 8 ) 5%

SINGLE ARC SEMI-AUTOMATIC (SUB-ARC) 12 J

SINGLE ARC SEMI-AUTOMATIC (INNERSHIELD) I 2

SINGLE ARC AUTOMATIC (SUB-ARC ) 15

TWIN ARC AUTOMATIC (SUB-ARC 1 2 5

/ TANDEM ARC AUTOMATIC (SUB-ARC) 1 3 0 1

TANDEM AUTOMATICS (SUB -ARC) O 18 BOTH WELDS O AND @ SIMULTANEOUSLY = 3 6 IN, $12 FILLET/MIN. ) ( 2 . 3 6 )

TRIPLE TANDEM AUTOMATICS (SUB-ARC) O 2 5 BOTH WELDS AND @ 2.50

J -wuLTANEousw = 5 0 IN. '/2 FILLEI/M1N) : FIG. 1 1 Many fabricating shops have realized substantial savings through step up in selection of welding process and equipment. This chart shows numerous ways to make the %" fillet weld, which is common to many large structural members.

1. I M P O R T A N C E O F PROPERTIES

Pill ma!vri:ils have certain properties which must he kno\vn in order to promote their proper use. These proper tic,^ art. t.sscntia1 to srlcction of the best material for a given mcmlwr.*

111 tlit: design of structural nrcmbers, the properties nf materials which are of primary concern are those that indicatt. matorial behavior tunder certain types of load. Some property of matcrial is called for in each of the hasic desigri formi~las.

I'rolwrtics corninonly found in angineering handbooks and suppliers catalogs are these:

1. ultimate tmsilc strrngth 2. yield streiigtli in tension ?. elongation 4, modulus of elasticity 5. compressivc strength 6. shear strength 7. fatigue strength Otlier properties such as modulus of resilience and

ultimate energy resistance, may also bc given. Tables I and 2 present physical properties and

c;l~rmical composition of various stecls. These are pro-

-. - Also see "Metals and HOW to Weld Them" by T. B, Jefferson

;iod G. Woods; J a n r s F. Lincoln Arc Welding kmdation.

prictai-y stwls that are not pmvidcd for by the ASTM specifications for basic steels used in the strtlctural field. The specification steels are covered in Srctio~i 7.1 on the Selection of Structural Stcel.

FIG. i Tensile test specimen before ond after testing to failure, showing maximum elongation,

T A B L E 1-Properties a n d Composition of Construct ional A l loy Steels

I Yield Uif Nominol Composition. % Producer

I Alloy point, Strength, E l m g . , C Mn si Cu Mo C i Nl

~ l i 04 % Other

Jooei & Lovghlin Jolloy-5-90 Jalloy-S-100 Jalloy-S-1 10

Lukcnr Steel / i - 1 100.000 115,000 18 0.15 0.80 0.25 0.35 0.55 0.60 0.85 V .8

Republic Sfeel 1 Republic 65 I 70

Youngitown Sheet 65,000 95.000 20 0 12 0.60 0.30 1 .OO 1.80 a iube

I

--Table courtesy PRODUCT ENGINEERING Magazine

2.1-2 / Load & Stress Analysis

TABLE ?-Properties and Composition of Wigh-Strength Low Alloy Steels

Yield Ult. Nominal Composition, %

Al loy Point, Strength, Elong.. c M, si cu Ma Cr Ni Other

031 0 4 ?6 Producer

Alon Woad Steel

Arrnco Steel H igh Strength No, I 2

Bethiehein Steel Mayor; R Medium Mangoneae Manganese Vonadium

Crucible Steel of America

Colorado Fuel & Iron

Joltcn No. i 2 R

Koirer Steel Kniroloy No. I 2 -

Structural High Strength

Cor-Ten Lukenr Steel

Nat ional Steel IGreat Loker

steel ond Weirton Steel]

V ~ A ~ X High Mangoncie

Pittsburgh Steel

Republic Steel

'it, Ten No, i

US Steel

Youngstown Sheet & lube

'"Icy 'aioy A242 'oloy E HSX 'olay EHS 'oioy M-k 'oiay M ~ B '010~ 45W 'oloy 5 0 W

Properties of Materials / 2.1-3

FIG. 2 A tensile testing machine applies a pulling force on the test piece. The moximum load applied before failure of the piece, divided by the original cross-section, equals the material's ultimate tensile strength.

The various properties are hest defined by a description of what happens when a specimen of the material is subjected to load during laboratory tests.

2. TENSILE PROPERTIES

In a tensile test, the machined and ground specimen of the material is rnarked with a centcrpunch at two points 2" apart, as shown in Figure 1. The specimen is placed iu a tensile testing machine, and an axial load is applied to it by pulling the jaws ho ld i~g the ends of the specimen in opposing directions at a slow and constant ratc of speed, Figure 2.

As the pulling progresses, the specimen elongates at a nnifol-m rate which is proportionate to the rate at which the load or pulling force increases. The load

, , . I I I I I I I I

0 0.025 0.050 0.075 0100 4125 0150 0175 Q200 4225 Strain, in./in.

FIG. 3 A stress-strain diagram for mild steel, showing ultimate tensile strength and other properties. Here, the most critical portion of the curve is magnified.

divided by the cross-sectional area of the specimen within thr gage marks reprcsrnts the unit stress or resistance of the rnatcrial to the pulling or tensile force. This sfrcss (a) is expressed in pounds per square inch, psi. The rlongation of the specimen represents the strain ( E ) induced in the material and is expressed in inches pcr inch of length, in./in. Stress and strain are plotted in a diagram, shown in simplified form in Figun: 3.

The proportional relationship of load to elongation, or of stress to strain, continucs until a point is reached where the elongation begins to increase at a faster rate. This poiirt, beyond which the elongatior~ of the specimen no longer is proportional to the loading, is the proporlionol elastic limit of the material. When the load is removcd, the specimen returns to its original dimensions.

Hryond the clastic limit, further movmnent of the test machine j a w in opposing directions canses a permanent elongation or defor~nation of the specimen ~naterial. In the case of a l o w or mediurn-carbon steel, a point is roaehcd h e y o ~ ~ d which the metal stretches briefly withont an incrcase in load. This is the. yield point.

For lo\v- and n1cdinn-c3rhon steels. the nnit stress at the yirld point is considered to be the material's tensile yield strcnclh (a,).* For other metals, the yield strength is the stress required to strain the specimen by a specifled small amount l~eyond the clastic limit. For ordinary co~nmereial purposes, the elastic limit is assumed to coincide with the yield strength.

Beyond the material's elastic limit, continued pulling causes the specimen to neck down across its diameter or widtl~. This action is ;~ccompanied by a

- "'The symbols conimonly used for yield strength, ultimate strerigth, and a r i d strain do oat indicate the type of load.


further acceleration of the axial elongation, which is now largely confined within the relatively short necked- down section.

The pulling force eventually reaches a maximum value and then falls off rapidly, with Iittle additional elongation of the specimen before failure occurs. In failing, the specimm breaks in two within the necked- down portion. The maximum pulling load, expressed us a stress in psi of tlie original cross-sectional area of the specimen, is the material's ultimate tcnsile strength (a").

Duct i l i ty and Efasticity

The two halves of the specimen are then put together, and the distance bctween the two punch marks is measured (Fig. 1). The increase in length gives the clongation of the specirncn in 2", and is usually expressed as a percentage. The cross-section at point of failure is also measured to give the reduciion in area, - which is usually expressed as a perccntage. Both elongation perccntage and reduction of area percentage indicate the material's ductility.

In the design of most members, it is essential to keep the stresses resulting from loading within the elastic range. If the elastic limit (very close to the material's yield strength) is exceeded, permanent deformation takes place duc to plastic flow or slippage along molecular slip planes. When this happens, the material is strain-hardened and tbercafter has a higher effective elastic limit and higher yield strength.

Under the same amount of stress, some materials stretch less than others. The modulus of elasticity ( E ) of a material simplifies the comparison of its stiffness

Strain, in./in.

FIG. 4 Stress-strain curves for several materials show their relative elasticity. Only that portion of curve displaying a proportional relationship between stress and strain is diagrammed.

with that of another material. This property is the ratio of the stress to the strain within tile elastic range:

Stress a -- - Modulils of elasticity E Strain c

On a stress-strain diagram, the modulus of elasticity is represented visually by the straight portion of the curve where the stress is directly proportional to the strain. The steeper the ctlrve, the higher the modulus of elasticity and the stiffer the material (Fix, 4 ) .

Any steel has a modillus of elasticity in tension of approximately 301000,000 psi. AISC in their specifications still llse a rnore conservative value of 29,000,000 psi for the modulus of elasticity of steel. The modulus of elasticity will vary for other metals. Steel, however, has the highexst value of any commercially available metal used in the stri~ctural field.

M P R E S S l V E S T R E N G T H

The general design practice is to assume that the compressive streligth of a steel is equal to its teusile strength. This practice is also adhered to in some rigidity d~s ign ~dculations, where the modulus of elasticity of the m;lterial in tension is ilsrd even though the loading is compressive.

The actual ultimate comprcssiuc strength of steels may be sonrewhat greater than the ultimate tensile strength. Tlic variation in coniprcssive valnes is at least partially dependent on the condition of the steel: the compressive strength of an annealed steel is closer to its tensile strength than would be the case with a cold-worked steel. (There is less of a relationship between the cornpressive strength and the tensile strength of cast iron and non-ferrous metals.)

A compressive test is conducted similar to that ior tensile propcrtics, but a sllort specimen is subjected to a compressive load. That is, force is applied on the specimen from two directions in axial opposition. The i~ltimate compressive strength is reachcd when the specimen fails by crnshing.

A stress-strain diagram is developed during the test, and values are obtained for compressioe yield strcngth and other properties. IIowcver, instead of the Young's modrrlus of elasticity conventionally used, the tungential modulus of chsticity (E,) is usually obtained. This will be cliscussed in Section 3.1 on Com- pression.

Compression of long colurnns is more complex, since failure develops under the influcncc of a bending moment that increases as tlre deaection increases. Geometry of the member has much to do with its capacity to withstand cornpressive loads, and this will

Properties of Materials / 2.1-5

FIG. 5 Fatigue test results ore plotted on u-N diogrom; stress vs, number of cycles before failure.

be dise~~ssed more completely under Section 3.1. With long columrrs, the effect of eccentric loading

is more severe in the cast. of cornpression than tension.

4. SHEAR STRENGTH

There is no r(u)gnizetl standard method of t<,sting for shear streugth of a material. Forhlnately, pure shrar loads are seldom encountered in structural mcrn- bers but shear stnwes frequently develop as a by- prodnct of principal stresses or the application of transverse forcrs.

The ultimate shear strvngth is often obtained from an actual she:tring of the metal, usually in a punch-and- die setup using a ram moving slowly at a constant rate of speed. The rnzrxim~~m load requirtd to punch through the metal is obsrrvad, and ultimate shear strength is calculated from this.

Where it is not practical to physically determine it_ the ultimate shcnr strcngth ( r ) is generally assumed to be 3/4 the material's ultimate tensile strength for most strurh~ral steels.

5. FATIGUE STRENGT

When tho load on a rncrnber is constantly varying in value, is repeated at relatively high frtquency, or constitntes a co~nplete reversal of stresses with each operating cycle, thc materiai's fatigue strength must be substituted for the ultimate strength where called for by the design formulas.

linder high load values, the variable or fatiguc mode of loading n:(lnces the matcrial's effective ultimate strength as thc n11rr11)t~r of cyclos incrtwes. At a givcn high str'ss value, the material has a definite service life, <,xprt:ssed 21s "Pi" cycles of operation.

.4 series of idcntird specimens are tcsted, each

rlndcr a specific load value cxprrssible as a unit stress. Tlie w i t strcss is plottcd for each specimen against the number of cycles before failnre. The result is a u-N diagram (Fig. 5 ) .

The cnnlz~rnncr! limit (usually u,) is the niaximum stress to which the material can bc subjected for an indefinite service life. Although the standards vary lor variot~s types of m<mbrrs and different industries, it is a commo~i practice to acccpt the assumption that carrying a certain load for sevcral million cycles of stress reversals indicates that loud can be carried for an indefinite time.

Theoretically the load on tlw test specimens should be of the same natr~ro :is the load on the proposed nicmber, i.e. tcirsile, torsional. etc. (Fig. 6) .

Since the geometry of the mcmber, the presence of local areas of high s t r m concentration, and the condition of the material have considerable influence on the real fatigue strength. prototypes of the member or its section would give thr most reliable information as tast specimt:ns. Tiiis is not always practical however. Lacking ;illy test data or handbook values on endurance limit, see Section 2.0 on Fatigue.

6. IMPACT PR

Impuct sircngfl~ is the ability of a metal to absorb the energy of a load rapidly delivered onto the member. A metal may h a w good tznsile strength and good ductility under static loading, and yet break if subjected to a high-velocity blow.

The t u ~ most irnportant properties that indicate the material's resistance to impact loading are obtained from the stress-strain diagram (Fig. 7 ) . The first of these is the modulus of resilience ( u ) which is a measure of how well the material absorbs euergy providing it is not stresscd al)ove the elastic limit or yield

-- LEVER

TEST SPECIMEN TURNBWKLE

VARUBLE CCCEN

WILSON FATIGUE TESTING MACHINE

FIG. 6 Typical setup for fatigue testing undel pulsating axiol stresses.

2.1-6 / Lood & Stress Analysis

FIG. 7 in the stress-strain diogrom for impact, the elongation ot moment of ultimate stress is a factor in determining the toughness of the material in terms of ultimate energy resistonce.

point. It indicates the material's resistance to deformation from impact loading. (See Section 2.8 on Impact.)

The modulus of rrsilienct: (11) is the triangular area OAB under the stress-strain curve having its apex at the elastic limit. For practiczrlity let the yield strength ( u ) be the altitude of the right triangle and the resultant strain (ei) he the base. Thus,

where E = n~odulus of elasticity.

Since tht: absorption of energy is ;rctually a volu- metric property, the 11 in psi = 11 in in.-lbs/cu. in.

When impact loading oxceeds the rlastic limit (or yield strength) of the material, it calls for toughness in the material rather than rrsilicnce. Toughliess, the ability of the metal to resist fracture under impact loading, is indicated by its ultimatc energy resistance (u,). This is a measure of how well the material absorbs energy withont fracture.

The ultimate mergy resistance ( I ) is the total area OACD under the strrss-strain curve. For practi- cality the following formula can be used:

where: u7 = mntrrial's shear strength cr, = material's ultimate strength E. = strain of the material at point of

ultimate stress

Since the absorption of cnrrgy is actually a volu- metric propeey, the 11, in psi = u,, in in.-lbs/cu. in.

Tests developed for dctrrmining the impact strength of n1att:ri:lls are often misleading in their rcsults. Nearly all testing is done with notched speci- mcns, in which casr it is more accnrately the testing lor noteh toughness.

The two standard tests are the Izod and Charpy. The two types of specimens used in these tests and the method o l applying the load are shown in Figure 8. Both tests can bc made in a nnivcrsal impact testing machine. The minimum amount of energy in a falling pendulum required to fracture the specimen is considered to be a measure of the material's impact strength. In actuality, test conditions are seldom duplicated in the working member and application of these test data is unrealistic.

FIG. 8 Typicol lzod (left) and

of opplying the test load. The V-notch specimens shown hove an included ongle of 45' ond o ---- bottom rodius of 0.010" in the notch.

1. IMPORTANCE OF SECTION PROPERTY

The basic formulas nsed in the design of structural members include as one factor the critical property of the material and as another factor the corresponding critical property of the mcmber's cross-section. The property of the section dictates how efficiently the property of the material will be utilizcd.

The property of section having the greatest importance is the section's area ( A ) . I-lowever, most design problems are not so simple that the area is used directly. Irlsteati therr is usually a bending aspect to the problem and, therefore, the rigidity factor normally is the section's moment of inertia ( I ) and the simple strength factor is the section moctulus (S) .

Another property of section that is of major i n - portance is the section's torsional resistance ( R ) , a modified valuc for standard sections.

2. AREA OF THE SECTION (A)

The area (A) of the member's cross-section is used directly in computations for simple tension, compression, and shear. Area ( A ) is expressed in square inches.

If the section is not uniform throughout the length of the member, it is necessary to determine the section in which the greatest nnit stresses will he incurred.

3. MOMENT OF INERTIA (1)

Whereas a moment is the tcndency toward rotation about an axis, the moment of incrlia of the cross-section of a structural member is a measure of the resistance to rotation offered by the section's geometry and size. Thus, the moment oP inertia is a useful property in solving design problems where a bending moment is involved.

The moment of inertia is needed in solving any rigidity problem in which the member is a beam or long column. It is a measure of the stiffness of a beam. Moment of inertia is also rcqnired for figuring the value of the polar moment of inertia (J ) , unless a formula is available for finding torsional resistance ( R ) .

The moment of inertia ( I ) is used in finding the section modulus ( S ) and thus has a role in solving simple strength designs as well as rigidity designs. The moment of inertia of a section is expressed in inches raised to the fourth power (;xi).

Finding the Neutral Axis

In working with the scction's moment of inertia, the ncutrul axis (N.A. ) of thc section must he located. In a member snhject to a bending load for example, the neutral axis extends through the length of the member parallel to the menrher's structural axis and perpendicular to the line of applied force. The neutral axis represents zero strain and therefore zero stress. Fibers between the nentral axis and the surface to the inside of the arc caused by dellection rmder load, are mider compression. Fibers between the nmtral axis and the surface to the outside of the arc caused by deflection under load, are under tension.

For practical purposcs this neutral axis is assumed to have a fixed relationship ( n ) to some reference axis, usually along the top or bottom of the section. In Figure 1, the refrrence axis is taken through the base line of the section. The total section is next broken into rectangular elements. The moment ( M ) of each element about the section's reference axis, is determined:

M = area of element multiplied by the distance ( y ) of element's center of gravity from reference axis of section

The moments of the various elements are then all added together. This summation of moments is next divided by tlie total area ( A ) of the section. This gives the distance ( n ) of the neutral axis from the reference axis, which in this case is the base line or extreme fiber.

Neutral Axis

Base Line

FIGURE 1


. . . . . . . . . . . . . . . . . . . . . . . . . ; . . . ( 3 )

where b = width of rectangle, and 8" d = depth of rectangle

F L I d--A k1.T

"6.

FIGURE 2

The neutral axis of the compound section shown in Figure 2 is located in the following manner:

1 n = - or s u n of all moments . . . . . . . . . . total area (1)

Thus, the neutral axis is located 6.8" above the reference axis or base line and i~ parallel to it.

Finding the Moment oi Inertia

There are various methods to select from to get the value of moment of inertia ( I ) . Four good methods are presented here.

Moment of Inertia for Typical Sections (First Method)

The first method for finding the moment of inertia is to use the simplified formulas given for typical sections. These are shown in Table 1. This method for finding I is the most appropriate for simple sections that cannot he broken down into smaller elements. In using these formulas, be sure to take the moment of inertia about the correct line. Notice that the moment of inertia for a rectangle about its neutral axis is -

Moment of lnertia by Elements (Second

In the second method, the whole section is broken into rectangular elements. The neutral axis of the whole section is first found. Each clement has a moment of inertia about its own centroid or center of gravity (C.G.) equal to that obtained by the formula shown for rectangular sections. (See Table 1.)

In addition, there is a much greater moment of inertia for each element because of the distance of its center of gravity to the neutral axis of the whole section. This moment of inertia is equal to the area of the element multiplied by the distance of its C.G. to the neutral axis squared.

Thus, the moment of inertia of the entire section about its neutral axis equals the summation of the two moments of inertia of the individual elements.

I Problem 2 1 Having already located the neutral axis of the section in F i y e 2, the resulting moment of inertia of the section (detailed further in Fig. 3) about its neutral axis is found as follows:

but the moment of inertia for a rectangle about its base line is - FIGURE 3

Moment of lnertio by Adding Apeas (Third Method)

With thc third method it is possihle to figwe moment of intirtia of 1111ilt-np wctions without first d i n ~ t l y making a calculation for thr, neutral axis.

This method is recommended for use with built-up girders and c~lumns 11txa11se thc designer can stop briefly as a plate is added to quickly find the new rnornent of inertia. If this v:iluc is not high enough, he simply continues to add more plate and again checks this value without losing any of his previous calculations. Likewix if the value is too high, the designer may deduct some of the plates and again check his resnlt. This is done in the same manner as one using an adding machine, whcrehy you can stop at any time during adding and take a sub-total, and then proceed along without disrupting the previous figures.

Using thc parallel axis theorem for shifting the axis for a momcnt of inertia, the momelit of inertia of the whole st:ction about thc reference line y-y is -

total moments about base - M Since * = total area - A

M and of course n2 = - AY

Substituting this back into equation (5 ) :

A M" Note: neutral axis ( n ) I, = I, - -- A2 1 has dropped out

Thus :

. . . . . . . . . . . . . . . . . . . . . . . . (6)

where:

I. = moinent of inertia of whole section about its nelltraI axis, n-n

I, = sum of the moments of inertia of all elements about a common reference axis, y-y

M -- sum of the moments of all elements about the same reference axis, y-y

A = total area, or sum of the areas of all elements of section

Although I, for m y individual element is equal to its area ( A ) multiplied by the distance squared from its center of gravity to the reference axis (y2),

Properties of Sections / 2.2-3

TABLE I-Properties of Standard Sections

scclioo

Modulus

S

bd' .... 6

. . . . . . .

bd' - 3

bd' - 24

bd2 - 12

lid3 - 32

n (D4--dd] -- 12 D

no'b -- 4

..... .

" Idb -Zd) 4 0

each element has in addition a moment of inertia (I,) about its own center of gravity. This must be added in if it is large enough, although in most cases it may be neglected:

The best way to illustrate this method is to work a problem.


FIGURE 4

The base of this section will be used as a reference axis, y-y. Every time a plate is added, its dimensions are put down in table form, along with its distance ( y ) from the reference axis. No other information is needed. It is suggested that the plate section size be listed as width times depth ( b X d ) ; that is, its width first and depth last.

Total I I I I

The above table has been filled out with all of the given infonnntion from the plates. The rest of the <:omputations are very quickly done on slide rule or calculator and placed into the table. Notice how easy and fast each plate is taken care of.

Starting with plate A, 10" is multiplied by 4" to givc an x e a of 40 sq. in. This value is entered into the table under A. Without resetting the slide rule, tl~is figure for A is multiplied by (distance y) 2," to givc 80 inches c u l ~ d . This value for the element's moment is placed under M in the table. Without resetting the slide rule, this figure for M is multiplied by (distance y) 2" again to give 160 inches to the fourth power. This value For the element's moment of inertia about the common reference axis y-y is recorded under (I,) in the table.

If the moment of inertia (I,) of the plate about its own center of gravity appears to be significant, this value is figured by multiplying the width of the plate by the cube of its depth and dividing by 12. This value for I, is then placed in the extreme right-

hand column, to be later added in with the sum of I,. Thus,

Usually the value of I, is small enough that it need not be considered. In our example, this value of 53.3 could be considered, although it will not make much difference in the final value. The greater the depth of 'my element relative to the maximum width of the section, the more the likelihood of its I, value being significant.

The table will now be filled out for plates B and C as well:

M 544 and n = - -- - A - 80

= 6.8" (up from bottom)

Plote

A recommended method of treating M2/A on the slide rule, is to chide M by A on the rule. Here we have 544 divided by 80 which gives us 6.8. This happens to be the distance of the neutral axis from the base reference line. Then without resetting the slide rule, multiply this by 544 again by just sliding the indicator of the rule down to 544 and read the answer as 3700. It is often necessary to know the neutral axis, and it can be found without extra work.

@ / 1 0 x 4 " 2- 1 40.0 80.0 160.0 - @ i 8.' 1 16.0 128.0 1024.0 1 85.3

@ / 6"nW 14" -47-336.0 -- -

A = b ; d in?

I Problem 4 1

Sire

To show a further advantage of this system, assume that this resulting moment of inertia (2359 i a 4 ) is not

Dirtonce y I - bdl z - 12 in."

M = A . y in.)

( = Ay' = M y in?


large enough and the section must be made larger. Increasing the platc size at the top from 6" X 4" to 8" x 4" is the same as adding a 2" X 4" area to the already existing section. See Fignre 5. The previous column totals are carried forward, and properties of only the added area need to be entered. I, is then solved, using the corrected totals.

FIGURE 5

New D b x ~ / 14" 1 8.0 / 112.0 1 1568.0 1 10.6

I I I I

= 7.45" (up from bottom)

Previous Section -- 80.0 -- .

Moment of lnerlio of

544.0

The fourih method is the use of steel tables found in the A.I.S.C. handbook and other steel bandbooks. These values are for any steel section which is rolled, and should be used whenever standard steel sections are used.

1 5888.0 I 170.6

Positioning the

The designer should give some thought to positioning the reference axis (y-y) of a built-np section where

it will simplify his computations. The closer thc reference axis (y-y) is to the final

neutral axis (N.A.); the smallsr will be the values of (I, and I,) and MYA. Hence, the more accnrate these values will be if a slide rule is used.

If the reference axis (y-y) is positioned to lie through the center of gravity (C.G.) of one of the elements (the web, fol- example), this eliminates any snbsequent work on this particular clement since y -- 0 for this element.

If the reference axis (y-y) is positioned along the base of the whole section, the distance of the neutral axis ( n = M/A) from the refercnm axis (y-y) then automatically becomes the distance (cb) from the neutral axis to the outer fiber at the bottom.

The following problem illustrates these points.

I Problem 5 1

FIGURE 6

It is very easy to incorporate a rollcd section into a built-up member, for exampl~ this proposed column to resist wind moments. See Fignre 6. Find the moment of inertia of the whole srction about its neutral axis ( I , ) and than find its section modulus ( S ) .

Choosing reference axis (y-y) through the center of gravity (C.C.) of thc web plate R makes y = 0, and t11us eliminates somc work for 8 R .

Propcrtics of the standard 18" W F 96# section ;>re given by the steel handbook as -

A -- W.22 in.' I, - 206.8 in." t, = ,512''


The handbook value of I, = 206.8 in.' can he inserted dircctIy into the following table, for the I, of this WF section C .

By adding areas aud their properties:

moment of inertia about neutral axis

-~ ~

A

B

A

distance of neutral aris from reference axis

- - -.925" from axis y-y

Sire

16"xZ"

l " x 3 2 "

18 WF 96# .-

distance from N.A. to outer fiber

Q, = 18.00 - ,925

= 17.075"

Totcll

section modulus (see Topic 4 which follows)

Y

-17.0"

0 .

+16.25& . --

= 1146 in."

92.22

4. SECTION MODULUS 6)

A

32.00

32.00

28.22 --

?he section modulus (S) is found by dividing the moment of inertia ( I ) by the distance ( c ) from the neutral axis to the outermost fiber of the section:

- 85.26 Since this distance ( c ) can be measured in two

directions, there are actually two values for this property, although only the rnalirr value is usually available in tables of rolled sections because it results in the greater stress. If the section is symmetrical, these two values are equal. Section modulus is a mcasure- ment of the strength of the beam in bending. In an unsymmetrical section, the outer face having the greater value of ( c ) will have the lower value of section modulus ( S ) and of course the greater stress. Since it has the greatcr stress, this is the value needed.

With some typical sections it is not necessary to solve first for moment of inertia (I). The section modulus can be computed directly from the simplified formulas of Table 1.

In many cases, however, the moment of inertia ( I ) must he found before solving for section modulus (S ) . Any of the previously described methods may be applicable for determining the moment of inertia.

f 19,652.8

M

-544.W .

0

1-458.74

1 Problem 6 1 Using a welded "T" section as a problem in finding the section modulus, its neutral axis is first located, Figure 7.

Using the standard formula ( j r l ) for determining the distance ( n ) of the neutral axis from any reference axis, in this case the top horizontal face of the iiange:

b +9248.0

0

+7456.62

FIGURE 7

IX

f 10.7

t 2 7 3 0 . 7

f206.8


M Sum of moments n = - - - - A - Total area of section

Next, the section's moment of inertia is determined, using the elements method (Figure 8 ) :

This value is slightly higher than the required I = 700 in.' because depth of section was made d = 15" instead of 14.9".

Finally, the section modulus ( S ) is determined:

-. 75.8 in."

5. RADIUS OF GYRATION (r)

The radius of gyration ( r ) is the distance from the neutral axis of a section to an imaginary point at which the whole area of the section could he concentrated and still have the same moment of inertia. This property is used primarily in solving column problems. It is found by taking the square root of the moment of inertia divided by the area of the section and is expressed in inches.

The polar monrcnt of inertia ( J ) equals the sum of any two moments of inertia about axes at right angles to each other. The polar moment of inertia is taken about an axis whiclr is perpendicular to the plane of the other two axes.

Polar moment of ine~tia is used in determining the polar section modulus (J/c) which is a measure

j'h

FIGURE 8

of strength nnder torsional loading of round solid bars and closed tubular shafts.

7. TORSIONAL RESISTANCE (R)

Torsiond resistance ( K ) has largely replaced the less accurate polar moment of inertia in standard design formula for angular twist of open sections. I t should be employed where formulas have been developed for the type of section. Thcsc are given in the later Section 2.10 on Torsion.

8. PROPERTIES OF THIN SECTIONS

Because of welding, increasingly greater use is being found for structural shapes having thin cross-sections. Thin sections may be custom roll-formed, rolled by small specialty steel producers, brakc-formed, or fabricated by welding. Propt:rties of these sections are needed by the designer, but they are not ordinarily listed among the standard rolled sections of a steel handbook. FJropcrties of thin sections customarily are found by the standard formulas for sections.

With a thin section, the inside dimension is almost as large as the ontside dimension; and, in most c a m , the property of the section varies as the cubes of these two dimensions. This means dealing with the differcnce between two very large numbers. In order to get any accuracy, it would be necessary to calculate this out by longhand or by using logarithms rather than use the usual slide rulc.

To simplify the problem, the section may be '.treated as a line", having no thickness. The property of the "line", is t l~en multiplitd by the thickness of the section to giva the approximate value of the section property within a very narrow tolerance. Table 2 gives simplified formnlas for nine properties of six different cross-sections. In this table: d = mean depth, b = mean widtli of the section, and t = thickness.


TABLE 2-Properties of Th in Secthns Where thickness (I) is small, 6 = mean width, and d = mean depth of section

bottom

e ( 4 b + d ) 6

bottom '

left side * 1

R

rr

max. or

min.

d' - 2 ( b + d )

down from top

dZ b + 2 d

down from top

= add t /2 to c for S )

The error in calculating the moment of inertia by An excellent example of the savings in design time this Line Method varsus the conventional formula is offcrcd by use of the Line Method exists as (column) represented by the curve in Figure 9, using a square Problem 4 in Section 3.1. tu1,ular section as an example. As indicated, the error Table 3 givrs the most important properties of increases with the ratio of section thickness ( t ) to additional thin sections of irregular but common con- depth (d) . figurations.

Properties o f Sections / 2.2-9

FIG. 9 Possible error in using Line Method is minimal with low ratio of section thickness to depth.

Ratio: thickness jt j t o depth Id]

For additional formulas and reference tables, see "Light Cage Cold-Formed Steel Design Manual" 1962, American Iron & Stet4 Institute.

9. SHEAR AXlS AND SHEAR CENTER

Since the bending moment decreases as the distance of the load from thc support increases, bending force f, is slightly less than force f2, and this difference (fy - f l ) is transferred inward toward the web by the longitudinal shear force (f.). See Figure 10.

I p a y 1 f, = f.' + . . . . . . . . . . . . . . . . . . . . 1, (11)

This force also has an equal component in the transverse dircction. A transverse force applied to a beam sets up transverse (and horizontd) shear forces within the secticn. See Figure 11.

In the case of a symmetrical section, A, a force ( P ) applied in line with the principal axis (y-y) does not result in any twisting action on the mcmber. This

FIGURE 10


TABLE 3-Properties of Typical Irregular Thin Sections Where thickness f t ) is srnaN, b = mean width, and

d = mean depth of secfian

shear force flow in the section

FIGURE 11

Properties of Sections / 2.2-1 1

FIGURE 12

is because the torsioud moment of the internal transverse shear forces (4) is equal to zero.

On the othcr hand, in the case of a11 unsymmetrical section, U, the internal tra~xverse shear forces (4) form a twisting moment. Thercfore, the force ( P ) must bo applicd eecccntrically at a proper distance ( e ) along the shcnr axis, so that it forms an exteinal toi-sional monierit which is equal and opposite to ti-.,' intrrtui torsional momimt of the transverse shear forces. If this pr~rc;iution is not taken, tlrcre will be a I ivisting action ;ippli:d to the member \vhich will twist under load, in addition to bending. Sec Figure 12.

Any axis of symmetry will also be a shear axis. 'There will be two shear axes and thcir inter-

section forms the shear ccnter (Q). A force, if applicd at the shear center, may be

at any angle in the plane of the cross-section and there will be no twisting moment on the member, just transverse shear and bending.

As stated pre\:iously, rniless forces which are applied transvetse to a int>rnbcr also pass through the shear axis, the mcmher \?;ill be subjected to a twisting moment as well as bending. .As a result, this beam should be considered as follows:

FIGURE 13

1. The applicd force I' should be resolved into a forcc P' of ttic same \dire passing through the shear ccntor ( Q ) and parallel to the origin:~l applied force P. P' is then resolved into the two components at light angles to each other and p;rrallel to the principal axes of thc section.

2. A twisting moinmt ( T ) is produced by the applied force ( P ) about the shear center ( Q ) .

The stress from tlw twisting moment ( T ) is computed separately and t h m silparimposed upon thc stresses of the two rrct:ingular componrnts of force P'.

This means that the shear center must be located. Any axis of symmetry will be onc of the shear axes.

For open sections lying on one common neutral axis (y-y), the location of the other shear axis is -

Notice the similarity between this and the following:

Reference oxis y-y

Y


which is used to find the neutral axis of a built-up section.

Just as the areas of individual parts are used to find the neutral axis, now the moments of inertia of individual areas are used to find the shear axis of a composite section, Figure 13. The procedure is the same; select a reference axis (y-y), determine I, for each member section (about its own neutral axis x-x) and the distance X this member section lies from the rcfcrence axis (y-y). The resultant (e ) from the formula will then bc the distance from the chosen reference axis (y-y) to the parallel shear axis of the built-up section.

Here:

Locating Other Shear Centers

4 +f + d 4

FIGURE 14

Normally Q might be assumed to be at the intersection of the centerlines of the web and the flange.

The James F. Lincoln Arc Welding Foun- dation also publishes collections of award- winning papers describing the best and most unique bridges, buildings and other structures in which modem arc welding is used effectively.

FIGURE 15

Here, at point M:

or, since areas have a common (x-x) neutral axis:

Y

d e b -

FIGURE 16

Properties of Sections /

Figure I7 suggests an approach to locating shear axes of some other typical sections.

Structural steel for Gateway Towers, 26-story Pittsburgh apartment building was erected in tiers of three floors each by two derricks. Shop and field welding combined to facilitate erection; nearly 15 tons of electrode were used.

FIGURE 17

2.214 / Load and Stress Analysis

Eighty-foot hollow steel masts and suspension cables help support the continuous roof framing system of the 404' x 1200' Tulsa Exposition Center. Welds holding brockets (orrow) to which cables are anchored are designed to withstand the high tensile forces involved in such a structure.

SECTION 2.3

I . TENSILE STRESS

The simplest type of loadirrg on a member is tension. A tensile load applied (axially) in line with the center of gravity of the section will result in tensile stresses distributed uniformly across the plane of the cross- section lying at right angles to the line of loading. The formula for the stress is -

where:

P = the tensile force applied to the member

A = area of cross-section at right angles to line of force

crt = unit tensile stress

A tensile load that is not applied in line with the center of gravity of the section, but with some eccen-

tricity, will introduce some bending stresses. These must he combined with the original tensile stresses.

2. TENSlLE STRAIN

The nnit clongation or strain of the member under tension is found by the following relationship:

where:

E = unit elongation (tensile strain)

cr, = unit tensile stress

E = modulus of elasticity (tension)

The total elongation or displacement is cqual to this unit strain ( E ) multiplied by the length ( L ) of the member.

Elongation = t , L

FIGURE 1

A welded tensile coupon (test specimen) measures Yz" x 1'P at the reduced section, and has two punch marks 2" apart with which to later measure elongation. Just after the test is started, a load of 10,000 lbs is reached.

Find (1) the unit tensile stress on the reduced section, and (2) the total elongation as measured within the two marks.

= 13,333 psi

and elon. = E . I, = 0.000444 . 2"

= 0.00089'' in 2"

In any calcr~lation for strain or elongation it is understood that the stresses are held below the yield point. Beyond the yield point, the relationship of stress to strain is no longer proportional and the fomula does not apply.

ELDING OF BUILT-UP TENSION ME

FIGURE %-Welding of Built-up Tension Members

ENDING STRESS

Any force applied transversely to the structural axis of a partially supported member sets up bending moments ( M ) along the length of the member. These in turn stress the cross-sections in bending.

As shown in Figure 1, the bcnding stresses are zero at the neutral axis, and are assumed to increase linearly to a maximum at the outer fiber of the section. The fibers stressed in tension elongate; the fibers stressed in compression contract. This causes each soction so stressed to rotate. The cumulative effcct of this movement is an over-all deflection (or bending) of the member.

FIGURE 1

The cantilever beam shown in Figure 1 is in tension along the top and in compression along the bottom. In contrast, the relationship of the applied force and the points of support on the member shown in Figure 2 is such that the curve of deflection is inverted, and the member is in tension along the bottom and in compression along the top.

FIGURE 2

Within the elastic range (i.e. below the proportional elastic limit or the yield point), the bending stress (u,) at any point in the cross-section of a beam is -

where:

A4 = bending nlornent at the section in question, in.-lbs

I = moment of inertia of the section, in.*

c z: distarlce from neutral axis to the point at which stress is drsiretl, in.

ub = bending stress, may he tension or compression, psi

TABLE 1-Beam Diagrams

Typed Beam Maximum Maximum Mmxirnum moment deflection shear ~A-.~ -..___. i

I Fixedend 1 1

bath ends added end

Fixed end 1 Free end 1

center I center I

Fixed end 1 1 PL P L3 M = - - I '=- 3

Fined end 1 svided end

both endr I cenler I

2.4-2 / Loud & Stress Anulysis

The bending moment ( M ) may be determined from standard beam diagrams. Table 1 lists several of these, along with the formulas for bending moment, shear, and deflection. A more complete presentation is included in the Hcfsrcnce Section on Beam Diagrams.

Normally there is no interest in knowing what the bending stresses are somewhere inside a beam. Usually the bending strrss at the outer fiber is needed because it is of ~naximum value. In an unsymmetrical section, the distance c must hr taken in the correct direction across that portion of the section which is in tension or that portion which is in compression, as desired. Ordinarily only the maximum stress is needed and this is the stress at the outer fiber under tension, which rests at the greater distance c from the neutral axis.

A standard rolled '"I? section (ST-6" wide flange, 80.5 lbs) is used as a bcam, 100" long, supported on each end and bearing a concentrated load of 10,000 Ibs at the middle. Find the maximum tensile and maximum compressive bending stresses.

Figure 3 shows the cross-section of this beam, together with its load diagram.

Referring to Tahlc I, the formula for the bending moment of this type of bcam is found to be-

PL M = -- and therefore 4

Since thc bottom portion of the beam is stressed in tension, substituti~ig appropriate known values into the formula:

=1 21,845 psi (tension) -. -. -

n = 1.47" 1, = 62.6 in'

P = 10,000 lbs

FIGURE 3

5,000 ibs 5,000 lbs

The top portion of the benm being in compression,

= 5,870 psi (compression)

FIGURE 4

Find the maximum deflection of the previous beam under the sainr loading. From the beam diagrams, Table 1, the appropriate iormula is found to he -

L:' and therefore Amax = 48 E 1

( 10,000) (100)" = f l r 6 - 2 q

=r. ,111'' -

. HORlZONTAL SHEAR STRESS

Moment

FIGURE 5

In addition to pure bending stresses, horizontal shear stress is often present in beams, Figure 5. I t depends

Anolysis of Bending / 2.4-3

on vertical shear and only occurs if the bending moment varies ;dong the beam. (Any beam, or portion of the bcam's length, that has uniform bending moment has no \wtical shear and thrtreforc no horizontal shcar).

Unlike: bending stress, thc horizontal shear stress is zero at thc onter fibers of the beam and is maximum at the neutral axis of the beam. It tends to cause one part of the heam to slide past the olhex.

The horizontal shear stress at any point in the cross-section of a beain, Figure 6, is -

where:

V == extem;il vrrtical shcar on bt:am, lhs

I = moinznt of incrtia of whole section, in.i

t = tbickncss of scctioil at plane whtm stress is desird, in.

a - arca of section hiyxid planc where stress is desired, in."

y = distance of wntcr of gravity of area to neutral axis of entire section, in.

I Problem 3 ]

FIGURE 7

Assume that the "T' beam in our previous example (Problem 1) is fabricated by wclding. Under the same load conditions,

( a ) Find thc horizontal shear stress in the plane wherc the weh joins the flange.

( b ) Then find thc size of co~itinuo~is fillet welds on both sides, joining the web to the flange.

From the beain diagrams, Table 1, the appropriate formula for vrrtical shear ( V ) is found to be-

r V = - and thus 2

i

FIGURE 6

The following values also are known or determined to he -

( a ) Substituting the above values into the formula, the horizontal shear strcss (7) is found:

V a y ,. = I t

= 1196 psi - ( b ) Since the shear force is borne entirely by the web of the "T, the horizontal shear force ( f ) depends on the thickness of the web in the plane of interest:

f = T t 'and thus

= I196 X 0.905

= 1080 Ihs/in.

There are two Met welds, one on each side of the "T" joining the flange to the web. Each will have to support half oi the shear force or 540 ibs/in. and its leg size would be:

This would be an extremely small continuous fillet meld. Bascd upon the AWS, the minimum size fillet weld for the thicker 1.47" plate would be 5/16".

If manual mtermittent fillet welds are to be used, the percentage of the length of the joint to be welded would he:


Amalysis of Bending / 2.4-5

fillct weld would satisfy this requirement because it- resnlts in 25% of the length of the joint being \vt4ded.

3. QUICK METHOD FOR FINDING REQUIRED SECTION MODUL S (STRENGTH) OR

OMEN+ OF INERTIA (STIFFNESS)

To aid in designing members for lxnding loads, the following two nomog;aphs have been consirncted. The first nomograph drtermincs the reqnirtd strength of a straight beam. Tlir st:cond nomograph deteimines the required stiffness of thc beam.

In both nornographs sewral types of beams are included for conccntratod loads as well as nniform

loack. The length of the hmm is sl~own both in inches and in feat, tllc loi~d in pnnds . 111 the first no~nogaph ( i . 8) an allo\v:rl,li: I~ending streLss ( u ) is shown rind the strmgth pi-operty of the hcem is read as see- lion modulus ( S ) . In the swo l~d nomograph (Fig. 9) an allowable imit deflection (A/I,) is shown. This is the resulting dc4ecti11ii of the 11e:ini dividtd by the lt~ngtli of the 11e;rm. The stiffness PI-operty of thc haam is read as monicrit of irrri-tia ( I )

13y using thrse nomogr:~phs thc designer can quiicidy find tliv required swtion moduhrs ( s t r c~~g th ) or rno~nmt of irwrtia (stilhcssj of the be;rm. We can thcrr refcr to a stecl handbook to choose a steel sectiori that will meet these rcqrrirc~ments.

If he wisli<,s to fabricate the section from welded steel, he may use any of the mcthods for building up a steel section having tlrc rtquirrd vah~es of section modulus or mointmt of incrtia discussed in Properties of Sections.

More than a carlood of welding electrode was employed in the fabrication of this huge bucket-wheel iron ore reclaiming machine at the Eagle Mountain Mine. Steel pipe was used extensively in the 170' long all-welded truss, of triangular cross-section, that is the main load-carrying member.


1. RIGIDITY DESIGN

Under a transvtrrse bcnding load, thc normally straight neutral axis of a bearn becomes a curved line. The deflection of interest is the linear displacement of some point on the neutral axis along a path parallel to the line of applied force. IJsually it is the maximum deflection that is of value on our com~mtations, although occasionally the deflection at a specific point is needed.

Rigidity design iormulas for use when bending loads are cxpt,rienced, are bawd on the maximum deflection being -

formulas arc, availahlc in the I'lcfercnce Section on Hmm Diagrams incli~dcd at the e i ~ d of this book.

Thrtre ;rrr s t w d m(&ods for finding the dcflection of a brain. Foin of these will be slrown:

1. Sncccssive intt.gration method 2. Virtnal n-ork method 3. Area momtint nrethod 4. Conjngatr beam method

2. FUNDAMENTALS OF BEAM DEFLECTION

A transvet-se load placed on a he:im causes bending rnomcnts along the length of the beam. These bending moments set up bcnding stresses (o) across all swtions of the beam. See Figwe l a , where at any given section:

-~

Two of the cornponerlts in this formula have been discussed pr~viously in dctail. The critical propcrty of the material is its modulus of elasticity ( E ) . In the case of all strels, this has the vary high value of 30,000_000 psi. The related property of the section is its mommt of inwtia ( I ) , which is &pendent on dimensions of the beam cross-section.

If the values for E and I are held constant, and the load (P) is a specifird value, the length of the beam span ( L ) is one variable which will influence the deflection. The constant ( k ) is a function of the type of loading and also the miinner in which th~: load is supported, and thus is subject to the desibmer's will. In practice "I" also is subject to the designer's will.

The several components of the basic forinnla arc best handled by eonstructing a bending moment diagram from the x t u a l beam, and then applying the appropriate sta~idard simplified bearn formula. These

It is usually asstimed that the 11rnding stress ( v ) is zero at the neutml :ixis and then increases lincarly to R maxinmm at the ont('r fibers. ( h e snrface is nnder compression, n-hilc the other sl~rfacc is under tension. Within the elastic limit, assmning a stritight-line relationship bctwrcn strrss and strain: the distribution of bending stress can be converted over into a distribution of strain. Corrospontiingly, th'ere would be no strain ( E )

along the neutral axis and the strain would increase linearly to a maximum at the outer fiber. See Figure l b where at any gi\.en scction:

Considering a segment of the beam having only a

7 L

Neutroi 4 ----- - OXlS

Tension it o 4 Extension - y p

Bending Stress (b) Sirain ( c ) Elongation

FIGURE 1


very srnall increment in lengtk (Ax), Figure lc, the clorigation a-itlrin this small incrernmt would be E (Ax). Also, here it c m be seen that the small angular rotation (AO) wo~rld be the clongi~tion at the onter fiber divided by the distance ( e ) to the outer fiber from the nentral axis.

This can he cxpri~sstid as -

€(AX) -- c ( A O )

E (Ax) M c (Ax) , , A .= - - ~

c E I c

or:

x - M, (4x1 ( @ A ) ---- -~ -----

I? Ix

In other words, the infinitesimal angle cl~ange in ally section of the bcarn is r q u d to the area under the moment diagram (M, Ax) divided by the ( E I,) of the soction.

The angular rotation relative to stress and strain is further illustrated by Figure 2,

Figure 2a represents a straight beam under zero bending moment. Here any two given sections ( a and b ) \+-onid p:irallel each other and, in a stress-free condition, ~vould then have a radius of curvature (R,) equal to infinity ( m ) . These two sections ( a and b ) can be set clost. together to define the segrnent of very small inwerncnt in length (Ax).

A t Figr~rc 2h, the beam is subjected to a bending rnonient and this small segrnent (AX) will compress on one side and will elongate on the other side where the onter fiber is in tension. This can bc related to a small ai~gular movement within this increment. It can be seen that sections a and b are no longer parallel

( a ) Beam With No Lood [no moment)

~ J I I ~ would converge at some point ( 0 ) in spa::ca. forni- ing a radius of curvature (H, )

In thc sketch to the right of Figure 2b, :lotted lilies ( a and h ) rcpresent the initial incrniltmtnl segment (Ax) with zero mitment; while the solid lines refiect the &ect of applied lnad: Ax (1 - e ) at the surfncc under compressioir.

The total angular change ( t i ) between any two poi~its ( a and h ) of thc hewn equals the sum of the incremental changes, or:

It is also ohscrved from Figure 2b that -

and since -

VV ( A x ) (AO) . E I,

thc reciprocal of the radins of curvatnre ( I / R ) at imy ~ i w n point (s) of the heam is -

The noxt logical step would seem to be application of the Snccessiw Integration Method to determine the heam d&ection.

(b) Beom Under Lood (with moment)

FIGURE 2

Deflection by Bending / 2.5-3

kEJ

Slieoi (V) --

Moment (Mj -

Slope (0)

Deflectmn , y

/'

3. SUCCESSIVE IPITEGRATlON METHOD

FIGURE 3

For any given hiram with any given load, if the load (w,) at any point ( x ) can be expressed mathematically as a function of ( x j and if such load condition is known for the entire beam, thcn:

load

and by successive intcpations -

shear

. . . . . . . . . . . . . . . . . . . . . . . . ( 5 )

. . . . . . . . . . . . . . . . . . . . . . M, - ( v , (dxj . ( 6 )

Beom-to-Column Continuous Connections / 5.7-31

FIGURE 59

are tr;ilisIiwrd into tlw colu~nn wel) within the con- Analysis of Required Web Thickness nection rcgioo as shmr. The unit shear force applied to thc web of the con-

It c:m be assurni,d that xilost of tbib vertical shear nection is- force ( V , \ of thr beain weh is tra~~sferred diucctlv into - ~

\ ., the flange of the supportiilg cohim~i arid does not enter V F, - Vp Mi Vq =.-=--- - - the web of tile corin(,ctioi~. d d c dud, d,

The Iiorizontal shear force (V,) of the upper columr~ will he translrrred through the web of the The resulliilg unit shear stress in the web of the connection illto tlie luw.er column if caused by wind; comcction is- or out across the beam to the adjacent column if ca~rsed by gravity load. T = - - v 1 ME

wi - w ( d d.

FIGURE 60

Thcsr: rcsuiting vcrtical ;imI liorizontnl shear forces cause a diagonal coin]?uessive force to act on the web oi tlic co~inection; xnd, if the \vcb is too thin cornpared to its width or depth, it may suEer some buckling action. SFC Figlire 61.

Thc following a~lalysis, based on plastic design concepts, rmay be used to chwk iliis condition.

Using plastic design concepts, the applied moment (MI) will become tlic plastic moment. For this valuc, thc allowable shear stress ( 7 ) will be based on the yield streiigtli of the steel. The value for the shear

FIGURE 61

FIGURE 6

scgrnc~~t of a vol~irnc. m -.= virtr~nl bt,nding nlfiment at m y point cansed Ijy thc 1-lb load In thc tri;ixi;rl rapr~~srnt;rtion, Figure 6, diagr;rins

for Lot11 th: rml moment ( h l ) divided hy E l and h'l real iiimtling mommt s t thi, s;mrta point the virtu:il moment j ~ n ) have ;I common hnse li~re (tire

I :: inii~ncmt oE im:rtia at this snmc point x axis j. T h M!EI curvt, for thc real hcndinr: moment

g<.omctric faccs. The \-oIumi: of :my c l~ment of tl~is solid equals the

area of tlw (.lrrncnt's h;wr% smftrce nrr~ltiplied by the verticd distarrcc froin tiir center of gravity of the hasc surface. to tile npprr flat surhcc. This vcrtical distance is shown hy a dotted line.

Thus, in Figrirr 7, with the M/EI ;rnd in diagrams lined up o w alxivc the other, it is necessary to litlow

FIGURE 7


ol load

moment jM) diaginm

, . 1 ,' . . I

Viiiuol Iood moment [mj diogioni

FIGURE 8

only tlrc height of the virtual nroinent diagram :tt the sanre dist;orcc ( x ) ;is on tlrc r ed moment diagram. The M;EI diagrerri is then dividcd into simple geometric shapes (in this case, riglrt trinnglrs), and the area of c:ich is found :md multiplied by the height of the rn c1i;igram ;tk~ng a line throng11 the particular Iv/EI arca's centcr of gravity.

t'ronr this the volume is obtained:

and sina::

Volume = I" . y

the deflection in inches is -

The n l u e of I can now be inserted iir this to give the defl~ction ( y ) in inches. Howcvcr, if the beam

Real b o d moment (M) diogiom

I + 30,000"$ t ,

FIGURE 9

has a v;iriable section, scveral values of I umr!d hiivt: to i~~ser tcd earlier in the cornputation-lor the srction taken tltrough the center of gravity of each geo- ini>tricnl arm of thc hIlI51 di:rgmm.

'To simplify this further, a mothod of cross- multiplying has hcwr found to give the samc rc.sults. Tho g v n t d nppro;rcI? is iilnstrated hy Figure 8, wl~ere somc scgmmt of the, rtxl irrornr~nt ( M ) diagram between points s, and x, is at the top and a correspond- irrg scgnlcnt of tlrr virtu:tl lnomerrt (rn) diagram is below.

Tlro rcquirrd ~oli inr t~ can be fonnd directly by inriltiplying Mi by rn, and W:, i)y m:: and then by cross- multiplying hl, by in, and Mr by mi using only ?-: of the products of cross-muitiplicatioi~. This is more fully related to the 1)asi~. iutegration eqoation hy the following:

whrre I, = the distance between points x, and xz.

Figure 9 s h o w :ipplic;itio~r nf this method to the original Problcin 1.

Defiectron curve

, .


From Figure 9:

5. AREA MOMENT METHOD

This a very nsefnl tool for engineers and is illustrated in Fignrc 10 by a gmcral inoment diagram and the L,~I-responding dcfl<,ctioli curvc. I l rrc points o and b reprcwnt any two points defining a sinrple geometric ;ire.? of an actual inorncnt diagram.

Tlie two flinda~nontal rules for of this mcthod are:

p i n t s ( a and 11) of n loaded beam equals the ;irtxa m d r r the nionwnt curm?, divided by E I, Ijetween these two points ( a and b ) .

tangent at point h oi the h~mm equals the moment of the arca undcr the moment diagram taken about point a, divided by E I.

FIGURE 13

Moment diogrom

Defiect!on curve s @

FIGURE 11

@ Load

FIGURE 12

For symmetrically loaded_ simply si~pported beams this is a conv~~tiirnt method with which to find the maximum deflection of the beam, because in this case the slope of t lh beam is zcro at the mid-span ( b ) and the distance from a to the tangent at b equals the maximum deflection we are seeking. See Figure 11.


From Figure 11:

I-Io\\:c\;er. for an i~iisyrnnietrically loaded beam, thr point of the he:un Iiaviiig zc?ro slope, or niasimum ileBection, is rrnk~iown (Fig. 12). There are ways of gctting :u-ound this.

The conditions of Problem 1 are here illustrated hy- Figrtrf 1:3. Tlir mimimts oi the nrca tmder the momcnt curve (from point zero to point 30) is takcn ;thout point zt-ro to givc thc \rcrtical distance betwerti point zero 2nd the taligent to the cleflcetion clime at point GO. This btw~mes y,, This is not the at:tual deflection, hecairse the slope of the clcB,ficction curve a t point 30 is riot lcvtd This slope i . y t to he found.

First firid the vc,rtical distmcc bctweeii pdn t 90 and the tarigcnt to thc defliactioii cnrvc at point 30. To find this distnriw [y,,,), take the momcnts. about point 90. of the area of the niomcnt cliagrarn from point 30 to point 90.

TABLE I-Ccmparative Conditions of Real and Coniuaate Beams

2, Fixed ends / 2. Free ends because - ai zero deflection o zero moment

R e d 8eqm

i Simple supported ends 0 ) zero deflection b) r nox im~m slopes

bl zero slope

I h. zero shear hcnce no support

- . 3. Free ends 3. Fixed ends because -

u] o maximum drf1e.rtion 0 , 0 m3xirnum moment b) a maximum rlnoc b; a moximum shear hence o

Conlu90+e Beam

i Simply supported ends b e i ~ u r e -- ai i e i o moment bl maximum shear

continuous beom / b i graduol chongc in shear

mum moment , ..~ .. ~~~ ~

1 ~ ~ ~~. -. ... ~ ~~ ~~ -

6 Either itu:icaliy dcfern?inate 6. A lwoy i staticoily determinote or stnticolly indeterminate

FIGURE 14

Tbc ; ~ n g l < ~ of this tangent line to the horizon (6',,) is thcn formd hy dividing this vertical distancc (yao) by the liorizontal distance between point 30 and l~oint 90.

Tliis angle (&,) is the same to the left of point 30, Figure 14, and dofines the vcrtical deflection ((y,) at point zero. This :inglc then, milltiplied by the horizontal distancc from point zero to point 30, gives the vertical displacement ( yi ).

Adding this to the initial displacement-

gives the total deflection ,it pomt /era of -

6. CONJUGATE BEAM METHOD

I n using this method, the bcnding moment diagram of tlic i-cal i~cam is constnrctrd. A sntxtitutiond beam or coiljugate heam is thm srt up; the load on this is the momrnt of the real heam divided by the E I of the real heain; in other w)rils it is loadtd with the M/EI of the rcal Iwam.

Five colditions milst be met: 1. The ltwgtli of the conjugate beam equals the

length of the rcal beam.

Deflection by Bending / 2.5-

TABLE 2-Typical Real Beams and Corresponding Conjug;ate Beams

Real Beom Conjugate Beam


FIGURE 15

Conjugate beom 30,000"+ t-

with i t s iood E i

2. Tlirrc arc two cqilntions of eqoilil,ri~~rn- The snm of forces acting in any one direction on tlic conjugate beam ~qnnIs zero. ?'he sum of momcmts ntmut an>- point of the cmjngate hcam t:qoals zcro.

3. Tho load at any point of the conjugate bean1 equals the moment of the r ed bcam divided by the Ii I of the rcal beam at the same point. The real bcam could imve vwiahle I.

4. Thc vei-tied shmr at any point of thr conjugate heam equals the slope of the red hrnm ;?t the same point.

5. The bending moment at any point of the conjugate heam r:qn;rls the deflection of thc rcal beam at the same point.

The conjugate beam n ~ ~ i s t be so sripportcd that conditions .1 :~nd 5 are sat isf id Thc abovr statements of col~dition may b i r e \ w x d

By knowing some of the conditions of the real beam, it will he possiblc to rwson the nature of the support of the eonjugate beam. 'i'l~e cc~~np:wativc statements of Table I will help in setting lip the conjugate beam.

Some osamples of re:d h e a m and tbeir corresponding cm~jr~gate beams are prcsentcd in Table 2.

\r<lticC! tliat lhc snpport of the conjngate beam can be wry unlike the support of the real bcam.

The last I in 'I'alde 2 is similar to the I'roblrm 1 brmn to n.liidl scvrml mrtliods of solving dc,flcction ha1.e alrcncly h : w ~ ;11:plied. Here the con- jiigati tmun i s hingpd at the point of ssccond siipport :IF r l~c rwl brarn, and wilhout this 11ingc thc Conjugate R(wn Metiiod would not hc workable.

, , Ihe same I'robltm 1 is illustrated in Figure 15, \?:hc~r thr rr.d hram momont is first diagrm~med. This is then dividcd by E I of t l x real beam lor tile load on the ~u~njugatc beam shown next.

To find the right 11in1d rcaction ( R ) take moments, about p i n t 30, on the conjngate beam between ~wints 30 ;ind 90. See Figuro 16.

This rrt.gaii\v sign mmns the re;iction is directed ~ p p ( l ~ i k to our original assnmption; hence it is directed do\vn\vard.

Since the snrn of vertical forces equals zero, VaO may be fonrrd:


This positive sign means original assumption was correct and sl~oar is directed upward.

The left hand mon~tmt (Mo) of thc conjugate beam may be fo11nr1 by taking moments of the isolated element, betwcen points zcr-o and 30. See Figure 17.

FIGURE 17

The d(&ction of the real hmrn at point zero (yo or A,,,,) t:qnals the moment of thc conjngate beam at this point (M,) ; lience:

This would be tlic solntion of this prn~hlt~m; however, to get the dcflcrtion at other points it wmdd be necessary to continuc this work and find tlie monient of the corbjugate bvam tlirouglwut its length.

Tire maximum d?flcdion of the real beam on the right side occurs at the same point ;is zero sllear of (he conjngatc beam. By ohsvrvation this \vonld occur somewhcrr between points 60 and 90, and the distance

FIGURE 18

of this poiltt of iwasimoni deflection from point 90 is set as x,. See Figure 18.

Since: Z V = O

and: Sl := 24.5"

Thr monier~t of tlir conjugate beam at this point 15 -

and therefore the maxiinrrm deficction (y,,, or A,n,,) of tlic roal beam, Figure 19 -

2,150,000 in.: - ynmx = ~

E I ' Ibs inct~cs

7. DEFLECTION OF BEA SECTION

The area moment method may be used vely nicdy to fiid tire ddlcction of beams in wliicli no portion of the beam has a constant moment of incrtia.

FIGURE 19


FIGURE 20

'The mgle between the tmgents at A and B = 0 == the area of the moment diagram between A and A, dividcd by El.

Subdividing this beam into 10 or more segments of equal length ( s ) :

FIGURE 21

Each segment of bending momcnt causes the beam in this sr.gment to bend or rotate. The angle of bend 0 = area of moment diagram of this segment divided by El, o'r -

The resultant vertical monrement (h,) of the load, at the left end of tlre beam, is -

i.:;1c11 segment of the beam bends under its indi- vidoal bcnding momcnt and its angle change causes the cnd of the hcam to drflect. S w l'igwe 72.

Tho total deflection at the end of the beam eqnals the sum of the deliections at the end of the beam caused hy the angle change of each segment of the 1,cam. Set, Figurta 23.

FIGURE 22

Re\tatn~g the preceding, the vert~cal deflection of B IS -

or:

hf,, x,, Note: - F - 1s found for eacb segment. These 1"

- values are added togr:tl~cr, and this sum is miiltiplied by s/E to give the total deflection.

(x)neosured from IeCt end of beam:B) where lnad<P>

FIGURE 23

The following tapcved beam is 30' long. It has 1" X 10" fiarrge plates and a 'h" thick \voh. It is 11" deep at the ends and 33" deep at centerline. It supports two 58kip loads at the 'h points. Find the maximum deflection of tlic Iicam. See l.'igiire 24.

Divide the length of thc btmn into 12 equal seg- n~ents. '1%~ greater the nnmher of segments or divisions, the more :iccrirnte will he the answer. Normally 10 divisions \vor~ld give a fairly acmratc result (Fig. 25)

eflecticn by Bending / 2.5-13

Moment diagram FIGURE 25

Here 5 - 10'' 8. DESIGNING FOR MULTIPLE LOADS

h'ft> x,> and A,,>+,, = Z ~ Normally, thr calculation of the maximum deflection E I"

of members suhjected to bending loads is very comples.

The moment of inertia of each scgment (I,) is Tilt: poiirt of maximum deflection must first be found;

taken at tlle sectional centroid of the segment. thw, from this; the mnxim~~m deflcctiorr is found.

~h~ formllla L.ompont~l,ts M,, x,, and 1,: are easier I h I ~ ~ s s tlx,r.re arc no more than two loads of cqnal

to hwdle in t&le form: vahir. and rqnal distance from thc ends of the hczm (Fig. 26), existing l~eam tat~les in handbooks do not cover this pn)hlem.

Total vertical d14iection -

FIGURE 26

For <~x,tniplc, most Ixarnc have mole than two loads (Fig. 2 7 ) . 7'11~ maxi~nuni dcflcction risrrally docs not nwnr at the rniddlr~ or ccntcrlinr of tlic bcarn (Fig. 28) . T\\w things can 1w donc to siniplify this problcrn.

First, consider only thc deficction at the middle or centerline of the mtmher, rather than the maximum ~lrfii:(~tio~i at sornc point which is dilficnlt to determine. This is justified, sirlce the dcflcction at midpoint or centerline is almost as great as tllc masimum deflection,


FIGURE 27

I I M c ; x i m m deflection Def lec t~on o! middle

FIGURE 28

the grcatest dcviatiori coming within I. or 2% of this value. For esnrnple, a simply supported h a m with a single concentrated load at the one-quarter point has a deflection at centerline r 98.5'1: of the maximum deflection.

Secondly, a simple method of adding the rtxpirtd moments of inertia required for each individual load a n be used.

For a given size member, Figure 29, it is found that each load, taken one at a time, will cause a certain amount of deflection at the middle or centerline. The total deflection at the cerrterlinc will equal the sum of these individr~al deflwtioris anisod by each load.

This principle of adding dcflcctions may be used in a reverse nralmcr to find the required section of the meniher ((I, Fignre 30. For a given allowable

deflection ( A ) at tht* centcrlinc, each individual load, taken one at a time, will rcqnire the member to have a certain section ( I I , I:, etc.).

The moment of inertia ( I ) of the beam section required to support all of the vertical loads within this allowable vertical ddlection ( A ) will equal the sum of the individual moments of inertia (I, ,) required for the several loads.

4ny torqnc or cor~plc, appiicd horizontal to the beam will cause it to d&ct vcitically. This can be lrandlcd in the same manner. The required moment of inertia of the member (I,,) lor vnch torqric acting selxmtdy is found and ;tddcd into !hi! total ri.qr~ire- ment for the pl-operty of the section ( I ) .

'The following two formulas may be wed to find the individual properties of the section ( I , , ) :

for each force

The two formrilas have been simplified into the fonnulas given below in which the expression K, now produces n constant ( 4 or B ) which is found in Table 3.

FIGURE 29 FIGURE 30

FIGURE 31-Required Moment of Inertia to Resist Bending


TABLE 3-Values af Constants (A and B) for Simplified Formulas (16 and 17)

for each force

for euch couple

The value of K,, is equal to the ratio a,/L, where a,, is thc distance from the point at which the specific force or couple is applied to the nearest point of support. I, is the span or length of beam between supports. From the value of K for arry givcn load ( P ) , the substitute constant A or B is obtained from Table 3.

\tihen a force is applied to the member, use the constant A aud substitute into the first formula. When a mi~p le is applied to the member, use the constant B and substitute into the secoud formula.

A shorter method would be to make use of the nomograph in Figure 31.

9. INFLUENCE LINE FOR REACTIONS

.\lax\veli's Theorem of Reciprocal Deflections may be usrd to 6nd the reactious of a continuous beam or frame, and is especially adaptable to model analysis.

Consider the continuous beam represented by the diagram at Figure 32a. The problem here is to find the reactions of the supports for various positions of the load (P,).

According to hlaxwell's theorem, the ddect ian at point 1 (A?,) due to the load (Pb) at point x, Figure 32b. eqnids the dc4ection at point x (A,) due to the same amount of load (PC) applied to point 1, Figure 32c. There is a similar relationship between an applied load or moment and the resulting rotation of a real beam.

Figures 32b and 32c constitute a simple reversal

FIGURE 32

eflection by Bending / 23-17

of points at which the pressure is applied. This concept supplies a very useful tool for finding influence lines lor reactions, deflections, moments, or shear. In this case, the interest is in reactions.

To find the value of the reaction ( R , ) at the left- hand support in Figure 32a, the support is rcnloved; this causes the left end to deflect ( A b ) , as at Figure 32b. 111 order to restore the left end to its initial position, an upward reaction (PC) must be applied, as in Figme 32c.

In extending h4awwell's theorem of reciprocal de- fiections to Figure 32b and Figure 32c, it is noticed:

if P, = P. then A,, = A,

However, in order to return the beam to the initial condition of Fignre 32a, Ad must be reduced until it i:quals A,. To do this the upward reaction (PC) must be rednccd by the factor: Ah/Ad And since A, = A,, this reduction factor becomes Ae/Ad.

A .'. RI = Yb-2 or, usmg Fignre 32a - Ad

This means that if the model bcam (as in Fig. 32c) is displaced in the same direction and at the same point

as the reaction in question, the resulting ddledion curve becomes the plot of the reaction as the load is moved across the Icngtli of the beam.

This is called an "iniiuaice cnrve". Considering the conditions of tlie rwl beam representlted by Figwe 32a, the reaction ( R , ) at point 1 due to a load (P,) at point x will be proportional to the ratio of the two ordinates at points x and 1 of the deflection ciirve.

In other words:

For continuous beams of constant cross-section, a ~vire model may be set up on a drawing board, with the wire beam supported by thumb tacks spaced so as to represent the supports on the real beam. See Figure 33. A load diagram of the real beam is shown at the bottom. Notice that the thumb racks used for supports of the wire must be located vertically so as to function in the opposite direction to reactions on the real beam.

The point of the model beam at the reaction in question ( R , ) is raised upwlu.d some convenient distanct,, for example 'h" or l", and the deflection curve of the wire beam is traced in pencil. This is shown immediately l ~ l o w the model.

The final value for tlie reaction ( R I ) is equal to

Thumb tacks

FIGURE 33


FIGURE 34

the sum of the actual applied forces mnltiplied by the ratio of their ordinates of this curve to the original displacement at RI.

The influence curve for the central reaction (Rn) may also be fouud in the same manner. See Figure 34.

Deflection curve of the wire model is shown Erst and then the load diagram of the real beam.

I Problem 3 1 A continuous beam has 5 concentrated loads and 4 supports. The problem is to find the reactions at the supporzs.

The reactions are found by comparing the ordinates of the deflection curve of a wire representing the beam. See F i y r e 35, where the critical dimensions appear on the (upper) load diagram.

For the ends, reactions R, and R4, displace the end of the wire a given amount as shown. The portion of each applied load (P) to be transferred to the reaction RI is proportional to the ordinate of the deflection curve under the load ( P ) and the given displacement at R,.

For the interior reactions Rz and R3, displace the wire a given amount at Rn. From the ordinates of this

FIGURE 35


FIGURE 36

deflected wire, determine the ratios of each applied load ( Y ) for the reaction at Rlr.

The cornputation of forces for the rcaetions R, and R, is as follows:

R2 = + ,695 PI + 1.11 P, + 5 6 Pa - ,352 P4 - ,296 Po

=z .695(2000#) f 1.11(2000#) + .56(1000#) - .352(15OO#) - .296(1500#)

= -C 3198 lbs

Rcactious R:, and R, can be found in like manner.

Application to Frames

This same method may be extended to the analysis of frames. If the frmr has a ninstant r~oment of inertia, a stiff wire may lie bent into the shapc of the frame. If the frame has a variable mornwt of inertia, the model may be made of a sheet of plastic or card- board proportioned to the actual moments of inertia.

FIGURE 37

Reactions, either horizontal (11) or vertical ( V ) at the supports, may he found by displacing the frame at the support a given amount in the direction of the desired reaction. Sce Figure 36. The outline of the displaced model frame is traced in pencil, and this becomes the curve showing the infinenee of any load (at any point) upon this reartion.

The displacement of each point of the model frame ( A ) u~herc a load is applied is measured in the same direction as the application of the load, and the resulting reaction may- be computed from the following:

horizontal reuction

vertical reaction

Moments at the ends of the frame (or at any point in the frame) may he found by rotating the point in question a given angle (+,) and again drawing the resulting displaced model frame. See Figure 37.

The displacement of each point of the model f ranc (A) where a load is applied is measured in the same direction as the application of the load, and the resulting moment may be comput~d from the following:

moinent at left-hand support

l t is necessary to displace the model a considerable distance in order that some accuracy may be obtained in the readings. Therefore, some error may be introduced because the final shape of the frame may alter the real load conditions. This error can be reduced greatly by me~suring the displacements between one


(a) Measuring dirplacerrrrni of model (b) Measuring displacement of model frame from initial condition i o dis- frame from one displaced condition ploced condition to an equal and opposite displaced

condition

FIGURE 38

condition and the opposite condition. See Fignre 38. This method of equal to opposite displacement

may also be applied to monrents in which the frame is rotated an equal ill both directions, and To dettel-mine the ddlection of the overhung portion

mcasnrcments taken from one extrclne to the other. of this trailer, Fignre 39, under the va r io~~s loads. As- sume a cross-section moment of inertia ( I ) of 2 X

E FOR D E F L E C T I O N

Iu like manner, the use of a wire model based on Maxwell's Theorem of Reciprocal Dcflec~ion is useful in finding the dcflectitnis of a bean1 under various loads or under a moving load.

If a 1-lb load is placed at a particular point on a beam, the resrilting ddection curve becomes the plot of the deflection ( A ) at this point as the 1-lb load is moved across ihc length of the beam. This is called the influence line for deflection at this particular point.

T A B L E 4-lncremenral Deflections of R e d Beam

Paint Ordinate Deflecsion At Free End ( In . )

------ ~

Total 3300 lbr -2.360"

11.82 in.' Using the standard beam formula for this type of

beam, the deflection of the free (right) end is detei- mined for a 1-lb load placed at that point:

A wire model of this beam is held at the two supports (trailer hitch and the wheel assembly) with tbnnrh tacks on a drawing board. The outer end is displaced an amount equal to 3.25 on a snitable scale. The dt4ection c t m e is traced in pencil from this dis- p l a c ~ d wire beam. The ordinates of this resulting deflection ciirvc become the actual deflections at the free md as the I-lb load is moved across the length of the beam.

Multiplying each of the loads on t!ie real beam by the ordinate at that point gives the deflection at the free end cansed by enc?~ load on the real beam. See Table 4. Summing these incremental deflections gives tluc total deflection:

A = 2.36" upward

DeSlection by Bending / 2.5-21

Drawing boord + 3.2:

FIGURE 39

Erection of the 32-story Commerce Towers in Kansas City, Missouri war speeded with the aid of modern semi-automatic orc welding. Field use of self-shielding cored electrode quodrupled the rote of weld metal deposition. The weldor shown here is mok- ing o field splice of two sections of the heovy building column.

2.5-22 / Load a n d Stress Analysis

Complex antenna systems needed in age of space communications are sensitive to bending deflections caused by high wind loads. Good engineering, including the specification of high strength steels and rigid welded connections, is essential to the satisfactory performance of such structures. In the parabolic antenna dish shown, 6400 sq fi of expanded metal mesh are welded to a space frame of tubular welded trusses.

SECTION 2.6

1. NATURE OF SWEAR DEFLECTION F ,

Shear stresses in :a buam section cause a displacement or sliding action on a plane normal to the axis of the beam, as shown in the right hand view of F i y e I. This is unlike the dofledion resulting from bending in a beam, which is shown in the left hand view of Figure 1.

Normally deflection due to shear in the usual .--.-. -----. - - - - -

- - beam is ignored hecansc it r~presents a very small percentage of the entire dt4ection. Figure 2 shows

L b J b--i+-i that the deflection due to shear increases linearly as FIG. 1 Deflection in beam caused by bending moment, the length of the beam increases, whereas the deflection left, and by shear, right.

Length of canti lever beom (1)

FIG. 2 Deflection caused by shear increases linearly as length of beam, but that caused by bending increases as the third power of beam length.

2 .61

2.6-2 / Load Stress Analysis

i r , = 0.3 [Poisson's rat io]

0 Y I I I

0 0 10 0 20 0 30 Sheot stroin [i ,) in in

FIG. 3 Shear stress-stroin diagram.

due to bending irxreases vcry rapidly as a third power of the length of the beam. For this reason the de8ec- tion due to shear is not an import:int factor except for extremely short spans where drAcctiorr due to bending drops off to a vcry sm;iIl valnc.

The deflection due to shear is dependent entirely on the shear distribution across the cross-section of

the member and also tihe value of the shear stress (7). Figure 3 shows the shcar stress-strain diagram which is similar to the usual stress-strain diagram, altE~ough the shear yield strength is much lower than the tensile yield strength of the same material. After the shear +d strength is reached, the shear strain (t,) ir~creases rapidly and the shear strength iricreases because of strain hardening.

INlNG SHEAR DEFLECTION

The theory of deflection caused by shear stress is rather simple. However, the actual determination of th,e shear stresses and their distribution across the heam section (which two factors cause the deflection) i~ more difficrllt. In all cases, some kind of a form factor (a) must be drtemlined, and this is simply a matter of expr~,ssing the distribution of shear stress throughout the web of the scction. Since there is pmctically no shear stvcss in the flange area, this particular area has negligible effcct on the deflection due to sheas ( A , ) .

The following formulas arc vdid for several types of hcams and loading:

Shear deflection of cantilever beom with concentrated load

Sheor stres (7 ) o r aiea beyond neutral onti

y I: dirtorice between center of c~rovity of this aiea and neutral o x i s of entrre croii~iection

A = total ore" of section

I =- moment of ineitio of section

t = tofol thickncis of web

FIG. 4 Form f a c t ~ r for shear deflection in built-up beams.

Shear Deflect ion i n Beams / 2.6.3

simply suppurled bcnn~; uniform load (w)

simply nrpported bcmn, conr entrutecl load ( P )

FIG. 5 Beam sections for which Eq. 5 applies.

confilecw bcant; uniform loud (u:)

where:

P = total load. lbr

A = area. of entirc sectkn~

E, = modulus of elasticity in shear (steel = 1 2 , O W ) O O psi)

w = distribntcd load, lbs/linc:ar in.

Welding was used extensively in the fabrication and erection of this steel- framed, 8-story, bolconized apartment building which features cantilevered cross beams in the upper stories. The building wor designed basically as a rigid structure with moin beoms designed plastically and light X-braces used to accommodate wind moments. The welded steel design cost 16@/sq ft less thon a reinforced concrete building would hove.

The slope of the deflection curve ( 0 ) is equal at each cross-seetioil to the shearing strain ( E , ) at the centroid of this cross-section. cr is a factor with which the avcrage shearing strcss ( ) must be multiplied in order to obtain thc shearing stress ( T ) at the centl.oic1 of the cross-sections.

On thi.s hasis, the form factor ( a ) for an I heam or hox beam would be:

where Figure 5 :ipplies. Don't compnto area ( A ) in this forruula b r c a ~ ~ s e it will canct.1 out when used in the formul:is for shear ddlection.

2.6-4 / Load and Stress Analysis

Both shop and field welding were used extensively in building the Anaheim Sta- dium, home of the Lor Angeles Baseball club-the Angels. The steelwork was designed as an earthquake-resistant frame, with high moment carrying capacity in both directions. Having very good torsional resistance in addition to bending strength in both directions, the tapered box section frames can be located more widely (45' centers along straight sides) and eliminate the need for conventional cross-bracing between bents.

OMENT METHOD FOR CURVED CANTILEVER BEAM

In Sect. 2.5, Fignres 20 to 2.3, the arca moment method was used to find the dtflrction of a straight cantilever beam of variable section. This same mcthod may be estcndt~l to a cwvcd cnntilr,vi-r heam of variable scdion.

As beforc, tho Bram is divided into 10 scgtnents of oclual length ( s ) and the nmnent of inertia ( I , > ) is determined for mch sepinmt. See Fi:nre 1.

The moinent applied to :my segment of the hcam is equal to the applied force ( P ) mnltiplied by the distance (X,) to the segment, inc;~surcd ~ I - U I X and at right angles to the line passing tlirongh and in the same direction as the load (1 ' ) .

‘-merit causes This moincnt (M,,) app l id to the sc, it to rotate ! O , , ) . and-

The resulting deflection (A,) at the point of the

beam where the deflection is to be determined is eqnd to the angle of mtation of this segment(@,,) mnltiplicd by the distance (Y,) to the segment, measured from and at right angles to the line passing through and in the sane direction as the dt~sired (leSlection(A)

F, I,, E I,.

The dist:n~crs X I Y ) and the moment of inertia (1,) arc dr.titrrnmin,rd for each of the 10 segments and placed in table form. In most cases, the dt,flectior~ to hc dctmnined is in line with the applied form so that thcsc. two di.stnnws :Ire equal and the formula 11ew)mt:s-

The valucs of X,,"/l,, we ionnd and totaled. From this the total defiection (A) is fuortd:

FIG. 1 To find deflection of curved cantilever beam of variable section, first divide it into segments of equal length.


........................ ( 4 )

A symmetrical beam forming a single continuous arc, for example, is comparable to two equal cantilever beams connected end to end. Thus, the pre- diction of dcflection in a curved beam can be approached in a manner similar to finding the deflection in a straight cantilever beam.

The total vertical deflection ( A ) is needed on a curved beam that will carry a maximum load (P) of 100,000 lbs. See Figure 2. Given the segment length ( s ) = 10" and the various values of X, and I., complete the computation.

Segment

216 1.04 23 358 1.48

4 29 550 i 1.53

Deflection of Curved Beams

5

Solving for defleclion

PS x: by using formula A =-E-C 7

f irst colculote value of X;/I,, 1

32 800

by using stiffness nomograph

grophicolly find value of P X ~ / E I ,

for use in fzimuio a = s z - E l

6 32 1 800 1.28 1.28

FIG. 2 For deflection of simple curved beam, use Eq. 4 or nomograph, Fig. 3.

7 8 9

1.53 1.48 1.04

29 23 15

21

550 358 216

10 i 5 119

FIGURE 3-Deflection of Curved Beam (Stiffness Nomograph)

Total load (P) on Curved Beam

I bs Moment 1,000,000 arm (X,)

3- A Feet Inches

Deflection o f curved beom

where I I X,= 50 in. i

Moment of inertio of section (I,)

i n.4

- I

Mul t~p ly the sum of these values by "st ' to get total deflec!inn of the curved

' i .00000,

beam


By using the stiH~wss nomograph, Figure 3, the computation can he collsiderahly shortened with no significant loss of accuracy The nomograph is based on the modified formula:

P X,,' 1 E , , , 1 . . . . . . . . . . . . . . . . . . . . . . . ( 5 )

Ileadirig are obtained from the nomograph for P X / I for each segment and cntered in the last column of the tahle. These are then addcd and their sum mdtiplied by s to give the total vertical deflection.

I Problem 2 I Use the same heam examplc as in Problem 1,

the same valzrrs for l', s. X,, and I,,; and the s u m form of table. Complrte the compiitation.

Engineers of the Whiskey Creek Bridge in No. California specified that the 300' welded steel girders across eoch span utilize three types of steel in order to meet stress requirements economically while maintaining uniform web depth and thickness and uniform flange section. High strength quenched and tempered sieel was prescribed for points of high bending moment, A-373 where moments were low, and A-242 elsewhere.

S E C T I O N 2 . 8

1. NATURE OF IMPACT LOADING

Impact loading resnlts not only from :ictual impact (or blow) of a moving body against the member, but by any sudden application of the load (Fig. 1). It may occur in any of the following methods: 1. A direct impact; risnally by another member or an

external body moving with considerable velocity, for example: ( a ) A pile clrivcr hammer striking the top of a pile. ( b ) The die striking the workpiecr in x drop forge

press or punch press. ( c ) A large rock dropped from a height onto a

tn1ck. 2. A d d e n npjilicution of force, witliont a blow being

involved. ( a ) The sudden crcation of a force on a inember

as during the explosive stroke in an engine, the ignition or misfirr of a niissile motor \&en moui~ted on a test stand.

( b ) The suddm~ moving of a force onto a member, as wlicn a lit~uvy loadrd train or trilck moves rapidly owr a bridge deck, or a heavy rock rolls from the b11cl;et of a shovel onto a truck without any appreciable drop in height.

3. The inertia of the mcml~cr rmisting high acceleration or deceleration. ( a ) Rapidly ret:iprocating levers. ( b ) A machinr sohject to earthquake shocks or

explosives in wa1-fare. ( c ) The bniking of :I heavy trailer.

2. APPROACH TO DESIGN PROBLEM

In many cases it is ditficult to evaluate impact forces 'lwantitatively. The analysis is grnerally more qualitative and requires recognition of all of the factors involved and tlwir inter-relationship.

The &.signer can follow one of two metilods: I . IWimate the m~xi~num force exerted on the re-

sisting mrmher hy ;ipplying an impact factor. Colisider this fol.ce to bo a static loitd and use in standard design formulas.

2. Estimate tlic cncrgy to hc : ~ b s o r h ~ d by the resisting memhrr, and design it as an o~crgy-absorbing member.

The propwtics of the nraterial and the dimer~sions of the resisting memhcr that give it maximum resistance to an energy load, we quite differcnt fi-om those that give the member maximum resistance to a static load.

Heovy rock :oiled from shovel onto frome without ony initial drop in height:

h = O F = 2 W

Fort moving, boded wogon par ing over supporting beom:

F = between W and 2 W

Sudden ignition of missile; or niisrile miifires and then re-ignites

F = 2 T (thrust)

FIG. 1 Types of impact loading.


KiNETiC ENERGY (E,,) is the omount of work a body can do by virtue of its motion.

POTENTIAL ENERGY (ED) is the omount of work o body can do by virtue of its position.

if the supporti~ig member is flexible ond deflects, this addi- 'ional movement must be considered as port of the total height the body con foil.

t is also the amount of work a body con do by virtue of its ;tote of strain or deflection.

F d E = -

d - - 2

Spring

3. INERTIA FORCES

FIG. 2 Formulas for kinetic energy and potential energy.

Inertia is the propcrty of a member which causes it to remain at rest or in in~iiorm motion miless acted on by some external force. Inertia force is the resisting force which inust be overcome in order to cause the member to accrlcrste or decelerate, equal hut opposite to--

where:

W, = weight ~f member. Ibs

a = acceleration or decelerntion of member, in./sec2 or ft/scc2

g = ac~deration of gravity (386.4 in./sec2 or 32.2 ft/se6

4. IMPACT FORCES

A moving body st]-iking a member produces a force on the member due to its deceleration to a lower velocity or perhaps to zero velocity:

Wb = weight of body, lbs

a = dreelrrntion of body, i n . / s e ~ ~ or ft/sec2

g = acceleration of gravity (386.4 in./se+ or 32.2 ft/sec2)

In tool rondtot1 At ,ni iont of irnpoct Maximum deflection

of member ond body t

FIG. 3 Efiect of member's inertia.

esigning for impact Loads / 2.8-3

Fortunatrly the mernber will dtbflcct slightly and allow a certain time for thc moving body (W,) to come to rest, therehy reducing this impact force ( F ) .

Since the time interval is usually ~nrknown, the above formul;~ cannot hr wed directly to find the force ( F ) . Ihvever , it is us~rally possible to solve for this force by finding thc nlnount of kinetic energy (EL) or potential encrgy (E,,) that must be absorbed by th,e memlwr (Fig. 2 ) .

This applied cncrgy ( E k ) or (E,,) rnay then be set equal to tbc energy ( U ) dxorhed by the member within a given stress (a), see Table 2.

LE I-Basic Laws Used in Analvris of l n r ~ a c t

Angular

d perpcndiculnr dis:onre f rom center of rolotion to line of force

5. POTENTIAL ENERGY OF V O N MEMBE

i rodivi oi point for which w in to be iound

(See Figure 3)

Potential encrgy of falling bodv ( W , ) :

Potential energy received by deHt:cted member:

Then:

F but K =r - being the spring constant of the beam A

to a load and & s i p as tl~ongh it were a stcady load. As the weiglrt of the snpporiing nriw&r ( V ) increases, this inlp;~ct factor of ( 2 ) becomrs less.

In a similar nmuler, it is possible to exprrss the resultant impact dcflsdion ill tc:rms of s k d y load deflection.

or since V .-: \/ 2 g b

If the body ( W,,) is suddenly applied to the member witliont any appreciable drop in height (h = 0 ) , the lnaximi~m force dne to inqx~ct is twice that of the applied load (W, , ) :

6. EFFECT OF MEMBER'S INERTIA

If the weight ( ) of the stipporting mcmbcr is relatively high, some of the applied encrgy will be ;~bsorlx.d became of the imrtin of the rnemher to mov~m:snt. A good txa~nple is the cfkct of the mass of T ~ I I S , it is cominor~ practice to apply an impact factor


TABLE 2-Impact Formulos for Common Member-Load Conditions

Energy stored in member, may be set equol to kinetic energy

Bending

D

simp y suppor e concentroted lood uniform section

(Coefficient = ,1667)

concentroted lood uniform section


concentroted load uniform section (Coefficient = ,1667)

uniform section (Coefficient = .500)

round shoft

E, = shear modulus of elasticity


u = simp y suppor e uniform lood uniform section

(Coefficient = ,26671

Bending W

uniform lood uniform section


uy1 I L U = -

10 Ec2

10 E uniform lood uniform section (Coefficient = ,1000)

simply supported

concentrated load variable section so o = constant volue


Torsion

I9 0,' R L U = ------

2 E, t,,,

where R = torsion01 resistance

open section


Designing for impact Loads / 2.

a concrete bridge deck in reducing the impact forces If the applied cnergy is expressed in terms of the transferred into the member supporting it. height of fall of the body ( h ) , the reduced velocity

If the applied energy is expressed in terms of the (V,,) may be expressed in terms of a reduced effective velocity of the body (V) , the reduced velocity (V,) height ( h , ) : at instant of irnnact is-

where:

This represents the effective height the body would have to fall in order to have the reduced velocity (V,) at the instant of inpact with the member.

Wb -- weight of the body 7. ENERGY-ABSORBING CAPACITY W, 2 equivalent weight of the member OF MEMBER

If the member were compact and anc cent rated at a point, the entire weight of the member would be effective in rtducing the velocity of thc body. How- ever: the supporting mernber is spread ont in the form of a beam or frame and therefore only a portion of its weight is effective in moving along with the body and slowing it down. Tinmhenko shows the portion of the weight of the member to be used is:

Simply supported beam with concentrated load at midpoint

* Cantilever beam with ~mmzntrated load at end

W, .;- ,236 W,,,

The reduccd k i~~e t i c energy (E,) applied to the n~embm cansing stress and deflection wonld be

(WI, + W,) Ve2 - Wb V2 Ek = -- - - 2 g

U n i t Stress

The allou~able energy load, or load that can be absorbed elastically (without plastic deformation) by the mernber in bending, is basically-

where (k) is a constant for a specific type of beam with a specific t y p of loading. Table 2 shows the application of this formula to various member and load conditions, with numerical values substituted for the ( k ) factor.

Obse~vation shows that the critical property of I ,, 2

the section is --,, while that of the material is -.~L c- 2 I;'

8. lMPACT PROPERTIES OF MATERIAL

The two most important properties of a material that indicate its ability to absorb energy arc obtained from the stress-strain diagram (Fig. 4).

0 5 .. D Unit strain [ r /

FIG. 4 Stress-strain diagram: basis far material's impact properties.


The modulus of resilience ( u ) of a material is its capacity to absorb energy within its elastic range, i.e. without permanent deformation. This is represented on the tensile stress-strain diagram by the area under the crIn7e defined hy the triangle 0 A B, having its apex A at the elastic limit.

Since the absorption of energy is actually a volu- metric property, the u in (in.-lhs/in.") = u in psi.

When impart loadmg exceeds the elastic limit (or ye ld stren@h) of the material, it calls for toughness in the material rather than resilience.

The ultimate energy resistance (nu) of a material indicates its toughness or ability to resist fracture nnder impact loading. This is a measure of how well the material absorbs rnergy without fracture. A material's ultimate energy resistance is represented on the stress- strain diagram by the total area OACD under the curve. Here point 4 is at the material's yield strength (cry) and point C ;it its ultimate strength ( r , , ) . For ductile steel, the uliimate energy resistance is approxiniately-

where:

6. =. dtiinate miit elongation, in. /in

Since the absorption of energy is actually a volu- metric property, u,, in (in.-lb~/in.~) = u,, in psi.

Impact properties of common &sign materials are charted in Tablc 3.

9. IMPACT PROPERTIES OF SECTION

The section property which is needed to withstand impact loads or to absorb energy in bending is I/?.

This is very important because as moment of inertia ( I ) increases with deeper sections, the distance from the neutral axis to the outer fiber (c ) increases ~ L S its square. So, increasing only the depth of a section will increase the section's moment of inertia but with little or no increase in impact property.

For example, suppose there is a choice between these two beams:

Section Properry

Steady load rtiength I 533.4 2096.4

S :=. -- = 88.2 in? ----- - - 175 i n ? 1 1.96

I I

Impact load strength I 533.4 -- 2096.4

14.6 i n 2 111.96!' -

Beom A 12" WF 65# Beam

I

The new be:m ( B ) with twice the depth, has about 4 times the bending stiffness ( I ) , and 2 times the steady load strength ( I /c ) , but for all practical puryoses there is no increase in the impact load strength (I /cY). In this example, there would be no advantage in changing from (A) to ( B ) for impact.

Beam B 24" WF76# Beam

10. IMPROVING ENERGY ABSORPTION CAPACITY

533.4 in?

The basic rule in designing members for maximum energy absorption is to have the maximum volume of the member subjected to the maximum allowable stress. If possible, this maximum stress should be uniform on every cubic inch of the member.

I . For any given cross-section, have the maximum amount of the area stressed to the maximum allowable. In the case of beams, place the greatest area of the section in the higher stressed portion at the outer fibers.

2. Choose sections so the member will be stressed to the maximum allowable stress along the entire length of the member.

For a member snbjected to iinpact in axial tension, specifying a constant cross-section from end to end will uniformly stress the entire cross-section to the maximum value along the full length.

2096.4 in?

Designing for Impact Loads / 2.8-7

TABLE L l m p a c t Properties of Common Design Materials

A beam can be designed fol- constant bending stress along its entire longth; by making it of variable depth. Although the cross-section at any point is not uniformly stressed to the maximum value, the outer fiber is stressed to the maximum value for the entire length of the member.

Material

1-1 Steel

FIGURE 5

Alloy Steel

Gray Coif l ion

Malleable Cost l ion

In Table 3 the member in tension (No. 4 ) has t h e e times the energy-absorption capacity of the simple beam with a concentrated load (No. 1). This is because the tensile member (No. 4 ) has its entire cross-section nnifor~nly stressed to maximum for its full length. In contrast, the maxinn~~n bending stress in beam No. 1 is at thc outer fibers only; and this bending stress decreases away from the central portion of the beam, being zero at the two ends.

Notice that decreasing the depth of the beam at its supports, so the n~aximnrn bending stress is uniform along the entire lcngth of the hram, doubles the energy absorbing ciipacity of the beam. See (1) and (9).

For a steady load, doubling the length of a beam will double the resnlting bending stress. However, for an impact load, doitbling the length of the beam will reduce the resulting impact stress to 70.7% of the original.

Two identical rectangular beams can theoretically absorb the same amonnt of energy and are just as strong under impact loading. The section property

which detemiines this is I/?, and this is constant for a given rectanqular area repaniless of its position.

* Bored on integmtor-rneoruicd area under rtierr-rtroin curve.

200,000 .

6.000 - 20.000

230,000 / 30x10' 0.12

0.05

0.10

. 20,000 15 X 10'

667.0 ...

1.2 ..

17.4

22,000

70

3,800 50,000 23 X 10'

2. / Load & Stress Analysis

FIGURE 7

The two tensile bars shown in Figure 5 have equal strength under steady loads; yet, the bar on the right, having uniform cross-section, is able to absorb much more energy and can withstand a greater impact Isad.

Summary

1. The property of the section which will reduce the impact stress in tension is increased volume (AL) .

2. The property of the section which will rcduce the impact stress in a simple beam is:

3. In a simple beam, a decrease in length ( L ) will decrease the static stress, but will increase the

stress due to impact. 4. In a simple tensile bar of a given uniform

cross-section, increasing the length (1) will not alter tho static stress yet it will decrease the stress due to impact.

11. NOTCH EFFECT ON ENERGY ABSOR CAPAC lTY

In Figure 8, diagrams e and f represent the energy absorbed along the length of a member. The total energy absorbed corresponds to the area under this diagram.

Assume the notch produces a stress concentration of twice the average stress ( d ) . Then for the same maximnm stress, the average stress will be reduced to % and the energy absorbed ( f ) will be of the energy absorbed if no notch were present ( e ) . For a stress concentration of three times the average stress, the enorgy absorbed will be t k

Notched bar impact test results are of limited value to the design engineer, and can be misleading:

( a ) The test is highly artificial in respect to severe notch condition and manner of load condition.

( b ) The results can be altered over a wide range by changing size, shape of notch, striking velocity, and temperature.

( c ) The test does not simulate a load condition likely to be found in service.

( d ) The test docs not give quantitative values of the resistance of the material to energy loads.

-I- 101 Tensile member. unifbrm section Tensile member with notch k! /Stress a t notch

7 1 ,,Sfrerr in member

FIGURE 8

Designing for Impact Loads / 2.8-9

12. GUIDES TO DESIGNING FOR IMPACT LOADS

1. Design the mr.m5er as an energy-absorbing system, that is have the maximum volume of material stressed to the highest working stress; this increases the energy absorbed.

2. For any given cross-section of the member, have the maximum area subjected to the maximum allowable stress; also stress the entire length to this value.

3. The property of thc section which will reduce the impact stress in tcnsion is increased volume ( A L).

4. The property of the section which will reduce the impact stress in bending is increased I/+.

5. Increasing the length ( L ) of a beam will increase the static stress, but will decrease stress due to impact.

6. Increasing the length ( L ) of a tensile member of uniform cross-section will not change the static stress, but will decrease stress due to impact.

7. Use the basic formula, or those shown in Table 3, as a guide to select the required property of section and property of material.

8. Select material that has a high modulus of resili- us2

ence n - - . Materials having lower modulus 9. F - -

of elasticity ( E ) generally have lower values of yield strength (us), and this latter value is more important becanse it is squared. Therefore steels with higher yield strengths have higher values of modulus of resilience and are better for impact loads.

9. The material should be ductile enough to plastically relieve the stress in any area of high stress corrccntration; and have good notch toughness.

10. Thc: material shonld have high fatigue strength if the impact load is vepeatedly applied.

11. The material should have good notch toughness, and for low temperatnre service, a low transition temperatnre.

12. Reduce stress concentrations to a minimum and avoid a b n ~ p t changes in section.

13. If possible, place material so that the direction of hot rolling (of plate or bar in steel mill) is in line with impart force.

14. For inertia forces, decrease the weight of the member, while maintaining proper rigidity of the member for its particular use. This means lightweight, well-stiffened members having sufficient moment of inertia ( I ) should be used.

15. One aid against possible inertia forces caused by the rapid movcment of thc member due to explosive energy, earthquakes, etc., is the use of

FIGURE 9

flexible supports, to decrease the ac~eleration and/or deceleration of the member.

Problem 1 Accelerating a load I

k Beam

FIGURE 10

Find the load placed on the supporting beam for a hoisting unit in the shaft of a mine if the 5000-lb load (W2) is accelerated upward to a velocity ( V ) of 1800 feet per minute in 5 seconds ( t ) . The dead weight of the hoisting unit is 1000 lbs (W, ) .

2.8-10 / Load & Stress An~lyris

acceleration

a = V2 - V1

on trailer have failed, and stops from a speed of 60 miles pcr hour within 15 seconds.

= 6 ft/sec' deceleration

force of accelcratio?~

= 931 lbs force of deceleration

total load on beam F = - a W WI i- wa i- Fa = (1000) + (5000) i- (931) g

= 6931 lbs - (40'000) (5.86) - (32.2)

r 7275 lbs

The king pin on the fifth wheel, connecthe the trailer to the tractor must be designed to transfer this

Asmme the truck brak~s the trailer, because brakes force.

V = 60 MPH 6------- W : 40.000 lb i

FIGURE 1 1

F = 7275 FIGURE 12

Designing for Fatigue Loads

1. ENDURANCE LIMIT

When the load on a member is constantly varying in value, or is repeated at relatively high frequency, or constitutes a complete reversal of stresses with each operating cycle, the material's endurance limit must be suhstitnted for the ultirnate strength where called for by design formulas.

Under high load valnes, the variable or fatigue mode of loading reduces the material's effective ultimate strength as the nnmbcr of cycles increases. At a given high stress value, the material has a definite service or fatigue life, expressed as N cycles of operations. Conversely, at a given nnmber of service cycles the material has a definite allowable fatigue strength.

The end:~raiicc limit is the maximum stress to which the material can be subjected for a given service life.

2. NATURE OF FATIGUE LOADING

Fatigue failure is a progressive failure over a period of time which is started hy a plastic movement within a localized region. Although the average unit stresses across the entire cross-section may be below the yield point, a non-uniform distribution of these stresses may cause them to exceed the yield point within a small area and catlse plastic movement. This eventually produces a minnte crack. The localized plastic movement fu r th~r aggravates tlie non-iuiiform stress ditribution, and frrrther plastic movcment causes the crack to pro- ge . s . The stress is important only in that it causes the plastic nrov~ment.

Any fatigne test usnally shows considerable scatter in the resnlts obtained. This resnlts from the wide range of time required hcfore the initial crack develops

in the specimen. Once this has occurred, the subsequent time to nltimate failnre is fairly well confined and proceeds in a rather uniform manner.

The designrr when first encountering a fatigue loading probleni will often use the material's endurance limit or fatignc strength value given in his engineering handbook, ~vithnut fd ly considcring what this value represents and how it was obtained. This pro- cadure wnld lead to scrioiis trouble.

There are many types of fatigue tests, types of loading, and types of specimens. Theoretically the fatigue value used by the designer should be determined in a test that exactly duplicates the actual service conditions. The sample used should preferably be identical to the member, the tcsting machine should reproduce the actnal scrvice load, and tlie fatigue cycle and frequency should be the same as wonld be enconntcri~d in actlid scrvice. For example, if thc problem is a butt xvdd in tension, the allowable fatigue strength used in thc design must come from data obtained from loading a hntt weld in axial tension on a pulsating type of fatigne testing machine, with the same range of stress.

3. ANALYZING THE FATIGUE LOAD

Fignre 1 illustrates a typical fatigue load pattern, the cnrve represeuting tlie applied stress at any given moment of time.

There are two ways to represent this fatigue load: 1. As a niwn or average stress (v,,,) with a super-

imposed variable stress (r,, ). 2. As a stress varying from maximum value (IT,,,,,)

to a minimum (IT,),,,,!. Here, the cycle can be represented by the ratio--

FIGURE 1

I Time ----+


One approach to this problem is to let the variable stress (u,.) be the ordinate and the steady or mean stress (urn) be the abscissa. When the mean stress (urn) is zero, see Figure 2, the varihle stress (u,) becomes the value for a complete reversal of stress (u r ) . This value would have to be determined by ,experimental testing, and becomes point b in the diagram. When there is no variation in stress, i.e. a steady application of stress, u, becomes zero, and the maximum resulting mean stress (u,,) is equal to the ultimate stress for a steady load (u, , ) ; this becomes point a.

FIGURE 2

where:

"2 = fatigue strength for a complete reversal of stress

u v = variable stress which is superimposed upon steady stress

USI = ultimate strength under stead load (Some set u, equal to the yiel g strength, u7)

urn = mean stress (average stress)

A line connecting points b and a will indicate the relationship between the variable stress ( u , ) and the mean stress (u,,) for any type of fatigue cycle, for a given f a t i y e life ( N ) . This straight line d l yield

FIGURE 3

conservative values; almost all of the test data will lie just outside of this line.

From similar triangles it is found that-

A Goodman diagram, Figure 3, is constructed from Figure 2 by moving point a vertically to a height q u a 1 to u,,; in other words, line a-c now lies at a 45" angle.

It can be shown by similar triangles that the same relationship holds:

esigning for Fatigue Loads / 2.9-3

The Goodman diagram of Figure 3 may bc modified so that the ordinate becomes the maximum stress (urn,,) and the abscissa becomcs the minimum stress (urnin); see Figure 4. It can be proved that all three diagrams yi'eld the same results. The American Weld- ing Society (Bridge Specification) uses this last type of diagram to illustrate their fatigue data test results.

If the maximum stress (urn,,) lies on line a-b, this value is found to be-

urnin where K = - urnax

The next diagram, Figure 5, is constructed with the values for complete reversal ( a , ) and the ultimate strength (u , ) for butt welds in tension. The fatigue data from test results are also plotted. Notice the values lie on or slightly above these straight lines for service life ( N ) of 100,000 cycles and that of 2 million cycles.

These "dependable values" have been reduced to some extent below the minimum values obtained in the test. A factor of safety is applied to obtain allowable values; these are shown hy dotted lines. This is expressed as a formula along with a value which should not be exceeded. In this case, the maximum allowable is 18,000 psi. This formula represents thc slanting line, but a maximum value must be indicated so that it ir not carried too far.

Figure 6 illustrates several types of fatigue cycles, with conesponding K values to be used in the fatigue strength formulas.

ABLE MAXIMUM STRESS

Fatigue strength formulas, for determining the allowable maximum stress for a given service life of N cycles, are presented in Table 1 for A7 mild steel, A373 and A36 steels, in Table 2 for A441 steel, and in Table 3 for T-1, quenched and teropered high yield strength steel.

Reqnircd fatigue life or number of cycles will vary but usually starts at several hundred thousand cycles. It is assumed that by the time the value of several million cycles is reached, the fatigue strength has

@ 100,000 cycler 2,000,000 cycles

Allowable values- - - - -

+ 1 0 + 2 0 + 3 0 + 4 0 + 5 0 + 6 0 + Minimum stress, ksi

FIGURE 5


leveled off and further stress cycles wor~ld not produce failure. For any particular specimen and stress cycle there is a relationship between the fatigue strength (o-) and fatigue life ( N ) in number of cycles before failure. The followmg empirical formula may be used to convert fatigue ytrengths from one fatigue life to another:

where:

= fatigue strength for fatigue life N.

ub --. fatigue strength for fatigue life Nb

N, = fatigue life for fatigue strength o-,

Nb = fatigue life for fatigue strength ub

Bane Metol in Tension Connected By Fillet Weldr But not to exceed

Bare Metal Compression Connected By Fillet Weidi

Butt Weid in Tension

But1 Weid Comprersion

Butt Weid in Shear

-- fillet Weids 0, = Leg Sire

The constant (k) will vary slightly with the specimen; however, 0.1:: has been widely used for butt welds and 0.18 for plate in axial loading (tension and/or compression ) .

The curve in Fignre 7 illustrates the general increase in fatigue life when the applied fatigue stress is reduced. As an cxarnple, in this case, reducing the fatigue stress to 75% of its normal value will in general increase the fatigue life about nine times.

Test data indicates a fatigue life of N, = 1,550,000 cycles when the member is stressed to oa = 30,000 psi. What would be the fatigue strength at a life of 2,000,000 cycles?

LE 1-Allowable Fatigue Stress For A7, A373 and A36 Steels and Their

2,000,000 cycler

--

@ 9.000 r = ----

K psi 1 - -

2

0 10.500 c = --------- psi

I - 2 1 3 K

0 18,000

d- = -- psi I - .8K

.

0 10.000

7 = -- K psi

i -- 2

0 18.000

'T = K psi 1 - - 2

But Not to Exceed

2 P, - I( psi

Pt psi

---

PI psi

Adopted from AWS Bridge Specificotionr. K = minlrnox P. = Allv.voble unit compressive stress far member. Pt = Allowable unit tensile stress for member.

FIGURE 6

esigning for Fatigue Loads / 2.

I I / " mln = + max K = + 1 - Time ---+- + (steady) -

I 1 " min = + 1/2 m m K = f 1/2

Time - - + -

min = 0 K = f l Time - - + -

4 : " I

mln = - max K = - 1

[complete - I reversal) -

FIGURE 7

For butt welds, k = .I3

Increase in fatigue life

2.9-6 / Load 8, Stress Analysis

Base Metal in Tension Connected By Fiilet Weidr

Bore Metal Compression Connected By Fillet Weldr

Bun Weld in Tension

Butt Weld In Shear

Fiilet Weidr w = leg liz

LE 2-Allowable Fatigue Stress For A441 Steel md i t s Welds

2.W0.000 I 600,000 cycler cycler

100,WO cycler

@ f = 8800 iblin.

i - f i R

But Not to Exceed

.- 23 pRI psi

PC psi

PC -- psi 1 - i/z R

Pt psi

* = 10,400 w iblin.

Adapted from AWS Bridge Specificotionr. * if SAW-I, use 8800 R = .in/mox load

p, = Allowable unit tenriie rtiesr for member P, = Allowable unit cornpierrive rtierr for member

TABLE 3-Allowable Fatigue Stress uenched ond Tempered Sfeels of High Yield Strength

. n - - lap.TT Fiilet Weld 6 360 W w = leg size

9,900 w f = 2-- Ibrlin. f = ------- 14,500 W

Ibrlin. f = Ibrlin. f = 26.1600 Ibrlin.

i - .A0 K I - .75 K 1 - .6O K

I I I I

Above valves adopted from "The Fabrication and Design of Structurer of 7-1 Steei" by Gilligon and Englond, United Stater Steel Cotporotion.

Designing for Fatigue Loads /

FIGURE 8 FATIGUE NOMOGRAPH

Since:

55 = ( ) (For butt welds, k = 0.13) or: W b

Given: Test data indicates a butt-weld fatigue life of N, = 1,550,000 cycles when the member is stressed to a, = 30,000 psi

Find: The weld's fatigue strength (ab] at 2,000,000 cycles (N,)

and since the butt weld's k factor is .13, the nomograph indicates

-- ah -- 96.8% 0-

or a, = 30,000 X 96.8% = 29,000 psi

ii 3 = (2-) and: 0,

Using logarithms* for the right hand side:

= 0.13(log 0.775) = 0.13(9.88930 - 10)

= 1.285fX9 - 1.3 (add 8.7 to left side and + 8.7 - 8.7 subtract 8.7 from right side)

9.985609 -10.0

The anti-log of this is 0.96740; hence:

= 29,020 psi at Nb = 2,000,000 cycles) - The nomograph, Figure 8, further facilitates such

conversion and permits quickly finding the relative allowable stress for any required fatigue life provided the fatigue strength at some one fatigue life is h o w n and that the constant k value has been established. Conversely, the relative fatigue life can be readily found for any given stress and any constant (k) . - * A log-log slide rule could be used to find the value of 0.775 raised to the 0.13 power.

/ Load & Stress Analysis

5. RELATIVE SEVERITY OF FATlG

In Figure 9, the allowable fatigue stress is the vertical axis (ordinate) and the type of fatigue stress cycle ( K = min/max) is the horizontal axis (abscissa).

The extreme right-hand vertical line (K = + 1) represents a stcady stress. As we proceed to the left, the severity of the fatigue cycle increases; finally at the extreme left-hand axis (K = - I ) there is a complete reversal of stress. This is just one method of illustrating fatigve stress conditions. The important thing to be noticed here is that actual f a t iye strength or allowable fatigue values are not reduced below the steady stress condition until the type of cycle (K = min/max) has progressed well into the fatigue type of loading.

In the case of 2 ndlion cycles, the minimum stress must drop down to '/z of the maximum stress before there is any reduction of allowable strength. In the case of 100,000 cycles, the minimum stress can drop to zero before any reduction of allowable strength takes place. Even at these levels, the member and welds would be designcd as though they were subjected to a steady load. The stress cycle must extend into a wider range of fluctuation before it becomes necessary to use lower fatigue allowables.

In other words, a fatigue problem occurs only if- 1. Stress is very high, 2. Anticipatrd service extends for a great number

of cycles, 3. Stress fiuctnates over a wide range. And it generally rcquires a11 three of these situa-

tions occurring simultaneously to produce a critical fatigue condition worthy of consideration.

The allowable fatigue strength values obtained from the formulas in Table 1 take all three of these into consideration, and it is believed they will result in a conservative design.

Several formulas are available for this consideration but very little actual testing has been done on this. In many cases there is not very good agreement between the actual test and the formulas.

1. Principal-stress theory -

2. Maximum shear-stress theory- --

we = $\r(w, - v,)~ +- 4 7.2

FIG. 9 Severity of fatigue depends on stress value and range of fluctuation, as well as service life.

esigning for Fatigue Loads /

TABLE &-Fatigue Strength o# Butt Summary of Results, Using %-In. Carbon-Steel Plates

FATIGUE STRENGTH I N 1000's OF PSI -- --

Ar Welded 1 22.3 1 14.4 1 33.1 I 22.5 1 53.3 / 36.9

Derctiptian of

Specimen

Reiniorcement On 31.9 Sties, Relieved

Reinforcement Mochined Off / 28.9 1 / 48.8 1 28.4 / 1 43.7 Not Strera Relieved I I

Reinforcement Mochined Off 1 24.5 1 16.6 / 49.4 1 27.8 1 1 42.6 Stress Relwed

TENSION TO AN EQUAL COMPRESSION

Reinforcement Ground Off 26.8 1 1 44.5 1 26.3 1 1 Not Stress Relieved

-- N =

100,OW

Plain Piole Mill Scoie On

TENSION TO TENSION

if> AS GREAT -- -

N = N= 100.000 2,000,000

N = 2,000,000

O

Ploin Plote Mili Scole Machined O i i

ond Surioce Poished

- N =

100.000

Bun Weld. Reinforcement and Miii Scoie Mochined Off

ond Suiioce Polished

- N =

2,000,000

3. Shear-stress-invariant theory- -

me = vux2 - UxU7 + fCTy2 + 3 rxy2

4. Combined bending and torsion. Findley corrected shear-stress theory for anistropy-

where ub/?- is the ratio of fatigue strength in pure bending to that in pure tension.

5. Combined tensile stresses. Gough suggests-

where: uo, = fatigure strength in (x) direction

a,, = fatigue strength in ( y ) direction

a, and uy = applied stresses

7. INFLUENCE OF JOINT

Any abrupt change of section along the path of stress Bow will reduce the fatigue strength. It is not welding that effects a reducing of the fatigue strength but the resultant shape or geometry of the section. It is for this reason that fillet welds have lower fatigue strength. simply because they are used in lap joints and all lap joints including riveted joints have lower fatigue strength.

TABLE 5-Effect of Transverse Attachments On Fatigue Strength -

I I 1 7 6 U

100,000 cycler 25.800 psi 25,400 pri I 22,900 p d

2,000,000 cycler 1 22,800 psi I 18.9OOpri I 13,100 pi

Stress Analysis

By means of Table 4, we can see that removing the reinforcement of a butt weld increases its fatigue strength to that of unwdded plate, also that stress relieving the weld has no appreciable effect on its fatigue strength.

Table 5 illustrates the effect of transverse fillet welds upon the fatigue strength of plate, this is %" plate.

The attachment causes an abrupt change in section, and this reduces the fatigue strength of the plate. It is believed these results could be duplicated by machining these joints out of solid plate, without any welding.

ING FOR FATIGUE LOADING

I. Usually a member is stressed to the full maximum value for only a portion of its fatigue life or cycles. For most of its fatigue life, the member is stressed to a much lower value, and not to its full rated capacity; hence, most fatigue loading is not as severe as it may first appear.

Consider actual stress rather than average stress. Reduce if possible the range of stress without

increasing the maximum or average stress. 2. Fatigue loading requires careful fabrication,

smooth transition of sections. Avoid attachments and openings at locations of

high stress. Avoid sharp comers. Use simple butt weld instead of lap or T fillet

weld. Grinding the reinforcr:ment off of butt welds will

increase the fatigue strength. This weld will have about the same fatigue strength as unweldt-d plate. Grinding, however, should not be specified unless essential, sincc it does add to the final unit cost.

Avoid excessive reinforcement, undercut, overlap, lack of penetration, roughness of weld.

Avoid placing weld in an area which flexes. Stress relieving the weld has no appreciable &ect

upon fatigue strength. DBiculties are sometimes caused by the welds

being too small, or the members too thin. 3. Under critical loading, place material so that

the direction of rolling (of plate in stml mill) is in line with force, because the fatigue strength may be higher in this direction than if placed at right angles with the direction of rolling. See Figure 10.

4. Where possible, form member into shape that it tends to assume under load, and hence prevent the resulting Aexial movement.

5. Avoid operating in the critical or resonant fre-

quency of individual member or whole structure to avoid excessive amplitude.

6. Perhaps consider prestressing a beam in axial compression. This will reduce the tensile bending stress and lessen chance for fatigue failure even though the compressive bending stress is increased to some extent.

7. Avoid eccentric application of loads which may cause additional flexing with each application of load.

8. Stiffeners decrease flexibility of panel and result in better fatigue strength, unless they cause a more abrupt change of section.

9. A rigid frame type of structwe or statically indeterminate type of structure may be better than a simple structure since the load is shared by other members; hence, the structure is less likely to collapse immediately if a fatigue failure starts in one member.

10. Avoid biawial and triaxial stresses, avoid restrained internal sections.

~ e c o m e ~ d e d method if fatique or impact ioodinq

Direit8on of hot rollinq ofsheets insteel mills

eecowend of Least on boitom h d f or thlrd,or w h o i e tank, s h e e t s be run lenqthwise with tonk

FIG. 10 Grain direction of sheet or plate should be in line with force, for greater fatigue strength.

SECTION 2.1

Torsional loading is the application of a force that tends to cause the member to twist about its simxtural axis.

Torsion is usually referred to in terms of torsional moment or torque ( T ) , which is basically the product of the externally applied force and the moment alm or force arm. The moment arm is the distance of the centerline of rotation from the line of force and perpendicular to it. This distancc often equals the distance from the member's center of gravity to its outer fiber (radius of a round shaft, for example), but not always.

The principal deflection caused by torsion is measured by the angle of twist, or by the vertical movement of one comer of the frame.

Steel, in rolled structural shapes or built-up sections, is very efficient in resisting torsion. With steel, torsionally rigid sections are easily developed by the use of stiffeners.

Here are the three basic rules for designing sbuctural members to make the best use of steel where torsional loads are a problem:

1. Use closed sections where possible. 2. Usc diagonal bracing. 3. Make rigid end connections.

When a round shaft is subjected to a twisting or torsional moment (torque), the resulting shear stress in the shaft is-

where:

T = shear stress, psi

c = distauce from centcr of section to outer fiber

T = torque, in.-lhs.

J = polar moment of inertia of sedion, = IX + I7 = 21

The angular twist of a round shaft is-

where:

B = over-all angular twist of shaft, in radians (1 radian = 57.3" approx.)

I, = length of shaft, in iuches

E, = modulus of elasticity in shear (steel E, = 12,000,000 psi)

In most cases, the desiper is interested in holding the torsional moment within the material's elastic limit. Where the torsional strength of a round shaft is required (i.e. the stress it can take without failure), the polar section modulus is J/c, and the allowable torque is thns-

J T = T,, -- c

where, lacking test data, the ultimate shear strength of steel ( 7 , ) is assumed to be in the order of 75% of the material's ultimate tensile strength.

The above three formulas are true for sdid round or tubular round shafts. For non-circular sections the shear stresses are not uniform, 'and therefore the standard torsional formulas no longer hold.

3. TORSIONAL RESISTANCE

Valucs of torsional resistance (K)-stiffness factor- have hem estahlish~d for various standard sections and provide more reliable solutions to torsional rigidity problems. Values of R are exprssed in inches to the fourth power.

Table 1 shows the formulas for shear stress and torsional resistance of various sections. The formulas for solid rectaiigitlar sections caU for valurs, of a and ,8, which are derived froin the ratio of section width ( h ) to depth ( d ) , as shown in the table.

Actual tests show that the torsional resistance ( R ) of an open section made up of rectangular areas, nearly equals the sun1 of the torsional resistances of all thc individual rectangular areas. For example, the torsional resistance of an I benm is approximately

2.10-2 / Lood & Stress Analysis

FIGURE 1

equal to the sum of the torsional resistances of the two flanges and weh (Fig. 1).

Figure 2 shows the results of twisting an I beam made of three equal plates. Calculated values of twist by using the conventional polar moment of inertia ( J ) and the torsional resistance ( R ) are compared with the actual results. This shows greater accuracy by using torsional resistance ( R ) .

This means that the torsional resistance of a flat

/ Angle of twist

Conventional

poior moment

Resistonce

FIGURE 2

TABLE I-Torsional Properties of Various Sections .- - ..

(for steel) Section / Shear stress R4orsionai Resistance

i b - = 1.00 1.50 1.75 2.00 2.50 3.00 4.00 6 for mlid d rectangular- - - -

jsections a 208 1.31 ,239 .246 .258

Use t4.s [&yo& Rz3.542 bracing l of

ning for Torsional Loading / 2*T&

! Angle of twist !

FIGURE 3

plate is approximately thc same whether it is used as such or is formed into an angle, channel, open tube section, ctc. This is illustrated in Figure 3. Samples of different sections made of 16-gage steel are subjected to torsion. The flat section twists 9". The same piece of steel formed into a channel ( b ) twists 9%". When rolled into a tube with an open beam ( e ) , it twists 11".

When the same section is made into a closed section ( d ) by placing a single tack weld in thc middle of the open seam, the torsional resistance increases several hundred times. When the tube becomes a closed section, the torsional stresses are distributed more evenly over the total area, thus permitting a greater load.

Notice the emor in using polar moment of inertia ( J ) for the angle of twist of open sections, and the good agreement by using torsional resistance (R).

The solid or tubular round closed scction is best for torsional loading since the shear strmses are uniform around the circumference of the member.

Next to a tubular section, the best section for re-

FIGURE 4

sisting torsion is ;i closed square or rectangular tubular section.

Tablr 2 provides formulas for dstexmining the torsional rt~sistarrce ( R ) of various closcd tubular sections. It also provides tire basic fomiulas for detemin- ing the shear stress ( T ) at any given point along the sidewall of any closed section regardless of configuration or variation of thiclaicss, and for determining the section's torsional resistance (R) .

T lk poorest sertions for torsional loading are open sections, flat plates, angle sections, channel sections, Z-bar sectioris, T-har sections, I-beam sections, and tubular sections which have a slot.

FIGURE 5

After the R values of all areas in a built-up section have becn added together, their sum is inserted into the following formula or n modification of it:

Torque ( T ) in in.-lbs may be obtained from one of the formulas in Table 3, such as-

63,000 X IIP T =. -- RPM

where:

HP = horsepower

RPM = speed of revolution

P I- applied force, lbs

e = moment arm of force (the perpendicular distance from the center of rotation to the line of force)

As an example, consider the torsional resistance of a closed round tube and one that is slotted. The tube has an O.D. of 4", and I.D. of 3", a length of 100f', and is subjected to a torque of 1000 in.-lbs.


Case 1 CA

From Table 1, the torsional resistance of the closed round tube is found to be-

R = 0.0982 (dyi - dl4)

= 0.0982 (4' -31)

and the angular twist is-

= 0.000485 radians, or 0.0278" --

FIGURE 6

Case 2

From Table 1, the tors~ollal resistance of the slotted round tube is found to bc-

LE 2-Torsional Resistance ( ) of Closed Tubular Sections

-= enclosed within mean dimensions. == length of p~ r t i cu ia r segment o i section = overage thickness of segment at point Is! = sheoi rtresi a t point (i! == torsion01 resistance, in4 = modulus of eloiticity in rheor

(steel = i2.000.000i 0 = onguloi twist lrodionr) L =; length of member (inches! f = unit shear force

R - 1.0472 t:! d


-- 0.018 radians, or 1.04"

Thus, the tube witlmut the slot is many times more rigid than the slotted tube.

1 Problem 2 1 Two 6" X 2" X 10%-lb chaniids are to be used in making a 100"-long frame, which will be subjected to a torque of 1000 in.-lbs. In what relationship to each other will these channels offer the greatest resistaxe to twist?

Case 1

These two channels when separated but fastened together by end plates do not have much torsional resistance.

FIGURE 7

From Tdhk 1 . the \.due of R for each of the flanges is found to b e -

Rl = 0.0306 in4

and that of each web is-

RP = 0.0586 in.'

and thus the total angular twist is-

= 0.0348 radians, or 2.0" --

esigning for Torsional Loading /

LE 3-Formulas ~ O P Determining Safe Torque Under Various

Case 2

When these two channels are securely fastened back to back, there is suitable n:sistance to any slip or movemcnt due to horizontal shear. Here the two webs are considercd as one solid web, and the top and bottom flanges are considered solid.

Based on tangential load:

Based on horsepower transmitted:

63,030 X NP r = RPM

--

Based on strength of shaft:

- where S, = 25,000

2945 dz4 - dl4 T = -- dz

Based on safe twist of shaft (.08"/ft):

Based on fillet weld leg size around ihaft or hub:

Based on butt weld size around hub:

T = 20,420 d2 t

FIGURE 8


From Table 1, thc value of R for each of the two conlposite flanges is found to he-

R1 = 0.066

and that of the composite web is-

R? = 0.459 in4

m d thus the total angular twist is-

= 0.0141 radians, or 0.81" -

~ohich is much less than in Case 1

Case 3

If these two channels were welded toe to toe to form a box section, the, torsional resistance would be greatly increased.

From Table 2, the value of Fi for a box section is found to be-


= 0.00027 radians, or 0.015" -

which is far less than in Case 2, which in turn was much better than Case 1.

Torsional Resistance Nomograph

A panel or other member may be sufficiently resistant to deflection by bending, and yet have very low torsional resistance.

The nomogl-aph, Figure 10, permits the designer to quickly find the torsional resistance of a proposed design. The total torsional resistance of a built-up design equals the sum of the resistances offered separately by the memhers.

On this nomograph:

Line 1 = Type of section, or element of a built-up scdion. Obscrve caution as to meaning of letter symbols. For a solid rectangular section use the ratio of wiclth ( a ) divided by thickness (b ) ; for a hollow rectangular section use width ( b ) divided by depth ( c ) .

Line 2 = Dimmsion (a) , in. Line 3 = Pivot line Line 4 = Dimension ( b ) , in. Line 5 = Torsional resistance of the section (R) , i n 4

Thcse values for cacli crlement are added together to give tho total torsional resistance of the section, and the resistances of the sections are added to give the total torsional resistance of the frame or base. This is used in the design formula for angular twist, or in the next nomograph, Figure 14.

In the ease of a member having a built-up cross- section, such as a T or I beam, read the Figure 10 nomograph for the R value of each element or area making up the section. Start at vertical Line 1 in the nomograph, using the scale to the right of i t that expresses the rectangular element's a/b ratio. i n the case of solid squares or rounds, and closed or open round tubes, go dil-cetly to the point on the scale indicated by the visnal represontation of the cross- section.

Notice that the meaning of a and b varies. In the case of a rectangnlar element, a is the longer dimen- sidn; hut in the case of a hollow rectangle, (I is the wall or plate thickness. The valuc of a or b on Lines 1, 2 and 4 must correspond, according to the type of section or element for which torsional rcsistance ( R ) is sought.

For hollow rwtangnlar sections (of uniform wall or plate thickotxs j , use the scale along the left of vertical Line 1 that expresses the ratio b/c. Here b - the section's width and c = its depth.

U M SHEAR STRESS IN BUILT-UP SECTIONS

The maximum shear stress of a rectangnlar section in torsion lies on thc surface at the center of the long side.

For the maximum shear stress on a narrow rectangular section or section element-

eaigning for Torsional Loading /


FIGURE 11

where:

Q, = unit angular twist of whole section (each element twists this amount), in radians/linear inch of member

t = thickness of rectangular section

R = torsional resistance of entire member, not necessarily just this one flat element

This formula can be used for a flat plate, or the flat plate of a built-up section not forming a closed section (i.e. channel, angle, T- or 1-beam section).

111 such a built-up open section, the unit angular twist (4) of the whole member is first found:

and then the maximum shear stress in the specific rectangular element.

'1 FIGURE 12

7-

I Problem 3 I A 6" X 2" X 10%-lb channel is subjected to a torque of T = 1000 in.-lbs. Find the shear stress along the web. See Figure 13.

Applying the fotmula for rectangular sections from Table 1, find the torsional resistance of each of the two identical 2" X %" flanges (R, ) and of the gr X 5/16" web ( R 2 ) :

Then:

= 2,580 psi

I Problem 4 1 Two 6" X 2" X 10%-lb cha~mels are welded toe to toe, to form a short box section. This is subjected to a torque of T = 100,000 in.-lbs. Find the horizontal shear stress at the toes and the amount of groove welding required to hold these channels together for this torsional load. See Figure 14.

From Table 2, the shear stress at mid-length of the short side is found to be-

T where:

Shear stresses tend to concentratc at re-entrant b = 6 - % = 5.625"

corners. In this case, the maximum stress valne should d = 4 - XB = 3.6875" be used and is- [A] = bd

- - .. 100,000 2(5.625 X 3.6817%

where a = inside corner radius. = 6420 psi

, FIGURE 13

Designing for Torsional Loading / 2.1

FIGURE 14

I

Two 6" x 2" x 10B# channels

The horizontal shear force is then-

f = 7 . t

1 6420 X ,375

= 2410 lbs/linear inch

Since weld metal is good for 13,000 psi in shear, the throat or depth of the continuous hutt weld must he-

The groove weld connecting the channels must have a throat depth of at least 3/16". Of course, if the - torsional load is applied suddenly as an impact load, it would be good practice to add a safety factor to the computed load. This would then necessitate a deeper throat for the hutt weld.

Check the following built-up spandrel beam supporting a wall 12' high, made of 4" of limestone and 9" of brick. The heam's span is 20', and the dead load of the wall is applied 6" off the beam's centerline.

FIGURE 15

4" limestone -t 9" brick = 140 lhs/sq ft Since the wall is 12' high, this is a load of 1680

lhs/lincar ft or 140 lbs/linear in. Or, use w = 1.56 Ihs/lin in. to include beam weight.

bending resistance (monwnt of inertia)

torsional resistance

= 442 in."

The eccentricity of the dead load applies torque to the beam. From torsional member diagrams in Refer- ence Section 8.2:

uniform torque

t = 150 lhs/in. X 6"

= 900 in.-lbs/in.

angular tzoist at center of beam

= ,00122 radians (or .07") k b ' = 8.5" -"f


torque at end total shear stress

torsional shcar stress

= 1410 psi

T T =

2 [A1 ts

unit shear force from torque

f t = . i t

= (1410) ('12)

= 700 lbs/in.

where:

t, = thickness of single web

unit shear force along N.A. from bending

v = w L/2

= (150)(120)

= 18,000 Ibs

FIGURE 16

-. - : 18,000) (10 x 4.5 + 1 x 2.0) -. (449.3) ( 2 webs)

total unit shear force on beam web (each)

f, = f t i- f t ,

= (700) $- (860)

= 1560 ibs/in.

= 4100 psi OK -

Then to determine the required size of Ulet weld between flange and web:

FIGURE 17

unit shear force at weld from bending

unit shear force at weld fvom torque

ft = 700 lbs/in.

total unit shear force at weld

f, = f t 4- f,, = (700) + (900)

= 1600 ibs/in.

required k g size of fillet weld (E70)

actual force w = - allowable force

However, because of the 1" flange, AWS Bldg. 212, AWS Bridge 217 and AISC 1.17.4 would require a x,,, h .

for Porrioslcll Loa

Tht, r i n i l e s of torsicii~ wliicli dctermin:: iht: bcst sectioi~s fur resisting twist apply to buil t -II~ fx~~lir~es. Just 1 1 t h torsio1t:il rcsist:rnw of the section i s i:qil:~l to the total of tlii. r~~sisi:~rices of its itidi~i1111;il arms, so is the torsional n'sist:u~ce of a fr:tme approxix~i:i!cIy equ;tl to thr totd I-r-ds!;rnce of it: jnrlivid~l:il p r i s .

Tlte tcasional rcsidance of the fvnmc nhos,: litrigi- t u d i d rn~.nibers art: two chan11i:ls wo~ild be :ippn)si- matply eq11,ll to twin, the torsi~ioal rvsistancc of wch channel section, Figure 18. T ~ I , (lista~iw betwwr thost. mentbers fur purpose of this ~,x;~mplt: is considered to have, no effect. Sincc t h ~ . c los~d sectioir is best for rc- sistirig twist, the torsional resistmce of this frame coulil be greatly increased by making t h o channels into rectangular box sections through the addition of plate.

A frame is made of two 6" standard pipes, spaced 24" between centers, and having a length of 60". Tl~is frame supports a 10-hp motor. running at 1800 lljm and driving a pump. Find the approximate twist of the frame undcr tho load.

FIGURE 19

The, 6" standard p i p h:is O.D. I fi.C;i?!ir' and I.D. = ROHi" , In finding t i i t . lorsioi~al r!%st:~nce of each tube:

The torque is easily found:

FIGURE 18

Then, adding together the X of each tube, the angular twist is:

= 0.0000156 radians, or 0.00089"

Maxinmm deflection in the frame is the vertical displacement ( A ) , which is the product of ailgular twist ( 8 ) arid frame width (W) between centers:


FIGURE 20

4 members t

The longitudinal members are now considered to TL TT .'. PL = - and PT = --- - make up a frame of their own. 'When the vertical force \V L (PL) applied at the corncr rcaches the proper value, the frame will deflect vertically the given distance ( A ) and substituting for PL and PT - and each longitudinal member will twist (81,). The same separate analysis is also made of the transverse A E, n~ RL A E, n.r Rr

PI, = -- W2 L

and PT = members. W I,"

By observation we find-

A = & W - - @ T L

Then:

A A & = - a n d & = -

W L

Since the external force ( P ) applied at the comer is the sum of these two forces:

and s~~bsti tut ing for 0,. and BT - where:

L = length of whole framc, in. A TI. L A 'pr l\rW - - . aItd ~... = W = width of \vhole frame, in. W - E, IIL RI. I, C, rrr Rr

RI. = torsional resisttince of longitudinal member, Then: in."

Using the common formula for angular twist-

TL 1. TT W . - - & = ----- ~- . and 81. =

A I<* IIL fir. A E IIT RT RT = torsional resistance of transverse member, T,, -- TT -5 W L W 1, in,4

. . . . . ( 4 )

Since the applied torque is-

E, n~ RI. E, n~ KT

nr* = numbor of longitudinal mcmbers

n r = number of transverse mcmbcrs

TL = PL W and TT = PT L P = load applied at comer, 1bs

esigning Cor Torsional Loading / 2.1

FIGURE 21

E, = modulus of elasticity in shear (steel: 12 X lo6), psi

A = vertical deflection, in.

It can be seen that the torque on a given member is actually produced by the transverse forces supplied by the cross members attached to them. These Fame forces subject the cross members to bending. In other words, the torque applied to a member equals the end moment of the crosq member attached to it. There is

some deflection due to bending of all the members, and this would slightly i~lcrcase the over-all deflection of the frame. For simplicity this has been neglected in this analysis.

p z z q To illustrate the use of the preceding deflection formula, consider a small elcvator frame 15" wide and 30" long, made of standard 3" channel, Figure 21. Find the

TABLE 4--Torsional Resistance of Frame and Various Sections

Deflection of Frame Under Torsional Lood Torsional Resistance of Common Sections 1

P L W 1 A = - Ln: - + - nT:]

R = 2 t t, ( b - t)2(d - t p

d L

b t + d t,- t2 - t12


Wall load

3%" X 13" box sectlo

8" X 8" box sectcon

FIGURE 22

vertical deflection of the unsupported comer when centerlines of the longitudinal members is 34.75", and under a load of 5 lbs. the latter are 82" long. Determine:

Using the appropriate formula from Table 4, a ) The approximate vertical deflection of the un- torsional resistance of the U channel cross-section supported comer, 1s - b) the shear stress in lougitudinal and transverse

members, and 2 ht," dtS3 - 2 htr3 + dtw3 R = -

c ) the size of the connecting weld between the 3 3 longitudinal and transverse members.

- -- 2 (1.875) (.3125)3 + 3( 1875)3 3 3 torsional resistance of longitudinal membe~s

Substituting actual values into formula #4:

The actual deflection when tested was-

2 b2 d? A = .030" RL = -- b d - + - ti, td

~ ( 3 ) ~ (113/4)= - The struchlral frame of Figure 22, simply supported - ( 3 ) + (11~47 at three comers, is designed to support a 17-kip load ( 1 (%) at its unsupported comer. Here the width between = 137.5 ia4

FIGURE 23

erigning for Torsional Loading / 2.1

tolswnal resistance of transoerse member (only one in this example)

FIGURE 24

oertical deflection of frame

P W L A = - - -. . - - 1 "s [+di + yT]

long side of its cross-section is -

= 3820 psi

shear stress in transverse member

In a similar manner it is found that the applied torque on the transverse member is -

See formula development, p. 2.10-12

Since the cross-section of the transverse member is a hollow rectangle of uniform thiclaess, the shear stress at mid-length along either side of the section 1s -

-- (438,500) ( 17,000) ( 34%) (82) - -- -- - i 1 I - Z(7.5 X 9.5)(%)

(12 X 10") (2) (137.5) + 11) (298.3) ( 343h) (82) = 6160 psi

= .35" size of connecting fillet weld

shear stress in longitudinal member

The applied torque on only one longitudinal member is -

TL = A Ea nL R1' See formula development, p.2.10-12 W L

- (35) (12 X 10" (l)(l37.5) - .. .- .

(31%) (82) = 202,500 in.-lbs, each member

The shear stress at midpoint of the longitudinal member, on the short side of its cross-section is -

= 2300 psi

and the shear stress at midpoint of the member, on the

Treating the weld as a line -

FIGURE 25

ming for Torsional Loading / -17

Resolving combined forces on weld at point of greatest effect -

Transverse member

FIGURE 28

Since 11,200 lbs is the accepted allowable load per linear inch of fillet weld having a 1" leg size, the minimum leg size for this application is -

3560 0 = --

11,200 - (E70-weld allowable)

The two main stresses on a member under torsional loading are (1 ) transverse shear stresses and (2 ) longitudinal shear stresses.

These two stresses combine to produce diagonal tensile arid compressive strcsses which are maximum at 45" At 45', the transverse and longitudinal shear stresses cancel each other. Therefore, there is no twisting stress or action on a diagonal member placed at 45" to the frame.

In a frame made up of flat members, the transverse shear stresses cause the longitudinal members to twist. The iongitudinal shear stresses cause the cross braces and end members to twist.

On a diagonal mcmber at 45" to axis of twist, the transverse and Iougitudinal shear stress components are opposite in direction to each other and cancel out, but in line with this member they combine to produce diagonal tensile and compressive stresses wlueh tend

L~ngthwise memoers and

, , cross members are subject ., \, to twisting action of the

\ shearhy stresses

/-\ diagonal \ brace) ,

There i5 no twisting action on 45'diagonal member since s h e a r components cancel out

Only dm gonal tensibn comprass/on a re formed, which place member in bending> I / member is very r ig id . V

FIGURE 29

to cause bending rather than twisting. See Figure 29. Since these two shear stresses cancel out, there is

no tendency for a diagonal member placed in this direction to twist.

The diagonal tcnsih: and compressive stresses try to cause this diagonal member to bend; but being very resistant to bending, the diagonal member greatly stiffens the entire frame against twisting.

Stiffening the Braces

Previous experience in designing longitudirral side mcinhcrs for bending is now used to design these diagonal n~embers.

It is important that the diagonal members have a high moment of inertia to provide suAicient stiffness so there will bo no f:~ilurr from local buckling, under srvcre torsional loads.

Since the diagonal brace is not subjected to any twisting action, it is not necessary to use a closed box section.

For short diagonal braces, use a simple flat bar. The top and/or hottom panel of the frame will stiffen this to some extcnt (Fig. 30). As the nilsupported length of the diagoilal brace becomes longer, it may becomc necessary to add a flange (Fig. 31). This is

/ Load & Stress Analysis

done by flanging one edge of the brace or using an angle kar or T section. The flange of the brace may also be stiffcncd to keep it from buckling.

For opcn frames with no Aat panel, it is better to use a channel or I beam section having two flanges (Fig. 32).

elative f ffectiveness of

Tests were made on scale models of typical machine frames to illustrate increase in resistance to twist as a result of the diagonal bracing.

FIGURE 31

FIGURE 32

FIGURE 33

esigning for Torisonal Lcadin

FIGURE 34

The top frame in Figure 33 has conventional cross A = . bracing at 90' to side members. It twisted 9".

(' F, Y3 (simply supported) 48 E I

The above frame is little better in resistance to twist than a flat sheet of the same thiclmess, as shown A - -- ' a - - F Y3 %==- in the middle. The plain sheet twisted 10". L 12 E I L,

The bottom frame has diagonal braces at 45" with side members. It twisted only 'A0. I t is 36 times as T

Since T = F L, then F = - resistant to twisting as the first frame, yet uses 6% less L

bracing material. T Y:j . ' . B = - - 6 E I L 2

(See Figure 34) i Since Y = fl L j An approximate indication of the angular twist of a 1 frame using double diagonal bracing (in the form of

;m X ) may be made by the following procedure. Here B = T(\/?;)'L' f i ~ ~ 6 E I L 2 - 3 E I

each brace is treated as a beam. T L ~ T L - T L

also 8. = -- Hence \ \ Ea R 3 E I - E , R

3 E I 'and R r= = 5.3 1 fi E8

For fixed ends, R = 21.2 I

For the usual frame, the following is suggested:

which appeared in Table 1. Therefore: For a double diagonal brace use R = -

10.6 1 and substitute this value into the standard

esigning for Torsional ~ o a d i n g /

FIGURE 38

Case 2 (Diagonal bracing) NECTIONS OF TORSI

since this is "doublez3 bracing, the ~ ~ b l ~ 1 formula When a member having an open section is twisted,

for this type of frame is used - the cross-section warps (see b, in Fig. 37) if ends of the mcmber are free. The flanges of these members

R = 10.6 I not only twist, hut they also swing outward (see c), allowing the member to twist more. If the ends of the

First find the moment of inertia for the cross-section flanges can be locked in place in relation to each other, of a brace, which is a simple rectangle, assuming the this swinging will be prevented. brace also is %" X 10":

b d3 I = - CONNECTIONS 12

where b = the section width (plate thickness), and d = the section depth

then substituting into the formula for R -

The angular twist on the frame is then-

= .0000152 radians or .00087" -

There are several methods of locking the flanges together. The simplest is to weld the end of the member to the supporting member as in ( d ) . If the supporting member is then neither thick enough nor rigid enough, a thin, squiue plate may he welded to the two Banges at the end of the member (e ) . Another method is to use diagonal braces between the two flanges at the two ends of thc member ( f ) .

Either of these methods reduces the angular twist by about %.

Members having a box section, when butt welded directly to n primary member, have the fully rigid end connections required for high torsional resistance.

I Problem 10 / A 12" WF 27-lb beam, 25' long, with a uniFormly distributed load of 8 kips, is supported at each end by a box girder. See Figure 38. If the beam is continuously welded to these girders, estimate a ) the resulting end


FIGURE 39

moments in the beam, b ) the torsional stresses in the girder, and c ) the weld size required to hold the box girder together. 8. = 0

torsional resistance of box girder

2 b2 d2 W L, R = M - -- b d (See Figure 39)

e - 12 ,+t, - - (8") (25' X 12")2

- 2(13.33)2(10%)2 12 - (13.33) (10%) -. 200 in.-kips

(%) -+pBq = 910 in.4 torque on box girder

See Sect. 8.2 Torsional Member Formulas. Torque in the central section of the box girder

support is equal to the end moment of the supporting beam.

end moment of beam

See Sect. 8.1 Beam Formulas.

Determine what torque must be applied to the central section of the supporting box girder to cause it to rotate the same amount as the end rotation of the supported beam, if simply supported (0, = ,0049 radians) :

If the beam is simply supported without any end restraint, the end moment (Me) is zero, and the slope T L,

8% = r~ of the beam at the end is -

= ,0049 radians A moment-rotation chart shows the relationship;

Now, if the ends of the beam are so restrained that see Figure 40. A straight line represents the end moment it cannot rotate, the end moment becomes - ( M e ) and end rotation (8,) of the supported beam

esigning for Torsional Loading / 2.18-23

FIGURE 40

under all conditions of end restraint. A similar straight line, but in the opposite direction, represents the applied torque ( T ) and angular rotation ( 8 ) at the central section of the supporting box girder.

These two lines arc plotted, and where they intersect is the resulting end moment (Me) or torque (T) and the angular rotation ( 8 ) :

Me = T = 190 in,-kips

0, = ,0002 radians

torsional shear stresses in box girder

d = I 03/a" FIGURE 41 1

= 1830 psi

torsional shear force on fillet weld

f i = rb tb

= (1830)(%)

= 690 lbs/lin in.

which must be transferred by the ellet weld joining the top and bottom plates to the side channels, lo make up the box girder.

l~orizontul shear force on fillet weld due to bending

- FIGURE 42

Half of the $-kip load goes to each end of the beam, or a Ckip load is applied to the central section of each box girder. And V = 2 kips.

2.10-24 / Load & Sfress Analysis

- - (F) (4.875) (594,) (468) (2 welds)

= 54 ibs/lin in.

total shear force on weld

f = f , + f, = (690) + (54) = 744 lbs/lin in.

required leg size of fillet weld (E70 weldsj

actual force 0 = --

allowable force

= ,066" (continuous)

However, AWS and ASSC would require a minimum fillet weld leg size of 3/1," (See Section 7.4).

If intetmittent fillet welds are to be used, the length and spacing of the welds would be-

% = calculated leg size of continuous weld actual leg size of intermittent weld used

= 35% or use 3" - 8"

Alternate Design

As a matter of interest, consider the support to be provided by a 10 WF 39-lb beam.

(See Figure 43)

FIGURE 43

torsional resistance of suppoiting beam

torque on suppoi-ting beam

Detelmine what torque must be applied to the central section of this supporting beam for it to rotate the same amount as the end rotation of the supported beam, if simply supported (0, = ,0049 radians):

The moment-rotation diagram, Figure 44, shows the resulting end moment on the supported beam to be 4.67 in.-kips. Thus, this beam could be connected as a

FIGURE 44

Rototion (81, radians

esigning for Torsional Loading / 2.10-25

simply snpported beam with just vertical welds on the 1. The volumes under tht: membranes will be pro- web si~fficicnt to carry the 4-kip shcar reaction. Thc portional to the torsional resistances of the correspond- end restraint is ahout 2.3%. ing srctions.

2. The slope of the membrane's surface at any imint is propor-tional to the shear stress of the section

Mcmhrane analogy is a very :isefnl method to mder- stand the behavior of open st,ctions mhrn subjected to torsion. To make nsc of this method; holes are cut into a thin plate making the outline of varions shaped sections. it membrne material s i~ch as soap film is spread owe tbc open surface and air prcssure is applied to the film. The mathematical expressions for the slope and volrnnc of this membranr or film cowring the openings rt:presenting diffr:rimt cross-sections are tho samt: as the expressions for the shcar stressas and torsional resistance of the actual member being studied. Tt is from this t p e of analysis that formulas for various types of open sections subjected to torsion have been developed and confirnred.

If several outlin<,s are cut into the thir plate and the same pressure applied to each membrane, the following will be tnie:

- - ;it this point.

3. A narrow section (thin plate) has practically the same torsional resistance rcgardltss of the shape of tht: scction it is formed into. Notice a, h, and c in Figure 45. For a given area of section, the volume under the membrane rcmains the same regardless of the sIi;ipr of the section.

It is possihlt? to dctcrminc the torsional resistance oE these opcrr st:ctions by comparing them witli a standard circle on this same icst plate whose torsio~ial resistance can readily he calculated.

fly comparing thc memhrarrc of the slottcd open tube, ( c ) in Figure 15, to that of the mt,mhrane of the closed t~~brx ( c ) , it is I-cadily seen why the closed tnhe is several hundred times morr. resistant to tu-ist, when it is renrembcred that the v o l ~ ~ m e under the membrane is proportional to the torsiol~al resistance.

FIGURE 45

2.10-26 / Load and Stress Analysis

Modern structural steel shops ore equipped with highly efficient equipment for the welding of fabricated plate girders. Here an automatic submerged-arc welder runs o transverse splice in 7/8" web plote to full width, with the oid of a small runout tab previously tacked in place.

This automatic submerged-arc welder mounted on o track-mounted, gantry type monipulotor runs o web-to-flange fillet weld the full 84' girder length. Welding generators travel with the monipulotor.

Prirzipal stresses are normal strcsses (tensile or compressive) acting on these principal planes. These

Structural members are often subject to combined are the greatest and smallest of all the normal stresses loading, such as axial tension and transverse bending. in the clement. These external forces induce internal stresses as forces Normal stresses, either tensile or compressive, act of resistance. Even without combined loading, there normal or at right angles to their reference planes. may be combined stress at points within the member. Shear stresses act parallel to their reference planes.

The analysis of combined stresses is based on the concept of a cubic unit taken at any point of intersection of three planes perpendicular to each other. The total forces in play against these planes result in proportionate forces of the same nature acting against faces of the cube, tending to hold it in equilibrium. Since any member is made up of a multitude of such cubes, the

Normal stress Sheor stress

I analysis of stresses at a critical point is the key to analysis of the member's resistance to combined ex- FIGURE 1 temal forces.

.6: ESS These stresses may be represented graphically on Mohr's circle of stress. By locating the points (cr,, 7.1)

Biaxial and triaxial stresses are tensile and com- and (u,, 7.1) on a graph, Figure 2, and drawing a pressive stresses combined together. circle through these two points, the other stresses at

Combined stresses are tensile and compressive various planes may be determined. stresses combined together. By observation of Mohr's circle of stress, it is

Principal pZanes are planes of no shear stress. found that-

Stress in Member Mohr's Circle of Stress

FIGURE 2

. I 1 4 / Load Stress Analysis

FIGURE 4

FIGURE 5

In this case, US and an are principal stress% ad, and u a , since they act on planes of zero shear stress.

For any angle of rotation on Mohr's circle of stress, the corresponding planes on which these stresses a d in the member rotate through just half this angle and in the same direction.

Notice in Figure 3, U, lies at + 180" from us in Mohr's circle of stress, and the plane ( b ) on which 0-2 acts in the member lies at + 90" from the plane (a ) on which u, acts.

Notice in Figure 4, T,,, lies at + 90" from u, and the plane ( b ) on which T,,,,, acts in the member lies at + 45" from the plane ( a ) on which us acts. In this case US and u3 are principal stresses because there is no applied shear on these planes.

This is a simple method to graphically show how stresses within a member combine; see Figure 5. On the graph, right, locate the two stress points (+ US, + 7,)

and (+ rrz, - TI) and draw a circle through these points. Now determine maximum normal and shear stresses.

By observation of Mohr's circle of stress, it is found that-

The above formula for the maximum shear stress ( T ~ ~ X ) is true for the flat plane considered; however, there are really two other planes not yet considered and their maximum shear stross could possibly be greater than this value.

This is a very common mistake among engineers. To be absolutely sure, when dealing with biaxial

Analysis of Combined Stresses /

FIGURE 6

stresses, always let the third normal stress he zero instead of ignorulg it, and treat the problem as a triaxial stress problem.

The example in Figurc 2 will now be reworked, Figure 6, and the third normal stress ( u l ) will he set equal to zero.

Here,

u3 = -k 12,000 psi T~ = 0

u2 = + 8,000 psi r2 - 0

On graph, right: Locate stress points (mi) (ua ) , ( U S ) and draw three circles through these points, Now determine the three maximum shear stresses.

There are three values for the maximum shear stress, each equal to half of the difference betweell two principal (normal) stresses. The plane of maximum shear stress (shaded in the following sketches) is always at 45' to the planes of principal stress.

Circle 3 t" 0-2 - ci

Tmax -= -- 2

- - - 8,000-0 2

= 4,000 psi

I t is seen that, in this example, the maximum shear stress is 6,000 psi, and not the 2,000 psi vali~c that would usually be found from the conventional formulas for biaxial stress.

3. TRIAXIAL STRESS COM STRESS (See Figure 7)

The three principal stresses (ex,,, u?,, r a p ) are given by the t h e e roots (u,,) of this cubic equation:

Circle 1

u 3 - UZ Tmax =

= 2,000 psi

Circle 2

= 6,000 psi

a = - ( u x + u 2 + ~ )

b = Flu* + c g r 3 + UlUj - 7? - 7 2 - 72 c = ulr,* f ~ 2 ~ 2 + u8r3* - uiu2u3 - 2 7 1 7 2 7 : ~

- 'Solution of Cubic Equation from "Practical Solution of Cubic Equations': G. L. Sullivan, MACHINE DESIGN, Feb. 21, 1957.

V y 3 - (Vi $. VZ t G - S ) ~ :

+ ( u ~ V ~ + G-aVa -1- VlUi 4;' - TS' - ~3~ - (ulG-9? + 2 i,iii:i - m,.;," <r_r.' - ~ ~ 7 2 ) = 0

. ( 4 )

For maximum shear stress, w e the two principal stresses (cr,,) whose algebraic diffrrmce is the grcatest. The maximum shear stress (r,,,,,) is equal to half of this diflerence.

*Since a, b, and c are coefficients of this equation:

2.1 1-4 / Load & Stress Analysis

T + 0.2 3

The ambiguous sign is opposite to the sign of Q (approximate, but very accurate).

For either Case 1 or Case 2

FIGURE 7

Then calculate-

N3 K = - as a test ratio. Q"

Case 1

When ( 1 + K) is positive (one real root) or when ( 1 f K) is zero (three real roots, two of which are equal)

ca lcu la tb

and compute the root-

Case 2

The additional two roots (u2,, u3,,) of the general cubic equation are calculated by solving for u, using the exact quadratic:

C 0 -2 - t ( a+u l , ) up - -= 0

TIP

Determine the maximum normal and shear stress in this web section, Figure 8:

0 3

FIGURE 8

where:

0-1 = 0 TI = 11,000 psi

US = - 13,650 psi T~ = 0

u8 = - 14,500 psi TZ = 0

Substituting these values into the general cubic equation:

uD3 - ( - 13,650 - 14,500)uD2 + [( - 13,650) ( - 14,500) - (11,000)2] o;, = 0

When ( 1 + K) is negative (three real and un- eaual roots) u,," 28,150 a, f 76,925,000 = 0

A

calcnlate-

T = q = x

and compute the root-

the tbree principal normal stresses are-

Ul, = 0

uz, = - 25,075 psi u3, = - 3,075 psi

Analysis o# Combined Stresses /

0, = - 14,500 psi ond a, = - 13,650 psi and ri = 11,000 psi 71 = 11,000 psi

FIGURE 9

b 4zp =- 25,075 psi (rnox) -1

and taking one-half of the greatest difference of two principal stresses:

25,075 - 0 rmax = 2 = 12,535 psi

These various values are shown diagramed on Mohr's Circle of Stress, Figure 9.

Checking Effect of Applied Stresses

The Huber-Mises formula is convenient for checking the effect of applied stresses on the yielding of the plate. If a certain combination of normal stresses ( U X and u,) and shear stress (r,,) results in a critical stress (uc,) equal to the yield strength ( u ) of the steel when tested in uniaxial tension, this combination of stresses is assumed to just produce yielding in the steel.

'4 - FIGURE 10

I Problem 2 1 For the beam-to-girder network represented by Figure 10, assume the combination of stresses represented by Figure 11.

FIGURE 11

Here:


The apparent factor of yielding is

This seems reasonable and under these conditions, the beam flange could be groove welded directly to the edge of the girder flange without trying to isolate the two intersecting flanges.

ENGTH UNDER CQM !NED LOADING

A very convenient method of treating combined load- ings is the interaction method. Here each type of load is expressed as a ratio of the actual load (P,M,T) to the ultimate load (P,,M,,T,) which would cause failure if acting alone.

axial load bending load torsional load

In the general example shown in Figure 12, the effect of two types of loads (x) and (y) upon each other is illustrated.

interaction curve

R, = constant R, = variable

0 .2 .4 .6 .8 1.0

R.

FIGURE 12

The value of R, = 1 at the upper end of the vertical axis is the ultimate value for this type of load on the member. The value R, = 1 at thc extreme right end of the horizontal axis is the ultimate value for this type of load on the member. These values are determined by experiment; or when this data is not available, suitable calculations may be made to estimate them.

The interaction curve is usually determined by

actual testing of members under various combined- load conditions, and from this a simple formula is derived to express this relationship.

If points a and b are the ratios produced by the actual loads, point c represents the combination of these conditions, and the margin of safety is indicated by how close point c lies to the interaction curve. A suitable factor of safety is then applied to these values.

Combined Bending ond Torsion

, Pure bending

Pure torsion

FIGURE 13

Combined Axial Looding and Torsion

FIGURE 14

Analysis of Combined Stresses /

Combined Axial Compression rrnd Bending The bending moment applied to the member (chosen at the cross-section where it is maximum) is

in this case, the axial compression will cause additional then multiplied by this amplification factor (k), and deflection, which in turn increases the moment of the this value is then nsed as the applied moment ( M ) in bending load. This increase can easily be taken care the ratio: of by an amplification factor (k) . See Figures 15 and

For sinusoidal initial bending moment curve

For constont bending moment

P P

Here:

FIGURE 15

FIGURE 16

FIGURE 17

bending

The chart in Figure 18 is used to determine the amplification factor ( k ) for the bending moment

FIG. 18 Amplification factor (k) for bending moment on beam also subject to axial compression.

k

1 2 .3 .4 5 7 ?/PC,


Top - panel

width b = 56" thickness t = $6"

Transverse load w = 185 lbs/in

FIGURE 19

applied to a beam when it is also subject to axial compression.

The resulting combined stress is found from the following formula:

A loading platform is made of a %" top plate and a 10-gage bottom shect. The whole structure is in the form of a truss, Figure 19.

Determinotion ot comb and bending) in top co

With L = 16%"

A = 21 in."

I = ,247 in.4

First the critical load-

= 272,000 lbs

Then the ratio-

The bending moment-

Obtaining the amplification factor ( k ) for the sinusoidal bending moment from the curve, Figure 18-

The actual applied moment due to extra deflection is found to be--

The resulting combined stress formula being-

of which there are two components:

( a ) the compressive stress above the neutral axis of the top panel being-

126,000 11,600( x6 ) Oc = - 21 + .247

=: 14,800 psi

( b ) and the tensile stress below the neutral axis of the top panel being-

= 2,800 psi

Determindion 08 Focfor of

The ultimate load values for this member in compression alone and in bending alone are unknotm, so the following are used.

For compression alone - L *Since - = 150 (where r = radius of gyration) r

assume P, = PC, = 272,000 lbs

For bending alone-- The plastic or ultimate bending moment is--

Elastic Plastic

FIGURE 20

These ultimate values are represented on the following interaction curve, Figure 21. Plotting the present load values at a against the curve, indicates there is about a 2:1 factor of safety before the top compression panel will buckle. - T h i s Ljr ratio of 150 is high enough so we can assume the ultimate load carrying capacity of the column (Pa) is about equal to the critical value (P..) . If this had been an extremely short column ( w r y low Ljr ratio), the critical value (Pa.) could be quite a bit higher than the actual ultimate value (Pa) .

Mu = 64,900 in-lbs

"M"-Applied bending moment, x 1000 in-lbs

FIG. 21 interaction Curve for Problem 3

.11-10 / Load & Stress Analysis

The Air Force Academy Din- ing Hall (seating the entire student body) at Colorado Springs was bui l t on the ground and jacked into position atop columns. The com- plexity of joints, the heavy cantilevered construction and large lateral forces offered unique problems in combined stresses. Welding was the only practical approach to the complex connections required to join members of this three-dimensional truss sysiem.

1. CAUSES 01: BUCKLING

Buckling of flat plates may be experienced whon the plate is excessively stressed in compression along opposite edges, or in shear unifo~mly distributed around all edges of the platc, or a combination of both. This uecessitates cstablishirrent of values for tile critical buckling stress in co~nprcssior~ (u,,) and in shear (r,,.).

The critical comprcssive stress of a plate when subject to compression (re,) can be found from the following:

FIGURE 1

where:

E = modulus of elasticity in compression (Steel = 30,000,000 psi)

t = thickuess of plate, inches

b = width of plntv, inches

a = length of platc, inches

v = Poisson's ratio (for steel, usually -- 0.3) k = constant; depends upon plate shape b/a and

support of sides. See Tables 1 and 3.

If the resulting critical stress ( u ) from this formula is below the proportional limit (u,,), buckling is said to he clnstic and is confined to a portion of the plate away from the supported side; this does not mean complete collapse of the plate at this stress. This is

represented by the portion of the curve C to D in Figure 2. If the rrsr~ltirig value ( u ) is above the proportional limit (u,,). indicated by the portion of the curve A to C:, hr~ckling is s:dd to he ine1;rstic. Here, the tangent modulirs (I?,) n~us t be used in some form to replacc Young's or secant modulus ( E ) in the fomxola for detcrminiug u,,,..

This problem can he simplified by limiting the maximum value of the critical buckling stress (ucr ) to the yield strength ( u ? ) . However, the value of the critical bncklirrg stress (u,,) may 1)c calculated if required.

Above the proportional limit (o,) , the ratio E = ~ J E is no longer constaut, hut varies, depending upon

LE 1-Compression Load on Ware

S u p p w i (long ploter) / d u e s for Plate Factor (k

to be Ured in Farmulo

Critical Strsrr on Plate to cause Bucklins (o',,)

r'm = $07

Bleich, "Buckling Strength of Metal Structures," p. 330


the type of steel (represented by its stress-strain diagram) and the actual stress under consideration (position on the stress-strain diagram). See Figure 3.

Above the proportional limit (u,,), the modulus of elasticity ( E ) must he multiplied by a factor (A) to give the tangent modulus (E,). The tangent modulus (Ei) is still the slope of the stress-strain diagram and Et = U / E , but it varies.

If it is assumed that the plate is "isotropic" (i.e., having the samc properties in both directions x and y ) , the critical buckling lorrnula hecomes-

where: I A = +

If it is assumed that the plate has "anisotropic" behavior (i.e. not having the same properties in both directions x and y), the tangent modulus ( E t ) would he used for strases in the x direction when the critical stress (u,,) is above the proportional limit ( u n ) . How- ever, the modulus of elasticity ( E ) would he used in the y direction because any stress in this direction would be bek~w the proportional limit (up). In this case, the above formula #2 would he conservative and

the following would give better results:

For steel, this becomes-

If the critical buckling stress (u,,) is less than the proportional limit (up) then A = Ei/E = 1 and formola #4 could he used directly in solving for critical stress (u~,).

However, if the critical huckling stress ( u ) is greater than the proportional limit (u,), then A < 1 and formula $4 cannot be used directly. It would be better to divide through by ?'x and express the formula as-

From the value of re,/ \/T;;formula #6 will give the value of re,. Obtain proper value for the plate factor ( k ) from Table 1 or 3.

Curve for A7 Steel

n, = 33,000 psi

oe = 25,000 psi

inelastic

= 2 . 7 0 ( $ 1 FIG. 2 Buckling $tress curve for plater in compression.

10 20 30 40 50 60

Buckling of Plates / 2.1

FIG. 3 Stress-strain diagram showing where tangent modulus need be applied to determine critical stress.

Determining Tangent Modulus Factor fX)

Bleich in "Buckling Strength of Metal Structures", p. 54, gives the following expression for this factor ( X = E,/E):

where:

rr, = yield point

u, =3 propostional limit

u,, = critical buckling stress

If we use a ratio of-

the expression hecornes-

Then, multiply through by

TABLE 2-Shear Load on Plate

I--- " -4 I I -Sleich, ',Buckling Strength of Metal Stiucturer." p. 395


See Figure 2 for curves representing these formulas applied to the critical buckling compressive stress of plates of A7 steel (u, = 33,000 psi).

UCKLlNG OF PLATES UNDER SWEAR

The critical buckling shearing stress (T,,) of a plate when subject to shear forces ( T t ) may be expressed by the formula in Figure 4 (similar to that used for the critical buckling stress for plates in edge compression).

where:

E = modulus of elasticity in compression (Steel = 30,000,000 psi)

t = thickness of plate, inches

b = width of plate, inches

a = length of plate, inches (a is always the larger of the plate's dimensions)

v = Poisson's ratio (for steel, usually = 0.3)

k = mnst,int, depends upon plate shape b/a an? edge restraint, and also accounts for the moduluz. of elasticity in shear (E.). See Tables 2 and 3.

I t is usual practice to assume the edges simply supported.

Shear yield strength of steel ( T ) is usually consid- 1

ered as - of the tensile yield strength (o,), or .58 uy " Since

ular Plates Supported On 4 Sides Between Stiffeners mnd

e Knee Between Stiffeners)

Load

CImnrrrslan

1 nir

Volver for Plate Factor (k) to be Used in Formulw

3, 4, 5, ond 6

when a, 1 k = 4

-- when a ;z 1 k = 7.7

when . 2 i k = 7.7 + 33 (1 - 0i9

Crilicol Stress 7'(. and S',,

Buckling of Plates / 2.12-5

Since the plate constant ( k ) can be adjusted to siort, in the irrelastic rangc the critical stress (u , , )

contain the 1'3 factor, this becomes- exceeds the proportional limit (u,,), and the tangent modulus (E,) is introduced by the factor ( h = Et/E).

2 Therefore, folmulas #5 and #6 would be used also

k + E ccr = 12(L - v2)(i) in the buckling of plates by shear.

Proper values for the plate factor ( k ) are obtained from Table 2, for purc shear load, and Table 3, for

As before in the buckling of plates by compres- shear load comhined with compression.

TABLE 3-Critical Stress #or Rectangular lpltes Supported On - Continued -

Volusr for Plate Factor (k) to be Used in Formulas

3, 4, 5, and 6

when $21

4 l where il = - + - 3 a'

when % - 5.5 l

'I3 i k = ( a + ) - I + q7] [ 4 a' + 5.34

where n = - !az + 1)'

when

5.34 + 41a' where 'i =

77

when % s = s l

k = 3.85 n 2 ~ f l + 3

2 I where q = - +' - - -

9 6 a'

when f i C a ( 1

J I k = 2 4 n m

1 2 where n = - + -~r

6 9 a'


4. SUMMARY FOR DETERMINING CRITICAL TABLE &-Buckling Stress Formulas BUCKLING STRESS OF PLATE 1Compressionl

1. The value of the plate factor ( k ) to be used in formula #5 comes from Tables 1 , 2 or 3, adapted from "Buckling Strength of Metal Strl~ctures", Bleich, pp 330, 395, 410.

2. Solve for u,,/ L I T from formula #5. ,

Portion Crilicol Buckling Compressive Foclar --- 01 / ''I / \&

Stress (nF,) Determined by Curve

I-' a. If u,,/\ h = uD, this is the value of ucx, SO go to step 4.

b. If u , , . / \T > u,,, go to step 3. 3. Insert this value (u,,/ \ /x) into formula #6,

and solve for the critical buckling stress (uc,). 4. After the critical stress ( ) has been deter-

mined, the critical buckling stress of the given plate (u',, or r',,) is determined from the relationship shown in the right-hand column of Tables 1, 2, or 3.

5. BUCKLING STRESS CURVES (Compression)

- - -

c to .I - 0". ."..I 6. = \/G

B t o C

The horizontal line ( A to B ) is the limit of the yield strength (u , ) . Here uc, is assumed equal to u,.

The curve from B to C is expressed by-

In regard to plates subjected only to compression or only to shear, H. M. Priest and J. Gilligan in their

(b/t) where: ucr = 1.8 uy - n "Design A4anual for High Strength Steels" show the n = -. cwrve patterns, Figure 5 (compression) and Figure 10 (shear). They have divided the buckling curve into

'I 1 4770

three distinct portions (A-B, B-C, and C-D), and have The curve from C to D is 75% of the critical bock- lowered the criticd stress values in the elastic buckling ling stress formula, Figure I, or: region by 25% to more nearly conform to actual test

3820 5720 - \,% to -x

r&ults. k r 2 E Values indicated on this typical curve are for U", = .75 12 ( 1 -.2,(t)'

ASTM A-7 (mild) steel, having a yield strength of 33,000 psi. - 4434 - -

The buckling curve (dashed line) of Figure 2 has been superimposed on the Priest-Cilligan curve for [%I comparison. All of this is expressed in terms of the factor

b i t o,, = 1.8 0, - n --

v'k where: \/-." " = -7-

4770

FIG. 5 Buckling stress curves for plates in edge compression.

b/t Ratio - s r Cri t icol buckl ing compressive stress [n,,) for A-7 steel having 0, = 33,000 psi

.I24 / Lood & Stress Analysis

TABLE 5-Factors for Eucklina Formulas - of Steel 4770

-. 3820 - 5720 - \6 --- \/<

--Limiiins Values of

Yield Side Strength Conditions

AiSC-American institute of Steel Construction AASHO-American Ariociotion of State Highway Ofiicials AREA-Amercon Railway Engineers Arrociotion

12

Both simply

Factors needed for the formulas of curves in Figure 5, for steels of vario~is yield strengths, are given in Table 5.

Figu-c 6 is just an enlargement of Figure 5, with additional steels having yield strengths from 33,000 psi to 100,000 psi.

For any given ratio of plate width to thickness (b / t ) , the critical buckling stress ( u ) can be read directly from the curves of this figure.

12 One simply 33,000

33,000 44

A suitable lactor of safety must be used with these values of b/t since they reprcscnt ultimate stress valnes for buckling.

Some structural specifications limit the ratio b i t to a maximum value (point B ) at which the critical buclding stress ( u ) is equal to the yield strength (u,). By so doing, it is not necessary to calculate the buckling stress. These limiting values of bit, as specified by several codes, are given in Table 6.

In general practice, somewhat more liberal values

13 & 16 supported; the .-

of b i t are recognized, Tablc 7 , extended to higher yield strengths, lists these limiting values of b/t.

7. EFFECTIVE lDTH OF PLATES I COMPRESSION

The 20" X %" plate shown in Figure 7, simply supported along both side<, is ~ubjectcd to a compressive

40

load

- other free 50,000

40 -. --

supported 50,000 36

Simply supported sides

/

-- -- 1 1 & 13 .-.

.- -

FIGURE 7 34

A-7 steel

o, = 33,000 psi

b = 20" t = %" k = 4.0

32

Under these conditions, the critical buckling compressive stress (u,,) as found from the curve ( a , = 33.000 psi) in Figure 6 is-

u,, = 12,280 psi

LE 7-Usual Limiting Valuer of b/t

Yield I One Edge Simply I Both Edger Strength Supported; the Simply or psi Other Edae Free Supported

This value may also he found fro~n the fonnulas in Tahle 4.

Since the ratio is 40.0 and thus exceeds

the value of 31.5 for point C, the ioilnwing formnla must be used-

= 12,280 psi

At this stress, the middle portion of the plate would be expected to buckle, Figure 8. The compressive load at this stage of loading would be-

FIGURE 8

The ovcr-all plate shonld not ~vllapse since the portion of the plate along tbe supported sides could still be loaded np to the yield point (cr,) before ultimate collapse.

This portion of the plate, called the "effectivti width" can be dete~mined by finding the ratio h/t when (u,,) is set equal to yield strength (u,) or point B.

From Figure 6 we find-

Since k = 4.0 (both sides simply supported), the ratio-

Since the plate thickness t = %" width, b = 42.0 t or h = 10.5".

This is the rffcctivc width of the plate which may be stressed to the yield point (o;) before ultimate collapse of the tmtirc plate.

The total comprcssive load at this state of loading would be as shown in Figure 9.

The total comprcssive load here would be-

Another method makes no aIlowai~ce for the central buckled portion as a load carrying member, it being assumed that the load is carried only by the supported portion of the plate. Hence the total compressive load would be-

or from Table 4 we find- FIGURE 9


" Critical buckling rheor stress for A.7 i teel hovng a, = 33,000 psi

FIG. 10 Buckling stress curves for flate plates in shear.

. BUCKLING STRESS CURVES (Shear) uckline Stress Formulas (Shear)

The Priest & Gilligan curve, corresponding to Figure 5, when applied to the buckling of plates in shear is shown in Figure 10. -

% , w e is expressed in t e r n (3). %e

Table 8. Comparison of Figure 10 and Table 8 with Figure 5 and Table 4 reveals the parallelism of critical buckling stress for compression u ) and for shear ( ~ c z ) .

Figure 11 is just an enlargement of Figure 10, with additional steels having yield strengths from 33,000 psi to 100,000 psi. Factors needed for the fmmulas of curves in Figure 11 are given in Table 9.

For any value of ( y i ) - the critical buckling shear . ~, stress ( rer) can be read directly from the curves of this figure.

A suitable factor of safety must be used with these values since they represent ultimate stress values for buckling.

By holding the ratio of (3) to the value at . ~~, point B, .r,, = T? and it will not be necessary to compute the critical shear stress (r,,). Assuming the edges are simply supported, the value of k = 5.34 + 4(b/a)" Then using just the three values of b/a as 1 ( a square panel), "I (the length twice the w-idth of panel) and zero (or infinite length), the required b/t value is obtained from Table 10 for steels of various yield strengths. The plate thickness is then adjusted as necessary to meet the requirement.

Notice in Figure 10 and Table &that the critical buckling stress in shear is given directly as (T,,). In Tabla 2 and 3 it is given &st as ( u ) and then changed to (T,,).

Portion Critical Bvckling Sheor Strerg Fccaor --

Of I Vi (T,,) Determined by

Curve

TABLE 9-Factors for Buckling Formulas (Shear)

Yiald Strength of Steel ar7 pri

Corresponding Shearing Yield

Strength r, = 3 8 o, psi

% g, ,,,,in+ 6 Vk

3820 -- - -- V 77

b l t - far point c \i k - 5720 - - -

V ~7

= %'3 4770

Buckling of Plates / 2.12-11

TABLE 10-Maximum Values 06 b/t To Avoid Formulas

Tensile b/o = 1 Yield Strength ($quore panel

PI psi

Maximum Value3 of b / t to Hold r,, to 7,

(Panels with limply rvpported edges)

Foul edges - rimply supported

k = 5 34 + 4[b/oj2

Four edges - fixed

k = 8 98 + 5.60(b/oj2

10 20 30 40 50 60 10

Rotto &i

FIG. 11 Buckling stress curves (plates in shear) for various steels.

.12-12 / Load and Stress Anolysis

United Airlines hangar a t San Fran- cisco features double-cantilevered roof over areas into which large jet aircraft are wheeled, nosing up to the 3-story inner "core" for servic- ing. Center girder section half (at left) i s completely shop welded. Large plate girders like this one are stiffened to prevent web buckling due to edge compression. Contilev- ered welded plate girders weigh 125 tons.

1. COMPRESSIVE STRESS

Comprcssivo loarli~lg of a mcrnb(ar when app l i ed (axially) touctintric with thc ccnter of gravity of the member's cross-s(,ction, results in compressive stresses distribi~ttd uniformly across tlir srctior~. This comprt+ sive unit stress is -

A short column (slendc,rnisss ratio L/r g u a l to aborit unity or less) tlmt is over1o;idrd in comprt.ssion may fail hy crusliir~g. From a desigri standpoint; short omp press ion nirrnhcrs pxsont little problt:rn. It is important to hold tlw compressive unit strcss within the material's colnpressirc strength.

For stccl, the \-ield and nltimate strengths are considered to bc tlrc same in compression as in tension.

Any liolcs or opcni~igs in the section in the path of force tmnsl;ition will u.cakm t l ~ c rnemlxr, rriiless sucli openings arc cuinp1atci)- filled iiy wiothcr member that \vilI wrry its sllarc- of the load.

Excessive comprc.ssirm of long columns may cause failure by buckling. As cornpressiw lo:iding of a long colmnn is increased, it r iw~ tud ly calms some ecc1.n- tricity. This in turn sets np ;I bending monwnt, causing the column to deficct or bucklc sliglltiy. Tliis deflection incre;isrs thc ecc~mtricity and this thc h i d i n g moment. Tliis may pnigrcss to whwe t11c bending moment is incre:ising at a rate greatel- than the ina-case in load, and ilie ct~luiirn soou fails by buckling.

2. SLENDERNESS RATIO

As t l ~ c me~nber becomcs longer or nmre slender, there is rnorc of a trndenty for dtirnntc failure to be caused by brickling. The most nintmon usay to indicate this t t d e n c y is the slenden~ess ratio which is equal to-

1, - r

where L = i~nsu~por ted length of mcniher

r = tile least radius of gyration of the section

I f tlw rrrmnbcr is made longcr, wing the same cross-s<.ctirin ;iud tlw sanrc conrprtxive I d , the re- su l t i~~g cori~pn:ssivr strr.ss u'iil rt?maili the same, d- tho~igli tlic tmdrmcy for buckling will increase. The ilcwd~~nwss ratio im.re;lsc\s as the radius of hyration US thi. section is nduc id or :is the length of the memhcr is incrrwwd. 'nie allowable compressive load which may h~ applied to tbr member deue:~ses as the slendimiess ratio inweasi:~.

The various columr~ formulas (Tablcs 3 and 4 ) givr tlic allowable :werage cornprmsive stress (5) for the culomn. Tlwy do not give the actual unit%ess devr~lopd in t lv column 11y tlir luad. Tlie unit stress resulting trorn tltiw forniu1;is may he multiplied by the cross-sectioniil arc:\ of tlir column to give the alliiwddr load \ ~ l ~ i c l ~ ma); be supported.

3. RADIUS OF GYRATION

Tlie riidius ol gyration ( r ) is thr' distance from the rreutral axis of a section to an imaginaiy point at which the w l d c awn of the section wrild be concentrated arrd still llavi, the same amonnt of inertia. I t is found hp the erpressimi: r = f l l / ~ :

in t l i? dosigir of ulrsy~n~nctrical sections to be used as mlumns, tht. le:rst r;tdius of gyration (r,,%,,) of the section must h t kriowrr in ordcr to make nse of the siendt~rnrss ratio ( l . / r ) in tlrc coliimn fo~mulas.

If the sc.cti~ir~ in question is not a standard rolled srr.tion tlrr priipc~ties of which are listed in steel hand- kioks, it will hi: uectwtry to mnpu te this least radius of gyration. Sincr the bast radius of gyration is -

the minimrim li~orneiit of inertia of the section must fir dvtermilned.

Minimum Moment of Inertia

T h ( ~ m;isiinllin moment of iiicrtin (I,,;;,,) ;ind t l~e mini- nxim monierit of inertia (I,,,,) of a cross-scction are and-

3.1-2 / Column-Reloted Design

V

FIGURE 1

Y

found on principal axes, 90" to each other.

Knowing I,, I,, and I,, it will he possible to find I,;,.

I Problem I I Locate the (neutral) x-x and y-y axes of the offset T section shown in Figure 2:

FIGURE 2

to locate neutral axis x-x:

where d = distance from center of gravity of element area to parallel axis (here: XI-XI)

and, applying fnrinula #I from Section 2.3, the distance nf neutral axis x-x from its parallel axis XI-XI is -

XM - 21.0 NA,., = - Z A = 12.0 = - 1.75"

to locate neutral axis y-y:

A -. - .. W x I " 6.0 0 ..r Total M ; 12.0 1 s ~ ~ - .

+ 9.0 ,- -

XM - + 9.0 - + 75" NA,., = -7- - ,A 12.0

product of inertin

It will he nwessary to find the product of inertia ( I ) of the scction. This is the area (A) times the product of distances d, and d, as shown in Figure 3.

(Set: Figure 3 on facing page).

In finding the moment of inertia of an area about a given axis (I , or I,), it is not necessary to consider the signs of d, or d,. However, in finding the product of inertia, it is necessary to know the signs of d, and d, hecnnse [lie product of these two could be either positive or negative and this will determine the sign of the resiilting product of inertia. The total product of inertia of the d i o l e scction, which is the sum of the values of the individual areas, will depend upon these signs. Areas in diagonally opposite quadrants will have prodncts of ineltia having the same sign.

The product of inertia of an individual rectangular area, the sides of which are parallel to the x-x and y-y axes of the entirc larger section is -

FIGURE 4

where:

a and b = dimensions of rectangle ( = A)

d and c = distance of area's center of gravity to the x-x and y-y axes (= d, and d,)

The product of ir~crtia of a T or angle section is - (See Figure 5) .

Analysis of Compression / 3.1-3 I

l x = A d: I - A d : i X y : A dx dy Moment of inertlo Moment of inertia Product of ine~t iu obout x - x axis about y y 0x1s about x-x and y ~ y u x c i

l i t Quadrant 2nd Quodront

l x y = + A dx dy i = -A dx dy " Y

3rd Quadrant dih Quadrant

1 X Y = i A d x d y iX" = -A dx d

FIGURE 3

Y Xow use formula given previously for product of inertia of such 21 section:

x a d t ( d - & ) ( a + t ) Ixy = - - 4 ( a + d )

-- ( 4 ) ( 5 ) ( % ) ( 5 - .- ~~ - 2.5)(4 ..~ + % ) -~

4 (4 + 5 ) r + 3.125 in.' - - ..

Y

FIGURE 5

Here, determine sign by mspection. 1 I 25"

Determine the product of inertia of this offset 'r section about the x-x and y-y axes:

I,, = ZA ( & ) ( d l )

= 2.5 ( - + 1) ( - 1 - ,555) + 2 ( - 1.25) (-- ,695)

= t 1.388 + 1.737

= + 3.125 in."

Y

FIGURE 6

3.1-4 / Column-Related Design

L)ett.rn~iiie the minimnm radius of gyration of the offset T sec t io~~ shown previously (Fig. 2 ) and repeated licrc:

FIGURE 7

moment of inertia about axis x-x

,, - '--.:-~--+ -

;') x 6'' ! 6 - 3 . 5 - I . I + 73.5t18.00 Total - pzlimp I= I , $ ~ 2 . 0 0 ~

ZM - -- 21.0 NA,., = - . -. -

A - 12.0 - - 1.75'' and ..

minimum moment of inertio

minimum radius of gyration

As a matter of interest, this r,,,!,, is about axis x'-x', the angle ( 0 ) of which is-

2 I,, tan20 = -. -- (See sketch below). sx - Iy

20 = -- 46.4" or + 133.6"

and 0 = -+- 66.8"

Any ultimate buckling could be expected to occur ahout this axis (x'-x').

1 Problem 4 1 Thc clian~icl section, Figtire 8, is to be used as a collinrn. Determine its radins of gyration about its X-x axx.

['sing the conventional formulas for the properties of the section -

Analysis of Compression / 3.1-5

FIGURE 8 FIGURE 9

area of the section Mean dimensions b and d are used, Figure 9.

A = bd - bldl = ( 6 ) ( 4 ) - (5.5)(3.75) -2-

= 3.375 i n 2 rx = b + 2d

distance of neutral axis

radius of gyration

If a slide rule had been used, assuming a possible error of - one part in 1(K)O for every operation, this ms\var co111d be as high as 1.336" and as low as 1.197". This represents an error of t 4.3% and - 6.6%. For this reason it is necessary, when using these conventional formulas, to make use of logarithms or else do the n:ork longhand. To do this rcquires about 30 min~ites.

The radios of gyration \ d l now he found directly, using thc properties of thin sections, treating them as a line. Sce Table 2. Section 2.2.

The exact value obtained from this formula for r is 1.279". The value obtained by using the conventional formula is 1.281".

Assuming a possible error of 1: one part in 1000 for every operation of the slide rule, it would be possible to get an answer as high as 1.283" and as low as 1.275". This represents an error of about Y4 of the error using the conventior~al fonnulas with slide rule. The time for this last calculation was 2 minutes.

oment of Inertia About Any Axis

Y

FIGURE 10 X

Sometimes (as in Problcm 3 ) the moment of inertia of a sedion is nedehl about an axis lying at an angle ( 0 ) with the cor~ventional x-x axis. This may be found by using the prodt~et of inertia ( 1 of the section about the conventional axes (x-x and p-y) \?,ith the moments of i~wrtizi ( I , ) and ( I , ) about these same axes in the following formnla:


/ pinned

FIGURE 11

4. CRITICAL COMPRESSIVE STRESS

The critical load on a column as given by the Euler- formula is -

where L, = eiivctive length of column. This can be changed into terms of average critical

s,roin , r I. :n,lnxid3

FIGURE 12

stress by dividing by the cross-sectional area of the column. Since A = I/r2, this hecomes -

Bccause this formula gives excessively high values for short columns, Engesscr modified it by substituting the tangent modulus (13,) in place of the usual Young's modulus of elasticity ( E ) .

The modified formula then becomes -

where:

Et - tangent modulus of elasticity, corresponding to the modulus of elasticity when stressed to ffw

r =: least radius of gyration of the cross-section

L, == effective length of the column, cwrresponding to the length of a pinned column that would have the same critical load. See Figure 11.

The Ihgesser fonnula is also called the Tangent hlodnlus formula and chccks well with expcrimeutal values.

5. TANGENT MODULUS

Use of the Tangent Modulns formula necessitates a stress-strain curve (preferably in compression) of the materid. See Figure 12, stress-strain cnrve for a quenched and tcmpered steel in compression. IVhereas the usual Young's modulus of elasticity represents a fixed value for stccl (30 X 10') according to the ratio

Analysis o(. Compression / 3.1-7

Slenderness Ratios: Quenched & Tempered Steel

TABLE 2 TABLE 1

ingcsrer of curve lioeloriir bending:

of stress lo t ra in lwlow the propoi-tiol~al limit, the tangent moditlus of t ~ l x t i d y tiikrs into corisidrrntion the cliirnciirrq eifwt of p1;tstic strain h ~ y o n d this point correspo~~tlinq to the actual s t r ~ ~ s ilrr.ol\-cd.

Notice; in Figure 1% tlw hrokrw lirws rt:pres~:nting the slopc For various v a l i r ~ ~ of tangmi modulus of elasticity (&) , iu this case from 1 X 10" psi up to 30 X 10". Tiit: c:omp~-iwiv~: strrss le\wl ( rr , . ) at which a given E, mluc applies is di:tcrrnine<l hy moving out par:iUcl from tlmt 1-eferencc inotluliis line ((lotted), by means of pardlcl rule or otller si~itable dcvice, until the strcss-strain cuwe is ii~tersrctcd at one point only. The line i s tar~grnt at this point.

The compressive stress-strain curve for any material KIII be superimposed on this graph and the values of E+. at a given stress level ( re) read by the same tecl~nique.

i t "<$ ( 0 , *

FIGURE 13

iCOOW."<. . " ' O I . , ; ,

FIGURE 14


and the critical slerrdcrncss ratio (I.,,/r) is determined for ~ w i m t s ~ d t r c s of strcss (c r , ) , restilting in Tables I and 2 for qucnchcd and teinpered steel only.

Table 1 givcs rorrwporlding \;altles of slendemcss ratio (I&) for given v;ilucs of strcss (u,,) above the proportio~i:il limit of ;I quimched and tempcred steel.

firlow tlrc m;itrrinl's propor-tiod limit, the use of Yot~ug's modt~lris (I.:) or tangrnt modiilos ( E , ) provide the sanrr vdite. Tablc 2 for qtienclied and tempcred stecl givcs ihc slerr~lernt*ss ratio (L,/r) for stress levtals (cr,) \viihin the prip~-tied portion of the stress-strain cur\,tr. Si~icc the o t i i i Eitler fornrula for cr,, iipplics here, this portioir of the crirvc is often called tho Eolcr curve

6. PLOTTING ALLBWA LE STRESS CURVE

These val~tes from Tabltx I and 2 arc now plotted to i'orm the cilrvc in Figurr 11. The Eulcr portion of the curve is cxtmded upward hy a hrokcn line to indicate the variance that would 11c obtxind by continuing to use the Euler formula beyond tlie proportional limit. This must be kept in mirid in designing compn%ion members having a low slenderness ratio (L/r).

A few test results are also sliown to indicate the close relationship hetwem thr Modulus formula and actual valiies.

Note that a correporiding wrvf has been plotted below the main citrve, r r p x w i ~ t i i ~ g the allowable

where:

TABLE 3-Allowable Compressive Stress (AISC)

For very rtiort :aluinns. t h foctor of iilfe?y !F.S., is to that of m m b c r s n ieniion ( i s . =. 1.67). For ior8gei ~ o l u m n r , the iofrty of foctoi ormenier giadunlly to o m o x m u v of F.S. = 1.92.

K -- effective length factor

Ronga of LI -Values

stress (cr) d t 1 ~ ;ipplyiug a factor of safety of 1.8. ~ .~

Average Allowable compra*,ive

un i t st,e,s (C) -

7. BASIC FORMULAS FOR COMPRESSION MEMBERS

In "lirirklirrg Strmgtli oi h?ctal Stnicttlrcs," page 53, 131r~icIr intnxliir~s a pit-:rbolic formtila to csprcss this tangent rnodiiltrs i:i~rvt. for comprcssiorr, i3y applying a factor of s;tfrty (F.S.). this Iitwmcs thc allowable cot~ipri~ssiv~~ strws, l ' l r t ~ hasir paralwlk: formula thus rnuilificd is -

o-, z proportiond limit

u -::: yirld point

F.S. : factor of s;~f(t!-

Any rcsidiml coniprcssive strcss (ir,, ) in the member tends to lo\ver tlie 171-oportional limit ( c r ) os straight-liw prirtio~~ of thc stri,ss-stmirr ciirvc, in rom- puessioir: \vitlioirt 2iff1,rting tl~t. yicld p i n t For the purposr of tlic ;thov<- fonnula, it is assumed that

Also assriming this value of residual co~npressive strcss is ahorit half of the yield point, or cr,, = '12 cr,, Formula 1113 becomes:

, . . . , . - F.S. 4 .ii" F.S.

This fonniil;~ Im)viilcs a paralxrlic curve, starting at a slrndrr~iess r;rtio of' ( r = = 0 ) with V R ~ I I C S at yield stress (rr,), ;urd mtc~iicling down to one-half of this strrss wli<~i-i. it hwonics taiig(wt \villi the I1uler curw ;it the iq> l j (~ litnit of (~lastic 11n1diny.

The slcrtdtwlcss ratic ;i t tllis point is:

l1)ovc~ tliis slc~tdcrrlt~s ratio, the 1:ulcr fonnula is I I ~ :

I-,. -. 2:3.925 . . for stecl r \,'cry

. . . ( 15)

Analysis of Compression / 3.1-

FIGURE 15

MAXIMUM WIDTH-TO-THICKNESS RATIOS

For Elements of Members Under Axsol Compieriicn or Compreiiior Due to Bendzng

Adopted from 1961 AISC, Sec 19 .1 o rd I 9.2

with ~epo~otor

The above rot ioi of b ' t may be exceeded i f , by u i n g n the coliuiationr a w d t h equol to the maxmum of these limits, the cornpierrive itreis value obtamcd ti wtthln the ol iowobe st ies

8. AlSC FORMULAS FOR COMPRESSION EMBERS

The AISC I r a i~rcorpoi-ati~d (1'363) tliesc h s i c column for~nitlas rlrdorsd hy the C:olumn R~w:ircl~ Corincil Report in its spc.eifientimis for structrrr-al buildings.

The slcnderrlcss ratio w111:r~ the liulcr and parabolic portions of the citrvc intrl-scct, Formula 15, lias been dcsigiiated in tlre AISC Specification as (Cc). This is also i~iwrl>oriitrd into Forrn~~la 13.

AISC itses n \ d ~ i c of ti =: 298,0O0,000 psi (instcad of the r~sual 30,000,000 psi) for tlre itrodrilus of elasticity of tecl . For the I r t i of the curve, Fornn~la 16, AISC uses a factor of safety of 1.92.

Tlre rcs~iltitig ncw 41S(: wlitnin forrr~ulas arc sho\v~r in Tol~lc. 3.

l';il~lcs 6 tlrro~~gli L1 give the AISC comprcwion ailo~vables for several strengths of structural stccl.

For v;ir-iow conditioils of colri~nn cross-section, Figure 15: there is a limiting ratio of element width to thickricxs (b / t ) . This ratio is rqressed as being C Y ~ I I ~ I to or 11,s~ than ( - ) a rwt~iin w l r l i . divicl~d by t1r.e sqlt:ir<, root of the, ii?;itcrinl's yicld strmgtl~. The r r l a t d 'l'ablc 4 pcrlirifs (lirrbct reading of ;I cornprcssion ~~lmnmt's b/t ratio for v:iriorrs yield strcngtl~s o i strel.

At times it may he desiral,lo to exceed the limiting 11-t I-atio of ;in clrwirwt. 'This air1 11e done if, in the calc~ll;rtiotis, substitriting t l ~ e sirort:,r ~nasimurn width allowed (by t l r Fig. 15 limits) wo~ild give n coi~iprcs- sivc ~mi t strtw valiic within the ;illo\r.iblr stress.

To 111'111 i n visii:ilizilrg rt,l:rtivc s:rvings in iirctal liy the ttsv of lrighrr-strrngtli steels, I'igui-c 16 indicates tlrc :illowable comprcssivc strc~igt l~ ( I T ) o1)tained from ttic Tahlc 3 formttl:rs for 8 difFertm< yield strengths. Notirc tlmt tlw adv:rrrtagc of the higlrer strengths drops oil 3s the coltmn becomes marc slender. I


TABLE 4-Limiting b / t Ratios of Section Elements Under Compression

Limits of Ratio of Width to Thickness of Compression Elements for Different Yield Strenrrths of Steel

Allowable Compressive Stress ( g ) based on I963 AISC Sec 1.5.1 3

whfch i s for steel of 36,000 pis

20 40 60 80 100 120 160 180 200

8,000

va,

10,000 -- b'a,

Slenderness iotio [ L l r ]

FIGURE 16

44.0 4 2 . 39.0 I 37.3 I )I 34.1 1 32.6 1 31.4 ~I 26.6 1 25.9 25.3 - - . ~.~ ~ .~ ~ ~ p~

i 55.0 1 52.6 48.7 47.1 46.6 44.7 42.6 40.8 39.2 33.4 / 32.4 / 31.6

Round off to the neoreit whale nurnbcr. * Quenched and tempered iteelr: yield strength at 0.2% aifret.

Analysis o f Compression / 3.1-1 1

If the allowable stress curve of quenched and tcrnpwed steel (Fig. 14) werc now sr~pe~imposed on this graph, thc ewn greater, strength advantnge of quenched and tenrpcred stcel at lower slcndcrness ratios would be rradily apparent.

The allowable compressive unit stress ( u ) for a given sicndcrncss ratio (KL/r) , from unityihrough 200; is qni~kly read from Tahlcs 6 thnjngli 11 for stwls of various yield strengths.

.%hove KL/r of 130, the higlier-strength stcels offer no advantage as to allowable con~prcssive stress (u) . - Above this point, nse Table 7 for the. rnorc economical steel of 36,000 psi yield strength.

9. OTHER FORMULAS FOR COMPRESSlON

MEMBERS

'Tal)l(. 5 givt,s t h A A S t f O fonnoias, which are appli- c:iblc to bridge design.

As a matter of gcnrr;~l interest, the colnmn formula r:sta'tjlishrd for use of qur:rrchrd and temperod steel on the Carqninez Strait Sridge (California) is -

TABLE 5-AASHO Al fowable Stress (.or Compression

H a v i n g Rigid Ends ond Concentr ic h o d s

A-7 and A373 j/4" m d under over 1%" to 4" I i i , = 50,000 psi 0, = 46,000 mi I a, = 42,000 ori

Steel skeleton for 10-story Buffalo, New York apartment building features unique shop-welded construction. Principal erection element is a "bent" consisting of a 50' floor girder or "needle beam" threaded through the web of column section near each end and welded. Girder is supported mainly by on angle bracket or "saddle" previously welded to the column web. Girders cantilever out as much as 13' from column.


TABLE 8--82,000 psi yield steel LE 9-45,800 psi yield steel

TABLE 10-46,000 psi yield steel


1. INTRODUCTION

The preceding Section 3.1 covers the general Analysis of Compression, along with an evaluation of the methods for determining stress aliowables.

This present section deals more specifically with the aciual design of colmnns and other omp press ion members. For purposes of illustration, the term "column" is uscd quite liberally. This is due partly to much of the material having been originally developed expressly for columns. However, the information is generally applicable to all compression members.

2. RESTRAINT A N MEMBER

Section 3.1 explained how a compression member's slendei~icss ratio (L/r) relates to its buckling strength. The degree of end restraint on a member results in its having an effective length wvl~ich may vary considerably from its actual unbraced longth. This ratio (K) of effective length to actual unbraced length is wed as a multiplier in determining the dfedive length (L,) of a compression member.

where:

L = actual length of the column

L, = effective length of the column to be used in column formulas

K = effective length factor

Table 1 lists theoretical values of K and the Column Research Council's corresporrding recommended values of K for the effective length (L,) of columns under ideal conditions.

Where End Conditions Can't Be Classified

In actual practice it will be more difficult to classify the end conditions. If classification is doubtful, the Column Research Council recommends the following method based on the relative stiffness of connecting beams and columns.

The stiffness factor of any member is given as I/L, its moment of inertia divided by its length.

These values are determined for the column or coli~mns in qr~cstion (IJL,.), as well as for any beam or other restraining member lying in the piane in which buckling of the column is being considered (IJL,).

The moments of inertia (I , and I,) are taken about an axis perpendicular to the plane of buckling being considered.

The values of G for each end ( A and B) of the column are determined:

TABLE 'f-Effective Length (L. of Compression Members

Buckled shape of member i shown by doshed line

Theoreticol K value -- Recommended design volue when ideal cond:tionr o m ooaroximoird

End condition

,totion fixed translation fixed

,ration free translotian fixed

,tation fixed translotion free

3totion free tronrlation free

'K moy be greater than 2.0 **Top end ossvmed truly rotation iree

From "Guide to Design Criteiio for Metol Cornpierrion Members" 1960, p. 28, Column Rereorch Council


094 0 boo d 999999 9 9 9

0GXOICW 0 d- M N 9 -

$Q'D" cu - 0

m (3 1 1 1 1 1 I 1 I l l I I I i I I I I I I I l l 1 1 1

o q o q q 0mcof:wIq d- i? N - do& n cu 8 a- -00000 0 0 d 0 0

m '&, l l l t l l , 1 (3

I I l l I I I l l I I I I I I I

Design of Compression Members / 3.2-3

where: sidesway prevented

I, - = the total for the columns meeting at L" the joint considered.

Ig - the total for the beams or restrain- '' - ing members meeting at the joint considered.

For a column end that is supported, but not fixed, the moment of inertia of the support is zero, and the resulting value of G for this end of the column would be z. However in practice, unless thc footing were designed as a frictionless pin, this value of G would be taken as 10.

If the column end is fixed, the moment of inertia of the support is cc , and the resulting value of G for this end of the column would be zero. However in practice, there is some movement and G may he taken as 1.0.

If the beam or restraining member is either pinned ( G = o: ) or fixed against rotation ( G = 0) at its far end, further refinements may be made by multiplying the stiIfness ( I /L) of the beam by the following factors:

far end of beam pinned = 1.5

far end of beam fixed = 2.0

sidesway permitted

far end of beam pinned = 0.5

For any given column, knowing the values (GA and G,) for each end, the nomograph, Figure 1, may be used to determine the value of K so that the effective length ( L , ) of the column may be found:

L , = K L This nomograph is taken from the Column Re-

search Council's "Guide to Design Criteria for Metal Compression Members", 1960, p. 31. The nomograph was developed by Jackson & Moreland Division of United Engineers and Constructors, Inc.

3. STRENGTH OF

A very convenient method of treating combined load- ings is the interaction method. (Also see Sect. 2.11, Analysis of Combined Stresses.) Here each type of

I Problem I I Find the effective ltmgth factor (K) for column

A-B under the following conditions:

Sldesway

prevented

FIGURE 2

Here:

= ,260

GB = o ~ ; use 10

From the nomograph read K = .76

Sidesway

FIGURE 3

Here:

= ,620

Gg = zero; use 1.0

From the nomograph, read K = 1.26


1 .o

Margin of hafety R, = constant

R, = vanoble

0 .2 .4 6 8 1 .O

R,

FIGURE 4

load is expressed as a ratio of the actual load to the ultimatc load which would cause failurt. if acting alone.

axial load

P R. = -- Pa,

bending load

M Rb = - Mu

torsionul load

T Rt = - T"

In the general example shown in Figure 4, the effect of two types of loads ( X and Y) upon each other is illustrated.

The value of R, = 1 at the upper end of the

Applied moment

- -

Induced secondary moment

M "?ox

Resultant moximum moment

FIGURE 5

vertical axis is the ultimate value for this type of load on the meniber when acting alone. The value of R, = 1 at the extnxme right end of the horizontal axis is the ultimate value for this type of load on the member when acting alone. These ultimate values are determined by experiment; or whm this data is not available, suitable calculations may be made to estimate these values.

The interaction curve is usually determined by actual testing of members undcr various combined- load conditions. From this, a simple formula is derived to fit the cnrve and express this rclationship.

If points a and b are tlrc ratios produccd by the actual loads, point c represents the combination of these conditions. Thc margin of safety is indicated by how close point c lies to the irrteraction curve. A suitable factor of safety is then applicd to these values.

Figure 5 illustrates this for axial compression and bending.

IIowever, the applied bending moment (MI) c a w s the column to bend, and the resulting displacement or eccentricity induces a secondary moment from the applied axial force. See Figure 6.

Assume that the moment ( M i ) applied to the column is s i ~ ~ a o i d n l in nati~re; Figure 7.

A siniisoidal moment applied to a pinned end member rcsults in a sinllsnidal deflection curve, whose maximum deflection is equal to -

Since the critical Euler load is -

FIGURE 6

this becomes

When the axial load (P) is also applied to this deflected column, a secondary moment is induced and this is also sinusoidal in nature, its maximum value being -

FIGURE 8

This slightly higher moment (M2 + MI) will in the same manner produce a slightly greater deflection (A2 + A l ) , etc. Each successive increment in deflection becomes smaller and smaller.

The final values would be -

since

M,., = MI + P Ail,,, then

Accommodating Increased Moment Due to Deflection

This increase in the moment of the bending load caused by deflection is easily taken care of in the basic interaction formula by an amplification factor (k ) :

esign of Compression Members / 3.2-5

Applied sinvsoidol moment

FIGURE 7

Resulting deflection Curve

The interaction Formula #4 then becomes -

(ultimate load condition)

Each ultimate load condition factor in the above formula is equal to the corresponding factor for working conditions multiplied by the factor of safety (n ) ; or

< = 1 and

where: subscript, is for working loads subscript A is for allowable loads

Notice:

?r2 E so: ue = - /&\"


Or, on a stress basis -

where:

o; = computed axial stress

ub = computed compressive bending stress at point considered

a. =: allowable axial stress permitted if there is no - bending moment; use largest (L/r) ratio, regardless of plane of bending

u, = allowable compressive bending stress per- - mitted if there is no axial force. (AISC Sec. 1.5.1.4)

The AISC Specification Sec. 1.6.1 uses the same amplification factor. They use the term (F',) which is

the Euler stress (u,) divided by the factor of safety ( n ) . The term (v',) is used here in place of AISC's (Ffe) .

AISC uses E = 29,000,000 psi and n = 1.92 in the above.

Here:

r, = radius of gyration about an axis normal to the plane of bending

L, = actual unbraced length of column in the plane of bending

TABLE 2-Euler Stress Divided By Factor of Safely

140

i 50

i 60

170

180

190

200

is = octuol unbioced length of column in the plane of bending iB = radius of gyration about the oxir of bending

- 7,620

6,640

5,830

5,170

4,610

4,140

3,730

7,510

6.550

5,760

5.110

4,560 .- 4,090

7,410 ....

6,460

5.690

5,050

4.510 .......

4,050

1 ---

7,300

6,380

5.620 -.

4,990

4,460

7,200

6,300

5,550

4.930

4,410

7.100

6.220

5,490 ... - .

4,880

4,360

4,010 3.930 3,970

7,010

6,140

5.420

4,820

4,320

3,890

..... 6.910

6,060

5,360

4,770

4,270

3,850

6,820 6,730

5,980 ......

5,290

4,710 - 4,230

3.810

5.910

5,230

4,660 .-

4.180 - 3,770

Design of Compression Members /

According to AISC Sec. 1.5.6, this value (o',) may be increased 'h for wind loads.

Table 2 lists the values of 5', (Eulcr stress divided

TABLE 3-Value of $ for Several Load Conditions

Core

KLb by factor of safety) for y- ratios from 20 to 200. ' b

These values apply for all grades of steel, hut are based on the conservative factor of safety = 1.92.

The derivation of the amplification factor has been based on a member with pinned ends and a sinusoidal moment applied to it. In actual practice these conditions will vary; however this factor will be reasonably good for most conditions. AISC Sec. 1.6.1 applies a second factor ( C , ) to adjust for more favorable conditions of applied end moments or transverse loads.

applied end momeflts

applied tranmerse load7

where:

MI and M2 are end moments applied to the column.

MI 5 M2, and the ratio (MI/M2) is positive when the column is bent in a single curve and negative when bent in reverse curve.

AISC 1963 Cornmentori

.. - (see Table 3 for values J, and C,, for several load conditions)

(AISC Formula 6) Here:

A = maximum ddection due to transverse load

L = actual length of member also used in deflection ( A ) calculation

M = maximum moment between supports due to transverse load

AlSC Formulas For Checking

When

When

the amplification factor must he used

Formula #8 now becomes-

(AISC Formula 7a) the influence of the amplification factor is generally small and may be neglected. Hence the following formula will control: This formula provides a check for column stability.

3.2-8 / Columm-Related Design

AISC formula 7b

-

In this exompie: A36 steel L i r = 80

-

-7 3 = 15,360 1

0, = 22,000

0: = 23,300 0, = 36,000

FIGURE 9

,

old AISC formulo

Bending compressive stress (ab)

I t is an attempt to estimate thc total bending stress in the central portion of the column and to hold the axial compressiw stress down to a safe level.

As L/r increases, this formnla will reduce the axial load carrying capacity of the column. This is because the Euler stress (o;,) decreases as L/r increases.

As C , increases, caused by a less favorable condition of applird and moments or transverse forces, Formnlx #I1 will reduce the axial load carrying capacity of the column.

The end of the member also must satisfy tho straight-line interaction formula:

1 ( AISC Formula 7h) I In this formula, the allowable for compression

(u,) is for a column having a slendemcss ratio of L/r - = 0, hence r, = .60 IT,. --

This formula provides a check for the limiting stress at the ends of the column, and as such applies

only at braced points. k Figure 9 is an example of the relationship of AISC

Formulas 7a and 7h in the design of a specific member, nnder varions loading conditions.

For bending moments applied about both axes of the column, these formulas become:

(AISC Formula 6)

I (AISC Formula 7a)

I (AISC Formula 7b)

esign of Compression Members / 3.2-9

4. DESIGN OUTLINES n~cinbers nnder coinpression in bending. Table 6 applies to hox members tinder compression in bending.

The design procedure is simplified by iollowing the Earh of these tl~ldrs categorize the mt:mber-load appropriate outline in Tables 4, 5, or 6. Table 4 applies conditions \\.hi& innst be satisfied, ; u ~ d then presents to compression mcinbers under combined loading (in- the nqoircd for~nulas with which to determine the teraction problems). Table 5 applies to open-sectioned ailowablc cornpressive stress.

LE 4---Design Outline for Compression Members Under Combined Loading flnteroction Problems)

category@ Coiumni in framer with computed momcnli moximum ot the ends with no transverse loading, and d e r w o y is permitted. Were the latcrol stability 01 the i inme depends upan the bending r t i f fne i i of its members.

v Siderwov permitted

Check #il and #12 Ma

using o, = - S

:ategory@ olumnr with computed mu:iioals ianimum a t the ends with no .onweire loading, and iderway i s pievented

Sideway orevented

Check #I i #12 M?

using a, , -- s

I (AISC Forrnulo 7oi

(AISC Forrnulo 7b)

.tegopy@ ornprersian members with idi t ionol tronrveire lood;;

example a compi~ is ive iord of o truss with onsverse loading between ippoit f (panel pointr!.

Tionrvene lood i

No tionriotion of iointr

). = max deflection due to t ianivei ie looding

= mox aoment between rupporir due to trans. loading

ie KL in computing or - ie Li, in computing moments (M)

Check #I i M, " r i n g a, = S

Check # i 2

M ou - 2

S

a,. oh ond .60 or moy be -- increoied $6 io r wind (AISC Sei iSd!


TABLE 5-Design Outline for Compression Members Under Compression In Bending

Members Which Are Symmetrical About An Axis i n Plane of Bending And Having Some Lateral Support of Compression Flange

Comprer%ion element8 which are not "campoct" but meet the lollowing AISC Sec 1.9 ieqvirementi

Having on axis of symmetry in the plane of its web: AISC 1.5.1.4.5

L when T 5 40 don't need AiSC Foirnuio 4

l i in addition. lateral sirppait of iamprerriui flange does not exceed:

A7. A373. A36 steels 13 bc

Other stronger steels

-- and compression elements meet the following AISC Sec i 5 . 1 4 . 1 "rampoct section" requirementi:

* This.mtio may be exceeded if the Lending stress, using a u d t h not cxcecding this limit, is within the allowable stress. t For "oompact" columns (AISC Scc. 1.5.1.4.1) which are s y n - rnetrical about an axis in the plane of bending, with the above lateral support of its con~piession Range and 0. = .15 a, use 90% of the moments applied to the ends of the column if caused by the gravity loads of the connecting beams. f For rolled sections, an upward variation of 3% may be tolerated.

In Tables 5 and 6: ment at the ends of the nilbraced length, taken abont

L = unbraced length of the compression flange

br = width of ~vmpression flange

d = depth of member treated as a beam

r = radius of gyration of a Tee section comprising the compression flange plus % of the web area; about an axis in the plane of the web. For shapes symmetrical about their x axis of bending, substitution of r, of the entire section is conservative

At = area of the compressiort flange

MI is the smaller and Mp the larger bending mo-

- the strnng axis of the member, and where MI/& is the ratio of end moments. This ratio is positive when Mi and M2 have the same sign, and negative when they have different signs. When the bending moment within an unbraced length is larger than that at both ends of this length, the ratio shall be taken as unity.

(but not more than 2.3 can conswvatively be taken as 1 .O)

Design of Compression Members / 3.2-1 1

TABLE 6-Design Outline for Box Members Under Compression In Bending embers Which Are Symmetrical About An Axis I n Plcrne o l Bendinq

No AlSC limit on laterol rupport of compresdon flange beiowe box section is torsionally rigid

Compiession elements which ore not "campad" but meet the following AlSC Sec 1.9 requirements (1.5.1.4.31

3000 * b/t = %

8000 * B/t = - %

Note: Al l notes from Table 5 apply equolly to this

Toble 6. gs = .60 a,

And if lotero! support doer not exceed:

A7, A373. A36 steels 13 bz

Other rtronger steels

2400 h i 20,000,000 A,

"' d <,

And compoiiion eiernrntr meet the following AISC Sec 1.5.1.4.1 "compoct section" iequliernentr;

I600 t b/t 5 ----

G 6000

B/1 5 .- V T

5 d" 5 *( 1 - 1.43 -2) t~ - fl

8000 but need not be lerr than -

.- V T --

a, = .66 a, t -

TABLE 6A

1600 1 fl .-

Width-to- 3000 - 9.5

thickncrr

rotio not 6000 - to exceed:

~

13,300 \K

yield strength of steel * * *

Lotero! support 2400 of compression 6 flonge of "compact" - sectionr not 20,000,000 Ar to exceed:

- --- -. a~ 4

C. =

1.18.2.3: mox. longitudino! rpocing between intermittent fi l let welds ottoching compression flonge t o girderr

4Wo S ~ - t ~ 1 2 E

*Quenched & Tempered Steels: yield strength at 0.2% offset Round off to nearest whole number

Allowable n = ,605,

bending

t t res e = .66 s,

33.000

20.000

100.000

60,000

46,000

27,500

22,000

36,000

22,000

65,000

39,000

42,000

25,000

90,000

54,000

60,000

36,000

50,000

30,000

66,000 24,000

45.000

27,000

95,000

57,000 ~-

55.000

33,000

28,000 62,700 29,5001 30,500 39.500 1 43,O0Oi 59,400 33,000 36,500


5. BUILT-UP COMPRESSION MEMBERS

The basic requirements of welds on built-up compression members, as specified by AISC, are summarizkd by Figures 10, 11, 12, and 13.

Welding a t the ends of buil t-up compression members bearing on base plates or milled surfaces (AISC 1.18.2.2) :

Weld odequote to transfer any calculated force

Continuous fillet weld at end of all elements in contact with each other (AISC 1.18.2.2)

Bearing or base plate or milled surfaces

FIGURE 10

Plate in contact with a shape (AISC 1.18.2.3):

Two rolled 1.18.2.3) :

shapes in contact with each other (AISC

n of Compression

lates and Lacing ,,.'8.2.5) 0"d (1

182.61

Main comprrsion member built-up from plates or shapes and czrrying a calculated force:

P

FIGURE 14

The spacing of lacing must be such (AISC 1.18.2.6) that -

S - of elemc-nt = (if whoL member rl

Single Double B!oiiriy C1:ocin~ FIGURE 16

For sil~glo bracing: For doubk bracing: Wlwn the, su:i~~irrz bctuwri intcrn~i.ttr:nt melds


Design laciug bar for axial compressive force (F) :

(AISC 1.18.2.6) \vhere:

n = number of bars carrying shear ( V )

Determine nllowablr compressive stress (ua) from - one of the following two formulas:

( A I S C Formula 1 ) I (Use Tables 6 through 14, Section 3.1)

ua from Form. #15 u. = -

. . . . . . . . . . . . . (17)

On continuous cover plates with access holes (AISC 1.18.2.7):

Typical Built-Up Compression Members

Figure 18 slrows a number of examples of compression members built up from common shapes by means of welded construction. As indicated in lower views, perforated plates are often substituted for lacing bars for aesthetic effect.

I Problem 2 / To cheek the design of the following built-up section for the hoist of a boom. The 15' column is fabricated from A36 steel by welding four 4" x 3%" x 'h" angles together with lacing bars.

- "For double brace, use .70 L,

Use net section for cornpierrion

I


FIGURE 18-Typical Built-up Compression Members

properties of each

A = 3.5 in."

r, = .72"

I, = 5.3 in.*

I, = 3.8 in.*

x = 1.0"

y = 1.25"

corner angle

moment of inertia of built-up section about axis 1-1

1, = 4(3.5)(5.75j2 + 4(5.3) = 484

moment of inertia of built-up sodion about axis 2-2

least radius of gymtion

slendcrncss ratio

Then from Tahle 7 in Sect. 3.1, the allowable com- prmsive stress is uc Z= 19,900 psi and the allowable compressive load is--

P = u , A - = (19,900) (14)

= 278.6 kips

Check slenderness ratio of single 4" x 3%" x %" angle between bracing:

= 22.4 < 30.6 OK - (AISC Sec. 1.18.2.6)

FIGURE 20

Design of Lacing

AISC specifies that lacing bars be proportioned to resist a shearing forw normal to the axis of the member and equal to 2% of the total compressive force on the member (Sec. 1.18.2.6):

v = 2% P

= (.02) (278.Ck)

= 5.57"2 bars)

The axial force on each bar is-

The unsupported length of the lacing bar between connecting welds is -

The least radius of gyration of the %" x l/z" bar is obtained tliusly -

A = 'I* in."

And the slenderness ratio of the lacing bars is -

= 56.3 < 140 OK single lacing - (AISC Sec. 1.18.2.6)

From Tahle 7 in Sect. 3.1, the allowable compressive stress on thc bas is -

uc = 17,780 psi -

The allowable compressive force on the bar is - F - U < A

= (17,780) (.25)

= 4.49 > 3.22" OK

If each end of each bar is connected to thc angles by two 1%'' long %<:/,,j" (ETO) Met welds, this will provide an allowable forco of -

F = 2 X I.% X 2100 lhs/in = 6.3k > 4.4Sk OK ---.

Design o$ Compression Members / 3.

I Problem 3 1 A multi-story building, having no interior columns, has a typical welded built-up cdumn with the section shown in Figure 21.

A36 steel and E70 welds arc employed. The following three load conditions are recognized:

Care A dead and iive loodr no wind

P = 2500 k i p Mr = 250 ft-kips M, = 0

Case C

deod ood iive loodr with wind in v-v with wind in x-x ~. . . . . ~~

direction direction P = 2700 kips P = 2800 kips

M, = 2200 ft-kips Mr = 250 ft-kips M, = 0 M, = i 200 ft-kips

properties of the 14" WF 426# section

A = 125.25 in.'

moment of inertia about x-x

Let reference axis be a-a here

L Outride face of column

=: 74,507 in.'

L I I ---A

= + 2.84" (from a-a)

moment of inertia about y-y

+ 76.570

FIGURE 21

Allowcrble Stresses

The various axial compressive stresses 'and bending stresses on the built-up cohlmn are checked according to Formulas #I1 and 12 (AISC Sec. 1.6.1, Formulas 6, 7a, and 7b).

When wind loads arc included, the basic allowable stresses are increased by %. provided the resulting section is not less than that required for dead load, live loads, and any impact (AISC Sec. 1.5.6).

Compression members are considered "compact" when syn~metrical about an axis in the plane of bending, with lateral support of the column's compression flange not exceeding a distancc equal to 13 times its width (A36 steel) (AISC Sec. 1.5.1.4.1). For "compact" columns, the engineer can use just 90% of moments applied to ends of the column if caused by gravity loads on connecting beams (no wind loads) and ua 5 .15 u,, - (AISC See 1.5.1.4.1).

If the section is not "compact", AISC Formulas 4 and 5 must be used to determine the allowable compressive bending stress (ubr and -. ub,).

check for lateral support

LC = maximum unbraced length of compression flange for "compact" section

+ 727 Total 25625


About strong axis [x-x) 1 check for "compact" section Bange half, width to thickness

I = B m 11" = 5720 L 13 ' 13'

( a ) outer flange plate

36" W 3004

(b ) inner WF section

@ 4;

check web depth to web tlzicknes

dm - 34" Actual - - - = 22.6 t, 1%

I - U 9 O . d = 405 8 - - /' L 50'

1 - 74,507 1n4 = 5720L- - - L - 13'

8000 but need not be less than -

V T

4 FIGURE 22 (a)

@

but need not be less than 42.1

42.1 > 22.6 OK

End V ~ e w of Bldg 'Not fixed

Therefore it is a "compact" section and following can be used:

rbr = uby = .66 uy or 24,000 psi - --

Euler stress (I+',,) and (u',,)

About strong axis (x-x):

From Table 2, read u',, = 133,750 psi.

About weak axis (y-y) :

From Table 2, read d,, = 50,400 psi.

ullowahle axial compressive stress

Sidesway being permitted, from the nomograph (Fig. I):

I< = 3.65 and

L , = K L

= (3.65)(13' x 12")

= 569"

Design ot Compression Members / 3.2-19

FIGURE 22 (b)

Sidesway being permitted, from the nomograph (Fig. 1):

K = 2.1 and

L . = K L

= 2.1 (13' x 12")

= 328"

This value of r, = 54.4 governs, and from Table 7 in Sect. 3.1 (A36 steel)

cr* = 17,970 psi

Column Analysis

The following three analyses of the column (Cases A, B, and C ) are for columns with computed moments maximum at the ends with no transverse loading and with sideswny being permitted.

This would be catezory A on Table 4. In this case (6, = .85) for both axes (x-x) and (y-y).

CASE A Dead and Live Loads; KO Wind

moment at support

FIGURE 23

applicd loark

P -- 2500 kips

M, = 250 ft-kips

M, = 0

applied stresses

= 9760 psi

3.2-20 / Coiumn-Related Design

- - (250 x 1000 X 12)(23.50) ( 74,507 )

= 947 psi (max at 4" x 20" flange fk )

= .15, .9M, can

b e x e d (Sec 1.5.1.4.1): but

allowable stresses

U S = 17,970 psi - Since it is a "compact" section laterally supported

witlun 13 times its compression flange width (Sec 1.5.1.4.1) :

u,, = 0

oi. = uby = .66 us = 24,000 psi

u',, = 133,750 psi

0.60 u, = 22,000 psi

u sib0 in this case, - = ---- - u* 17,970 - '54

= 54 > .15To full value of h4, must be used.

checking against Fornzula #I4 (AISC 7a)

Here C, = .85 because sidesway is permitted

checking against Formula #15 (AISC 7b)

CASE B Dead and Live Loads; Wind in Y Direction

applied loads

p = 2700 kips M, = 2200 ft-kips My = 0

applied stresses

P = K

- .- - 2700 lo0O = 10,520 psi 256.25

= 8330 psi (max at 4" X 20'' flange ifi )

We cannot use .9 M,, because wind loading is involved; hence full value of M, must be used.

allowable stresses

ua = 17,970 X 1.33 M7ind in addition .- (Set 1.5.6)

ubx = 24,000 X 1.33 Wind in this direction -- (Set 1.5.6)

vex = 133,750 X 1.33 Wind in this direction (Scc 1.6.1 and 1.5.6)

checking against Formula #14 (AISC 7a)

FIGURE 24

checking against Fornizrlti $15 (;1lSC 7b) . i\4g ~ o Obi li

m,, -. h --. I . I .() 0.6 w, + F,, I V,,? . .

(10,520) -- -- . -- (8330) 14.500 1'" ; m i x ; i t fi;nigc of WF section) (22,000 x 1.33) ~2-t.(nx) x~ ~ i .33 )

,621 < 1.0 OK - or

CASE C Dead and I ivc I,o;ds; Wind in S Direction 1.5.',00 pi (irr;ix :it outrr c r f ~ c . of 4" X 2wR)

We cailrlot I I W .Y hl, bec:iuw: wind loading is / Y involved; hm<v f~ill \ ; h e of (M,) ;md (M,) must be

used.

allowable st r twrs

o;, = 17,070 ;,< 1.33 Wind in addition (SK 15.6)

cr,, = 24,000 No wild in this direction

uby = 24,000 >: 1.33 Wind in this direction (Sec 1.5.6)

utCx z z 13X750 No wind in this direction

5 = 50,400 >< 1 3 Wind in this direction

checkins apiirlst I'oi.rnr11a #11 JAISC 7nj

FIGURE 25

applied loads

P 2Y00 kips

M, 2,70 ft-kips

M, 1200 ft-kips

: 10,920 psi

olumn-Related Design

Torsion on Built-Up Column

One item left to investigate in the built-np column is the twisting action applied to it. In Case C, the wind in the x-x direction causes a moment of M, = 1200 ft-kips because of the restraint of the spandrel beams.

( 1 ) One way to analyze this problem is to assume that this moment (M,) is resisted by the elements ( the 14" W F section and the 4" X 20'' flange plate) of the built-up column in proportion to their moments of inertia about axis y-y. See Figure 26.

Since:

The moment resisted by the 4" X 2 0 flange plate is-

= 346 ft-kips = 4,153,000 in.-lbs

This moment is to be transferred as torque from the 13" W F section to the 4" X 20" plate through a

4" X 20" R J

Torque box -V

FIGURE 26

torque box, made by adding %"-thick plates to the built-up column in line with the beam connections.

This torque box is checked for shear stress; Fig- ure 27.

= 6600 psi OK -

( 2 ) Another method of checking this twisting action is to consider the moment (M,) as applying torque to the built-up column. See Figure 28.

This applied moment may be considered as two flange forces: in this case, 411 kips iu the upper and the lower flanges of the spandrel beam, but in opposite directions. Since these forces are not applied at the "shear center" of the column, a twisting action will be applied to the column abont its longitudinal axis within the region of the beam connection where these forces are applied; there is no twisting action along the length of the column in between these regions.

Since an "open" section such as this built-up


FIGURE 27

FIGURE 28

No twisting action

Twisting oction o section

Shear oxis I I

Torsue box

3.2-24 / Column-Related

P = 1000 lbs A

column offers very little torsional resistance, two plates will be added within this region to form a closed section about the shear axis to transfer this torque. See Figure 29.

If this torque had to be transferred from one floor to the next, these plates would havc to be added the full length of the column. How-ever, this torque is only within the region of the connecting beams which apply these forces, hence plates are only added within this short distance.

In our analysis of the column under Case C loading conditions, a transverse force of 1 kip was assumed to be applied in line with the web of the WF section of the built-up columu (this is the position of the spandrel beams). This cross-section is in the plane of the top flange of the spandrel beam. Just below this, in the plane of the lower flange of the spandrel beam,

this 1-kip force will be applied in the opposite direction. Treating this short section of the built-up column

as a bcam, the shear forces due to this I-kip force will he analyzed on the basis of shear flow. In an open section it is not difficult to do this because there is always one or more starting points, the unit shear force a t the outer edges alwtys being zero. But in a closed section such as this, it is necessary to assume a certain value (usually zero) at some convenient point, in this case at the midpoint of the web of the WF section. The unit shear forces are then found, starting from this point and working all the way around the section using the general formula-

V a y q2 = q, + I

where:

V = transverse force applied to srction (Ibs)

I = moment of inertia of built-up section about the axis normal to the applied force (h4)

a = area of portion of sectiou considered ( in2 )

y = distance between center of gravity of this

erign 06 Compression Members / 3.2-25

area and the neutral axis of the boilt-up section (in.)

% = unit shcar force at the start of this area (lbs/in. )

q a = unit shear force at the end of this area (Ibs/m. )

This work is shown as Computation A. Relow, in Figure 30: the total shear force ( Q ) in the various areas of this section are found; thcse are indicated by arrows. This work is shown as Computation R. By Computation C, thesr shear forces are seen to producc an unbalanced moment oi 70.519 in-lhs, which if nn- resisted will cause this section of the colurnn to twist.

In order to couiiterbalancc thiq moment, a negative moment of the same value is set up by a constant shear force flow of-

q = -51.1 1bs per linear inch

When this is sr~perimposed upon the original shear flow, Figure 30, we obtain the final %ow shown in Figure 31. The resulting shear stress ( r ) is obtained by dividing the unit shear force (q ) by the thickness of the section. Also the valucs must bc increased because the actoal forcc is 111 kips instcad of 1 kip, the work and resulting shcar stresses are shown as Compu- tation D. Sce Figuw 37 also. These shear stresses seem reasonable.

FIGURE 30

FIGURE 31

olumn-Related Design

Computation A

1.q. = 0 0

v L 1 ~ - o + (1000)(7.83 X 1.8751(3.921 = + 5,01 = 2.q.=0+I-

11,491. 5.01

3. qa = 0 0

v 0 Y 4. qe' = qs + - = 0 + IlOOO)i8.35 X 3.03%!7.83) =

+ 17,24 = I 11,491.

17.24

5. q." = qr + q,' = 5.01 + 17.24 = 22.25

" a = 22.25 + 110003(8.35 X 3.03W.83) = 22,25 + 17,24 = 39,49 6. qa = q," + T 11.491.

" - 39.49 + i10001l28.64 X '/2)!9.095) = 39,49 + = 7. qir = qa + I - 11,491.

8. qp = 0 0

V o Y l1000)1.905 X 4)(9.548) = + 2.99 = 9. qc' = q. + 7 = 0 + 2.99 11,491.

10. qr" = qt' + qt = 2.99 + 50.82 = 53.81

I I. q. = q." + = 53.81 + 11000)(9.095 X 4114.5481= 53,81 + 14,40 = 68,2, 11,491.

Computation B

12. Om. = (3 X 0 + ]/5 X 5.01) 15.66 = 26.1 #

13. Qsa = (% X 17.24 X 8.35) + 22.25 + 39.49 2

X 8.351 = 329.7 #

14. Qas' = 39.49 X 1.265 = 50.0 #

15. Q a t = 39'49 + 50'82 X 28.64 = 1293.2 # 2

16. Q u = (36 X 68.21 + % X 53.81) 18.19 = 1153.4 #

Check I: V == 0

Computation C

Now, take moments about @

The unboionred moment ir 70,519 in-ibs

Make 2 M, = 0 o constant shear force flaw, which must be added to iarm o negative moment of - 70,519.

The resulting aheor force is -

Where [A] = aieo enclored by renterline of web, flonges, and [A] = (15.66)(8.35) + (18.19)(28.64) = 651.7 in'

This giver the true rhea? flow (Fig. 31).


FIGURE 32

FIGURE 33

(@ 1450 psi

FIGURE 34

Reentrant Corners (Figures 33 and 34)

The only other concern on this built-up construction is the sharp reentrant corner at points ( d ) and (f) .

Timoshenko in "Theory of Elasticity", p. 259, indicates thc following shear stress increase for a reentrant comer:

Sharp reentrant corner

FIGURE 35

In structural steel. any stress concentration in this area probably would be relieved through plastic flow and could he ncglectcd nnlcss fatigne loading were a factor or there were sonic amount of triaxial stress along with impact loading.

Of course if a fillet weld could be made on this inside corner, it would eliminate this problem. See Fignre 35. This is possible in this case, because these plates for the torque box ;ire not vcry long and the welding operator could reach in from each end to make this weld.


ELDS FOR FABRICATED COLUMN

The melds that join the web of a built-up column to its inside WF seetion and its ontside flange plate, me subject to longitudinal shear forces resulting from the changing moment along the length of the column.

As an example, continue with the conditions stated for the preceding Problem 3.

The bending force in the flanges of the girder applied to the colunm is found by dividing this moment (M,) by the depth of the girder:

- - 2200 ft-kip X 12" . 35"

= 754 kips

Thc point of contraflexure, or zero moment, is assumed at about midheight of the column. The horizontal force at this point, or bansverse shear in the column, may be found by dividing half of the moment applied to the column at the connection by about one- half of the column height. This assumes half of applied

Wind

i

T -* J Midheight

h

moment cnters upper colt~mn and half enters 1owcr column.

M F,, = -- '6 h

- 1100 ft-kip 6.5'

= 170 kips

The moment and shear diagrams for the column when loaded with dead and live loads and wind in the y-y direction (Case H ) are given in Figure 38.

This shear diagram indicates the transverse shear within the region of the beam connection is Vz I= 584 kips, and that in the remaining length of the column is V, = 170 kips.

The size of the connecting weld shall be determined for the larger shear within the region of the beam connection, and for the lower shear value for the remaining length of the column. The minimum fillet weld size is aiso dependent on the maxi~num thickness of plate joined (AWS Building Article 212 a 1, and AISC Sec. 1.17.4).

Moment diagram

FIGURE 36

Shear diagram

This is also o picture of the amount and location of the connecting welds to hold column together

Design of Compression embers / 3.2-29

where:

A = 256.25 in.'

I, = 74,507 in.*

The following allowable shear force for the fillet weld will be used:

f = 11,200w (A36 steel and E70 weld metal)

We will not reduce the shear carrying capacity of the 61let weld due to the axial compressive sbess on it.

weld @ in the way of the beum connection

- (584k) (125.25) (1515) - ( 74,507) ( 2 welds)

7450 leg size w = ------ 11,200

= .665" or use W

weld @ for the remaining length of the column

Vs = 170" or 29% of V2

hence use 29% of the leg size or ,192". However, the

maximum thiclmess of plate here is 17/e", and the minimum size of fillet weld for this thickness is W' (AWS Bldg Art 212 and AISC: Sec. 1.17.4). IIcncc use - 33"

Weld @ in line with the beom connection

- -- ( , 5 s lk ) (SO) - (21.84) (74,507) ( 2 wc4ds) - 6860 lbs/in.

6860 leg size w = ------ 11.200

weld @ for the remaining length of the column

V1 = 170L or 29% of Vz

hence use 29% of thc above leg size, or leg s i ~ e w = ,178" or 3/16"; however, the maximum thickness of plate here is 4" and the minimum size of fillet weld for this thickness is 'h" (.4WS Bldg Art 212 and AISC Sec. 1.17.4). Hence use M".

When the column is subjected to the dcad and live loads and wind in the x-x direction, bending is about the y-y axis. Here the inside and outside portions of the colurrni arc continuous throughout the cross- section of the colimm, and the connecting welds do not transfer,any force; hence, the weld size as dcter- mined above for Case R would control.

Perhaps w'ld 9 should be further increased within the region of t e beam connection, to transfer the horizontal forces of the hcam end moment back into the column web. The horixontal stiffeners in the colurnn at this point, however, would undoubtedly take care of this.

7. SQUARE AND RECTANGULA SECTIONS FOR COLUMNS

Square and rectangnlar tubnlar shapes are now being hot rolled from A7 (33,000 psi yield) and A36 (36,000 psi yield) steel at about the same price as other hot- rolled sections.

These sections have exceptionally good compressive and torsional resistance. See Tables 7 and 8 for dimensions and properties of stock sizes.

Many cngineers feel that the round tnhular section is the best for a column since it has a rather high radius of gyration in all directions. This is much better than the standard W F or I sections, which have a much lower radius of gyration about the weaker y-y axis.


Unfortunately the usually higher cost of round tubular sections prohibits their universal use for columns.

However, a sqnare tube is slightly better than the round section; for the same outside dimensions and cross-sectional area the square tube has a larger radius of gyration. This of course would allow higher corn. pressive strcsses. Consider thc following two sections, 12' long, made of A36 steel:

FIGURE 38 FIGURE 39

3%" extra-heazjy pipe 4" x 4" square tubing

A = 3.678 in.' A = 3.535 in.'

Wi = 12.51 lbs/ft W, = 12.02 lbs/ft

r,,, = 1.31" r,,bi,, = 1,503"

ue = 11,670 psi - u, = 13,500 psi -

In this example, the square ttlbe has 3.9% less wcifiht and yet has an allou&le load 11% greater. Its radius of gyration is 14.7% greater.

For another rxamplc, consider the following A36 Techon:

FIGURE 40 FIGURE 41

uc = 15,990 psi - uc - 19,460 psi - P = (15,990) (9.71) P :: (19,169) (9.18)

= 155,0k = 184.3"

The 32-lb/ft 10" square tubular section has a radius of gyration which is more than twice that about the weak y-y axis of the 33-lb/ft 1 0 W F section. This results in an allowahlr compri:ssive load 19% grcater.

The second advantage to the square and rcctangu- Iar sections is thc flat surface they offer for connections. This results in the simplest and most direct type of joint with minimum preparation and wclding. Also by closing the ends, there would be no maintenance problem. It is common practice in many tubular structures not to paint the inside.


Four all-welded multilayer Vierendeel trusser make up the exposed frame of the beautiful Rare Book Library of Yale University. Weld- fabricated tapered box sections are used in the trusses. Good plan- ning held field welding to o minimum, the trusses being shop built in sections. Here, a cruciform vertical member of the grilled truss is field spliced.

S E C T I O N 3 .3

1. BASIC REQUIREMENTS

Rase plates are reqnirtd on the ends of columns to distribute the concentrated compressive load (P) of the column over a much larger area of the material which supports the column.

The base plate is dimensioned on the assumption that the overhanging portion of the base plate acts as a cantilever beam with its iixed end just inside of the column edges. The upwnrd bending load on this cantilever beam is considered to be uniform and cqual to the bearing pressure of the supporting material.

c r i t i c $ Sec t i on in Bending

FIGURE 1

AISC suggests the following method to determine tho reqnired thiclmess of bearing plate, using a maximum bending stress of .75 cry psi (AISC Scc 1.51.4.8):

1. Determine the required minimum base plate area, A = P/p. The column load ( P ) is applied uniformly to the base plate within a rectangular area (shaded). The dimensions of this area relative to the column section's dimensions are .95 d and .SO h.

The masonry foundation is assumed to have a unifonn bearing pressure ( p ) against the full area ( A = B x D ) of tho base plate. See Table 1 for allowable vah~es of p.

2. Detmmine plate dimensions f3 and D so that dimensions m and n are approximately equal. As a guide, start with the square root of required plate

area (A). Tablc 2 lists standard sizes of rolled plate used for bearing plates.

3. Determine overhanging dimensions m and n, the projection of the plate beyond the assumed (shaded) rectangle against which the load ( P ) is applied.

4. Use the larger value of m or n to solve for required plate thickness ( t ) by one of the following formulas:

Derivafion of Formula # I

The primary fnnction of the plate thickness is to provide sufficient resistance to the bending moment ( M ) on the overhang of the plat(, just beyond the rectangular area contacted by the column. Treating this over-

LE 1-Masonry Bearing Allowabler (AlSC Sec 1.5.5)

On sandstone and limestone p = 400 psi

On brick i n cement mor to i p = 250 pi1

On full oiea of concrete support p = 0.25 f'.

On ?$ orec of concrete support p = 0.375 f',

where f', ir the specified iarnpicir ion strength of the concrete a t 2 8 doys !In this text, a', ir used as equivalent to AISC'i Pi.)

LE 2-Standard Sizes of Rolled Plate For Bearing Plates

I / 2 8 x 3 4 4 x 6 6 0 x 7 7 2 X 9!j

1 4 X I l l 2 2 8 X 3% 48 X 5% 60 X 7 % 7 2 X 10

1 6 X 1'12 3 2 X 3 ' / 2 4 8 x 6 6 0 x 8 7 8 X 9

16 % 2 32 Xi4 48 X 6Il2 66 X 7% 7 8 X I0 20 i 2 36 X 4 52 X 6 66 X 8 8 4 X 9l/2

20 X 2112 36 X 4% 52 X 6% 66 X 8% 84 X 10

2 0 X 3 40 X 4112 52 X 7 66 X 9

24 X 2 40 X 5 56 X 61/2 72 X 8

24 X 21/2 44 X 5 56 X 7 72 X S1/2

24 X 3 44 X 51/2 56 X 8 72 X 9

3.3-1


hang (m or n ) as a cantilever beam with M being maximum at the fixed or column end:

bending moment

p m' M = ---- parallel to thc column's x-x axis and 2

M = - parallel to the column's y-y axis 2

bending stress in plate

where, assuming a 1" strip:

I (I") t' S = -- 6

and by substitution:

- 6 p m V p m m ' - - and

2 u u

t = m )r Formnla #1

(similarly for dirncnsion n )

Finishing of Bearing Surlaces

AISC Sce 1.21.3 prescribes that colunin base plates he finished as follows:

"1, liolled steel bearing plates, 2" or less in thickness, map be used withont planing, provided a satisfactory contact bearing is obtained; rolled steel bearing

FIGURE 2

plates over 2" hut not over 4" in thickness may be straightened by pressing; or, if presses are not available, by planing for all bearing surfaces (except as noted under requirement 3 ) to obtain a satisfactory contact bearing; rolled steel bearing plates over 4" in thickness shall be planed for all hearing surfaces (except as noted under requirement 3) .

"2. Column bases other than rolled steel bearing plates shall he planed for all bearing surfaces (except as noted undcr reqnirement 3 ) .

"3. The bottom snrfaces of bearing plates and column hnses which are grouted to insure full bearing contact on fonndations need not be planed."

The above reqnirements assume that the thinner base plates are sufficiently smooth and flat as rolled, to provide full contact with milled or planed ends of column bases. Thicker plates (exceeding 2") are likely to be slightly bowed or cambered and thus need to be straightened and/or made smooth m d flat.

2. STANDARD DETAILING PRACTICE

Fignre 2 shows typical column bases. Note the simplicity of these designs for arc-welded fabrication.

Designs a and h are intendcd for where column and base plate are erected separately. The angles are shop welded to the column, and the column field welded to the base plate aftcr erection. Design c is a standard of fabrication for light colnmns. Hwe the base plate is first punched for anchor bolts, then shop welded to the colnmn.

If the end of the colnmn is milled, there must be just sufficient welding to thr. base plate to hold all parts

Column Bases / 3.3-3

securely in place (ATSC Sec 1:15.8). If the end of the colu~nn is not milled, the connecting weld must be large enough to carry the co~npressive load.

Welding Practices

In most cases, during fabrication, the columns are placed horizontally on a rack or table with their ends overhanging. The base plate is tack welded in place (Fig. 3) , using a square to insure proper alignment, a d is then finish welded.

As much as possible of the welding is done in the downhand position because of the increased welding speed through higher welding currents and larger electrodes. After completing the downhand welding, along the outside of the top flange, the column is rolled over and the downhand welding is applied to the other flange.

FIGURE 4

It is possible to weld thc base plate to the column without turning. Sce Figure 4. With the web in the vertical position and the flangm in the horizontal position, the top flange is weldcd on the outside and the lower flange is welded 011 the inside. This will provide sufficient welding at the flanges without further positioning of the column.

FIGURE 3

3. ANCHOR ATTACHMENTS TO COLUMN BASES

Anchor bolt details can be separated into two general classes.

First, those in which the attachnrents serve only for erection purposes and carry no important stresses in the finished structure. These include all columns that have no uplift. The design of these columns is governed by direct grnvity loads and slenderness ratios set up by specifications for a givcn column formula.

IIere the columns can be shop welded ctirectly to the base plate, unless the detail is too cumbersome for shipment. The anchor bolts preset in the masonry are made to engage the base plate only. See Figure 5a. I.arge base plates are usually set and levelled separ- atcly bclore hcginning column erection. In this case d ip angles may hz shop welded to the column web or Nanges, and in field creetion the anchor bolts engage both base plate and clip angle. See Figure 5b.

Secondly, those in which the attachments are designed to resist a direct tcnsion or bending moment, or some combination in which the stability of the

(a) Base plate shop welded to (b) Bose plate shipped separate-attaching column. angles shop welded to column.


finished structure is dependent on the anchor attachments. These include all columns having direct loads combined with bending stresses, caused by the eccentric applications of gravity loads or horizontal forces; for example, wind, cable reactions, sway or temperature, etc. These are found in everyday practice in such structures as mill buildings, hangers, rigid frames, portals and towers, crane columns, etc.

In large structures that extend several hundred feet between expansion joints in each direction, the columns at ends and corners of thc structure may be plumb only at uormal temperature. As temperatures rise and fall, milled-end bearing conditions at edges or corners of the column base may prove very unsatis- factory, even though shop work were pcrfect. Such columns should have anchor bolt details designed to hold the column firmly fixcd, in square contact with the base plate.

The combined efiects of the direct load and over- turning moments (due to wind, cranc runway, etc.) can always be considered by properly applying the direct load at a givcn cc~ent r i~ i ty , even though the bending stresses sometimes occur in two directions simultaneously. Design of the anchor bolts resolves itself into a problem of bending and direct stress.

If there is any appreciable uplift on the column, angles may be welded to the base of the column and anchored by means of hold-down bolts. Under load., the angle is subject to a bending action, and its thickness may be determined from this bending moment.

Trcating the cross-section of the angle as a frame, the problem is to know the end conditions.

Some engineers treat the horizontal leg as a cantilever beam, fixed at one end by the clamping action of the hold-down bolts. See Figure 6. This is not quite a true picture because there is some restraint offered by the other leg of the angle.

FIGURE 6

Otlrer engineers have assumed the horizontal leg of the angle acts as a beam with both ends fixed. In this case the resnlting moment at either end of the portion being considered, the heel of the angle or the cnd at the bolt, is only half that indicated by the previous approach. St:e Figure 7.

However, i t might be argued that the vertical leg is not completely fixed and that this will increase the moment in thc horizontal leg near the bolt. The fo1low~- ing analysis, made on this basis, is probably more nearly correct. See Figure 8.

FIGURE 8

1. Considering first just one angle and temporarily ignoring the eRect of the other, the upper end of the vertical leg if not restrained would tend to move in horizontally (A,,) when an uplift force (P,) is applied to the column.


The resulting moment is

M = P, b and

area of moment diagram AhY = - E I X moment arm

2. Since the opposite angle does provide restraint, a horizontal force (PI,) is applied to pull the vertical leg back to its support position. The resulting moment is

M = P,, d and

area 1 X moment arm I A,, = E I

drea 2 X moment arm 2 t - E I

Since the horizontal movement is the same in each direction:

3. Combining the initial moment resulting from the uplift force (1) and the secondary moment resulting from the restraint offered by the opposite angle

( 2 ) :

Substituting into the previous equations:

at the heel of the angle, and

which is the critical moment and is located at the hold- down bolts.

Required Thickness of Angle

The leg of the angle has a section modulus of-

or required thickness of where:

M S =-

u

or, see Figure 9, where the vertical leg of the angle is welded its full lcllgth to the column ~roviding a fixed- end condition (Case A ) ; here formula #3 applies-

or where, the vertical leg of the angle is welded only


FIGURE 9

at its toe to the column (Case B); here formula #5 construction. Aim included are dimensions of s tandad applies- bols. (Tablc 3.4).

5. BASE PLATE F R COLUMN LOADE 1, 13b + d ) u MOMENT

Allowable Stresses

Table 3 presents the allowable stresses for holddown bolts used in building (AISC) and in bridge (AASHO)

TABLE 3-Allowable Stresses for Hold-Down Bolts

Aliowoble unit tension and $heor itrerier on baltr and threaded ports (psi of unthieoded body oieo):

Tension Sheor AlSC 1.5.2.1 (Building) psi psi

A307 boltr ond threaded parts of A7 ond A373 rteei 14,000 10.000

A325 boltr when threading ir

excluded from shear planer 40,000 15.000 A325 bolts when threading

excluded fiom rheor ~ l ane r 40,000 22,000 A354, Grode BC, boltr when

thieoding ir not excludcd from rhear ploner 50.000 20,000

A354. Grode K , Y h e n threading excluded from rheor planer 50,000 24,000 - - .

AASHO 1.4.2 (Bridge) psi

tension - boitr ot root of threod 13,500

shear - turned bolts 1 1.000 beoring - turned bolts 20,000 tffeitive beorjog o m o of o pin or bolt iholl be its diometer multipiicd by the thickness of the metal on which it beoir.

When a moment ( k t ) is applied to a column already srihjectcd to an axial compressiveforcc (P,), it is more couwbnicnt to exprcss this combined load as the same axial forcc (PC) applicd at some eccentricity ( e ) from the neutral axis of the column.

t-e+

, (4 lbl

FIGURE 10

In either representation, there is a combination of axial compressive strcss arid bending stress acting on a cross-section of the column See Figure 11.

Multiplying this stress by the width of the Range (or the thickness of thc web) over which the stresses are applied, gives the following force distribution

Column Bases /

TABLE 3A--Standard Bolt Dimenrionr

Compressive stress

= $

Bending stress

P, e " = - S

Total stress

P PC e a = ' + -

A S

FIGURE 11

across the depth of the column. This force is transferred to the base plate. See Figure 12. This assumes that the column flanges are welded directly to the base plate.

FIGURE 12 FIGURE 13

If anchor hold-down bolts transfer the tensile forces, then-

The column is usually set with the eccentricity ( c ) lying within the plane of the column web (ads y-y), as in Figure 11. Thus the column Aangcs will carry most of the resulting forces because of their having relatively greater cross-sectional arca, and being located in areas of higher stress. See Figure 14.


FIGURE 14

If the eccentricity ( e ) is less than % D, there is no uplift of the base plate at the surFace of the masonry support (Figure 15):

section modulus of base plate

stress in base plate

UT = TI compression t T? bending

When the eccentricity ( e ) exceeds % D, there is uplift on the base plate which is resisted by the anchor hold-down bolts. The beariug stress on the masonry support is maximum at thc extrcme edge of the bearing plate. It is assumed this stress decreases linearly back along the plate for a distance (Y); however, there is some qucstion as to how far this extends. One problem analysis approach treats this section as a reinforced concrete beam.

FIGURE 15

There are three equations, and three unknowns (Pt) , (V, and (5,):

l . ; r ; V = O

M Y u , B - P t - P , = O

and

where: cr, = pressure supplied by masonry supporting material

2. 2 M = 0 (About N.A. of column)

aud

......... (Qb)

FIGURE 16 3. Representing the elastic behavior of the concrete

support and the steel hold-down bolt (see Figure 17) :

Also where:

A, = total area of steel hold-down bolts under tension

us = stress in steel bolt

Es = ah in s t d bolt

E. = modulus of elasticity of steel bolt

then and: 7, o: = stress in concrete r t - support

a A, - Pt 6 = - Twc-n

eC = strain in concrete support

E, = modulus of elas- and from similar triangles ticity of concrete

D SUPP0l.t

- - Y + f n = modular ratio of ; = 2 elasticity, steel to Y concrete

* * *

Substituting formula #10 into formula #8a:

Substituting formula #9a into formula #11:

Column Bases /

FIGURE 17

Solve for Y:

This reduces t ( t -

or to express it in a manner to facilitate repetitive use, let-


then-

There are several ways to solve this cubic equation. Perhaps the easiest is to plot a few points, letting Y = simple whole numbers, for example, 9, 10, etc., and reading the value of Y on the graph where the curve crosses zero.

Having found the effective hearing length (Y) in this manner, formula #9b can be used to solve for the tensile force (P,) in the hold-down bolts. Formula #10 then gives the amount of bearing stress in the masonry support.

FIGURE 18

Another approach to determining the effective bearing length, involving less work, assumes the same triangular distribution of bearing forces from the supporting masonry against the bearing plate. However, the center of gravity of the triangle, or the concentrated force representing this triangle, is assumed to be fixed at a point coinciding with the concentrated compressive force of the wlnnln flange. See Figure 18.

From this assumption, the overhang of the hearing plate, i.e. the distance from the column flange to the plate's outer edge, is seen to equal the effective bearing length.

FIGURE 19

Figure 19 shows a column base detail. The columns have a maximum load of 186 kips, and receive no uplift under normal wind. See Figure 19. Under heavier wind load and in combination with temperature, they may receive up to 20 kips dircct uplift. See Fibwe 20. Four bolts are provided, attached by means of 6" X 6" X %" clip sngles, 11" long on a 4" gauge.

To be effective, the angles must carry this load on the anchor bolts into the column web. This causes a bending moment on the outstanding legs of the angles. Analysis follows that for formula if3. The bolt tension fixes the toe of the angle against the base plate and causes LUI inflection point between the bolts and the vertical leg of the angle, so that the bolt load is cantilevered only about halfway.

To compute the bending stress in the angles:

diagram

FIGURE 20

where:

ub = s t res in outer fibers

M = hcnding moment

c -- distance to neutral axis

I = moment of inertia

Since:

= 19,400 psi

Hence, thc. dfstail with %" angles is OK for this load.

Check Welds to Column Web

The angles are welded to the column web with 'h" fillet wclds; this will now be checked.

The heel of the angle is in coinpression against the wt:b of the column and is equivalent to an additional weld across the bottom for rcsisturg moment. On this basis, the section rnodulus of the weld is calculated. For simplicity, the weld is treated as a line without any cross-sectional area. From Table 5 ; Sect. 7.4, the section modulus of a rectanzular connection is:

and liere:

Normally, section modulus is expressed as inches to the third power; however, here where the weld has no area, thc rcsultirrg swtion modulus is expressed as iiiches squared.

When a stmdard bending formula is used, the answer ( ) is strcss in lhsjin.\ however, when this new section modulns is used in the bcnding formula, the answer ( f ) is forcc on the weld in lbs/linear in.

bending

M fl, = -

S,

- - (l0.000* x 4") -- (78 in.')

shear

P f"

leg size of (170) fillet weld

actual force = . - - - - - allowable force

= .06"

but 3k"thick angle requires a minimum of Ydl

(Table 3, Section 7 3 ) .

If it is dcsircd to incrrasc the anchor bolt capacity of the d ip angle &tail, tllicker arrgles should be used with large plate w~ishcrs on top of the angle. The ;ittaclrmc~lts s h o ~ ~ l d be maclc to the column flanges, sincc the welds arc more accessible there and the bolts Iiave better leverage.

To ilhistrnte how the colnmn Aange can lx: checked to clctcmiine whcther or not it is too tliin, considcr a clip angle mchored with two 1%" bolts centered 2?W out l'rorn the face of the cohimii flange; see Figure 21. The angle is att;iclied to the column flange by fillet ~velcls across the top a i d down each side.

The capacity of thc two lx~lts at 14,000 psi allowable stress on nntlircaded area (AISC Sec 1.5.2) is-

2 (1.2") (14,otl()) =: 31,400 lbs > 28,500 lbs OK -- Tlie hending nioment on tire ~ c l d is-

(28,500 lbs) ( ~ ~ h ) , ) = 71,250 in.-lbs

n-Rela ted Des ign

FIGURE 21

As in the previous example, the heel of the angle is in compression against the web of the column and is replaced with an equivalent weld. The welds are treated as a line; and the section modulus of ihe welded connection is found to be--

= 78 in.= (See Problem 1 )

The bending force is-

- 51,250 in.-lbs -

58 in."

all along the top edge of the angle, pulling outward on the column flange. This is the force on the hori-

zootal tor, weld. At the ends of the angle, the force - - (915)(3) - couple is - --- -- - 1370 lbs centered 1" below the 2

top toe of the angle. See Figure 22. This is the force on each of the vertical welds at

ends of the angle. Since these forces are not resisted by anything but the flange, they have to be carried transversely by bending stresses in the flange until they reach the resistauce in the column web.

The bending moment in the column flange is com- putod as follows:

Force along top of angle = 915 X 5.5 = 5040 lbs

M, = 5040 X 2.75 = 13,860 in.-lbs

M, = 1370 X 5.5 = 7,535 - i d b s

Total M = 21,395 i d b s

If we assume a 6" wide strip of the column flange to resist this load, this moment will cause a bending stress of 45.300 psi in the 14" WF 87-lb column with a flange 1% ," thick.

This is calculated as follows:

= 45,300 psi

Obviously, since this stress distribution along the welds is capable of bending the column Aange heyond the yield point, the cvlnmn Aange will deflect outward sufficiently to relieve these stresses and cause a redistribution. Thr resultant stresses in the weld metal on the toe of the clip angle will be concentrated opposite the column web.

FIGURE 22

Column Bares /

Thus, the capacity of this anchor bolt detail is e = ( 175,000) (12) - limited by thc bending strength of the column flange ( 130,000) even alter the clip angle has bccn satisfactorily stiffened. = 16.15"

The force back through the column web is: The load on the bolts is- F = (915 lbs/in.) (11") + 2 (1370 lbs) (130,000) (9.49) F = .-

= 12,800 lbs (15.66)

= 78,800 lbs A 'h" fiUet weld 3 inches long on the top of the

angle opposite the column web will satisfactorily resist The area of the thrce lWrdia. bolts in the un- the force couple: threaded body area is-

F = (3") (5600 lbs/in.) E70 welds A = (3)(2.074)

= 16,800 ibs. OK = 6.22 in.2 --

The tensile stress in the bolts is: For greater anchor bolt capacities than shown in

Figure 22, either horizontal stiffeners or diaphragms u = -- (78;800) shonld be provided to prevent bending of the column (6.22) flanges. = 12,700 psi < 14,000 psi OK -

A rather simple detail, whereby a wide-flanged channel scrves as a stiEener, is shown in Figure 23.

This detail was used with three lSk"dia anchor bolts on a 14" X 87-lb mill building column designed to resist a wind bending moment of 175,000 ft-lbs combined with a direct load downward of 130,000 lbs.

The tension on the bolts is determined by taking moments about the right-hand wmpression flange of the colrrvnn after first determining the eczatricity at which the direct lond will cause a moment of 175,000 ft-lbs about the centerline of the column. The eccentricity is-

(AISC Sec 1.5.2)

The compression Aange reaction ( R ) is the sum 01 the 130,000-lb c:Arrmn load plus the 78,800-lb pull of the anchor bolts, or 208,800 lbs. The 13" ship channels are st:t up just clear of the bearing on the base plnte so that the end of the column will take the compressive load of 208,800 lbs without overloading channels.

Bearing stress on masonry

The hearing stress on the masonzy support is maximum at the extreme edge of the bearing plate, and is assumed to decrease linearly back along the plate. This bearing stress would resemble a triangle in which

FIGURE 23


@ 8 = 24"

@ Anchor

@ hold-down bolts ore inactive on compression side

78.Ek

FIGURE 24

the altitude is the maximum hearing stress at the edge of the plate, and the base of the triangle is the effective bearing length ( Y ) against the plate. (See short method described on page 10.) Since the area of this triangle has a center of gravity % Y h e k from the altitude, the bearing pressnre may be resolved into a concentrated force at this point. This point will be assumcd to lie wh'ere the column flange's concentrated compressive load of 208,800 1hs is applied.

FIGURE 25

Hence, the distance from the compressive force of the Range out to the edge of the bearing plate (in oth,er words, the overhang of the bearing plate) equals 'h the effective distance of the bearing support. See Figure 24.

arm of triangle

A = % u , Y

= PC + Pt

effectice beuring length of base plate (from formula #8)

= 23.2" 1 = .25 (3000 psi)

Y I = 750 psi and - - 7.73" overhang

3 -

.'. D = 7.73" + 13.31" f 7.73"

= 28.77" or use 28%''

Bolt load

The load on the bolts is supported by the top flange of the 13" channel, reinforced by four 3%" X 'ii' s t B - cner plates welded between the channel flanges. See Figurc 23.

The two interior plates each support a full bolt load of '/, (78,800 Ibs) or 26,300 lbs. Thesc stiffeners are attached to the channel web with four I" X intermittent fillet welds on each side of the plate, and to both flanges by continl~ous 3$,j" fillet welds on each side of the plate. See Figmo 25. The welds at the chnnncl flanges transmit the moment to the channel flangcs, and the welds at the channel web support most nf the shearing load.

Thc 2" eccentricity of the bolt load to column Range is trar~sposed to a force couple acting on the channel flanges. This couple is obtained by dividing


the momeut by the depth of the stiffeners:

This is a hori~ontal load acting at right angles to the column flange. I t is delivered as four concentrated loads at the tops of stiffeners and then carried horizontally by the channel flange to a point opposite the column web where it is attached to the column with a 2%'' x M" fillet weld.

2%" X 5600 lhs/in. = 14,000 lbs.

The concentrated load valucs are 2015 lbs at each end stiffener for one-half a bolt load, and 4030 lbs at each interior stiffener.

The total moment on the flanges is:

(2,015) (7.5) = 15,200 in.-lbs

(4,030) (2.5) = 10,100 in.-lbs - M = 25,300 in.-lbs

I t causes a bending stress in the channels 4" X %" top flange section of approximately-

= 15,800 psi

To keep the channel section from sliding parallel to the column flange, the direct vertical pull of the bolts is supported by two 13" X continuous fillet welds between the edge of the cnlumn flanges and the web of the 13" channel section. The shear on these welds is-

The problem in Figure 23 has been analyzed on the basis of simple levers with the compression load concentrated on the colnmn flange. It ignores the compression are:> under the web of the column and illustrates the prohlcrn where the channel flange of the anchor bolt attachment does not bear against the base plate.

For simplicity, this analysis has assumed that the effective bearing length (1') was such that the center of gravity of the triangular bearing stress distribution, C.G. a t % Y, lies along the centerline of the column Bange where the comprcssive force of the colunm is applied.

\With the same column base detail as in Problem 3, we will now m e the original derivation for this effective bearing length ( Y ), treating the analysis as a reinforced concrete beam and solving the resulting cubic equation. The work may takc longrr, hut rcsults are more accurate. See Figun: 26, temporarily ignoring the anehor- bolt channel attachments.

FIGURE 26

Here:

e = 16.15"

f = 9"

D =z 283/4"

B = W


four %" X 3%" R ' s

Tensile stress

in bolts FIGURE 27

Compression stress at outer 1 edge of channel st~ffcners

E n = = 10 (E, = 3000 psi)

Ec

15h" bolts

A. = 3 (2.074)

= 6.22 in.' (bolts under tension)

Q, = 130 kips

from formula #13 (cubic ~quat ionj

Y 3 + K 1 Y Z + K 2 Y + K 3 = 0

where:

. 1 = 3 ( ~ - $ )

( 28% = 3 16.15 - - 2

= 5.33

6 n A, K' = -- B ( f + e )

- - 6 (lOj(6.22) 24

( 9 + 16.15)

= 392

Plotting these three points, the curve is observed to pass through zero at-

Y = 13.9" - which is the effective bearing length.

from fornula #9b

which is the tensile load on the hold-down bolts.

from formula #8b

= lOiiO psi Therefore. substitutinr into formula &13: ~ "

which is the bearing pressore of the masonry support E3 + 5.33 Y2 + 392 Y - 9160 = 0 against the bearing plate.

Letting Y = +lo, --1-12, and +15 provides the follow- If the anchor hold-down bolt detail is milled with ing solutions to the cubic equation as the function of the column base so that it ht:ars against the base &ite, - Y: it must be made strong enough to support the portion


of the reaction load (PC + P,) which tends to bear upward against the portions of the bolt detail outside the colu~nn flange. This upward reaction on the com- pre.ssion side (PC + P,) is much larger than the downward load of the bolts on the tension side (P,).

The area of section effective in resisting this reaction includes all the area of the compression material-column Bange, portion of column web, the channel web, and stiffeners-plus the area of the anchor bolts on the tension side. See shaded area in Figure 27.

The anchor bolts on the compression side do not act because they have no way of transmitting a compressive load to the rest of the cohunn. In like manner, the column flange and web on the tension side do not act because they have no way of transmitting a tensile stress across the milled joint to the base plate. The tension flange simply tends to lift off the base plate and no stress is transmitted in the tensile area except bv the hold-down bolts attached to tllc column.

Determining moment of inertia

To determine the moment of inertia of this effective area of section, the area's neutral axis must he located. Properties of the elements making up this effective area are entered in the table shown here. Moiamts are taken about a reference axis (y-y) at the outermost edge of the channel stiffeners on the compression side (Fig. 27). See Section 2.2 for method.

Having obtained the 1st totals of area (A) and moment ( M ) , solve for the location ( n ) of the neutral axis relative to the reference axis:

- - (199.98 + 2 1 n") (27.36 + .42 n )

= 6.93" distance of K.A. to rcf. axis y-y

.'. c = 6.93" distance of N.A. to outer fiber

Now, having the value of n, properties of the effectivr portion of the column woh can he fixed and the table completed. With the 2nd totals of area (A) , momcot ( R ) , and also ~noinents of inertia. (I, + I,), solve for the moment of inertia about the neutral axis ( I n ) :

Smce the concentrated compressive load (P,) is applied at an wxent~icity ( e ) of 16.15" to provide for the wind moment of 175,000 kips, the moment arm of the 130-kip load is-

9.15" from face of column gauge

5.15" from outer edge of channel stiffeners

12.08" from neutral axis of effective area

compressioc stvess a t outer edge of channel stiffeners

= 8220 + 4300 = 12,150 psi

I Dirtonce: C.G. to ref. mi. y y I Moment

4.688 + n 2 Poition

= .21n2 -- 4.615 of web

- - . -- Column flonge 4.344 42.83 1 86.05

~- - Channel web 3.812 6.00 22.87 87.19 - -- . .. . .-

Chonnel stiffenen 2.00 7.25 14.50 29.00 7.92

Fict Totol -t

By substituting value of n = 6.93":

Second Totol +

27.36 + .42 n

30.27

199.98 + .21 n' -

210.07 2789.93


tensile stress in hold-down bolts

M c PC - where c is distance of ut = -

I A N.A. from extreme fiber of tensile area

= 15,500 psi - 4,300 = 11,200 pd

total force in hold-down bolts

P* = A, 0-t

= (6.22) (1 1,200)

= 69.6 kips

e!ds Attaching Stitfeners to Channel

Compressive force is carried by each of the four channel stiffeners. The average compressive stress on these stiffeners is-

5.15'' a (8220 psi) + 4300 psi " - 6 . W

= 6110 psi + 4300psi = 10,410psi

This co~npressive force on cach channel stiffener is transferred to the c11aiinr:l wcb by two vertical fillet welds, each 11" long. The force on (:a& weld is tllus-

r 856 lbs/linear inch

and the rtqnired Gl1t.t wcld Icg size is-

856 OJ 7-

11,200 - for E7O welds ('firhlr 5, Sect. 7.4)

= ,076" or use $iG"h (Table 2, Sect. 7.4)

With this 1r:g size, intermittent welds can be used instead of contiriuous wdding-

elding Channel Assembly to Column Ftonge

Sa = d212b + d l 3 i b + d l

- - 1131212 X 14.5 f 13) 3114.5 + 13)

- - 86.1 in. 2

M i a = -

S,

- l174.2001 - - 186.11

- - 2020 lbslin.

v i. = -

L (1 23.4001 - -

2(i3) + 04.5i - - 3050 ibdin.

i. = v' ib2 + isn 7 = f(2020,Zf;3050) - - 3670 ibdin.

actvol farce 0 =

cliawabie force

(36701 = - 111.200) t E70%

= ,328'' or 5/16" A

d2 S, = bd + -

3

- (13)' - ll4.5)(13) + -

3 - .- 242.2 in.'

M f --

Sx, I 1 74,2001 - - -

(242.2) - - 720 Ibdin.

v f. = -

L f123.4001 - ..

2(13 1- 14.5) - - 2240 ibd in .

f. = d (8" f e z

== fx-. +(211;;;;2 - - 2350 Ibsiin.

uctual force " = . ollawoble force

.- (23501 - - i11.2001

- - ,210.' or *,, A

d2 s - -. ," - 3

- (131" - - 3

- - 56.3 in."

M i" = --

Sr

- ( 1 74.2001 - - 156.31

- - 3100 lbdin.

v f - -

L

- I 1 23.4001 - - 2 (13)

- - 4750 ibslin.

i? = V' f,,2 .+ i*z = '"i3100li + i475012 - .- 5680 Ibrlin.

aituol force " = aliowabie farce

- 156801 - - 111.2001

- - .506" or X" A

- - 114.51li3)

- -- 185.9 in."

M i s = -

S,

- - -. I 1 74,2001 (185.91

- - 935 ibslin.

v f e = -

L 1123,400)

- - - 2 114.5)

- - 4260 Ibdin.

f , = V fb2 + /.? - \/1937t;4260iz -. - 4360 ibnlin.

octucl force (11 =

oilowobie force


5. USE OF WtNG PLATES

or a total length of 4%" of 3/16" fillet welds on each side of each stiffener.

Id Connecting Channel Assembly t o Column Flange

The average compressive stress on the channel web is-

= 3700 + 4300 = 8000 psi

total compressive force on channel assembly

F = 48,000 + 4(18,850)

=r 123,400 Ibs

The fillet welds connecting the assembly to the column flange must transfer this total compressive force into the column flange. There are four ways to weld this, as shown in Table 4. Assume the welds cany all of tlie compressive force, and ignore any bearing of the channel against the column Aange.

FIGURE 28

First find the moment applied to the weld, Figure 28, which applies in each case of Table 4:

M = 4(18,850 lbs) (2.187") + (48,000 1bs) (3116") = 174,200 1%-lbs

Then, making each weld pattern in turn, treat the weld as a line to find its section modulus (S,), the maximl~m bending force on the weld (f,), the vertical shear on the wcld (f,), thc resultant force on tlie weld (f,), and the required weld leg size (o).

Perhaps the most efficient way to weld this is method ( d ) in which two transverse 'h" fillet welds are placed across the column Aange and channel flange, with no longitudinal welding along the channel web.

When large wing plates are uwd to increase the leverage of an anchor bolt, the detail sho~rld always be checked for weakness in bearing against the side of the column flange.

I F 1

FIGURE 29

Figure 29 illustrates a wing-plate type of column base dotail that is not limited with respect to size of bolts or strength of colnmn flange. A similar detail, with bolts as large as 4%'' diameter, has been used on a large terminal project.

The detail shown is good for four 2Yd'-dia. anchor bolts. Two of these bolts have a gross area of 6.046 in.' and are good for 84,600 lbs tension at a stress of 14,000 psi.

In this detail, the bolt load is first carried laterally to a point opposite the column web by the horizontal bar which is 5%'' wide by 3" thick.

section modulus of section a-a

- - 8.25 in."

bending moment on bat-

rcsulting bending stress

= 18,000 psi


At the center of the 3" bar, the bolt loads are snpported by tension and compression forces in the 1" thick web platcs above and below the bar. The web plates are attached to the column flange, opposite the column web, by welds that carry this moment and shear into the column.

The shear pnd moment caused by the anchor bolt forces, which are not in the plane of the weld, determine the size of the vertical welds. The welds extend 15" above and 3" below the 3" transverse bar.

The properties and stresses on the vertical welds are figured on the basis of treating the welds as a line, having no width. See Figure 30.

FIGURE 30

Take area moments about the base line ( y-y) :

moment of inertia about N.A M"

I, = I, + I, - -- A

2 w e l d r X 1 5 "

Total

= 11.5" (up from base line y-y)

distance of N.A. from outer fiber

cbotbm = 11.5"

- 30

36

section moddus of weld

= 112 in.'

( 1288) S,, = --

(9.5)

15.3

= 135.5 in."

-- 405.0

414.0

-. I

maximum bending force on ueld

5467.5

shear force on weld

562.5

resultant force on weld

6048

required flkt weld size

3000 a =- 113J0 WI E70 allowable

This requircs continuous fillet welds on both sides for the full length of the 1" vertical web plate. If greater weld strength had been required, the 1" web platc could be made thicker or taller.

For bolts of ordinary size, the upper portion of the plates for this detail can be cut in one piece from colnmn sections of 14" flanges. This insures fnll continuity of the web-to-flange in tension for carrying the bolt loads. By welding across the top and bottom edges of the liorizontal plate to the column flange, the required thickness of flange plate in bending is reduced by having support in two dircctions.

6. TYPICAL COLUMN BASES

In ( a ) of Figure 31, small brackets are .groove butt

olumn Bares /

FIGURE 31

y stiffeners moy be

\voided to the oirtcr edges of thc colnmr Annges to develop greatcr moment resistance for the attachment to the bas? plate. This will help for moments about either the x-x or the y-y :tsis. A single bovel or single V joint is preparcd by beveling just the edge of the brackets; no hcveling is done on the column flanges.

For colnnrn flanges of nominal thickness, it might he easier to simply add two brackets, fillet welded to the base of the column; see ( h ) and ( c ) . No beveling is required, and handling and assembling time is reduced hecat~se only two additional pieces are requirod.

In ( b ) thc bracket plates are attached to the face of the coluin~r flange; in ( c ) the p1atr.s are> attached to the outer edge of the column Nange. In any rolled section used as a column, greater berrtling strength and stiifiress is obtained about the x-x nxis. If the moment is ahont the x-x axis, it would be better to attach the additional plates to the face of the column as in (b ) . This will provide a good transverse fillet across the n)lumn flange and two longitudinal fillet welds along the outer edge of the column flange with good acct%ssihility for melding. Thc attaching plates and the welds connecting thein to the base plate are in tho most effcct~vc position and location to transfer

this moment. The only slight drawback is that the attaclring plntcs will not stiffen the overhung portion of the base plate for the hending due to tension in the hold-down bolts, or due to the upward hearing pressure of the masonry support. Mowevrr if this is a problem, smxll hrackrxts shown in dottrd lines may be easily added.

The plates can he fillet wrlded to the outer edges nf thc column flange as in ( c ) , although there is not good accessibility for the welds on the inside. Some of these inside fillet welds can be made before the unit is assembled to the base plate.

For thick Ranges, clctail ( a ) might represent the lrast amount of \velding and additioml plate material.

Short lengths of pipe have been welded to the outer edge of the cohnnn flange to develop the necessary moment for the hold-down bolts; see (d) . The length and leg size of the attaching fillet welds are sufficicnt for thc moment.

In ( e ) two channels with additional stiffeners are wc ldd to the cohnnrr flanges for the required moment from the hold-down bolts. By setting this channel assenibly back slightly from the milled end of the column, it does not have to be designed for any bear-


ing, but just the tension from the hold-down bolts. If this assembly is set flush with the end of the column and milled to bear, then this additional bearing load must be considered in its design. Any vertical tensile load on the assembly from the holddown bolts, or vertical bearing load from the base plate (if iu contact), will produce a horizontal force at the top which will be applied transverse to thc column flange. If the column flange is too thin, then horizontal plate stiffeners must be added between the column flanges to eflec- tively transfer this force. These stiffeners are shown in ( e ) by dotted lines.

In ( f ) built-up, hold-down bolt supports are welded to the column flanges. These may be designed to any size for any value of moment.

In (g), the attaching plates have been extended out farther for very high moments. This particular detail uses a pair of channels with a top plate for the hold-down bolts to transfer this tensile force back to the main attaching plates, and in turn back to the column.

One of the many possible details for the base of a built-up crane runway girder column in a steel mill is shown in Figure 32. Two large attaching plates are fillet welded to the flanges of the rolled sections of the column. This is welded to a thick basc plate. Two long narrow plates are next welded into the assembly, with spacers or small diaphragms separating them from the base plate. This provides additional strength and stiffness of the base plate through beam action for the forces from the hold-down bolts. Short sections of I beam can also be welded across the ends between the attaching plates.

7. HIGH-RISE REQUIREMENTS

A 14" WF 426# column of A36 steel is to carry a compressive load of 2,000 kips. Using a bearing load of 730 psi, this would require a 30" X 60" base plate. Use E70 welds.

For simplicity, each set of lxackets together with a portion of the base plate formed by a diagonal line from the outer comer of tlir plate hack to the coh~snn flange, will be assrsmcd to resist the bearing pressure of tho masonry snpport; see Figure 34. This is a conservative analysis because the base plate is not cut along these lines and thcse portions do not act inde- pendently of each other.

Columns for high-rise buildings may use brackets on their base plates to help distribute the column load out over the larger area of the base plate to the masonry wpport.

This portion of the assembly occupies a trapezoidal area; Figure 35.

/+hi = 167"

t

Li-b, = 50' -4 FIGURE 35

P = A w

= (690 in." (750 psi)

= 516 kips

Determining thickness of base plate

To get an idea of the thickness of the base plate ( t ) , consider a 1" wide strip as a uniformly loaded, continuous beam supported at two points (the brackets) and overhanging at each end. See Fignre 36.

From beam formula #6Bh in Section 8.1:

-w a2 M,,, (at support) = 2

Since:

M = a S

or:

where: t = I a = 7 5 a, (ALSC L.J.1.4.8)

= 5.51" or use 6"-thick plate

Check bending stresses & shear stresses in base plate bracket section

Start with lYzf'-thick brackets ( 2 x 1M" = 3" flange thickness) at right angles to face of column flange. Find moment of inertia of the vertical section through brackets and base plate, Figure 37, using the method of adding areas:

moment of inertia about N.A.

FIGURE 36


distance of N.A. to outer fiber

cb = 9.27"

bending stresses

M Cb Vb = I

= 4370 psi

= 9770 psi OK -

n~aximum shear forcc at neutral axis

Bendtng stress [a) Shear force (f)

PI (4

FIGURE 37

corresponding shear stress iu brackets

= 8400 psi OK -

shear force at face of 6" base plate (to be transferred through fillet welds)

= 24,630 llx/in. ( to be carried by four fillet welds at 1%" thick brackets)

leg size of mch fillet wdd joining base plate to brackets

l/g (24,630) W =---- (11,200) - E70 allowable

= ,545" or use %/,Br'[l --- (The minimum fillet wcld leg size for 6" plate

is WB .)

Determining vertical weld requirements

In determining fitlet weld sizes on the usual beam seat bracket, it is often assumed that the shear reaction is uniformly distributed along the vertical length of tho bracket. The hvo unit forces resulting from shear and bending are then resolved together (vectorially added), and the resultant force is then divided by the allowable force for the fillet weld to give the weld size. This is of course conservative, because the maximum unit bending force does not occur on the fillet weld at the


same region as does the maximum unit shear force. However the analysis docs not take long:

bending force on weld

f, = u t

= (9770 psi) (1%")

= 14,660 lbs/in. (one bracket and two fillet welds )

or = 7330 lbs/in. (one fillet weld)

vertical shear force on weld (assuming unifolm distribution)

resultant force on weld

required leg size of certical fillet weld

actual force 0 =

allowable force

FIGURE 38

Alternate method. In cases where the forces are high, and the requirement for welding is greater, it would be wcll to look further into the analysis in order to reduce the amount of welding.

In Figure 37, it is seen that the maximum unit force on the vertical wt:ld due to bending moment occurs at the top of the bracket mnnection ( b ) in a rcgion of very low shear t~msfcr . Likewise the maximum unit shear force occurs in a region of low bending moment ( c ) . In the following analysis, the weld size is determined both for bending and for shear, and the larger of these two values are used:

ccrtical shear requirement (maximum condition at N.A.)

fl = 25,200 lbs/in.

to be carried by four fillet welds

actual force 0 =

allowable force

= ,562" or %,/,," bending requirement (maximum condition at top of bracket)

actual force = -. allowable force

Hence use the larger of the two, or 3/4" fillet welds. .4lthough this altrrmate method required a slightly smaller fillet weld (.654") as against (.758"), they both endod up at %'' wheu they were rounded off. So, in this particular example, there was no saving in rising this method.

Column stiffeners

A rather high eompr~~ssive force in the top portion of these brackets is applied horizontally to the column Range. It would hs wcll to add stiifenors behveen the column flanges to transfer this force from one bracket through the column to thc opposite column flange; Figure 38.

It might he argncd that, if the brackets are milled to brar against the column flanges, the bearing area may then be considered to carry the compressive horizontal force bctwecn the bracket and the column flange. Also, the connecting welds may then be considered to

/ Column-Related

FIGURE 39 Slight tensile prestress

Unit sheor ' between bracket in weld before load is

force on weld ond column flange applied

carry only the vertical shear forces. See Figure 39, left. If the designer questions whether the weld would

load up in compression along with the bearing area of the bracket, it should be remembered that weld shrinkage will slightly prcstrrss the weld in tension and, the end of the bracket within the weld region in compression. See Figure 39, right. As the horizontal compression is applied, the weld must first unload in tension before it would be loaded in compression. In the meantime, the bracket bearing area continues to load up in compression.

This is very similar to standard practice in welded plate girder design. Even though the web is not milled along its edge, it is fittpd tight to the flange and simple fillet welds join the hvo. In almost all cases, these welds are designed just for the shear transfer (parallel to the weld) between the web and the flange; any distributed floor load is assnmed to transfer down through the flange (transvrrse to the weld) into the cdge of the web which is in contact with the flange. Designers believe that even if this transverse force is transferred through the weld, it does not lower the capacity of the fillet weld to transfer the shear forces.

Refer to Figure 37(b) and notice that the bending action provides a horizontal compressive force on the vertical connedng wclds along almost their entire length. Only a vcry small lcngth of the welds near the base plate is subjected to horizontal tension, and these forces are very small. The maximum tensile forces occur within the base plate, which has no connecting welds.

shear force on certical weld (assuming uniform distribution)

516.5k f - .------- s - 4 x 30" = 4310 lbs/in. (one weld)

t;crtical weld size (assuming it to transfer shear force only)

bnt 3" thick column flange would require a minimum lhr' h (Table 2, Sect. 7.4).

If partial-penetration groove welds are used (assuming a tight fit) the following applies:

allowables (E70 welds)

compression: same as plate

shear: 7 = 15,800 psi

shear jorce on one weld

f. = 4310 lbs/in.

required effective throat

i j using bevel ioint Y6 ,ik

t = t, + '/a''

= ,273'' 4- W" = ,398"

raot face (land) = ll/z" - 2(.39Wr)

= ,704'' or use - -- W'

if using 1 joint k- %"4

1 %" t = t, "

= ,273"

root face (land) = 1Yz" - 2(.273")

= ,954" or use '/8"

A portion of the shear transfer represented by the shear force di~tribution in Figure 37 ( c ) lies below a line through the top surface of the base plate. I t might be reasoned that this portion u a ~ l d be carried by the base plate and not the vertical connecting welds between tire bracket and the colnmn flange. If so, this triangular arcs would approximately represent a shear force of

?5. (24,63O#/in.) 6" = 73.9"

to be deducted:

516.5& - 73.9' = 4426&

However, in this example, the column flange thickness of 3" would require a %" fillet weld to be used.

Brackets to column flange edges

The base section consisting of the brackets attached to the edge of the column flanges, Fignre 40, is now considered in a similar manner. From Illis similar analysis, thc brackets will be made of 1W-thick plate.

Figure 41 shows the resulting column base detail.

FIGURE 40 FIGURE 41

COLUMN BASE PLATE DIMENSIONS (AISC, 1963)

- COLUMN BASE PLATES / For c Dimensions for maximum II column loads

L--?Q Base nlaien, ASTM 1116. h - 2 7 ir i Cuacilic, ,'< - 30UO or,

'Or / COLUMN BASE PLATES Dimensions for maximum

column loads mT . 1.-

Bare OaiPs, hSTM A16. F,, = 27 kr, coacrsts. l, - 3OM nri 1 . J .- -

Wt. P" Fi. - ib .

1w 161 133 120 106 99 92 85 79 72 65

58 53

50 45 40

I12 100 89 77 72 66 60 54 49

45 39 33

67 58 48 40 35 31

28 24

20 17

~-

tn.

61: 16 W

4 X 14% W

1 X 12 W

1 X 10 W:

1 x 8 W

~. Note' i

SIlO Wht -

-This and following toblei prenenisd here by cauttery of American Institute of Steel Conltruction.



E 5! I S r , s 8

. 2 a a a F Y . L D F F F

xk X; x x r xs xz x m x X S x x X- X- X- X- - - - a " a L D - - - a m F " ? "

ases / 3.3-31

Column base plates for the 32-story Commerce Towers, Kansas City, Mo., were shop-fabricated and shipped separately. At the site they were positioned and bolted to the concrete. The heovy columns were then erected ond field welded to base plates. This was facilitated by use of semi-automatic arc welding with self-shielding cored electrode wire. Process quadrupled the speed of manual welding and produced sounder welds.

Ten-ton weldments were required for tower bases on lift bridges along the St. Lawrence Seaway. Edges of attaching members were double- beveled to permit fuil penetration. Iron powder electrodes were specified for higher welding speeds and lower costs. Because of high restraint, LH-70 (low hydrogen) E7018 electrodes were used on root posses to avoid cracking, while E6027 was used on subsequent passes to fil l the ioint.


In designing a scenic highway bridge with 700' arch span, near Santa Barbora, Col., engineers called for tower columns to be anchored to the concrete skew- backs by means of 1%" prestressing rods. The bottom of the column is slotted to accommodate the base, an "eggbox" grill made up of vertical plates welded together and to the box column. The towers suppoFt heavy vertical girder loads but also safely transmit horizontal wind and seismic loads from the deck system to the foundation.

1. INTRODUCTION

.41SC specifies that, where full-milled tier-huitding coliirnns are spliced, there shall be suflkicnt welding to hold them securdy in place. These connections shall be proportioned to rcsist any horizontal shear forces, and any tension that would be developed by specified wind forces acting in conjnnction with 75% of the ea1c:ulated dead load strws and no live load, if this condition will prodrice more tension than full dead load and live load applied. (AISC: Sec 1.15.8).

Figures 1 and 2 show various designs of column splices mhicli diminate punching of the columns. Note that these details require only llandling and punching of small pieces of angles or plates v&ch are easily carried to, and welded to, the columns in the shop. The details provide for temporary bolted connections in the field prior to making the permanent welded connections.

Sometimes the column connections are placed about mid\~ay in height, in order to get the connection away from the regiorr of heavy bending moment caused by windloads, etc. The resnlt is a . ~wnncction sufficient to hold tlre columns in place and designed for horizontal shear m d axial compresion only

2. TYPES OF SPLICES

In Fignre I ( a j , a plate m d two :mgles are punched or, if nccessary, drilled. The plate is shop welded to the top of the lower colrrmn. The two angles are shop welded to the web at the lower end of the npper rolnmn. The r r p p ~ ~ column is erected on top of the louw column and eroction bolts are inserted. The tipp'r c~lnrnn is then &.Id \velded to the mnnecting plat?. Where additional clc.ar;mce is needed for erection of beams framing into the web o i the lower c,olumn, it might be nccessary to shop weld the plate to the upper col~m~rr and tlicn field weld in the over- licnd position to the lo\vcx colun~n.

If tlre nppm and lowcr colnrnns differ in size, the conn<z~.ting phti. is dcsi~ned as a member in bending due to misalignm~~nt of the fiangcs, and its thickness is dctcrrnincd from this; Figure l ( b ) . If the lower coltnnn's section is mrirh dceper than the upper column, stiffeutm c:m he wcldcd directly helow the flanges of the rlppor coli~mn. Tllese stiffeners will reduce the required thickness of thr i.onnccting plate*; Figure l ( c j .

A splice for heavy coliimns is shown in Figure I ( d ) . Turo small platcs arc prmcl~ed with holes aligned as indicated. They are then carried to the column sec-

FIG. 1-Typical Column Splices

.Q-2 / Column-

Cc) FIG. 2 - Typical Column Splices

tions and welded thereto. In the field the colun~n sections arc bolted temporarily prior to welding, as indicated at ( d ) .

In Figure 2 ( a ) the ends of both column sections are first milled for a square bearing surface. Then the two lower ewction splice angles are shop welded on opposite sides of the web of the heavier w lum~i section, so as to project past the end of the column. The outstanding legs of these angles are provided with holes for erection bolts to engage the outstanding legs of the other two angles that are shop welded to tlie 11pper column section. In this type of detail where lighter con~iecting material projects from heavy main sections, care should he taken in handling to prevent damage to the lighter material.

The flangcs on the lower end of tlie upper column section are partially beveled or "J" grooved, and this partial pelletration groove joint is then welded in thc field.

The ~ u r p o s e of the angles is to splice and hold the two adjacmt columns together kemporarily while they are being fir:ld welded.

These erecting angles may be placed horizontally

LE 1-Allowables for Weld Meta l in Partiol-Penetration Groove Welds

For Field Splices of Columns

E60 Welds E70 Welds SAW-I SAW-2

campreision some or piate some os plate ..... . ~ ~ .-

lendon ironsverse to cross- section oi throat oiea 15.800 psi -- .~~ 1: 2: 1 1 5 , 8 0 0 p

AWS Building Por 20510: a n d AiSC Scc 1.5.3

on ttw ~ r v h of thc colririms. Figwr '(b). Trie advantage of this position is that tlwy do not i~ t i :nd hcyond the eiids of the coliimri for possihlc drm~iige dr~ring transit or ertrtion.

F m r plntcs xi-e piiiichctl, timi shop welded he- t\veen the A:inges of tlrc two colurrin sections as sliown i r ~ Figure 2 ( c ) , lraving enorlgh space hetween the back of the, platc.s and tlic colt~mn web to insert a \vrtmcl~. Two splicc plates art: also punchcd and shop wrldcd to the l o u - < ~ coli~mn sc~ctiori hcfore siripping to the crcction sit<,. .After bolting in the field as indicated, the permanent coii~iwtitm is in:& by welding.

Tlic splico in Figr~rc 2(1l) is similar to that at ( a ) but is lor coiinccting two coliimiis of differrnt sizes. The flanges 01' tht. r~ppcr columlr lic inside of thc flanges of the 1ov;ol- colririm Rcfort, shop \vtIding tile erecting arlglcs, spiicc phies art, first shop fillet welded to the ir1sid.r. face of ihc ilarigc 01' the lowcr colrunn. Tliey are milled with tlw lowcr col~imn section. As an altrrnate to this, spliw plates with their lower edges prepared for wcldiiig are slrop fillet wi-oided to the outside face of tlrt. fiarigcs on the uppcr column.

In case only m ~ c side of the idumn is acccssil)le, far example wlim new stecl is crccted adjacent to an old stmcture, a cornhination of this procedure may bc usrd. Placc the lowcr splice plates on the inside face of the lo\vcr coliinln a i d the ~ ~ p p e r splice plate oii tlw oi~tside face of thc r~ppcr colr~mn; See Figure 2 (d ) . In this ma~i~ier all fiold w\.olds on both a)!umn flmgcs can he maclt from the one side.

\t'Iisrc splice platc,s arc used and filler plates are needed l~ecanse of the diflerencc in sizes of the upper and lower columns, these plates are welded to the iippcr coliiinii. Sre Figiirt, 2( tS) . This allows the greater amount of \velding to ljc do i~c in the shop where larger electrodes arrd higher \velding currents used in

Column Splicer /

FIG. 3-Pariiul-Penelrotion Welds

the fiat position result in higher welding speeds and lower cost. After erection the splice plate is Iicld welded to the lower column.

Two attaching plates are shop welded to the upper end of the lower column. The column may be hoisted by attachiug the cable to the erection holes of these plates. After erecting the upper columns, these plates are field welded to the upper column.

3. WELD ALLOWABLES

Both the AWS Building Code and the AISC Specifi- cations allow partial-penebation groove welds, either a bevel or a J preparation, to be used on column field splices.

For a J joint, the effective throat (t,) is equal to the actual throat ( t ) .

For a beveled joint, the eflective throat (t,.) equals the actual throat ( t ) less '/a". This reduction in throat is made because the weld may not extend all the way down into the very root of the joint. The Ye" reduction is very conservative. No reduction is made in the throat of the J preparation because there is no problem in reaching the root of the joint.

.4 beveled joint is usually flame cut along the end of the column flange. A J groove must be machined or else gouged out by tbc air carbon-arc procvss. Although it may seem that the beveled groove might require more weld metal because it must be Ya" deeper than required, the J groove on the other hand must start with a %" radius and an included angle of 45". There may be no reduction in the amount of weld metal by using the J groove; see Figure 3. A decision on joint design should be made only after all factors are carefully evaluated.

Since it is impossible to properly read radiographs of this partial penetration groove joint, because of the

unwe!ded portion, these field splices should never be subject to radiographic inspection.

. EXAMPLES

Figure 4 illusbates a typical field splice used on columns of the Detroit Bank & Trust Buiiding in Detroit, htichigan. These fabricated columns were spliced by partial-penetration bevel joints in the column

BUILT-UP COLUMN

BUILT- UP COLUMN FIELD SPLICE

FIG. 4-Typical column splice on Detroit Bank & Trust Building.

3. / Coiumn-Related

flanges. These A36 steel columns were welded with E70 low-hydrogen electrodes. Notice the schedule of u-eld sizes. The angle were sliop welded to column ends and field bolted during erection, using high-tensile bolts. These bolts were left in place and carried any horizontal shear in the direction of the column web, hence no field u&ling was required on the web of the columns.

Figure 5 illustrates the field splice of columns in the Michigan Consolidated Gas Co. Building in Detroit, Michigan. These fabricated A36 steel box-shaped columns were field welded with E70 low-hydrogen electrodes. Partial-penetration J-groove welds were used on all four flanges around the periphery of the column. Notice the schedule of weld sizes.

FIG. &-Typical column splice in sections of some depth. Plate on the web i s for bolting to facilitate erection.

BUILT- UP COLUMN


FIG. 5-Typic01 column splice on Michigan Con. solidoted Gos Co. Building.

FIG. 7-Field splicing of column flanges, using vapor-shielded arc welding process.

Figure 1 illustrates a suggested detail for a pin connection at the cnd of a built-up compression member of an arch bridge, subject to a reaction of 90 kips.

FIGURE 1

There are many approaches to this type of problcm and, of courso, many solutions. This is simply one analysis and one solution. One of the design requirements in this i~artierllar example is to have a smooth- appearing surface on the outside or faeia side of the arch compression member,

Notice in tlie sketch of thc cross-section of the built-up compression member, Figure 1, that the center of gravity is ,935'' in from the outer face.

By selecting an attaching plate of sufficient tliick- uess for its ccnter of gravity to line up with the compressio~~ ~nernber's center of gravity, the compression load will be transferred in a direct line without any eccentricity.

Thc bearing pin is subjected to a double-shear load: 90,OOO lhs on two areas, or 45,000 lbs cach. See Figure 2. .4c(:ording to AASI-IO (Scc 3.4.2), the allowable stress on this pin is 13,500 psi.

= 3.33 in.+equired pin area

or use a 2%"-&a pin having A = 3.98 ia2 -- --

The next step is to compute the thickness of the connecting plate. This is based oil the minimum required bearing area of the plate because of the pin reaction against the plate, Figurc 3. The 90,000-lb load is divided by the allowable bearing pressure, which in this case is 24;000 psi assuming no rotation, (AASHO 3.4.2) and the minimum bearing area comes out to be

Smce thc pm's diameter has been computed to be 2%", the rcquired plate thickness to make up tbis bearing area would bt-

= 1.67"

hut nse 2"-thick plate .~ ~~ -~ ..~.. -

since this will also line up with the center of gravity of the compression member (CG = ,933').

The next step is a simple determination of the required depth ( d ) of this courrecting plate. See Figure 4. In this analysis, some structural designers consider this connecting plate as a beam supported at the center, or pin. and withstanding the tvmpression loads transmitted from the compression tncmber.

In most cases, the compression load (here 90 kips) is assumed to bc ~qual ly distributed tllroughout the

3.5-2 / Column-

various parts of the compression memher by the ratio of the individual areas to the total area. Accordingly, the compression load carried by each angle wodd h e -

= 16.9 kips "

and the compression load carried by the 5h" X 20" web plate would be-

= 56 kips

throughout its entire width. Dividing this load by 2G" results in a uniform load of-

= 2.8 kips/linear in.

Treat this connecting plate as a cantilever beam from the centcrline with these two loads:

( 1 ) the concentrated load of 16.9 lups at 8.75" from center, and

( 2 ) the unifonn load of 2.8 kips/in. for a distance of lo".

The resulting bending moment i.; then computed:

= 288 in.-kips

FIGURE 4

Since the required section modulus is in tenns of ( d ) :

M:=, ,S

.- (288,000 in.-lhs) - ..

(20,000 psi)

Since

and the minimum depth of upper plate is found to b e -

d = 6.58"

or 7" deep beyond the pinhole would he sufficient.

. FINALIZING + The final detail has k e n sketched in Figure 5. The outer leg of each angle might be triinmed back slightly so as to fit to the 2" connecting plate. Whether this is cut back or not, there will be a loss of 25h1t of the angle leg. This area ( A = 2 X 'h" X 2.625" = 2.625

is made up by additional attaching stiEening plates. These have been chosen to be two %" X 3" plates ( A = 4.5 in.2) and two 'h" X 13h" bars ( A = 1.375 in2) . The total added area is thus 5.875 square inches. The entire built-up compression member has an area of 20 square inches. These additional attaching plates simply mean that the cross-sectional area in contact with the 2" cunnecting plate is in excess of the required 20 square inches.

After the compression member has been welded, its end might he nulled to provide a Bat, smooth surface for bearing against the 2" plate. If this is done, the entire section would not have to be welded 100% all the way through. Under these conditions, it is suggested that a bevel he made part way through these plates of the compression member and that a groove weld be made on the outside. Reinforcing Ellet welds should then be made on the inner side of this compression member where it co~mects with the 2" plate.

lost at connection; replaced by adding

FIGURE 5

/ Column-Relate

Bearing-pin connections like those shown on this bridge over Michigan's John C. Lodge Expressway must be designed to transfer the compression load without eccentricity. Note simplicity and beauty of the welded rigid frame employed in this bridge design.

1.

In the past, when engineers required steel columns of heavier section than those commercially available, they designed the columns to be made by riveting eover plates to the flanges of 14" WF rolled sections. See Figure l ( a ) . The cover plates w e e si7ed to produce the required additional section area.

In recent years, fabricating shops have simply substituted fillet welds for rivets and produced the same FIGURE 2

column section; Figure l ( b ) . This practice has presented a design problem in getting an efficient transfer of forces on the beam-to-column weld. of tensile force from the beam flange through the cover The best design is a completely welded built-up plate into the column without pulling the cover plate column, Figure l ( c ) . This gives the exact section away from the column flange. The cover plate, being required without any increase in welding, and there attached only along its two outer edges, tends to bow is no problem in transferring tensile forces from the outward; Figure 2. This results in uneven distribution beam flange through the column.

FIGURE 3

FIGURE 4

For very large column sections, 4 plates can be welded together to form a box section; Figure 3 (a ) . Sometimes a web plate is added to this box for additional area in the lower part of a building; Figure 3(b) . Moving up the bnilding, the point is reached where this web plate can be omitted without changing the outer section dimeiisions.

There are two general requirements for the welds holding the plates of the columns together; Figure 4.

a. The cntire length of the column must have sufficient welds to witlistand any longitudinal shear resulting from moments applied to the column from wind or beam loads; Figure 4 (a ) . Notice at the left the rathcr h ~ w change in moment along most of the colu~nn length.

b. Within the region where the beams connect to th,e col~imn, this longitudinal shear is much higher because of the abrupt cl~ange in moment within this region; Figme 4 (b ) . .41so the tensile force from the beam flange will be t ransfc~~ed through a portion of this weld. Thcse two conditions require heavier welds in the connection region.

Varioris t n x s of welds are employed in fabricating: a. Fillet u;el& (Fig. 5) require no plate prepara-

tion. They can be madc to any size simply by making more passes. However, since the amount of weld metal varies as the square of the leg size, these welds can require a large amount of weld metal for the larger sizes. For nominal size welds (approx. 'h" to %"),

fillet welds are usually used. When their size becomes too large, they are replaced with some type of groove weld because iess weld metal is required.

FIGURE 5

b. Bevel and Vcc groove welds (Fig. 6 ) require joint edges of the plate to be beveled, usually by the oxygen cutting process. On larger size welds, this additional preparation cost is offset by the reduction in weld metal required. AWS and AISC deduct the first %" of weld to compensate for any slight lack of penetration into the very bottom of the bevel joint, if welded manually.

FIGURE 6

c. J und l T groove udds ((Fig. 7 ) require the plates to be googed or machined. Machining is seldom used in thc structural field, although air carbon-arc gouging is becoming more popular. The J and U welds may not require as much weld metal as the bevel or Vee weld. AWS and MSG allow the full throat or depth of groove to be used.

FIGURE 7

a FIGURE 8

P~uiial-penetration groove welds are :illowed in the Building field. They have many applications; for cxample, field splices of coliiinns, built up columns, built-up box sections for truss chords, etc.

If a vee J or U groove is used, i t is assumed the welder can easily reach the bottom of the joint. Thus, the effective tliroat of the weld (t,?) is equal to the actual throat of the prepared groove ( t ) , see Fig. 8 ( b )

If a bevel groove is used, it is assumed that the weldor may not quite reach the bottom of the groove, therefore AWS and AISC drdu'ct %" from the prepared

FILLET WELDS

tor any direction of force' 7 = 13,600 psi 7 = 15,800 psi I i = 9 6 0 0 ~ .- ~ 1 ! = 1 1 , 3 0 0 "

PARTIAL PENETRATION GROOVE WELDS

sheor 1 r , 13,600 pi i = 15,800 psi

##tension transverse to axis o i wcld

! o = 13,600 I o 1= 15.800 psi

tension poial le l to axis of weld 1 some or piote 1 scme or p o r e

COMPLETE PENETRATION GROOVE WELDS

te l l i on compression bending I some o i piate 1 same oi piote

' low hydrogen E60 8 S A W 1 rruy be ,,red for fi l let weldr & pa i t io l penctrofion groove weldr on A242 or A441 steel. (at the lower ollowobfe r = 13,600 psii

$ dy for iplier or connections a i or other members subject p r i l la r i l y 10 axial camprrs5ion stress

groove. Here the cfiective throat ( t , ) will equal the throat of the groove ( t ) minus 'In", see Fig. 8 ( a ) .

hE 2-Partial-Penetration Groove

I // ~ " ' j b....a.~.>J

depth of

leg sire of f i l let weld

force - fb i per l i n in r rmch - upper volue A?, A373 ifre! & €60 welds l o w : d u e H36. A441 steel & E70 weldr

weight of weld me fa - Ibs per foot.

Tcnsion applied parnllel to the weld's axis, or compression in any direction, has the same allowable stress as the plate.

Tension appliccl transverse to the weld's axis, or shear in any dinxtion. has reduced allowable stress, equal to that for tlir throat of a correspanding fillet wcld.

Jnst as fillet wclds have a minimum size for thick - platcs becaiise of fast cooliiig and greater restraint, so partial-perietmtion .:move welds have a minimum effective throat ( t , ) of-

TABLE 3-Portiol-Perpetration Groove Reinforced by o

of f i l let weld leg size

1st value force ibs per l ineor Inch A7, A373 sitel & E6O welds 2nd value loice ibr per l ineor inch A36, A441 steel & E70 weids 3rd valve weight of weld metol lbr per foot

where:

t, - thicknc~s of t h i ~ ~ n e r plate

LD METAL REQUIREMENTS

Table 1 lists the AWS and AISC allowable stresses in welds iiscd on Buildings. Vaiucs for both partial- pcnetratio~i and full-pciletration groove welds and for fillet welds are included.

Table 2 tr:inslates the Table 1 values into allowable forces (Ibs/linear in.) and required weld metal (Ibs/ft) h r fillet wclds and scveral types of partial-penetration groove welds. These values cover weld sizes from M" to 3".

Table 3 provides allowable forces for partial-penetration groove welds reinforced by a fillet weld.

Table 4 directly compares a number of joints to carry a giveil force, illustrating their relative requirements in weight of weld metal.

LE 4-Joints to Carry Force o# 2

IlillMG WELD TYPES

There arc! several w:rys in which different types of welds can be combined in economically fabricating built-up colunins to meet the two basic rtqiiirements: a ) welds from end-to-end of column to withstand longitudinal shear resulting from (wind and beam load) applied momonts, and 11) hcavier wclds in connection rcgions to withstand higher longihdinal shear due to abrupt change in moment, and to carry tensile force from the beam flange. The following cases illustrate combinations that permit optimum use of automatic welding:

Region of beam to column connection

FIGURE 9

If the weld sizes are not too large, the column may be first fillet welded with -hw!ld ( a ) along its entire length. Second, additional passes are made in the mnnection region to bring the fillet weld a p to the proper size for weld ( b ) .

n o Region of beom to

Weld o ,,, column connection

Double beveled entire length

The wcb plate is txvdcd to the proper drpth on all 4 edges dong tllc ci~tirc length. Croovr weld ( a ) is iirst made :iIoiig the rntire Icngill. Second, fillet weld ( b ) is made over tilo groove \veld within the connection region to hiilg it rip to the propvr size.

Region of beam to

( coiurnn carinecfion

Beveled only within coni?ection region

FIGURE 11

The web plate is beveled to tbc proper depth dong short lcngths within tho connection region. First, groove weld ( h ) is made flrish with ihe surface within the connwtior~ region. Second, fillot weld ( a ) is made along thc entire lmgih of the column.

Additlono! beveling in

region of beom to (column COnneCTiOn

FIGURE 12

Thc web plate is beveled to tbc, jxopcr depth on all 4 edges along the entire lcygth. \Vithin the co~snection I-egioii, the \vcb is furti~cr l w ~ i , l i ~ I to a dcepcr depth. First, groove weld ( b ) is I I I X ~ C within the connection region until the plate edge is built rip to the heigllt of the first bevel. Second, groove weld ( a ) is made

FIGURE 10 ;iIong the entire Icrigtli.

FIGURE 13

In colunin bos sections, J and U gl-oovo welds may be substituted fol- bevel and Vee grnovix welds if the fabricator is eqnipped to gouge anti profrrs to do so rather than bevel. Since bevelirrg is a cutting method, the plates must bc beveled before :rsscmbling them together. Gouging, Irowevcr, may be done either before or after assembling. Further, heavy J or U groove welds normally nq~ i in : less wcld mctai than the bevel or V1.1: groove wvlds.

Some fabricators, in making hrilt-isl> box sections; have ass(~mb1ed ;illd liglitly t:r& weldrd the plates together witliont ;iny prqxration; Figurc 13(a) . The joints are next air carbon-arc g o n g ~ l to the desired depth for very slsort distalices and fr~rther tack welded; Figure 13(b) . Next, the longer distances in between.

tack welds are air carbon-arc gonged. Whcn this is completed, the entire length is ;~utomatically submerged-arc welded togeth'er; Figure 13(c) .

At first glance it might he thought that the rcquire- mciits for a bc;trn Range welded to the flange of a 1111iit-up box colmsin, Figure 14(;r), would be similar to the beam h i g c nelded to the flange oi an I shaped colnrnn, Figun: 14(b). This is because the box colnmn flangc is treated as ;I beam simply supported at its two miter edges, Figmr 14(c); it has the same maximum bending nroment as the W F columz flange treated as a beam supported at its center, Figure 14(d) .

The follo\virig analysis of a beam flauge welded to

FIGURE 14

a box column, Figure 15(a) , is based upon a simila analysis of a line forcc applied to a cover-plated WF column, i'igure 15(1)). The latter analysis was made by Dr. T. R. Higgins, llirrctor of J",ngint:ering and Research of the AISC.

The following assrlmptions are made: 1. The length of the box column Aange resisting

this line forcc is limittd to a distance equal to 6 times its thickness abovc arid below the application of the line force. See Figure 16.

2. T l ~ e edge welds oirer no restraining action to this Clmge plate. 1.11 oilier words, these two edges are just supported. The nppcr and lower bo~uidary of this portion of the column flange are fixed.

3. The tensile line force applied to this Aange area is urriiormly distributed.

At ultimate load (P,l), it is assunied that this roctirngdar plate has failed as a mechanism with plastic binges Forming along thc dotted lines.

The internal work done by the resisting plate eq11aIs the summation of the plastic moments (M,)

FIGURE 15

ini~ltiplied hy tlie angle change (6) along these edges. 'I'he exten~al work done equals the ultimate load

(P,,) rnrrltiplied by the virtual displacement ( A ) . By setting those two exprrssions equal to each

othcr; it is possible to solve for the ultimate load (P,,) which may be applied to this portion of the flange plate.

FIGURE 16

At ultimate loading (P,), plastic moments (M,) will build up along the dashed lines (Fig. 16) to form plastic hinges. The iutemal work done, when this plate is pulled out, will be the plastic moment (M,) multiplied by the corresponding angle changes (+) along these lengths:

an& +I along @-@ & @-@ angle +, along @-@ angIe 4, along 0-0, 0-@, @-a &

GI-@ With reference to Figure 17:

Distance @-@ = J aZ + 36 tz

@-m -e az + 36 t2 a

6 t or distance = - \/ a' 4- 36 t2

a

Now find the angle changes (+) along the hinges at ultimate load:

A +I= 5-t

A + 2 = 2 + 1 = - 3 t

and sirice

Sectiori x-x

a or distance @--a -. - \/ a2 + 36 t2 6 t

FIGURE 17

p Columns I'

A ;, ,$, = +3 + +,, = - &Ctt3;-;;~- allowable force

6 at extend work = internal work

internal ~ o r k

. .-

= M. [ m , 2 ( 2 a + b ) + ~ b + m , * d a ~ + 3 8 t ' ]

A Applying a load factor of 2, and using the yield

strength (u,), the allowable force ( P ) which may be applied to the plate would be-

where the plastic moment (M,), in in.-lbs/liuear inch is-

T t

FIGURE 18

external work

= P" A

FIGURE 19

Example

Here:

t = 31/2''

a = 5 "

b = 14"

u = 22,000 psi

calculated tensile force on beam flange = 386 kips

The allowable force:

(3%) (38 kips/sq in.) - - 12

= 1178 kips > 386 kips OK -

Equitable Life Asmrcmce Building

Colurnns for tlm Equitab1.e Life Assmxnce building in Sun Francisco, an earthquake area, were built and erected in 3-story lcngtl~s. The columns were uniformly tapered :$$, in./ft from the base to the 14th story.

Exterior columns started with a 42" web at the bottom, tapering to a 1.2" web at the 14th story level; Figure 20. Flanges were 18" X 3" at the h e . The tapered columt~s were fabricated by welding two flange plates and a web together. L-shaped columns were used at the corners of the building.

C.IL. House

The 32-story C.I.L. House in Montreal, Caiiada has the heaviest TI" section columns ever constructed. The fabricated columns weigh as much as 2,000 lbs/ft. A t y p i ~ d column, Figure 21, consists of two 7%" X 28" fiange plates welded to a 5" X 16%" web plate.

FIGURE 20

FIGURE 21

FIGURE 22

Automatic submerged-arc welding was used in fabricating these columns; Figure 22. Simple continuous fillet welds of about 3/4" leg size join the column flanges to the web. Because of the greater forces $thin the beam-to-column connection region, these welds were increased in size by beveling the web.

The depth of the bevel for this double beveled T-joint varied with the forces to be transferred, hut ranged from a minimum of Yz" on each side of the web up to 100%. Less than 10% of these groove welds required 100% beveling. The grooved joints extended in length slightly above and below the depth of the connecZing beam and ranged in length from 2' to 5'.

Joint preparation involved beveling with oxygen cutting equipment at a 22" to 30" angle to the correct depth. After tacking the Range to the web, the weldor lightly air carbon-arc gouged the bottom of the joint prior to welding to open it up for the root pass; the result was a modified J-groove.

The columns, 2 stories high, range from 22' to 34' in length. Flange and web plates were clamped in heavy fixtures to maintain proper alignment during welding; Figure 22. After tack welding, trunnions were

Designing Built-Up Columns / 3 . 6 1 1

FIGURE 23

attached to the column ends so that all welds could be deposited in the Bat position. The columns with trunnions attached were then transferred to the automatic welding unit. After preheating to the correct temperature, using natural gas torches, the shorter- length groove welds were made first. The remaining length of unwclded ailurnn was then fillet welded.

After welding, trumions were removed and the column ends machine facod to proper length. Con- nection plates were attached after machining, with most weids positioned downhand to achieve maximum wclding spced. Preheating preceded the manual welding of these plates in position, using low-hydrogen electrodes; Fi@re 23.

Inland Steel Building & N o ~ t l r Carolina h7alional Bunk Building

Elimination of interior colnmns in a building designed for wclded coiistruction is not unique, but

nsually reqnires the design and fabri~lltion of special colnrn~~s; Figure 24.

The ~ o l u m n design on the right was used in the Inland Stet:] Bidding in Chicago. The inner portion of the built-up colt~rnn is a standard WF section; the outer portion is a flat plate from 1" to 3" thick. A web plate, From %" to 1'W thick, joins thcse tw-o segments. Notice that a section of the main girder was shop welded to the fabricated column. Dotted lines show the spandrel bean~s and remainder of the girder that were fidd welded to prorluce a rigid vonnection. The main ginlrrs span 60'.

On t t ~ left is n typic;il column from the North Carolina National Rank B~~ilding in Ch;dotte. A spc- cially rolled V\'F sertion is tlic innin s q p e n t of this column. Wing plates have bix+*rri addrd to one flange and a mvcr plate to the othel- to d w d o p the necdvd ~.olrimn proportics. The m;iin girrl<~-s and spandrels (dotted sections) were later att:~ched by field welding.

FIGURE 24

3.612 / Column-Related Design

Fabrication of special colnmn seetiom demand low cost, high production assembly and welding techniques. Submerged-arc automatic welding is uscd ex- tensivcly in fabricating these columns. The welding head, Figure 25, is mounted on a universal, track traveling type welding ma~ripuletor. The manipulator,

FIGURE 26

ifux recovery nnit, and welding generators are mounted on a self-propelled carriage having a G5 ft track travel distance. Two identical welding fixtures are positioned parallel to and on either side of the carriage track. This has rcduced handling time for setup and re- positioning of the columns.

During fabrication of columns for the North Caro- lina National Rank Rnilding, they were placed in a specially designed trunnion fixture; Figure 26. This stood the columl~s on end. Shop welding of connection dotails could then be performed in the fiat and horizontal position. This, facilitated use of semi-automatic, submerged-arc welding and minimized weld costs.

Commerce Towers Building

Columns of similnr section configuration were used in the 32-floor Commerce Towers Building in Kansas City. Here, heavy floor loading due to the modern electronic business machines to be installed necessitated very heavy sections.

Column sections were built up by first welding plates into an I section and a T section, and then joining th'e end of the T section web to the middle of the I section web. The typical column length is 34' and the lower columns use 5" Aange plates and 5" web plates.

Tanden-arc automatic sobmerged-are welding was used in joining the Aange plates to web; Figure 27. The basic weld was a Yz" fillet deposited at 32-36 ipm. Preheat torches ran ahead of the arc.

In joining together the I and T sections, they are assembled in an air-clamping fixtnre and tack welded; Figure 28. Automatic submerged-arc welding is then used, with the fixtwe on a rail-mounted carriage.

esigning Built-up Columns / 3.6-13

FIGURE 27 FIGURE 28

41/811 4 4 4 % L

First Federal Savings b Loan Co. Building

On this project in Detroit, Michigan, the engineer originally detailed the fabricated columns to the 17th Soor as built-up box sedions, flush around the outside periphcry. U-groove welds were to be used; Figure 29(a) . This would have meant grooving the platcs for the entire length of the column.

Tile falxicator, chose to set one set of plates slightly in or out; Figurc 29 (h ) . This w-odd allow use of continuous fillet welds for the basic welding. The fabricator obtained pcrmission to exceed the original outside column dimension in one direction by '1'4''. Any further adjustment was prccluded because of the already de- iailed curtain walls, etc.

The original outside dirncnsions of the columns were 18" X 22" to the 5th floor, 18" X 20" to the 11th floor, 18" X 19'' to the 13th floor, and 18" X 18" to the 17th floor. Above the 17th floor, W F sections were used. The modified box section on the lower floors were then built up from two 18%" X 4S/s'' flange plates, with two 12%'' X 4%" web plates recessed slightly to permit tlie fillet welding. Above the 5th floor, the

smaller plates were set out slightly. In general, these full-length welds were 'h" fillets;

with %'' fillets for plates 2%" or less in thickness. This eliminated plate preparation except for short distances in the region of the beam-to-column connections. Here the plates were previously beveled, to the required depth, varying from 3/8" to 5/1,j'' depending upon load requirements. The typical joint consisting of the beveled groove weld topped by the continuous fillet weld extended 9" above and below the beam-to-column connection.

. FIELD SPLICES

Partial-penetration groove welds; either single bevel or single J, may he used for the field splicing of columns. The information presented previously under ''Partial- Penetration Groove Welds" will apply here.

Attaching angles shop-welded to the coh~mns serve to temporarily hold the column sections in alignment. For the II colum~i in Figure 30, using high tensile bolts, this connection was considered sufficient to transfer any horizontal shear force across the

3.6-14 / Column-Reloted

BUILT-UP COLUMN

I I I I 2. & under


LA FIGURE 30

web in this dir<,ction. Tlx. colnmn field splice, consisting of two sirrglr bevel. partial-penetration groove welds, wonld transfer any horizontd shear in the other direction.

BUILT- UP COLUMN

BUILT- UP COLUMN FIELD 5PLICE

FIGURE 31

For the box colnmn in Figure 31, the column ficld splice consisted of a partial-penetration J groove weld on all four sides of the column. These four welds would transfer any horizontal shear in the column splice. The attaching angles here were used simply to facilitate erection.

Partial-penetration welds on colornn splices pemut fast semi-automatic welding techniques to be used in the field. In the Commerce Towers project, semi- automatic arc welding with self-shielding, cored electrode permitted dqxxition of 100 lbs/mam/8-hour day; Figure 3%.

. COPICLUSION

The full econoinic impact of welded steel built-up columns in constn~ction of t d l multi-story btiildings, can be realized by carefully considering the major cost factors. These are colnmn design, placement of welds, joint design, weld size, and procedure. The dominating objective is the fullest use of automatic arc welding lncthods in the shop, with an extension of these henefits into the field l ~ y usc of semi-automatic arc welding for beam-to-column connections and for field splices.

FIGURE 32

Designing Bu i l t -Up C a l u m ~ s / -1 5

Built-up columns are a key design feature of the 28-story Michigan Consolidated Gas Co. Building in Detroit. Welding was considered to be the only procticol method for fabricating these columns which carry a maximum load of approximately 6800 kips. Photo shows a field splice of the column, revealing the shop beveling that facilitated welding. Clip angler shown are for temporary use during erection.

Typical splice Alternate splice Typicof splice

for builbup column for built-up ralumn for WF colvmn

Splice details from the Michigan Consolidated project show how maximum use was made of material at minimum weight.

/ Column-Refated Design

Automatic submerged-arc welding was used extensively in shop fabricating the unique and complex built-up columns for the 500' space tower which overlooked the Seattle World's Fair. Approximately 50% of ol l shop welding was with the submerged-arc process: 25% with self- shielding cored wire, semi-automatically; and the remainder manual stick electrode. At the top of the tower is a five- story observatory and restaurant, The structure required 3400 tons of structural steel.

Plate girders arc fabricated for requirements which exceed those of a rolled beam, or a rolled beam with added cover plate. The usual welded plate girder is made of two flange plates fillet welded to a single web plate. Where needed, web stiffeners are attached to one or both sides of the web. Box girders are made of two Range plates fillet welded to two web plates. Internal stiffening of these is accomplished with diaphragm plates.

The flange-area method is used to get an approximate dimension of the girder. This assumes that the flanges will carry all the bending moment and the web will carry all the shear forces.

The required web area is-

where:

V -- vertical shear applied to cross-section to be considered

T = allowable shear stress on web section

The formula for required flange area is derived froin properties of the girder:

For simplicity, this assumes web depth is equal to ( d ) , the distance between the centers of gravity of the two flange plates.

Also,

Therefore, the required flange area is-

where.

M = bending moment applied to section

u = allowable bending stress

d = distance between centers of gravity of flange \ plates

This method will require some approximate knowledge of what the girder depth should be an+ some adjustment of the resulting figures before the design is finalized.

The previous AISC specification held the depth of girders to a minimum value of 1/24 of the span. The Commcutary on the new AISC specifications suggests, as a guide, that the girder depth should not exceed the following:

Floors: u, / 800,000 times the span Roof purlins: IT, / 1,000,000 times the span

This translates into the Table 1 limiting values of depth-to-length lor girders used in floors. These values are for general guidance only.

*Quenched & iempcred steels: Yield strength ot 0.2% ofiret.

Camprerrion elements which ore not " i on~pac t ' but meet the ioilowing AlSC Sec 1.9 requirements-

box girder tension (1.5.1.4.31

a = .60 o, ~~~ . - .

compression (1.5.1.4.3)

. .. (AiSC Formuio 4) (AiSC Formula 5)

Use the larger of @ or @ but not to exceed .60 a, L

i f - < 40, don? need to w e @

reduction in o lowable compressive bending stress due to possible ioteroi displacement of web. (1.10.6)

d 24,000 when 2~ < -- s,, = oliowoble cornprerston

tw cry stress from obave

(AiSC Farmulo l li

*?his ratio may be cxweded i f the camproiaive bending stress, using a width not this limit, is

within the oi!owable stress, i n e above toble does not include tho higher bending rtreir to = .66 <,I for ":ompart" sections because most fabricated piate and box girders will exceed the widtli-thickness ratio of ' ' c o ~ O C ~ C ~ ' ' 5ections.

ending Stresses

Table 2 suinm;irizes tho AISC allowable bending stresses for plate and box girders.

I In Table 2:

L = s p a n or iinlxaccd length of compression flange

r = radius of gyriitiml of ;I Tw section compris- o-, = aiiowable compressive bending stress from in7 tlic cornprcssioir flarigc plus 1/6 of the nhn.,a ---"" ~ ~ 1 3 ;rrea, about the y-y axis ( in the plane of thc we11). For girders symmetrical about MI is the smaller, und Mz is the larger bending tlieir I-x ;%\is of hending, substitution of r, moment at tl,e ends of the onbraced length (L) , taken of ilrc: enlirc section is conse~ative about the strong axis of the member. M1/M2 is the

At = area of the compression flange ratio of these end moments. When MI and Mz have

Bme Girders for

the same signs, this ratio is positive; when they have different signs, it is negative. When the bending moment within an irnhraced Imgth is larger than that at both nids of this Icngth, the ratio is taken as imity.

Figrire 1 is a graph showing t11c valrie of C,, for any given ratio of MI/M2.

When the bending moment within an rillbraced length is larger than that at both ends of this length, the ratio shall be takcn as unity, and C,, becomes 1.0.

Loads applied to beams and girders cause bending moments dong the Icngth of the member. When these moments are non-uniform along the length of the member, both horizontal and vertical sliear stresses are set up because shear is equal to the rate of change of moment.

The horizontal shear forces worild cause the f l a n ~ e of a platc girder to slide past the web if it were not

for t h e fillet welds joining them. Thrse liorixontal and vc:rtical sllear st~rsses com-

bine and prodwc both dingo~ral tcnsiori and compression, c;wh at 45" to the shmr strcsscs. i n steel structr~res, trmsion is not thc problrrri; howev-er, the diagonal eomprcssion could be high enough to cause the wtkb to bwk1,c. StiRmrrs arc used to prevent the web from buckling in ribgions o i high shear s t r ~ s .

The ratio of wch thickness to clear depth of web in the oldrr spccificatioiis \rxs bascd on predications of file plat^, buckling tlrcory: tire wch being subjected to shear throughoi~t its daptl~, and to rompressi\,e berid- i i~g ,iiesscs o w r a portion of its depth, See Figure 2.

The plate buckling tlrcory assumes the portion of the web 11etwt~~ii stiil 'c~l~rs to be an isolated plate; l~owovcr, in thr plate girdcr, the web is part of a built-rip n~emher. When tllc critical buckling strcss in the wcb is rcacbcd, the gilder does not collapse. This is because the flangcs carry all of the bendirrg moment,

1 , C . ,. . .

,--- ,. . - ,.- - - -----w- ,...-.

Diogonol compresson Compresswe f i om sheor forces bending sireis

FIGURE 2

FIGURE 3

Transverse stiffeners act or compression struts

the buckled web then serves as a tension diagonal, and the transverse stiffeners hecome the vertical compression struts. This in e%ect makes the plate girder act as a truss. See Figure 3.

The carrying capacity of the plate girdcr is greater under this analysis, being cqual to that supported by the beam action shear (Fig. 2) and that supported by the diagonal tension field in the web (Fig. 3 ) . AISC Formulas 8 and 9 will meet this requirement. These formulas appear further along on this page.

ABSC Specifications

Intermediate stiffeners are not required when the ratio (d,/t.) is less than 260 and the maximum web shear stress is less than that pcimitted by AISC Formula 9 (AISC 1.10.5.3).

Figure 4 partially s~.immarizes the AISC specifications for intermdiate stiffeners.

These requirements apply: 1. If single s tf i l lers are used, they must be

welded to cumprcssion flange (AISC 1.10.5.4). 2. Intermediate stiffeners may be cut short of

tension flange for a distance less than 4 t, when not

needed for bearing (AISC 1.10.5.4). 3. For intcmmittent falet welds, clear spacing ( s )

between lengths of weld must L 16 t , and L 10'' (AISC 1.10.54).

4. Welds joining stiffeners to web must be SUE- ci.ent to transfer a total unit shear force of-

f, = d, (AISC 1.10.5.4)

This shear force to be transferred may be reduced in same proportion that the largest computed shear stress (T) in the adjacent panel is less than that allowed by AISC Formula S (AISC 1.10.5.4).

5. If lateral bracing is attached to stiffener, u d d s connecting stiflrner to colnpression flange must be SUE- cirnt to transfer a horizontal force (F) = 1% of flange force (AISC 1.10.5.4).

Wlreri intermediate stiffeners are required, their maximunr spacing ( a ) depends on three items: a/&, d,/t,., m d shear stress ( 7 ) .

The largest average web shear stress (T,, = V/A,) in any panel between transverse intcrmdiate s t i fhe r s shall not exceed the following (AISC 1.10.5.2):

Cut short of tension

flange < 4 t, f, = d,

FIGURE 4

late Girders for

when C, < 1.0

. . (3a)

This provides an allowable shear stress ( T ) up to about .35 u, and takes advantage of tension field action.

when 6, > 1.0 or when no stifenem are used

This provides an allowable shear stress (7) within the range of ,347 o; to .40 o; and does not take advantage of tension field action.

where:

a = clear distance between transverse stiffeners, in.

d, = clear distance between flanges, in.

t, = thickness of web, in.

a, = yield strength of girder steel, psi

when C, < .8

when C, > .8

when a/d, < 1.0

when a/d, > 1.0

Above, the one C, formula picks up exactly where the other leaves off. The value of C, may be read directly from the nomograph, Figure 5, without separately c~mputing the value of k.

Both ASIC Formulas 8 and 9 contain a basic factor

5 0 a, C, which you will notice is the same as r

or (.347 a? C,). The expression (.60 u,) is recognized

as the basic allowable tensile stress and as ( 7 ~ ) . , " -,

For greater depth to thickness of web (d,/kV) and greater stiffener spacing (a/d,), the values of (C,) will become lower. Thir will result in lower values for the allowable shear stress in the web. For these conditions, AISC Formnla 8 has an additional factor which takes advantage of the increased carrying capacity provided by the diagonal tension field and results in a higher shear allowable. When C, = 1, this factor becomes zero and AISC Formula 8 becomes Formula 9.

The ratio a/d, shall not exceed (AISC 1.10.5.3):

nor

These arbitrary values provide a girder which will facilitate handling during fabrication and erection.

When a/d, exceeds 3.0, its value is taken as infinity. Then AISC Formula 8 reduces to AXSC For- mula 9 and k = 5.34 (AISC 1.10.5.2).

This work can be greatly simplified by using the appropriate AISC Table 3 for the speci6c yield point of steel. See AISC's "Specification for the Design, Fabri- cation and Erection of Structural Steel for Buildings" and Bethlehem Steel Corp's Steel Design File on "V Steels-Recommended Allowable Stresses for Building Design."

In end panels and panels containing large holes, the smaller dimension (a or d,) shall not exceed (AISC 1.1053)-

where T is the computed average shear stress in the web:

i t is necessary that the stiffeners have sufficient cross-sectional area for them to act as compressive struts to resist the vertical component of the tension field in the web.

This cross-sectional area, in square inches, of intermediate stifFeners when spaced in accordance with

0 - ----------

one w, arge o e

FIGURE 6

AISC Formula 8 (total area when in pairs) must not T .. = allowable web shear stress from AISC be less than (AISC 1.10.5.4)- Fonnnlas 8 or 9

u,, == allowahle bending tensile stress -

(7 ) I t can he shown that this formula will result in- a ) full bending tensile stress allowable, if the con-

current shear stress is not (Treater than 60% of

(See the appropriate AISC Table 3)

where:

yield point of web steel y = _--..-- - - -- y~eld point of stiffener steel

D = 1.0 for a pair of stiffeners 1.8 for a single angle stiRen'er 2.4 for a single plate stiffener

When the greatest shear stress (T) in a panel is less than that permitted by AISC Formula 8, this area (A,) requirement may be reduced in like proportion (AISC 1.10.5.4).

The moment of inertia of a pair of stiffeners or a single stiffener, with reh:rence to an axis in the plane of the web, shall not he less than (AISC 1.10.5.4)-

See Tabies 3, 1, and 5. Plate girder webs, subjected to a combination of

hending tensile stress and shear stress shall be checked according to the following interaction formula:

where: v

T = computed average wcb shear stress = -- A,

- the full allowahle value, or

b ) full shear stress allowable, if the concnrrent bending tensile stress is not greater than 75% of the full allowable value.

See Tahle 6B €or abbreviated Fonnula 12 lo w e for a specific yield strength of steel.

Concentrated loads cause high compressive stress at the web toe of the fillet along a distance of N + K for end reactions, and N + 2K for interior loads.

If there a r e a 0 boaring stiffeners, this compressive stress shall not exceed (AISC 1.10.10.1)-

for cnd reactions

- t,(N + K ) = ' . . . . . . . . . . . (10a) (AISC Formula 14)

for interior loads

n < 75u, t,JN + 2 K ) = ' . . . . . . . . . . . ( lob )

( AlSC Formula 13)

Also, the sum of the compressive stresses from concentratsd and distributed loads on the compression edge of the web plate not supported directly by bearing stSeners shall not exceed (AISC 1.10.10.2)-

f ABLE 3-Minimum Moment 04 Inertia

of intermediate Stiffener

i ,. = > p14 50

d, I. d, I. d, I. d, I. d, 1,

W i d t h of bor

(d)

-11t- oment of inertia of n-i-

ese Volues tor St Sides 04 Girder

t B( Inertia of Sing

se Vatu'ues tor St Sides BP Girder

Thickness of ongle rtiffener0)

1 ,,, 1 1/*11 1 j 1 1 y 2 1 x 1 3 j ~ - ( XP 1 1/4"

Angle size

FIGURE 7

if flange restrained against rotation

if JEange not restrained against rotation

Concentrated loads and loads distributed over a partial length of panel shall be divided by either the product of the web thickness and the girder depth or the length of panel in which the load is placed, whieh- ever is the smaller panel dimension. Any other distributed loading, in lbs/iinear in. of length, shall be divided by the web thickness.

If the above stress limits are exceeded, bearing stiffeners shall be placed in pairs at unframed ends and at points of concenixated loads, Figure 8.

12 t* [or less]

4 25 tw

[or less)

[a) Single pair of [b] Single pair of st~ffeners at end stiffeners - interioi

Bearing stiffeners with the above sections of web are designed as columns (AISC 1.10.5.1).

These requirements apply: 1. Bearing stiffeners shall extend almost to edge

of flange (AISC 1.10.5.1). 2. Bearing stiiFcners shall have close bearing

against flange or flanges to which load is applied (AISC 1.10.5.1).

3. Clear spacing of internittent fillet w e < 16 t, < 10'' (AISC 1.10.5.4.).

4. Deduct leg of fillet weld or corner snipe for width of stilfenev (b,) effective in bearing at 90% o; (AISC 1.5.1.5.1). If parts have different yield strengths, use the lower value.

5. The limiting ratio of stiffener width to thickness shall be-

- -- - b" 3300 (AISC 1.9.1) ts - s 6. Use I,, 2 3/4 dw for slenderness ratio (L,/r) of

coltrmn section to determine allowable compressive stress (AISC 1.10.5.1); r is figured about an axis in the plane of the web.

[or less) (or less)

(c) Double pair of (d) Double pair of stiffeners - interior stiffeners at end

FIGURE 8

If intermittent fillet welds are used in plate or box girders, their longitudinal clear spacing shall not exceed-

tension flange (AISC 1.18.3.1)

(12)

compression flung8 (AISC 1.18.2.3)

FIGURE 9

The longitudinal shear force on fillet weld hetween flange and web is-

V a y f = Ibs/linear in. I n

where:

V = external shear on section

a = area of flange held by welds

y = distance between center of g area held by welds, and neutr section

ravity of fiange a1 axis of entire

1 = moment of inertia of entire section

n = number of fillet welds holding flange area, usually 2 welds

Table 6 summarizes the principal AISC specifications in (,asy to use form, permitting direct readout of the limiting value for the specific yield strength steel being used.

Design a welded plate girder to support a 120-kip uniformly distribnted load, and a 125-kip concentrated load at midspan; Figure 11. Girder is to be simply supporkl, have a span of 50', and have sufficic.nt lateral support for its compressive flange. Usc A36 steel and E70 or SA-2 weld metal.

Plate Girders Cor

125 k i r s uniformly distributed

FIGURE 11

L = 50' = 600"

bending moment for the unifoim load,

for the concentrated load,

Total M = 97,750 in.-kips

shear

V = 122.5 kips

Design Procedure

1. Design the girder web for the shear requirements, assuming it held to a depth of 66".

c / ACSC Formula 4 (1.5.1.4.5) 1 A15C Formula 12 (1.10.7)

* Quenched & tempered ileels; i v yield brength ot 0.2% offset. r = averoge shear sties in web =-

A,

/ irder-Rekted Design

Consider the following average shear stress ( T ~ , )

and maximum panel length ( a ) for various web thicknesses (t,):

Although the Y4" thick web would result in a reasonable shear stress of 7430 psi, the greatest stiffener spacing ( a ) allowed would be 97% of the web depth (d,); this would require more intermediate stiffeners. It would be more practical, in this example, to increase the web thickness to x6", thus allowing a greater distance between stiffeners.

2. Design the flange to make up the remainder of the moment requirements. Assume a bending stress of about cr = 21,000 psi.

section modulus required of girder

- - (27,750 in.-kips) (21,000 psi)

= 13W in.3

distance from neutral axis of girder to outer fiber assuming a flange thickness of about 1"

6 = 'h d, + ti = (33") + (1")

= 34"

total moment of inertia required of girder

I t = S c

= (1320)(34)

= 44,380 in.4

remaining moment of inertia required of flanges

If = I, - I=

= (44,880) - (7487)

= 37,393 in.4

and since

If = 2 Af cr2 c, = 33'' + W'

area of flange required

= 16.67 in.2

or use two 17" X I" flange plates.

final properties of girder

I = 2 (17 in.=) (33.5")2 + (%6")(66")3 12

= 46,766 in.' > 44,880 i n 4 OK -

= 1375 in." 1320 im3 OK - actual bending stress in girder

= 20,200 psi

reduced allotuahle compressiue bcnding stress in jiange due to possible lateral displacement of the web in the compression region (AISC 1.10.6)

UL, 5

- -

- -

where:

u,, = - - - -

21,347 psi > 20,200 psi actual OK -

allowable bending stress

.60 o; 22,000 psi

,V = 122.5 kips

FIGURE 12 k d

3. Design the Wansverse intermediate stiffeners. Figure 12 is a shear diagram of the girder.

end panel distance between intermediate stiffeners (AISC 1.10.5.3)

45.6" or use 45"

nzazimum shear just inside of this stiffener

V = (12.2.5 kips - 62.5 kips) ) + 62.5 kips

= 155.6 kips

maximunl spacing between remaining intermediate stiffeners (AISC 1.10.5.3)

required number of panels

WO" - 2(45") = 510"

so use 6 panels of a = 85" each.

check the allowable shear stress in the web and determine required area of stiffener

Shear diagram

Since the girder web's ratio is-

d,/t, = 211

and the ratio of panel width to web thickness is-

the maximum allowable shear stress (T) to be carried by the girder, web and the total area of stiffener (A.) to resist this shear are found from Table 3-38 in the following manner:

Within the above limited area of the 1;uger AISC table, the values in the four corner cells are read directly from the AlSC tal~lc. Then the rerpirt,d values obtained by interpolation ax: filled into (he center cell. Within each cell, the upper value is the allowable shear stress ( 7 ) and the lower value is the required area of stiffener (A,).

Thus, for our problem:

T = 8.0 kips or S O N psi > 5950 psi OK

width of stificner ( i f using t, = 3h")

(2.16) I Since: - - -. --

2(?18) A, - 2bS t, . .

= 2.88" or use 3?i"

4.1-16 / Girder-Related

also check AISC Sec 1.9.1:

b. 3% - -- - t, %

required moment of inertia

actual moment of inertia

I, = ( 2 x 31%'' + %,")"" - 12

4. Determine the size of fillet weld joining intermediate stigeners to thr girder web.

unit shear force per h e a r inch of stiffener

or f, = 1140 ibs/in. for a single fillet weld (one on each side).

leg size of fillet weld

,r = ,102" or use "./I6 cont~nuous fillet

or, for a "/10" intermittent fillet weld

.102" % = - 9{#''

[\ = 58.8% or use v 3 . 5 or --TJ&-

or, for a 3'4'' intermittent fillet weld

5. Check the combined bending tensile stress and shear stress in the girder web according to

wherever the ealciilated shear stress exceeds 60% of that allowed according to AISC Formulas 8 and 9.

The allou-able shcar stress was found to be T = 8000 psi and 60% of this would be 4800 psi. ~-

This would correspond to a shear form of

V = 7 A , -

= (4800 psi) (%, X 66)

= 99.0 kips

and would occur at x = 125". The bending moment at this point is-

and the bending stress is-

- 13,750 in.-kips -- --

1375 in."

= 10,000 psi

I t is only when the shear stress exceeds 60% of the allowablc that the allowable bending stress must be reduced according to AISC Formula 12.

Since the calculated bending stress at this point (x = 125") is only 10,000 psi or 45% of the allowable, and it rapidly decreases as we approach the ends, there will be no problem of the combined bending tensile stress and shear stress exceeding the allowable values of AISC Formula 12.

6. Determine the size of fillet weld joining flanges to the girder web, Figure 13.

FIGURE 13

(AISC Fonnula 12)

FIGURE 14

force on add portion of i ~ e b acting with stiffeners to form column

, .

- - ( 122.5 kips ) (17 i n 2 ) (33.5") (46,776 h4) ( 2 welds)

I- = 746 lbs/in. 17"

FIGURE 15 leg size of fillet weld

746 W =

11,200 -

= ,066" - 12 t,

but because of 1" thick flange plates, use Xo" - 12 (%,") = 3%''

Bearing Stiffeners

6. Check to see if bearing stifleners are needed at awn of this web portion

the girder ends (AISC 1.10.10.1); Figure 14. := (3%") (

= 1.17 in.' compressitje stress at web toe of girder fillet

R required arm of bearing stiffeners = - t d y -t K) 6.10 - 1.17 = 4.93 in."

- - (122.5 kips)

~ -- -~ ~:h6(lo" + If stiffeners extend almost the full w-idth of the

flange, a wkltli of 7" will be needed on each side. = 34,700 psi > 27,000 psi, or .75 uy

This stress is too high; bearing stiffeners are needed. Try a singlc pair and treat the stiffeners along with a portion of the web ns a (.ohinn. Assume an acccptable cotnpressive stress of about 20,000 psi.

7. Determine size of bearing stiffeners.

sectional ureu required to cawy this stress

- (122.*kips) -

(20,000 psi)

A, = 2 (7") t,

= 4.93 in."

= ,352 or use %" thiclrness

8. Check stiffener proiile for resistance to compression (AISC 1.9.1).

?'Iris ratio is too hizh, so m e 11 pair of 7" x 7/10" hearing stiffeners.

9. Check this bearing s t i f h e r area as a coliimn; Figure 16.

FIGURE 16

= 106.8 in.'

A = (7$6)(14%0) -I- ( 3 7 4 6 ) ( % e )

= 7.3 in."

slorderncss ratio

& __ 3h(66") - r ' (4.6")

= 10.6

allowable comprcssivc stress

u =: 21,100 psi, from Table 6 in Section 3.1

and

R = u A

= (21,100) (7.3)

= 154.0 kips > 122.5 kips actual OK - 1.0. Determine tlie size of fillet weld joining bear-

ing stiflencvs to tl-ic girder web.

length of weld

L := 4 d,

= 4 ( 6 6 " )

= 264"

force on tceld (treufilzc weld us a linej

R f = -- L

( 122.5 kips ) - ... . - -- ... (264")

leg size of fillet weld

11. Check bearing stress in these stiffeners.

beoring area of stiffenel. (less comer snipes)

(7" -- 1") 7/;8" = 2.62 h2 each

bearing stlass in stiffener

.- ..- (122.5 kips) -. 2("62)

= 23,400 psi < 27,000 psi or .75 u? OI(

12. In a similar manner, cheek the bcaring stifE- encr at cciiterliire for resistance to 125-kip load. I f irsing the same s t i f h e r size as at ends, Figure 17:

FIGURE 17

= 106.8 in.'

A = (7/,,")(14%0") + (7.8" - 7/16")(%0")

= 8.56 in.'

elded Plate Girders (or Buildings / 4.1-1

Uniformly distilbutrd loud of 120 kius

FIGURE 18

nllotcablr compressitje stress

v = 21,000 psi, from Table 6 in Section 3.1

and

F = u A

= (21,000) (8.56)

= 179.5 kips > 125.0 kips actual OK - so use the same ainouiit of fillet welding as before.

heriring stress in center stiffener F

u = - 4

- .- (125 kips) 2(7" - 1") (5,")

= 23,800 psi < 27,000 psi or .75 u, OK - 13. C11ei:k the compressive stresses from the uni-

foririly dis~rihi~t id 1o;id of 120 kips on thc comprwsion edgr of tlw a.eb pint? (AlSC 1.10.10.2). See Figure 18.

Bearng sttffeners lntermediote stiffener

rillolonblc r:o?npressice stress ugninst web edge assiiming flange is not restrained :ig:rinst rotation

-C .- 990 psi

rictual presszrrc of uniform loiid against web edge

(120 kips) = . . (600") ( 24,")

=: 640 psi < 990 psi allowable OK - 14. Consolidate these findings into the final girder

design, Figure 19. As a matter of interest, rcducing the web thickness

to Yn" would have saved about 143 lbs in stml. I-Iow- wer, this would have required 13 pairs of stiifeiiers instead of 9 pairs, Figure 20. The additional cost in fitting and welding the extra 4 pairs of stiffeners probably would exceed any savings in steel.

Increasing tbc web thiclmcss to %" would only rednce tlre iiuinber of stilfeners by 2 pair, Figure 21. However, this would iiicre:ise the weight by 287 lbs.

Bearing stiffeners Bearing stiffeners 2 - R 7 : ' ~ V,&,' 2 - R 7" x Vt;/ia"

125 kips / intermediate stiBenei 1

FIGURE 19

66" X 36'' web

16" X I " flange FIGURE 20

-. 66" X %" web ~ n n i ~ u I i I

FIGURE 21

Many tinrt.s access Irolcs must be cut into the wrbs of beams a d girders for dnct u.ork, etc. If snirrciently large, they must be reinforced in some manncr.

Sinrr: the flanges carry most of tlrr bending forces, the loss of web arca docs not p w n t much of a problem. Howrver, sincc thc shear (V) is carried for the most part by the web, any reduction of web area must Be checked. See Fignre 22.

If the hole is located at midspo ( b ) , the shear is minimum and may have little cffcct on the strcngth of the girder. If the liolc is located near the support in a region of liigh shear, tfic additional bending stresses produced hy this s11c;tr milst bc added to the conventional bending stresses froin tile applied beam load. See Figure 23.

An irrsidt: Iiorizontal f laug~ may be added to the Tee scction in (11-dm to give it sufficient bending btrength, or sufficient comprc~ssive buckling strciigtli.

Applied load

FIGURE 22

When this is done, it must he rernem1)cred that this Range bemmes a part of the Tee arm 311~1 is subjrctrd to tlie same axial tension (F , , ) and con,prt:ssio~ (F,) force causcd hy tho bending mon-rvnt ( M , ) from the external loiiding. Tlievefore, tliis flange must extend iar monglr beyond tire web opcwing to effectively transfer this portion of tlic axial force hack into the main web of the girder; see Figure 24. Of course in the region of low inomflit ( \ 4 x ) , this iixial f o r c ~ may he low a~rd not req~iire tliis extra length of Range.

FIGURE 23

If t11cw ;ii.wss Iiolcs in tlic \rcb are close cnoi~gh togctlicr. the portion of the wrh between the holes beha\-cs iir tlw s;rii-re rriatiner as tlrc vcrtical mcmbrrs of a V ic~r rndd truss. Scr Figure 25.

I'nlcss the bmding stress at the corner of the accrss hole is r;ltl~cr low, rt:inforcernctit of this corner sho111d b(. consic!r:cd:

1. liccalisc 01' t l r ? a h n ~ p t change in section, there is a stress co~iceritriiti~~~r scwral times the average stress valrie. Sec Figlire 76.

2. Tlw Tce scrtion at this inside corner behaves similar to a ciirved lxwm i n t1i;rt thc neiitrxl axis shifts in ton-srrd this i n r greatly increasing the bendiiig stressrs on this i~iward face. This increase is gre:itcr with a smnllcr r;?diiis of corner.

111 tlie us~ial aiialysis of a Vicre~rdeel truss, the horizontal slicar ( ) along the neutral axis of the

6.1-24 / Miscellaneous Structure Design

STEP 7: Determine Properties of tlrf Elastic .4rea

area of elastic urea

b A, _ ~~~~ ~ log, -~ 11.

( L - 11%) 11,

Li- 1 = 200" -4 Topered beam

Moment of inertia

1

1 1 c, = 134.30" -

Elastic orea

0 FIGURE 30

cornpl-ession must be checked against biickling according to AlSC l .<J.l:

FIGURE 29

If tlitx resnlting bcriding st]-ess in the stem is excessive, it must he rcinfort:ed by an insi(1e flangr or stiffener.

Cornim of the liolr slio~ild always llc round m d snrootli. A ~~iininir~in cornel- r;idii~s of Y is recom- meridrd \rIwn i l ~ e hole is not stifl 'iwd

lisirally it is assu~ncd Lhi: point of conti-:18cxnre of t l ~ a rnmncnt in thr top and l~ottenn povtioirs prodiiced by tlir shear ( I ' , ) and ( I? , , ) is allout ~nit ls t~t ion of the Irole ( g ) . It is also assnmed t l ~ c total vcrtical shcar

is 11ividt:d b c t w ~ ~ n these two sections in proportion to tlioir depths. For Tccs of equal deptli, Vt = V ,, - - " . 2 VI.

The top ~ n d bottom Tee sections must be capable of withstanding this conihiiiecl bending stress, and the vcrtical slirar.

A flange may be added arornld the edge of the web openi~rg to gi\.c LIie Tee section snfficient strength for the bending inomcxt. An aciditioiial plate may bo addcd to the \vch of the Tee to give it sufficient strengtli for the wrtical shear ( V ) .

7. COVER PLATES

It mi) bc ;idv;rntageous in some cases to use parti;il-lengtli cover plates in the beari~ig regions of a beam or girder, to reduce tlie required thickness of the iiaiige plate extending from end-to-end of the mrcnher.

Related disciissioli will hc ioiind forther along in this tmt iinder Section 4.3 on 1Vi:ided Plate Girders for 131-idges (sac Topic 12) ;ind iinder St.ction 6.1 on Design of Rigid Franics (see Topic 3 ) .

'The te,niiination of partial-lcngth cover platcs for Ix~ildings is govcme:d by I S ( : SIC 1.10.4. The fol- l owi~~g l~u,-agr;il~lis sunnn:~rin~ t lmc reqniremeiits.

Pit1-tii~l-1~11gtli COVIY pli~tcs sliiill crtcnd beyond the tlicorctic:11 nit-oil' point for ;i distmci~ a ) , di4inetl Iwlo~r. Tliis e~str~~itl(d pnrtinii ( a ' ) s11;iil he attaclicd to tlie h<.;ini or girtlev \vitlr siiffii.iw~t fillet wcids to d e i h p the uwri- pIati.'s pc~rtioii oS tho bending force

FIGURE 30

tote Girders for Buil

in the heam or girdel. at ihe theoretical cut-off point d r i ch is equal to-

Q = statical moment of cover plate area ahout neutral axis oi covrl--plated beam section

I = nromel~t of inertia of cover-plated beam section

The moment, coinputed by equating gis to the L

c:ipaeity of the connecting fillet welds in this distance (a') fxom the actoal c.nd of the cover plate, must equal or exceed the moment at the theoretical cut-off point. Otbel-wise, the size of the fillet welds in this teiminal

s t r t i o ~ ~ (a ' ) milst ),<' i~icnxsed, or the aciual end of t l ~ c cavcr plat<, rnlist ht, ~ ~ s t c ~ ~ ~ d r d to a point of lower momclit.

The lcwgtl~ ( r r ' ) l l l ~ : l ~ r l ~ < Y l from the actual end of t l i ~ cowr platc shall l1c:

1. A distnnco eipinl to the* width of the cover plntc when t l i t ~ t ~ is a colrtiiir~orls fillri weld i:qual to or larger tlmr 34 oi' tlw pl;itc, tliickitcss across the end I thr plate :ind (xmtin~tr,cl \\.<,Ids along hoth edges (11 the cover plate iu tlw Itygth ( i t ' ) ,

2. A distancr r q u d to 1 % timrs the width of the w v c ~ plate h i tiicw is ;I coiiiinnoi~s fillet weld smaller tlian 3h of tlw plirtr. thickness across the end of the plate and continnd \v<,lds along hoth edges of the (,over plate ill the lmgth (a ' ) .

3. A disimce eyud to 2 tiines the width of the cover platc wl~en there is no weld across the end of the plate but continuous wclds along both edges of the cover plate in the lengtll (a ' j .

I+".? I Top secton

B e n d ~ r , ~ stress from Resuking bending stress oppiied beam load

FIGURE 31

4.1-24 / Girder-Related Design

M, = moment ot n n r i end of I teiminol develooment / M, = moment at theoretical

:f beyond theoietz

I Moment dtagram

development cut-off point 6 Theorelicol cut~off point

t I J

I I I I

I I

8 I If inner end of teiminal development lies beyond theoreticol cut-off point

M , ~ Y End weld -+ F = - ---- f = x;i-, \ I

J f

I If terminal development starts at theoretical cut-08 point

,

I . . I Inner end of

%Theoretical cut-off point terminal development

M,a y -+:,A 1 f = vw.

End weld - r F = Mi 0 y 7 ~ E n d w e l d + F = 7-

Inner end of Theoreticnl cut-off p o t i i t d - 1 ! h ~ 4 terminal development

Inne terminal developmen

FIGURE 32

e lded Blare Girder for Buildings / 4.1-

elded Plate Girders $or rrildimgs / 4.1-27

/ Girder-Related Design

elded Plate Girders for Buiidings / 4.8-2


Access holes cut in girder web must be reinforced. In regions of high bending moment, flonges must extend far enough beyond web open i~g to effectively transfer forces into moin web of girder. Semi-automatic welding, with self-shielding cored electrode wire, is used here in ottaching reinforcements at double the speed of manual welding.

Every plate girder must havc several properties: 1. Sufficient strength, as measured by its section

moduins ( S) . 2. Sufficient stiffness, as measurcd by its moment

of incrtia ( I ) . 3. Ability to carry the shcar forces applied to it,

as measured by its web area (.4,). 4. Ability to withstand web buckling, as indicated

by the empirical relationship of the web depth to web thickness-

-,

In some cases, the depth ( d ) must be held within a certain maximum value.

Also, the choice of Aange and web plates should not result in any n11usua1 fabricating diEcuIties.

An "efficimt" girder will satisfv all of these re-

with any advantages of tlrc altered design, such as increased head room, less fill a t bridge approaches, ete.

In order to simplify the derivation of the efiicient girder, it u-ill he necessa~y to assume the depth of the web plate (d,) is also the distance between the centers of gravity of the two Range plates as well as the overall depth of thc girdcr. Sec Fignre I.

In the case of welded plate girders where the thiclmcss of flange plates is vory small compared to the girder's depth, this assumption doesn't introduce very much of an error while greatly simplifying the procedure and resulting fom~ulas.

The moment of inertia of the girder section is-

I dw3 S = -- - A, d + 01

d/2 - 6 K - quircments with the minimum weight.

An "econon~ical" girder will satisfy these same S dW2 Af = - - also

requirements and in addition will be fabricated for d , 6 K the least cost for the whole structure. This may not dW2 necessarily be the iowest weight design. A, = t, d, =

Most structural texts sr~ggest a method of girder K

design in which some assumption is made as to the depth, usually from % , to I/,, of the girder length ( a rninimum of ? h 5 ) . Knowing the web depth, the wcb thickness is the11 found. This is kept above the value A .

't required for web area (A,-) to satisfy the shear forces and also to insure that the ratio K = d,/t, will be below the proper value.

Table 1 lists the AASHO (Bridge) limiting values of K == d,/t, for common materials, with or without transverse stiffeners. I 2. DESIGN APPROACH

It might he well to investigate thc efficient girder design on the basis of minimum weight. If done simply, it would offer a good guide or starting point in any design of a girder. An estimate of weight that is obtained I

quickly would allow the designer to deviate from the efficient depth to a more shallow girder when neces- s ay . He would then balance off the additional weight

Assume: dw = d, = db

FIG. 1 Girder description

TABLE 1-Limiting Ratios cf Web Depth to Thickness

d, - web depth . - = - web thickne3r AASHO (Bridgar)

I I I Low Ailoy Steel I I Mild Steci

A441 or Weldable A242

I A373, A36 46 000 pri 50,000 psi i 1 1 h e l d / yield

No tronrverre stiffenerr

K C 6 0 1 K - 5 2 K 5 53

(1.6.80) / i

Longitudinal stiffener with ironweire rfiffeneri

Therefore, the total girder area is- Also, the total area of the girder is-

2 S d,' d," A t = 2 A , + A , " = - - - m + X

d,"

Now differentiate with respect to the depth (d,) K

and set equal to zero: ... I A , ] . . . . . . . . . . . . . . . . . . . . . . . . . (4)

also

This indicates that the efficient girder has half its weight in the w& and half in the flanges. Based on steel weighing 3.4 lhs/linear ft/sq in. of section area, the efficient girder's weight is-

Figure 2 contains two curves showing the weights . (2) and depths of girders for a given set of requirements;

in this case a section modulr~s of S = 5,000 in." Curve '4 gives the weight (Wc, ibs/lin ft) and

depth (&, inches) of the girder for any given value of K.

These two values come from Formulas 2 and 5 :

Since 6.8 dWY and W, = ...

S d " TY K Af =---

d," G K These combi~le to form- 2 d," d ' - *-

3 K d , G K -1 . . . . . . . . . . . . . . . . . . . . . . . . (6)

. . . . . . . . . . . . . . . . . . . . . . . . . . ( 3 ) which is the weight of girder not including weight of

FIG. 2 Relationship of efficient girder weight and depth for given requirements (here, 5=5,000 in.").

Weight of ef ic ient

girder for d

different values of K = Z tW

min weght for mclxmurn value of I<:

W, = 9.80

70 80 90 100 110 120 130

Deplh of web ( d W j in .

stiffeners. It is seen that larger values of K result in lower

weight (Wt) and increased depth (d,?) of girder. Con- versely, lower val~ies of K will produce heavier and more sl-tallow girders. This represents the lowest weight design for any given value of K.

Assuming the weight of stiffeners will be 20% of the web waight, and since in the efficient girder, the web represents half of the girder weight, the stiffeners would increase the girder weight by lo%, or-

-\ , . * . , . . . . . . . . . . . . . . . , , , , ( 7 )

which is the weight of girder including weight of s t8 - eners.

Effect of Changing Dinlensions

In an efficient girder the depth of which is determined by Formula 2-

the weight decreases as the ratio (I<) increases; hence use as large a K ratio as is possibic (see Table 1 ). Once the flange area ( A f ) is determined, the actual profile

of the flangc (thicknms to width) has almost no .effect on the resulting girder weight (Wt).

Occnsionaily the girder depth may be restricted because of head room or some othcr reason. The shallow-depth wcb thrii innst he thickcr in order to make UP the wch area required for the shear forces; in this case, it may he possible to further increase the web thicl;~less, \,cry slightly, to arrive at 1/60 of its clear depth and thus eliminate thc transverse stiffeners. If this is thc case, the decision not to use stitfeners should be made at the start of the design rather than later. For example, See Figure 3.

Hcre on the left side, the efficient girder using stiffeners ( K = 170) \veighs 188 ibs/linear ft. Taking this same dcsign and incrrasing the web thickness to 1/60 of its dcpth to cliininate the stiffeners, would increase its weight to 328 Iibs/lincnr ft, or 1.74 times. On the other hand if the emcient depth is first determined using no stifimrrs ( K = HI), the weight is increased to only 243 ibs/linenr ft, or 1.29 times. In this particular case, the design which eliminated the stiffeners at the start (right-hand girder) weighs only 74% as much as the dcsign which eliminated the stiffeners after the dcpth was determined (center girder).

The graph in Figure 4 show-s the direct effcct of changing web depth. Changing the combination of flange diniensions, but using same depth of web (d,)

Percent of e f i c i e n t depth used (doid,)

FIG. 4 Effect of changing web depth on girder weight.

must he used. d,, c 1- + tf 2. For web thickncss, use 2

3. Check the resulting values for

T .I? . . to use valrws of t, and d , that will provide

the highcsf allowable valrre of I<. If resulting A , erjnals or excccds the given rqui rcd value, procecd to Stcp 4 of Method A; if not; jump to Step 3A of Method H.

4. Kow compute the web's moment 01 inertia:

5. Select a flango tliicklress and wmpirte the distance from the cntire section's neutral axis to the outor fiber ( c ) , and tlrcn coinputc c,: FIG. 5. Girder description.

3 = a , SUE

Efficient PBaiie Girders / 4.

6. With this, compute the section's total reqnired moment of inrrtia:

7. Now select a flange width from the following:

J Since:

and use the next larger corrvenicnt plate width for flange width ( b r ) .

8. Then c h e ~ k

i p -- 2 11~ tt cr2 and

I, = I, + 1, and

Tliis final value of section modulus (S) must equal or exceed the value initially stated as a requiroment to resist the bending moment.

overpls Design 08 Girder

If the xveb arm (A,) cornpted hack in Stop 3 does not equal or exceed the givcn required arno~urt; take these addition;rl steps before proceeding with Step 4 of Mrthod A.

3A. Calculate the web thickness (t,) and web depth (d,>,) from the required web area (A,T) and rrrpired depth-to-tliickness ratio ( K ) , wing the iollowing formulas:

and

3R. Usi~ig this its a glide, adjnst the thickness (L ) and drpth (d,, i of thr web plate to satisfy the ahove coiiditio~~s a r ~ d also the following:

> t, d, = A,"

which must equal or exceed the rcqnirrd value of A,v (= V/r); and

a.hich rnttst q n a l or bc l c ~ s than tlic maximum allowable \drw of K.

Ha\irrg s<,lccttd d, i t i d t,v, n,tum to Step 4 of Metlrod 4 and follow t h r o ~ ~ g h to completion (Step 8 ) .

Short-Cut iVomographs

The first nomograph, Figurt: 6, will quickly give tlir girdcr's cflicimt u r b deptl~ its wrll as its estimated wriglrt (lhs/lin f t )

On this r~ornograph: Line 1 =. r q u i r d section n~odrilus ( S ) I.,inr 2 - reqnired ratio of web (ltytln to web thick-

nrss ( K ) Linc 3 = (read:) rlficient web depth (d,) I h e 4 = required vatio of web &yth to web thick-

rrrss ( K ) Line 5 = (read:) estimated weight of girder (W,) Line 6 = (rrad: ) d1~1wable shear carried by web (V)

on the, basis of r = 11,000 psi (bridges)

l f the right-hmd line G shonld indicate an allowable shear value ( V ) for the efficient web which is lcss than the a(,tuaS value, thc girder design must he hascd on the shcar-carrying capacity of the web. This is done by going to the second nomograph, Figurt* 7:

Here: Line 1 = actrial shear value which ~nirst be carried

hy the usel.) (V) Line 2 = requii-cd vatio of web depth to web thick-

ness ( K ) Line 3 = (red) we17 thickness to be used (t,,.) Line 4 = reqnirtd ratio of wab depth to web thick-

ness (K) Lint: 5 = (mtd : ) wvb daptlr to 11c used (d,)

The weight of this slicar design may he estimated by the third noniograplr, Figure 8. Two valnes of weight are obtained; tlrc:c rnrlst be added together.

Ilrre, for first weight: Lint l a = rrqnircd section rnodr~lus ( S ) Lint %I web drptlr ( d ) Line 3 == (,-cad:) cstir~iated weight (W,)

For t l ~ c s t~mnd \wight: 1,inc. l b := shrnr to be c;~rriwl by w-el> (V) Line 2)) =: allo\vd~le shwr stress ( T )

1,irrc 3 := (rcad:) esti11n;rtcd weight (W,) The slim of thcsc two weights still does not inclnde

the weights of stifi'mers if required.

Problem 1

Design a hridge girder for the follo\ving loads:

Ivl 7~500 ft-kips

V -- 600 kips

For A36 steel, AASIlO Sec 1.6.75 (see Table 1) requires the K ratio of web depth to thickness (d,/t,) to be not more than K = 170 using transverse stiffeners.

Then:

- (7500) (12) --

(18 ksi)

- - (600) (11 ksi)

= 54.5 in.2

Following the suggested outline for designing an efficient girder:

or use an 1 l / l a u thick web, 11V deep

3. Check these proposcd dimensions:

= 160 < 170 O.K.

A, = t, d,

= (11/16) (110)

= 75.6 in.2 > 54.5 in.' O.K.

= 76,255 in.4

5. Let flange thickness be t, = 2":

= 16.65"

or use 17.0'' wide x 2" thick Range plates

8. Then, to find properties of the actual proposed section:

Then, to find the weight of this designed girder:

2 A, = 2(2")(17") = 68.0

A, = (11,/16")(110") = 75.6 - 143.6 in.'

.'. Wt = 488 Zbsllin f t of girder, on the basis of steel's weighing 3.4 lbs/lin ft/inl.' of cross section,

To show that this does result in the n~inimunl girder weight, nine other combinations have been figured, from a web depth of 70" up to 120", as shown by Cwe B in Figure 2. In the example just worked, the various dimensions were rounded off to the next

FIG. 8 Weight of Plate Girder When Design Is Governed by Sheor

size fraction based on available plate. The actual plate is increased to V = 1000 kips. This will illustrate the girder t:xample using a web depth of 110" weighed work to he done where shear ( V ) would govern the 488 lhs/ft, yet the efkient girder for this same depth design. should weigh 473 lbs/ft.

Four other combinations of flange Jimensions were Here: figured, using the same web depth (d, = 108.45"), V but there was little difference in girder weight. The A" = -i thinner and wider flanges result in a very slight rednction in weight. -

( 1000) - (11 ksi)

= 90.9 in.'

Consider the same girder in which the shear load Following the suggested outline:

Efficient Plate Girders /

In the previous problem, this led to a web 11/16" X 110"; however-

In this case the '%6" X 110" web plate has insufficient area to carry the shear load. So, switching to Method B:

or use a W-thick web plate.

or use a 124" deep web plde

3B. Check:

A, = t, d,

= (3/q)(1%)

= 93.0 in.' > 90.9 i a 2 OK

Now returning to the basic Method A outline:

5. Let flange thiekness be tt = 2":

= 12.65"

or use 13" wide x Y thick flange plates

8. Then, to find propertics of the actual proposed section:

Then, to find the weight of this designed plate girder:

4.2- 12 / Girder-Related

142.0 in."

WL = 462.8 lbs/lin f t of girder

Find the approximate web dimensions and weight for the same girder, using the nomographs, Figures 6, 7 and 8.

Given:

S = 5000 in."

d, K =- = 170 tw

read:

d = 108"

Given:

read:

Wt = 470 lbs/ft

and:

V = 750 kips allowable

Using an actual depth of 110" as in Figure 1 would increase this estimated weight to 483 lhs/ft as read on the nomograph. In Problem 1, the weight was computed to be 488 lbs/ft; this slight increase is due to the increase in web thickness from the required ,638" to the llext fraction, 11/16".

2nd Nomograph

If the shear value is increased to V = 1000 kips as in Problem 2, this exceeds the allowable value of 750 kips mad from the &st nomograph. Therefore, shear governs the design and the second nomograph must be used.

Given:

V = 1000 kips

read:

t, = ,725" or use Vi"

Given:

read:

d, = 126" or use 124"

Given:

S = 5000 in.Y

d = 124"

read:

Wt = P 275 lhs/ft

Given:

V = 1000 kips

T = 11,000 psi

read:

Wt = + 210 lbs/Ft Total = 485 lbs/ft

In Problem 2, the weight was computed to be 482.8 lbs/ft.

If the valuc of u,, resulting from the above formula is eqnal to the yield point of the steel in nni-axial tension (what is commonly called the yield strength, u r ) , it is assumed this conhination of stresses will just produce yielding in the miiterial. Hence, the nse of this formula will give some indication of the factor of safety against yielding.

(a) Cross-sections of test specimens

(b) Comporison: ultimote ond critical loads of

bending rests

FIG. 1 Eiiect of web thickness on ultimate carrying copocity of the girder.

Transverse intermediate stiffcners shall preferably be in pairs. They may be either single or double, and be plates or invertrd tees. When stiffcners are used on only one side of the web, they shall be welded to the compression fiange to give it proper support.

The nioment of inertia of the transverse stiffener shall not be less than-

I -= minimum required moment of inertia of stilf- cner, in."

where:

a, = required clear distance befween hansversc stiffeners, in.

d ' J = 2 j - . ~ - 2 0 = 5

a.

a, = ach~al dear distance between transverse stiffeners, in.

. . . . . . . . . . . . . . . (3)

d, = uninpporied d q t h of web plate between flanges, ID.

t, = web thickness, in.

When transverse stiffeners are in pairs, the moment of inertia shall he taken about the centerline of the weh plate. When single stiffeners are nsed, the moment of inertia shall be taken about the face in contact with the wcb plate.

The width of n plate stiffener shall not he less than 16 times its thickness, and not less than 2" plus 1/30 of the girder depth.

The distanct~ bctwcen transverse stiffeners shall not exceed-

1. 12 feet 2 the clear nnsupportcd depth of the web (d,)

where:

T = average unit shear stress in the web's cross- section at the point considered, psi

4. LONGITUDINAL STIFFENERS MASH 1.6.81 )

The longitudinal stiffener shall lie along a line 1/5 d,

la te Girders tor

(a) Longitudinol stiffeners on inside of girder

FIG. 2 Placing longitudinal stiffeners on outride of girder and transverse stiffeners inside saves fobricafing time.

/ Longitudinal stiffener

Longitudinal and

tionsverse stiffeners

do not inteisec,

from thc compression flange. Its moment of inelZia shall not be less than-

These stiffeners do not nwessarily have to bc continuous, but may be cut where they intersect transversc intermediate stiffeners if they lie on the same sidc of the web.

5. BEARING STIFFENERS

Transverse stiffeners shall I>F wed over the end bcarings or along the Icngth of tire girder wherc concentrated loads must he carried, and shall hc designed to transmit thc n:actions io the web. They shall extend as nearly as ixaeticahlc to ihr oi~ter edge of the flange, hut not to excwd 12tiilncs their thiclcness. (AASIIO 1.6.17)

Some ixidges have longitudinal stiffeners on the inside of the girders, otircrs orl the outside. If the longi- tuclinal stiiIrr~ers arc on the inside, along with the transverse stiffeners, it loaves the ontside of the girder smooth; Figure 2 (a ) . This, of course, means the iongi-

(b) Longitudinal stiffeners on outside of girder

tudinal stiffener mnst he cut into short lengths and then inserted betwccsr the transverse stiffeners. This results in inrreascd welding tirnc and production costs.

Some states havc used longitudi~riil stiffenci-s on the outside and transvrrsib on the insidc; Figure 2(b) . Tf~is method saves on fabricating time and aL~o allows the use of automatic welding trchniques to join the Iongihldinal stiffeners to thc girder web, thereby substantially incrrasing welding speed.

C OF STIFFENERS

AASIIO (2.10.32) will allow the welding of stiffeners or attachments transversc to a tension flange if the bending stress is 75% or less than the al1owal)le.

.4WS Bridge (225 c j will allow the welding of stiffeners or attachments transverse to a telrsion flanga if thc bending strrLss in the f h g e is held to within those of the fatigot. formulas ( I j, ( R ) , or (5) for the welding of atiachnrents hy fillet vmlds; sw Section 2.9, Fable 1.

Figure 3 illustrates the eflcct of transverse attachments wclded to a plate when tested from tcnsion to an cqual compression (I< = -I ) .* .~ -

"Fatigue 'Tests of Weliid Joints in Structural Steel Plates", Bull. 327, University of Illinois, 1941.

FIG. 3 Effect of transverse attachments on fatigue strength of member

Some engineers have felt this reduction in fatigue strength is due to the transverse fillet welds; however, it is caused by the abrupt change in section due to the attachment. It is believed these plates would have failed at about the same value and location if they had

machined out of solid plate without any welding. This same problem cxists in the machining of stepped shafts used in large high-speed tur lkes and similar equipment.

Figure 4 illustrates the effcct of welding transverse stiffeners to tension flanges.* Tests, again a t the Uni- versity of Illinois, were made from tension to zero tension in bending ( K = 0 ) and at 2 million cycles.

Eliminating the weld between the stiffener and the tension flange incrsased the fatigue strength of the beam. In addition, leaving the weld off the lower quarter portion of the web in the tension region gave a further increase in fatigue strength.

Later tests at the University of Illinois** took into consideration not only the bending stress in the flange, but also the resulting principal tensile stress in the wcb at critical locations, such as the termination of the

connecting fillet weld of the stiffener. See Figure 5. It was discovered that the fatigue failure in the

stiffener area did not necessarily occur at the point ol maximum bending stress of the beans. Failure stailed at the lower termination of the fillet weld con- rlecting ths stiffener to the web. When the bottom of thr stiflerrer was also welded to the tension flange, failure started at the toe of the fillet weld connecting the stiffesner to the beam flange. After the flange had failad, the crack wonld progrrss upward into the web. Ilerz, the failures usnally occurred in the maximum moment section of thq heilm.

This test indicated fairly good correlation when the results were considerod in terms of the principal tensile strcssis (including the effect of shear) rather than simply the bending stress. The 'angle of the fatigue failme in the web generally was found to be about

" "Flexural Strength of Steel Uenms", Bull. 377, University of Illinois, 1948.

** "Fatigue in Weldcd Beams and Girders" W. H. Munse & J. E. S t a h e y e r , Highway Research Board, Bull. 315, 1982, p 45.

min. _ K-*.- 0

2000,000 CYCLE5

INTERMEDIATE

I& 400 psi 26,600 psi.

WELDED m COMPREJSIOU R A N E E AND TO UPPER

JZ.700 psi.

FIG. 4 Effect of welded intermediate stiffener on tension flange.

safe Girders for

WE 'A" TYPE '8' TYDE P . TYPE I T T/Pt 'E' TYPE 'F.

(a) Details of various stiffener types

FIG. 5 Effect of stifiener type on fatigue strength of member.

(b) Sigma-n diagram for maximum principol tensile stress at failure section.

20% less than the computed angle of the principal strcss. AASHO Specifications (2.10.32) state that trans-

verse intermediate stiffeners shall fit sufficiently tight to exclude water after painting.

Some insprctors interpret a tight fit to he onc in which the s t i fhc r s must be forced into position. Many fabricators frel this is an unnecessary dcterrent since it takes extre time to force the edges of tlie flanges apart to allow the stiffeners to be inserted.

There err two gencra! methods of fitting these stiffeners to the plate girder (Fig. 6 ) :

1. Use a stiRener that does not fit too tight. Push it tightly against thc tension flange. \Vt,ld it to the girder web and to the compression flange.

With this method, tlie fitting of the stiffener will comply with the above AASHO spec.;; yet it is not welded to the tension flange, nor is it a problem to insert. An alternate mcthod is to-

2. Use a stiffener which is cut short about 1". Fit it against the compression flange and weld it to the web. If it is a single s t i fher , also weld it to the cam- pression flange:. It is not v d d e d to the tcnsinn flange. Experience indicates thc 1" gap at the lower tcnsion FIG. 6 Fit of stiffeners to girder.


flange will present no maintenance problem. Although this does not cornply with the above AASHO requirement, many girders for higl~way bridges are fitted with stiffeners in this manner.

Plate girder research at Lchigh University* has indicated the stiffener does not have to contact the tension flange to develop the ultimate capacity of the girder. They recommended the stiffeners be cut short a, described in the alternate method above (2). The distance between the lower and tension flange and the stiffener is set at 4 times the wcb thickness; see their recommcndations in Figure 7.

There is no clear-cut answer as to whether continuous or intermittent fillet welds should be used to attach the stilfencr to the web. The latest research at Illinois on stifIeners indicated that fatigue failurcs occurred at the terminations of fillet welds, regardless of whethrr they were continuous or intermittent. Natur- ally, a continuous weld \ d l have fewer tcnninations, hence fewer aaras for potential fatigue cracks.

Where lwge, intormittent fillet welds are specified, %" for example, roplacement with %" continuous fillet welds made by automatic welding equipnrent achieves a considerable saving in cost. Where small intermittent

*"Strength of Plntc Cirdcrs", Hrmio Thurlimm, AISC Proceed- ings 1958; "Plate Giriicr Rcsr:rrch", Konrad Resler & Bruno Thurlirnan, AISC Proceedings,, 1059.

fillet welds are specified, 'h" possibly, savings from the introduction of continuous welds and automatic equipment become qumtionable.

With thin, deep web plates, a smaller size weld may tcnd to reduce distortion. In this case, automatic welding would be of benefit, provided this substitution of continuous welds for intermittent welds does not increase weld length to any major extent.

7. FLANGE-TO-WEB WELDS

These welds hold the flanges to the web of the plate girder. They are located in areas of bending stresses and must transfer longitudinal shear forces between Ranges and web. Some restraining action may develop with thick flange plates, but any resulting transverse residual stress should not reduce the weld's load-caw- ing capacity. This bcing parallel loading, the actual contour or shapf: of the fillet weld is not as critical as long as the minimum throat dimension is maintained.

Shop practice today usually calls for submerrged- arc automatic welding equipment to make these welds. For the usual thickness of web plate, the two fillet welds per~etrate deeply within the web and intersect as in Figure 8(1>), giving complete fusion even though simple fillet \welds are called for, as in ( a ) . A few

one a two sided

FIG. 7 Summary of design recommendations relative to girder stiffeners

e l d e d Hare Girders @or

FIG. 8 Flange-to-web welds.

states recognize this perlctration and are now detailing this weld with cornplctr fusion. 'Tlris proves no problem on the rrormal web thicknas. In thc futurr, however, if the same detail is showrr on much thickcr web plates, the fabricator will have to use a double-bevel edge preparation to obtai~r the intersretion ( c ) , wen thongh detail ( d ) is sufkient.

It sho~dd not he necessary to detail groove welds for this ioiot from a dcsign standpoint. Selection of a groove T-joint design should be Ilased on a cost comparison with filkt wrlds. The groovid l'-joilit requires abont ?b the arnonn? of weld metal compared with fillet welds (assuming full-strength welds). However, the grooved joint has the extra cost of PI-eparing thi. double hevcl.

In respect to the physical perfonnaiice of cither tiit> fillet or the groovd T-joint design, tests liave been made, hy .4. Ncum:mrr, of these \velds nnder fatigue hending from 0 to tcnsion, K - 0, at 2 111illion cycles.*

FIG. 9 Both weld types showed same fatigue strength.

No ciifkrenec was iirdicat~cd for thr: fatigue strength of the beam using cither joint dcsign, with both types dernopstrntiilg a f:ttiguc strcugth iri the beam of 22,000 to 24,000 psi (hvirding strcss); Figure 9.

From a dcsign sta~xlpoin?, thm: welds may be quite small. Their achrd size is usually established by the minimum allowable leg size for the thickness of

For Vorious Plate Thicknesses (AWS)

THICKNESS O F THICKER M I N I M U M LEG SIZE PLATE T O BE JOINED / O F FILLET WELD*

THKU % inch over in. *IW" $5 in,

over y4 i n *hi" 1% in. Ovoi 1% in. thru 21,: in . Over 21/4 in. t h r u 6 in. I Over 6 in. 1

3 / 1 6 in. lh in. 5/16 in.

),'a in. '/> in. % in.

Need not the th i r kncs i of the i h i n n e i plotb - the fiangc plat(%. T;rblc 7 lists tile minimum size of fillets for various platc tliickuwses as established by rlM'S Sprdficntions. 1,cg sizc ilicri'ases to take care of thc fastt,r cooling rate and grisatc.r rcstrairlt that exists in thicker platcs.

On tliickcr plates. with rrniltiple pass wclcls, it is desirable to gel as nindr hwt input into the first pass as possible. This means 1iight:r ucldiiig currents and siower urlding spwds. L.ou--11ydrogcn olt:ctrodes are bettor'for manual wcldirrg in this work. 'The lmv-hydro- gm characteristics of a submerged-arc wclding deposit gives this welding mrthod ;I si~nilar advaiitagt:.

~~ - "Discussion at the Syinposium on Fatigue of Wuided Struc-

tiircs" The British WtMing Joonial, August, 1900.

/ Girder-Related

TABLE 3-Allowable Shear Forces O n Fillet Welds For Various Fatigue Loodings

100,000 600,000 1 2,000,000 CYCLES 1 CYCLES I CYCLES

8800 o f = -- lb/in. K K

i - - 2 2

but rhoil not exceed f = 8.800 o (€60 or SAW i welds) f = 10.400 o (E70 or SAW 2 welds1

-- -- Where.

MiNlMUM K = (sheor (V) opplied to girder1 MAXIMUM

w = leg size of fiile,

Determination of Combined Stress

mbined stresses in a fillet weld between the and flanges is seldom considered for the

following reasons: 1. The maximum bending strcss for a simply sup-

ported girder docs not occur at the same region as the maximum shear force. For a continuous girder, however, the ncgative moment and shear force are high in the same region near the support, and perhaps the combined forces in this fillet weld should be checked.

2. The maximum bending stress in the outer surface of flange is always designed for something less than the allowable (Bridge code = 18,000 psi). The weld lies inside of the flange and is stressed at a lower value. Ex: If the weld is in an area of 15,000 psi bending stress, this additional normal stress would reduce, theoretically, the allowable shear force for the weld from f = 8800 w to f = 7070 w, or about 80% of what it would be if just horizontal shear were considered (E60 or SAW-1 welds).

3. Usually these welds must be larger than design requirements because of the minimum weld size specifications listed above.

Nevertheless, if desirable to determine the com- binell stresses, it can be theoretically shown that the

axial normal stress from the bending, applied to the fillet weld, would increase the maxin~um shear stress applied to the tlrroat. For a given applied normal stress (u), the resulting ~naximwn valuc for the allowable force ( f ) which may be applied to the fillet weld of a given leg size (a) under parallel loading is expressed by the formula:-

( E N or S.4W-1 welds)

(I370 or SAW2 welds)

This formulatio~~ still pennits the maximum shear stress ren~lting from the combined shear stresses to be held within thc allo\vable of T = 12,400 psi ( I 3 0 or SAW-1 welds) or 14,700 psi (E70 or SAW-2 welds).

Allowable Fatigue Strength

Table 3 contains tho formulas for establishing the albwahle shear foucc that may hc applied to fillet welds under various conditions of fatiguc loading.

8. FLANGE BUTT JOINTS

In nearly all welded plate girdms, the flange is a single plate. These plates are stcpped down as less area is required. A smooth transition is made between the two, by reducing either the thickness or width of the larger flange to comqxmd to that of the smaller.

When this tra~xition is rnade in thickness, the end of the larger flange is hevelcd by a flame-cutting torch. There is a practical limit to the angle of bevel, but this slope, according to AWS Bridge Specifications, should not be greater than 1" in 2l%" (an angle of 23"). On the Calcasieu River bridge, this slope was decreased to about 1" in 6" (an angle of about 9%"). Transitions also e m be made by varying the surface contour of

FIG. 10 Plate bevels made by flame cutting.

(a) Beveling end of flange (b) Beveling end of flange plate for groove butt plate for tronsition in held thickness.

Fatigue Strengths in Suit l o i n f s

1 100,000 1 600,000 2,000,WO CYCLES CYCLES I CYCLES

BUTT WELD IN TENSION 1 -- - .7 K i - 8 K

(not to exceed 18.000 psi1

BUTT WELD IN COMPRESSION inor to exceed p1

(a) Straight-line transition in width Where: (p) is the allawobie ian;piciiivi itrerr far the

member involved.

BUTT MINIMUM K = - (bending stress or bending moment1

(WELD MAXIMUM

(b) Curved transition in width

rather than in thickrsess. This advantage undoubtedly would bt: greater if the transition in width wert: made more gradual; however, both methods are sound and acceptzible. Fatigut, values for these transitions are found in Figure 12.

Allawabie Fat igue Strengths FIG. 11 Method of transition in width affects weld's allowable fatigue values. Croove wt~lds in hntt joints of equal platc thiek-

ness. if the rcinforcmnent is finished smooth with the

the groove welds. The usrial method of flame rutting a bevel in the

preparation of a wcldcd joint is to cnt down through the surfaw of the plate at the proper angle. lkcause of the wide angle needed for this transition in thickness, it is often better to flame-cut back from the edge of the plate after the flange platc has been cut to length. Scc Figure 10.

When the transition is made in width, the end of the wider flange is cnt back at an angle, again with the flame-cutting torch. There is no prohlcm in cntting in this matn~er, and any slope rnay be used; many tinrcs 1 in 12, hot usually a maxiinom slope of 1 in 4. Often this tapar m;ry extend back for several feet.

Gent~ally, it is fctt that the straight-line transition in width is sufieient, ;md in the case crf fatigue loading the allowable fatigue va1ut.s for butt groove welds in tension or compressior~ are used. See Figure 11. If a curve tangent to thc edgr of the rtarrow flange at the point of twinination is used, it may be assumed the flanges h a w eqnal widths. Thus, for equal plate thicknesses and with the \veld reinforeern::nt removed, the butt groove meld may he assigned the same allo\vable strcss as the tiangc plat<?, nntler :my condition of fatigue loading.

Studirs at the Utiivcrsity of Illinois have intlicatcd a slight advantage in rnaking a transition in width

surface, rnay hc ;rllowcd the same fatigue strength under any type of fatigne loading as the base metal. For plates of nnrrpal thickness where the transition slope is not grcata than 1 in W 2 , the formulas found in Table 4 may bc used.

transition in thickness I I

FIG. 12 Making a transition in flange width rother than thickness has a slight advantage in fatigue strength.

4.3-10 / Girder-Reloted Design

FIG. 13-Summary of Bridge Plate-Girder Specifications AWS & AASHO

Neutroi axis of girder

ARV OF BRIDGE SPECIFlCATlO

In order to aid thc bridge rrrgineer in designing a welded plate girder, the pertinent .4WS and AASHO Specifications liavt; been brought together into a single drawing, Figiire 13, and related text, below. The corresponding numbers are inclrided so the engineer may refer back to the original speciiicntions.

This summary can also serve as a checkoff list, so that nothing will he inadvertently omitted.

The following requirements apply: 1. Extend bearing stinener as near as practical to

outer edge of flange. Proportion for hearing. Welds to web must transmit end reaction. (1.6.79)

2. Width of bearing stiffener mist not exceed 12 times stiffener thicliness ( 1.6.17).

3. Space (horizontal) longit~idinal stiffener Si, ~ 1 , ~ from compression Range (1.6.81).

4. Dimension longitudinal stiiicncr for required moment of inertia, using-

about edge of stiffencr (1.6.81). 5 Mill or grind bcnring stiffener ends For even

bearing to iiange. StifFcner may be welded without rnilling to comprrssion flange, or to tcnsion flange if less than 75% terrsile strength (2.10.32).

6. Do not wcld transverse intermediate stiffener to tension flange if stressed over 75% (2.10.32) or unless stress is within that of fatiguc formulas 1, 3 or 5 of Art. 228 ( 2 2 5 ~ ) .

7. Fit intermediate stitYcner tight to flnnges to excludc water aftm painting (2.10.32).

8. Consider placing intermtdiatt: stiffeners at points of conccntrated load to transmit reactions to the web (1.6.80).

9. Use transverse intermediate s t i f h e r preferably in pairs on opposite sides of web. If only one side of web, wcld ends to compression flange and intermittent weld to weh (1.6.80, 22%).

10. The minimum moment of inertia of transverse intermediate stinener shall be (1.6.80)-

where:

d - .- actual , distance between stiffeners, in.

d, = required distance bctween stiifeners, in

d , = w-eb depth, in.

t, = web thickness, in.

T = average shear stress in web

11. Girder ffange shall not extend beyond 12 times its thickness (1.6.17).

12. Ilistance betwem stiffeners must not exceed

12', d,, or l ~ o o O (1.6.80) \F

T '

13. All shop groove butt welds in flange and web plates shall be made before final litting and welding into girder (404f).

V a y 14. Web-to-flange lillet weld leg size = 17,600 1

15. Width of tr'msverse intermediate stiffeners must not exceed 16 times stiffmcr thickness, or 2" plus K O of girder depth.

Also, deflection due to live load plus impact shall not exceed 1/800 of the span; for cantilever arms, 1/300 of the span (1.6.10).

lute Girders for - 8 8

MINIMUM WEB THICKNESS (twl

i I i f long. ond tiani. stiffeners / t , ~ = - - dil / tr = dSv I tr = -- dx

340 290 1 280

Also. ratio oi depth to length of span shall prefcr- in the above t a l h for the more coiilrnolr steels. ably not be less than :;is; for lowor depth the saction shall be incrcxrscd so that the maximum dt:flection will

ENSlONAh TOh

not 1)e grcatcr than if this ratio llad not b w n cxceeded Tho dimensional tolcrmces ill Figurc 14 have been set ( 1.6.11). lip for welded plate girdcrs by the AWS Bridge Speci-

Also, wrh thiekr~css shall meet requirements given fications.

FIG. 14-Maximum Dimensional Tolerances AWS 407

dapthr up to %'inel.

= i " Oerio,ion F r m Flotncrr of Gird" Web in a b q i h

depths wrr 3be+O 72" iml. ' Between Stiffeners a a h g t h Eouol to dmths over 72" + C - & * Depth oC Girder

Fignre 15 illustratt:~ several types of diaphragms used, and rcliresent the extremes in designs and fabrication. Diaphragm ( a ) , although so simple in design that no shop welding is rqnired, must be fitted and welded in the field. Diaphragm ( h ) , although mnch more complicated, may he mass-produced in the shop: The anglcs are shcared to length; and the plates are shcared and pnnched. Thcse are placed into a simple fixture and welded together at low cost. Thc field crection is simpler, since the ciiaplu~~gms are put into position, held by an ervction bolt, and then weldcd into place.

. COVER PLATES

Using A-441 sted (previonsly A - a ? ) , it may he ad- Yantngeous in some cascs to use two plates, a flange plate and a covcr plate, to make np the flange. This will pcrmit use of thinner plates and take advantage of the higher allo\n~~ble stresses. This stcd has the following allowable tension in mcmbers subject to bending:

Many methods have bcrn suggested for twinination of cover plates. Thc existence of at lcast four conditions which affect this makes it irnpossiblc to recommend one specific covrr plate m d which will hcst meet all conditions.

First, the tensile forces, assnmed to be uniformly distributed across the width of the cover plate, sllould be transferred simply and directly into the corresponding flange of the rolled beam withoi~t cansiug any stress concentmiion in the beam flange. In general, a large tmnsversc fillet wrltl across the end of the cover plate dors this in tlv, simplest manner.

Second, there must bc a very gradual change in the beam sertion at the mid of the cover plate, in order to develop a similar gradual change in bending stress of the beam. Any abrupt change in beam section

THICKNESS

FIG. 15 Diaphragms used in modern bridges: (a) angles cut to length and dropped into place; (b) Shop welded diaphragm, field welded to girder stiffener; (c) angler ottoched to siiffeners; and (d) channel welded to web ond stiffeners.

ALLOWABLE

%" and under i 27.000 psi

over ?/," to Ilh" 24.000 psi j over 1 % " to 4" 22.000 psi

elded Plate Girders for Bridges / 4.3-1

FIG. 16 Cover plates extending beyond width of beam flange.

will rcducr the bcam's fatigue strength. This would tend to favor a gradual tapered w-idth ithat the end of the cover plate.

Third, some caution slhould he txerciscd relative to terminating the cowr plate in the narrow zone of the flange that is in direct line of the beam web. This is a rigid portion with little chance for localizrd yielding to pnwmt the build-up of possible high stress concentration.

[:ntrrilz, the selectt.d joint should be rconomically practical to make and answer functional rtrquircments. For cxample:

1. Continuons welds may be needed to provide a positivc seal and prevent moisturc from entering underneath the plate and causing connection deterior- ation.

2. Ilinimum appcai-ai-icc stanrlnrds may eliminate solno joint designs.

Early fatigur tosting at the University of Illinois* on rolled lwams \\-it11 covrr platcs indicatcd that:

- 8ulietin No. 377

1 . In geiwral, continnous fillet welds were better than intermittent fillet welds for joining cover plates to the beam Aange.

2. On covar plates extending beyond the width of the heam flangr and conncctcd with longitudinal ,xij" continuous fillet welds, adding a "/,, fillet weld across the end of the cover plate produced a slight increase in fatigue strength (from 8900 psi to 9300 psi at 2 million cycles). Omitting thc welds for a distance at each corwr of the cover plate increased this valnc up to 11,000 psi; see Figure 16

Thc intersection of the longiturlil~al and transverse fillet welds conld present a point of wrakness if not properly made. This "cross-over" usually results in a very shallow concave weld. By eliminating this weld for 1" back from cach comer, the fatigue strength is incrcased. This does not apply if the cover plate lies within the brain flange, since the weld does not have to " C ~ ~ I S S O V ~ . " . * Bid1 No. 377, J a n 1'348.

FIG. 17 Cover plates lying within width of beam flange.

I / , loo

no t e h made w i t h the : r a n s v e r ~ e fillet w t l d l e f t off

Un iv~ rs i t y of nl inois - Bullet in No. 377

FIG. 18 Effect of cover plate terrnin- aiion on fatigue strength. Calculations based on 4" x %" cover plate and 1/4" filiei weld.

3. For cover plates lying witl-rin tho width of thc bmm flangv, incrraseil fillet i \ d d sizt across tiic end of the covrr p l n i ~ pr(x111cd o gradual increase in fatigut. strength. h ";,;" fillc~t weld iiad n strength of "3100 psi at 2 millioii cycles. a :ib" fillet weld 11,000 psi, and a 3/h" X 1'' fillet weld tip to 12.600 psi. This piilrticular size of (wvcr plate \ms not testid with the transverse fillet \I-ild omittrd; scc Figriri. 17.

Tiir latmt work reportcd at thc University of Floi-ids on stcady 10:rding of 18'' WF XI# 1)eoms with 5" "s" covcr p1:ites showcd that th(, beam flange within the. wvrr-plated I-egion was stressed Iouw when a ad' fillet weld W;IS pIiiv(id acwss the end of the covcr plat? as coinp;u-cd to that wit11 no tmnsvarse \veld. 'i'hc trarrsvorsc wt~ld nlso prod~rccd a more uniform distribution of s t r ~ s s acrnss tllc covcr pliitc as \ v ~ l l as the ],cam Aairgc, and dlowed tlic platc to pick up its share of tlic, 11mm lorcv in a shorter distance However, all of these factors occlir within the cover-plated ragion of grcatrr stvtion modulus and lower hcnding stress, so this is not vcry scrions.

What is inore important is thc effect the transverse weld and shape of tlrc cover plate's end has on thr s t x s i i l ~ J I C I I C ~ I I ~ flange adjacent to where the covczr plate is nttaehed. This is the region of lower section modol~is and higher bending strcss and is much more critic;rl than any regirnl within the cover plate.

The drawing, Figure, 18, illristratcs variations of cover plate tcrnrin:~tiorts.* 7 ' 1 1 ~ data stiinlnarizes recent tests on t h fatigiic strciigth of l~rains with partial cover plates. mndi~ctid nt tlrr i!nivcmity of illiirois. Although llle comnioll inr~tllod of tcrrniliatirig the cover plate dircctly across thr Hmgc wit11 a transverse fillet weld is satisfiicton, and ;rcceptable hy the AWS Bridge Specifications, this data worild sccm to indicate that tapering thc end of tire cover platc and eliminating transverse welds across the end slightly increases the fatigue strength.

~

" "Fatigue in Welded Beams and Girtleis", W. Ii. Mume and 1. C. Sta lheyer , lfighway Rescarch Board, Bull. 315, 1962, p. 45.

lare Girders for ridges / 43-15

FIG. 19 Effect of transverse fillet weld size on fatigue strength.

higher s t ress conccn~ration ,n beam flange w i t h smaller transverse f i l l e t weld

It should be noted that a small 'A'' fillet weld was used across the end of the 'h" thick cover plate. The results might have been different if a larger transverse weld had heen used. Most states require continuous welds on cover plates and across their ends, thereby limiting the selection to termination types u or b. Since the data indicates that tapering has little effect, final selection between o or b would have to h e made on the basis of some other factor such as appearance, or lower dead weight.

In summary, it would appear that the short section of the transverse weld across the end of the cover plate directly over tha web of the beam ( I ) is restrained and ( 2 ) wlien tested under severe fatigue loading may reduce the fatigue strength of the connection unless it is made large. A large transverse fillet weld, especially in this central section, would more uniformly transfer this force through the surface of the beam Aange into the end of the cover plate. See Figure 19.

Summary 06 Cover Plate Speciticationr (AWS Art. 225)

I l i e 4WS Bridge Specifications limit the thickness of cover plates to I'h times the thickness of the Aange to which it is attached (225 e 1).

For partial-length cover plates, their end shall extend beyond the "theoretical e n d (theoretical cut- off point) which is determined by the allowable stresses from fatigue formulas ( I ) , ( 3 ) , or ( 5 ) of Section 2.9, Table 1.

The ends of thc cover plate shall extend beyond this "theoretical end" a sufficient distance to allow "terminal development" (ti-ansfer of cover plate bending force into the beam aange) by either of the following two methods:

A. With square ends and a continuous transverse

cflangc. of beam

fillet weld across the and and along both edges of the cover plate, the minimum tenninal devrlopment length measnred from the actual end of the cover plate to the tlicoretical m d or cut-off point shall be 1% times the width of the cover plate.

B. With f apwcd cuds having no transverse wcld across the end but welds along both tapered edges, tapered heyorid the terminal rnd to a width not greater than ?6 the width, but not ICSS than 3", the tennilla1 development length sllall be 2 times the width of the cover platit.

Nonnally the inner end of the tcrminal development lerigth will lir :it the theori:ticrtl cut-off point; see Figun: 9.0, ( A ) and ( R ) . However, the cover plate may be extended farther so that tlie distance between the actual knd the theon:tical cut-off point exceeds the requircd t t~minal developrrlent length. In tlus case only the r~rjnired tci-minnl development length shown in ( A ) and ( 8 ) shall be used for the length of connecting weld when determining weld size, rather than the actual length hctween the actual and theoretical cut-off point; see (A') and ( R ' ) .

Fillet welds bctween terminal de\&p~nents along the cover plated length, shdl be continuous and be designed to transfer the horizontal shear forces:

- (for mch weld, there are 2 welds along the edge of the cover plate)

Fillet welds within the terminal development zone (between the inner crid of the terminal development and the actual end of tbe covcr plate) shall be continnous and be dcsigncd to trnnsfer the cover plzte portion of the bending force in the beam at the inner

-16 / Girder-Related Deri

teirn,nol development i f

beyond cut-off point

Momenf d i o g ~ m I I

Theoreticol cut-off point %

I , I

Cover plated beam 1 f = k Y 2 1 M, Y

I End weld: F = - 1 I I

3 FIG. 20 Relationship of terminal develop- & c,,,~ p ! I I I IAi

poinis. rv,, a y

,- End weld: F = --7----

C " -- - -

.j J ment to weld size. Required terminal

I

end of the terminal development length (usually the (0) theoretical cut-off point):

-1 , . . . . . . . . . . . ..... . . . . . . . . . . . . (8) Cut-0ff "=ner end of terminal development

- - M Z ~ Y

M y - I u = ---

I (A')

. . . . . . . . . . . . . . . . . . . . . . . . . . ( 0 ) Inner end of termtnol develo~ment

, ,

where:

V = vertical shear at section of beam under consideration

a -- area of cover plate connected by the 2 fillet welds

y = distance between C. 6. of cover plate and the N.A. of the total section

I = moment of incrtia of the total section

MI = moment applied to beam at the section of the theoretical cut-off point

Ma = moment applied to bean at the section of the inner end of the tem~inal development

The allowable to be used for these fillet welds would come from formulas ( lo ) , (14), or (18) of Table 1, Section 2.9, and shall conform to the minimum

development length (A and 0) is used rather thon actual length (A' and B') Clih W-4

Cut-off end of term~nol development beiween actual and theoretical cut-off . ,, %, A ,

W Cover R i I (0'1

Cut-off point Inner end of terminol development

fillet weld size of Table 2. AASHO (1.6.74) specifies that the length of any

cover plate added to a rolled beam shall not be less than-

(2d + 3 ) feet

whrre

d = depth of beam (feet)

It has been pointed out* that the sloping bottom flange of the parabolic haunch has a vertical componcnt of its compressive force and this will reduce the shear stress (r',.) in the girder web in this region. In addiiion, the concave compression flange produces a radial compressive stress ( u ? ) in the web depending on the radius of curvature of the flange.

In contrast, the fish belly haunch provides no appreciable reduction in shear in the critical portion of the wcb near the support. This is because the slope of the bottom fiange is small in that area. Also, the convex compressive flange produces a radial tensile stress (u,) in the web, w-hich is greater than the radial compressive stress in the parabolic haunch. This is because of the sharper curvature of the fish belly haunch.

I? is seen by observation of the Huber-Mises formula that both of these factors will result in the yield criterion (we,) having a lower value in the ease of the parabolic haunch. This result con~pared with the yield strength of the steel (in uniaxial tension) would indicate a higher factor safety.

(Huber-Mises Formula) uer = d ur2 - u, u). + u? + 37,y2

Haunched girders do not present much increase in cost for welded construction for longer spans. The web plates are normally trimmed by Aame cutting, so that a gradual curve would add little to the cost. In most cases the curved flange plates can be added without prior forming; the flat Aange plates are simply pulled into place against the curved web. Although the bansverse stiffeners u~ould vary in length, this should be no problem. The flange can still be automatically fillet welded to the web by placing the web in the horizontal position. The portable automatic welder would then ride against the curved flange.

* "Design of the Bridge Over the Quinnipiac River" by Roman Wolchuk.

FORCE VALUE

The horizontal force (F,,) in the sloping flange is equal to the bending moment at that section divided by the vertical distance between the two flanges:

Or, this force may be found by multiplying the flange area by the bending stress in the flange using the stictiol~ modulus of the girder. This method will produce a more accurate value.

From this value, the actual force in the Aange (F,) may be found, as well as the vertical componcnt (F,) of this force:

2 - Fh F ---- - and

cos B d cos B

M F, = Fh tan 6 = - d tan 0

This vertical componcnt (F,) acting along with the shear force in the web resists the external shear ( V ) at this section.

Modified shear is the resulting shear force in the web after the vertical component of thc flange force (F,) is substracted or added, depending upon whether it acts in the same direction or opposite direction as the shear in the web.

Fish belly Haunch Parabolic Haunch

FIGURE 1

Resistance of web

FIGURE 2

eslstance o f bottom Fv = Fh tan B flange due to i ts

vertical component of tensile force

Simply Supported Girder Staoighf os Curred

See Figure 2. Here the external shear is-

ontinuous Parabolic Hounched Girder Sce Figure 3.

Here the external shear is-

M M V = A, rv + - tan 0 V = A. rw + - tan B

d d

and the niodified shear is- and the modified shear is-

M = V - - t a n 0 M

d = V - - tan 0 d

In this case the vertical component is subtracted In this case the vertical component is subtracted from the web shear. from the web shear.

Resistance of bottom

f cornprerrive force

FIGURE 3

FIGURE 4

FIGURE 5

FIGURE 4

I

------+ 4 Resistonce of web

due to its shear

Fish Belly liaunch Parabolic Haunch

See Figure 4.

Here the extend shear is-

M V = Aw T~ - - tan B d

and the modiIied shear is-

In this case the vertical component is add& to the web shear.

osatinuous Fish

See Figure 5.

Mere the cxternal shear is-

In this case the flange force has no vertical component; hence, there is no reduction of shear in the web.

Check the haunched girder section (a t poini of support) shown in Figure 7, to detennine the difference

between the fish belly haunch and the parabolic haunch in the area of the compression 5ange near the support.

See Figure 6.

Conditions include the following:

Use of A431 steel

M = 55,000 ft-kips

V = 1200 kips

I, = 3,979,000 in.'

FIGURE 7

Analysis of Porobolic Haunch

aocrage bending stress i n louer flange

= 21,150 psi compressini~

Range forces

F, = c* Af

= (21,150)(25/8 x 36)

= 2,000 kips

F, = F,, Van B

= (2000) (.l763)

= 353 kips

F,, F = cos B

1 2030 kips

s lzar stress in web

Siiice the external shear is-

V = A,,. 7," + F, or

V - F, Tw z

A"?

stress in U:I& ut lower jfli~nge (it support

FIGURE 9

- (55,000 X 12)(126) .- - - - p~ ~~~~

(0,979;000)

= 20,900 psi, eompressio~~

These stresses in Figure 10. Irft-]land side, must now be rotated 10" to line 1113 with the sloping ilange in order that the radial cornpressive stress may be added. This is shown on the right-hand side of Figure 10. '%is may 11e analyzed by one of two methods:

I. Graphically, using Molrr's circle of stress: (Fig. 11) a ) Dmw thc gi\,en st]-cssrs (w,', u,', and 7') at the

two points (a') nrid (b ' ) h ) Constrni:t a circlc thro~igh these two points c ) Rotate clockwise ilirongli an angle o f 20 or 10" d ) Read the ncw stresses (c,, u,, and 7 )

2. Analytically; woi-k is 1)rrforrncd as follows:

0 = -

FIGURE 11

sin p - ,0886

cos p = ,9961

7 = m sin /3 = (11,540) (.0886)

= 1020 psi

n == m cos /3 = ( 11,540) (.9961)

= 11,500 psi

o ; = k + n

= (10,450) + (11,500)

= 21,950 psi, compression

v 7 = k - n

= (10,450) - (11,500)

= 1050 psi, tension

radial force of l o o m compression @nge againat w e b

FIGURE 12

= 846 ibs/linear in.

resultant radial cornpresshjc stress in uocb

This produccs the final sircss condition o f :

d-Y U, = - 21,950 psi

FIGURE 13

critical stress

Using the IIuber-Miscs formula:

,--~ ~~

ucr,, = V urZ - 0; O; -t wTZ + 3 T~~~

. . -- . . - . = \ (-21,Q50)2-(-21,050)(-180)+(-180)' +3(1020)Z

= 29,000 psi --

This results in an indicated factor of safety against y~elding of-

Analysis of Fish

NOW wing the same load conditions on t l ~ c fish belly hannch with the same web and flange dimensions:

FIGURE 14

At this point: crx = cr,, & F, = Fh

stress in weh or lower flange from bending moment

= 20,900 psi, compression

average stress in lotoer ftange from bending moment

= 21,150 psi

force in lower flange from bending moment

F, = Uf Af

= (21,150)(2% '/a 36)

= 2000 kips

radial tensile force of lower compression flange against web

restiltur~t radio1 trnsile stress in web

r; 2420 psi

6930 psi

combining strcssrs to f t ld fhi, critical dress

Using tlic IIuhi-r-Lliscs formula:

ridge Plate Girders

This rcs~ilts in an iidicatcd factor of safety against yiolding of-

F.S. =- u, IT, r

I t is apparrnt fmm this that tha paxii1,olic haunch lins a sligl~tly lowcl. criticirl stress and, ihiwforr, a slightly 11ighi.r fiwtor of sixfcty.

3. WELDS CONNECTING SLOPING FLANGE TO WEB

f,, f __ . . ~~~~

cos 8

but the distance dong this s lqw for I W ~ l~orizoni~il inch is-

i" - - cos H

s o that t11c s11mr f ~ ) r w on th i~ wt,ld iilwrg this sloping Hang(, is obt;iiried froin i h ~ , :ii)ovr: fonnrilii for the lrori- zontnl flange, using the rnoiliiird v;rlue of \":

Erection view of New York State Thruway bridge shows haunched girders. Siraight- ness and true camber of the lower fianges are apparent. Note veriicoi stiffeners and suspended (235') span bearing suriaces at girder junctions.

Portion of 295' span of bridge on Connecticut Turnpike being settled onto supporting piers. Note continuous parabolic haunched girder construction.

1. RECENT PROJECTS

Today, it is accepted practice to design and fabricate plate girders with horizontal curves when necessary. Several such bridges or freeway overpasses have been built within the past several years.

A series of 4 lines of curved welded plate girders with 90' spans are a part of the Pasadena-Golden State Freeway's interchange in the Los Angeles area, Figure 1. These have a curve radius of 400'. They were fabricated in Kaiser Steel's plant at Montrhello.

e One of Milwaukee's new expressways has a section of 4 continuous spans with n total lengtli of 345' in which tlie two orrtcr girders have a 9' horizontal curve and the 2 inner girders are straight.

Bristol Steel & Iron Works, Bristol, Tennessee, rt:cently fabricated several curved girders for the South- west Freeway-Inner Loop in Washington, D. C.

2. DESIGN AND FABRICATION

Although there are torsional stresses within the curved girder, usually the degree of curvature is not overly high and these additional stresses arc- offset by the diaphragms connecting the girders. The number of diaphragms has occasionally been increased for this reason, and sometimes the allowable stresses have been reduced sligl~tly.

FIG. 1 Welded plate girders, having a 400' radius of curvature, dominate the interest in Los Angeles interchonge of Pasadena-Golden Stale Freeway. Curving girders permit economies in deck system by keeping overhangs uniform from end to end of curve.

Curved flange plates are laid out by offsets and flame cut from plate. By cutting both edges at thc samc time, there is no bowing from any unbalanced shrinkage tBect of the flame cutting. The web plates do not have to he prcfonned, usually being rasily pulled into alignment along the ct.nterline of the flanges.

Caution must he ustad in placing attaching plates for thr diaphragms to the webs and flanges. The proper angle for these plates may vary along the length of the girder. Shear attachments are added mainly to accomplish composite action between the concrete dcck and steel girder, and thereby increase torsional rigidity. During erection, a pair of curved girders is usually attached togethcr by moans of the dinpluagms and then hoisted into position as a unit.


FIG. 2 Bridge plate girders being weld fabricated. With flanges flame-cuf on a curve, weight of the rolled web is utilized in making i t conform to desired radius.

FIG. 3 A two-span continuous box girder and curved ramp construction provided the answer to space iimitotions in reaching elevated parking area at busy New York terminal complex. Smooth, clean lines, without outside stiffeners, demonstrate oesthetic possibilities inherent in welded design.

The use of tapercd girders has hecome widespread, especially in the frarning of roofs ovrr large ;ireas where it is desirable to minimize ihe number of interior colnmns or to clirniriatc them ;iltogelhcr. They permit placing maximum girdrr depth whm: it is needed, while rpducing tho dcpih consiclrrably ;it points whcrr it is not necdcd.

Tapred girders are fahricatcd either 1) by welding two flange piates to a t;ipcmd \vch plate, or 2 ) by cutting a rolled WE' b u m kmgthwisc along its wcb at an angle, tnrning onn half r d for md2 arid then wt:lding the two h;ilm>s back togct1tt.r again along tila web. Sea Figure 1..

Gtlniber can he built into the tapend girder when required. Wlien thc girder is made from WF beams, each half is clamped into the propcr canher during asscmhly. Then the h i t joint dong the web is groove welded while the girder is held in this shape. Sincr the weld along the 1)earn web lies along the nentral axis, no bcnding or distortion will result from welding, and the girder nil1 retain the shape in wltich it is held (luring wtlding.

When the girder is made of two h n g e plates and a tapered web, the proper caniber can ?it: ohpained by simply ciitting thr wel, to the p q w r wmbrr outline. The flange plat<,s during nssombly are then pulled tightly against the web, into the proper camlier. The four flllot welds joining the flanges to the web are l>alanced about the ncuiral axis of the girder and as a result there shodd he no distortion p r o ? h n .

Application of Tapered

When the tapered girders are used with the sloping flange at the top, their t a p r in both dircetions from the ridge will provide t l ~ c slo:,e needed for drainage. By varying the depth ai the ends of successive girders, the deck can bc canted to drain tow:lrd roof boxes in thc valleys betwecn adjacent galikd spans and at flank- ing parapet walls.

For flat roofs, the girders are inverted, with their tapercd flange down. Thcre art: inany combinations of roof framing systcins possible. For example, on a three-

slxm dc*sigil, the central span can use the tapered flange lip, forming thcb slop!: of the roof; the two ndjaccnt spans usc the taperrd liangc rlo\vn to provide a flat roof, hnt tiltrd to in. t l ~ swn<. slope as the cmrtml swtior~.

Th? pro1)lrnl of 1ntt.r;il srrpport for the top ?om- prisioii Wnng~s of tapcrrd girders is 110 different than with other lirnms and gird:,rs. C~~nrral ly the roof deck is s:rfficit?iitly rigid to function as a di:ipl~ragm, ;md it's only neetxary to attach the deck to the top flange. Tl~ci-e's appnrcntly no advantage in clrsigning with a rodticcd stross :illow:~blc, in aieord:mce with AISG Foi-inol:is 4 or 5, in order to pwinit a greater distance between bracing points ;kt thc top ilange.

Whmc iapcred girdrrs are critical, Section 5.11 on Rigid Fr;nn<> Kriccs g o c ~ into more detail rclative to stresstss (elastic design).

Bcca~lsc of the rrduccd dcptli at the ends of thi.

FIGURE I

eided Structures

Required depth, Required depth,

(a) Conventional beam (b) Tapered girder

FIGURE 2

Curve of required section modulus [S) has same shape as moment diagram for uniform load on simply supported beam

Moment d i a g ~

(a) Conventional beam (b) Tapered girder

FIGURE 3

tap(:red girders, their connection to supporting colum~ls may offer little resistance to horizontal forces. For this rcason, sonre knce braces may l x required ur~less the roof deck or a positive system of bracing in the plane of the roof is stiff enorigh to transmit these forces to adeqr~atcly braced walls.

At first glance, there appears to bc quite a weight saving in tapered girdcr; how?ver, this is not always as great as it might seem:

First, the flange arca remains the same; the only weight saving is in the web. See Figure 2.

Second, the depth of the tapered girder at midspan r n ~ ~ s t he iricrcased over that of the conventional straight beam to he sofficicnt at thc critical section (about "4 span). This is necessary to dcvelop the required section rnodulus along the full length of the tapered girder.

This will slightly offset the initial weight saving in the? wcb. See Figure 3.

FIG. 4 For f lat roofs, tapered girders are used inverted, with tapered flange downward. Fre- quently the girder i s tilted to provide a slope to the roof or roof section.

itders / 4 . 6 3

2. DETERMINING CRlTlCAL AND SLOPE

The critical depth scction of a tapered girder is that section in which the actual depth of the girder just equals the minimum d ~ p t h required for the moment. It would be the highest skessed section of the girder in bending.

In the case of a uniformly loaded, simply supported girder, its sloping flange must be tangent to the re- pired-depth cilrve at this point in order for the beam to havc sufficient depth along its length.

Setting thc slope of the tapered girder flange so that the critical section is located at the V4 span will result in about the minimum wcb weight. See Figure 5.

The properties of this critical section are-

[depth between I- CG, of flanges)

df

FIGURE 6

FIG. 7 Tapered g i rde rs used with the tapered flange a t the top provide for roof drainage in both directions from the ridge. Multi-span designs often call for combinations of girders having tapered flange up and others having tapered flange down.

This formula for section n~odulus can be simpliIied with little loss in accaracy, by letting-

dw = dl = dl,

I I

If the section modulus required to resist the bending moment is known, the required beam depth ( d ) is solved for:

For a simply mpported, unitormly loaded, tapered girder-

w = 50 lbsiin uniform lood

4 L b

FIGURE 8

or to find the depth in one step-

To find the slope of the critical-depth curve forined by points d, along the girdcr length, this expression for depth (d,) is digcrentiated with respect to the dis- tanccs ( x ) :

3 w . --- (I , - %I dd 2 t, u 8 = ---x = - . - - dx A, ( L - x)

w

It is simpler to find the slope at Y4 span, letting x = L/4:

Also, at x = L/4:

and:

. . . . . . . . . . . . . . . . . . . I = d, 4.- 4 tan B 4 1 ( 5 )

. . . . . . . . . . . . . . . . . . . d, = d, - tan 0 (6)

Since loading on the girdcr is not always ouiform, the ~ h o v c formulas do not always apply. Table 1 sum- marizcs the working formulas to use for various conditions of loading, as w d l as locating the critical depth.

Fignre 9 shows the effects of placing lnultiple loads npon a simply-s~rpportrd tapered girder. These effccts on the hending rnonxnt and the critical depth of the girder can be explained as follows:

In the case of the single contcntrated load ot midspan, the critical dcpth section is :it midspan, and the maximum slope is 8.

* In the casi: of 2 cqual conccntratcd k~ads applied at 'h points, the critical depth section is at the p i n t s of lotid application and the m;~xinnlrn slope is 0. .lssi~rn- ing the slope n w e to pivot itbout this criticnl depth section, any slope lcss than this value \ rm~ld cause ihc dcpih at the end to incrmisi. at twice the rate at which the depth at centerline is dctrcasing. Sincc such a shift would incrt:;isr the web weight, this maximum slope vahle of 0 should be nsed initially.

If morc dt:pth is ncedcd at tllc end because of higher vcrtical shear, do this by pivoting about this critical depth section. This will rcwlt in thc least increasv in \vet) wcight. It can IIC shown that, nnder this condition, the rcst~liing depth at centerlinc will be-

3 d, - d,, d, = - - . . . . . . . . . . . . . . . . . . . . . . . . ( 7 ) rn * In tho case of 3 equal concentratsd loads applied

at 'A points, the critical depth section will he chosen at U4 spa^ Thr slope of the girder mnst lie sonrcwhcrc bctwcen 0 and 4. For any ar~gle l~etwecn these two values, the wcight of the web will rcmain tlw same

8.1-12 / Reference Design Formulas

Influence Lines

Effect of position of force (F) upon moments Ma, MI, M2 and upon kmax

0 .1 .2 .3 .4 .5 6 .7 .8 .9 1.0

Position jo) of applied force F

M S = - u

- (1687.5) - - ( 22,ooq

= 76.7 in."

To use an "eficient" section (Sect. 4.2, Topic 2), the efficimt depth would be-

It would be prefcra1,le not to have to use transverse intermiitcwt stiflei~crs. 1,ooking in Section 4.1 on i'latc Girders for Rnildings, Topic 2, it is secn that these stiffeners are not n:rjuircd if:

a, :I) The ratio K = ,- is less than 260

rw b) The shear stress (7) does not exceed that of

AlSC Formula 9. This means the values of K and shear sircss (7)

shall fall within the values of the right-hand column of AISC Tahlc 3-36, in Section 4.1, page 25.

Assume a value of K = 70 at the end of the girder; herc the shear (V) is highest. Assume a value of K = 170 at midspnn; here the shear (V) is very low. This means at 34 span (the critical section under consideration) K would fall halfway between these two values, or K = 120.

therefore, the eficicnt depth

required flung6 area (&cicnt section)

=. 2.4 in.' or usc Yz" x S' flange, the area

of which is Af = 2.5 i a 2

u e b thickness

= .W' or use a 3/,6" thick plate. Then-

ratio of tccb's depth to thickness

And from Table 3-36 in S<.ct. 4.1; since wi& no stiireners a/& = n (over 3 ) , allowable shcar is 7 = 5000 psi.

nctual shear stress

v 7 = -

A,

(7.5 kips) = (3/16)(24) = 1670 psi < 5000 psi OK

required slope of tapered girder

= ,0852 radians, or 4.88'

required depth of web

L = d, + - tan 0 4

= (24.0) + -- (m) (.08538) 4

= 24.0 + 12.8

= 36.8"

eck Shear Stress at End

A, = 3/16 (11.2)

= 2.1 in.'

- (15 kips) -

(2.1)

= 7140 psi

flcre:

d, K = - t,

- (11.2) - ( 3/16) = 60, and from Table AISC 3-36 in Section 4.1,

page 25 it is dctelmined tha't no stiffeners are required.

Check Section of Midspan

d, IC = t,

- (36.8) - rn) = 196 < 260 OK

Also, practically no shear here.

W L2 M9 = -8-

- (50) (600)' -

8

= 2250 in.-kips

tu dW2 S, = At d . + ---

6

(3/.L6) (36.8)2 = (2.5) (36.8) + 6

= 134.4 in."

Ma cr* 'e- - ss

- .- ( 2250 in.-kips) -- (134.4 in3)

= 16,750 psi < 22,000 psi OK

Alternate Design

FIGURE 1 1

To make this tapered girder by splitting a WF rolled beam, and weiding back together aftcr reversing one-half end for end.

Since the reqoircd section modulus of the critical section at '/a span is-

S = 76.7 in."

an 18" M;F 50.11, bcam could be used

properties of this rolled beurn

A, = (.57)(7.5)

= 4.27 in.'

d, = 18.00 - 2(.57)

= 16.86"

8 = 89.0 in."

shear stress at 'h span \I

= 1240 psi OK

slope of tapered girder

= ,05415 radians or 3.10'

L dg = d , + tan 0

L d, = d, - tan 0

4

Before going further, check the sheav stvess at i hc end of beam-

A, = t, d,

= ( 3 8 ) (8.8-i)

= 3.17 in.'

ing point for flame cutting the WF beam to prepare a tapered girder.

- (15R) - (3.17)

Check Girder Section at

= 4730 psi OK

depth of beam

sturling poini of cut

= 2.0014 a and

Also, practically no shear here.

= 13,500 psi OK

26.12 a = - 2.0014

EFLEGTlON OF TAPE

= 13.06" The area-moment method may be used with good results to find the deflection of tapered girders, where

or use the dimension ( a = 130") to determine the start- no pori~on of the rnember has a constant mo~nent of

FIG. 12 Turn o n e - h o f f end for end, and submerged-arc weld this web ioint without rpecid edge p repara t ion . Trim ends.

4.6-10 / Girder-Relaled Design

Depth of web ot end of centerline

d = 11.2" dw = 36.8"

FIGURE 13

inertia. This method is described under Topics 5 and 7 of Section 2.5 on Deflection by Bending.

To compute the deflection of the tapered girder shown in Figure 13. This girder has a uniform load of 50 lbs/in., and a length of 50' or 600".

Usin the area-moment method, the distance of point from the tangent to point equals the moment of the area under the moment diagram taken about point @ , divided by the EI of the section.

Divide the girder into 10 equal lengths ( s = 60" long). The greater the number of divisions, the more accurate the anywer will be.

For each division, the moment of inertia (In), moment (M,), and distance to the end (x ) are determined and listed in table form.

.3,76" 14.26" 346.in." 427.5in.-k 37.2

90" 18.88" 19.3W 669.in.' i147.5in.-k 154.6 - 150" 24.00" 24.50" l I 17.in.' 1687.5 in.-k 226.7 - 210" 29.12" 29.62" 1702.in.' 2047.5in.-k 253.2

270" 34.24.. 34.74.. 2439.h." 2227.5 in.-k 246.7 -- -

FIGURE 14

Total +

Here, for each segment:

918.4

Since: * , - 3.0 in.=

t* =

-

Tbe above formula, in this problem, reduces to:

Since:

and:

Dramatic savings can be obtained from an often for- gotten design conccpt. The opcn-w-ob expanded bcam has already paid substmtial dividends for various engineering firms. It shonld hc considertd on many more projects.

The opening up of ii rolled beam i~icre~scs iis section moclnlus and rnorrient of incrtia, results iir greater strmgth a i d rigidity. Thc reduction in bcam wright has a chain cfFiict on savings throughout ihc structure.

The open-wcb expanded beam is made economically by flime cutting a ri)l:ed henrn's weh in a zig-zag patiwn along its ccnt~~rlinc. S<v Fig~irc 1. One of the, two equal l~alvcs is then tnmed end for end and arc welclcd to the other half. The rwnlt is a deeper bium, stronger and stiffer than thc original.

Rolled beam cut along web

Welded back together to produce open-web expanded beam

FIG. 1 Result: a deeper beam, stronger and stiffer than the original. Design starts with a lighter beam for immediate savings in material and handling costs. It often eliminates need for heavy built-up beam.

Starting the design with a lighter rolled heam realizes immediate savings in rnatcrial and handling costs. There is no waste material with this mcthod. It often clirniitatcs the ~ iccd for a hmvy built-up beam.

In the design of hnildings, the web opcning is frequcrrtly oscd for duct work, piping, etc. which con- ventio~ially are suspmtled below the bearrr. See Figure 2. On this Basis for cqnivalcnt strength, open-web ex- pandcd 1x:nms usnally permit a reduction in the distance between wiling hclow and floor dmve and thus providcs savir~gs in Iniilding hcight.

Oxygen Barnc cutting of the light heam wcb is

FIG. 2 Use semi-automatic arc welding to rejoin the two halves. A 100% fully penetrated butt weld can often be mode with a single pass on each side of web withoiit beveling.

relatively easy on ;I template-rrjuipped machine. The !is<: of stm-automatic arc wclding to rcjoin

the two hnlvcs onablcs good, soirnd welds to be made faster, more economically. M7i>lding is confined to a portion af tho web's total length. A 100% fully pene- tratcd butt wcld c m usually be made with a single pass on each side of thc wrh, without prior beveling of the cdges. See Figure 2.

18" W 5 0 2 ~ opened up to 27"

Duct work inside Wetghs 65%, saves 3" tn heqhf

FIG. 3 Opening in web used for duct work, piping, etc., normally suspended below beam. For equivalent strength, open-web expanded beam usually reduces distance between ceiling below and floor above.

Cutting the zig-zag paitmn along a slight angle to the beam axis results in a tapercd open-wih cx- panded heam. See Figlire 4. This has many applica?ions in roof framing, etc.


FIG. 4 Cutting the zig-zag patlern along an axis at slight angle to the beam results in tapered open-web expanded beam. This has many applications in roof framing, etc.

Two opm-wd> i,xp:ud(:d bcams can sornctirncs be nested togatl~er to form a coltrrnn l~avirig ;I liiglr rnoment of inertia alxnrt lrotll its x-x and y-y ; ix t~ . Sce Figilre 5.

EOMETRY OF C U T I N G PATTE

The zig-zag cutting pattern and the rrsiiltirig geometly of the web cut-or~t help determine prtipr,rties of the section.

f Cut W benm olong rig-zag line

FIGURE 6

tan & = - rn In gencrd, the angle (4 ) will be within about

45" rninirnrrm and about 70" n~axirnu~n, with 45" arid 60" beir~g most commonly used. This angk: must be

Tied together with plates

FIG. 5 Two open-web expanded beams can sometimes be nested logether to form a column having a high moment of inertia about both its x-x and y-y axes.

si~fficient to kecp thc horizontal shcar stress along the web's nentral axis Eroiri txcrciling the allowable; see Figurc 7.

FIGURE 7

The distancc ( c ) may 11r varied to provide the prop"- \wh opmirig for duct work, ctc., and/or the pro pi:^ dist:iircc for ~ ~ l d i l l g between openings. Set: Figure 8. I-Iov~~\.cr, as this distarrce ( e ) increasrs, the b(wding strt:ss witl~in the Tce st,ctioir dtrc to the applied shear forw ( V ) iricr~~ases. Thus. t h c is a limit to bow largr ( e ) rnay be.

irders / 4.7-3

FIGURE 8

. RESISTANCE 10 A

Since the bmrn flanges carry most of tbr 1)rncliiig load, the loss of well area is not much of n prn!~lc.m as far as mor t i t~~t is c o n c ~ w ~ c ~ l . However, s l~ear (V) is carried by the web, and must he considered.

.4t cuch we!> op2ning, two Tee scciions act as members of a framr in resisting vertical shcar forces.

At midspnn b , Figure 9, the shcar ( V ) is minimum and may have little rftnct on the beam's strength. Approaching the srrppori in the rcgion of high shear a , the hcnding strcss produced by this shear on tlic shallow Tee st~dion must be added to the conventional bending stress f n m the applied beain load.

The bending moment due to shear is diagrammed in Figure 10. Usually, thr point of inficction in top and

Auulied load

Looded open-web expcnded beam

d-

Shear dicgiom

Moment diogrorn .-

FIGURE 9

bottom Teo scctions doc, to thc rnommt prodi~ccd hy shear. is ;iss~irnr~l to ba at inid-scction of the opcning (c.'2). It is furtl~cr :mnmed that thc total vertical shcnr ( V ) at this point is divided ccpally bctmcen tbcst: two Tre scctions. sincc they arc of rqunl depth.

Actually, thc dcsign and st]-css bchzrvior of an opcn- weh expandid heam or girder is wry similar to that of a Vicrci~dm>l truss. Thc primary d('sig11 consider:itions ;in. as follows:

I . The top and bottom portions of the girder are suhjectcd to coinpression arid tixnsion bcnding stresses from ihr m:iin bcnding moment. u,, = hf/S,,. Thcrr must be ;r continuity of thew sections tl~rougbout the girder lcrngtk to transfer tlrcsr stresses. In addition, the comprssiio~ portion most hc cl~ccked for lateral sup-

FIGURE 10

4.7-4 / Girder-

Point of inflection

4 0, k t' -s

/ t~ompress ion

Bending stress of Resultant (total) Bending stress of Tee section beom section due bending stress ( 0 ) due to application of vertical to load on beam sheor at point of inflection

FIGURE 11

port, niinimurn width-to-thickness ratio, and ;rllowahle compressive stwss; scc the left end of Figure 11.

2. The vertical shcar (V) in tho girder i q carried by tile web, and producrs vertical shear stresscs in the wch section, both in the solid portion of the web, and in tho stein of thc Tee scctiou of tlic open portion.

3. In the open portion of the web, the vertical shear ( V ) is divided equally between the top and bottom Tee sections (assuming same depth of Tee sections). Assuming the shear is applied at the midopening, it will produce a bending moinent 011 the cantilevrrtd Tee section; see the right-hand end of Figure 11. The resulting secondary bending stresses

must be added to those of the main bending moment, Item 1. If needed, a flange may be added around the inside of the web opening to give the Tee sections added strength.

4. The horirontal sliear force (V,,) applied at tho solid portion of tlic web along the girder's neutral axis may subjcct this portion to buckling. SIX: Figure 20. The resulting co~nprcssive bending stress on this un- reinforced web scction is important because of the possibility of this w:b scction buckling under this stress.

5. The solid portion of the web may trnnsfcr a vertical axial force (compressive or tensile) tqiial to one-half of thc cliffermce between the applied vertical shears (V,) aild (Va) at thc cnd of any given unit panel of the girder. See Figure 27.

6. There should be 100% web depth at the points

of s~~ppor l . Bcauing stiffeners m;iy hr needed at the t:n& of th? ~ i r d c r w1icr.e rmctions an: applied.

4. TOTAL BENDING STRESS IN t

? ' h ~ main bending stress ( r , ) Itern 1, acting on ;I

section where tile open Tre swtion stabs. is assunred to increasc linearly to a rnaxiinu~u at tlw outer fihcr. To this stress must be :~ddwl or snbtractc& depcndiilg up011 signs, the secondary boridii~g stress (u.~,), Itein 3. See cerrtr;il portion of f:iguw 11.

~t point @

Second:rry hendir~g strcss at stem of Tee due to vertical shear ( V j at Section @ , atidcd to main bending stress at stcm of l'ce d11c to inair1 moment ( M ) at Section @ :

A* point @

Secondary brnding stnlss at fiange of Tee due to vertical shcar (V) at Section @ , added to the main bending stress at flange of Tee* du? Lo main moment (M) at Section @ :

Open-Web Expended Beams ond Girders / 4.7-5

Research at the University of Texas- indicated these main bending strcsses in the Tee scacfion do not increase linearly to a maximinn at thc ontar film of the flange, hut in some casrs the revt:rse is true; the stress along the stem of the Tce scction is high(,r than that at the outer f i l m of thc flange. For this rcason, in their analysis, they calci~latcd the bending forcc 17 = M d using the moment ( M ) on thc girder at Section , .- . .~ ~-~ ~

d " "Experimmtul Investigntions of Espencicd Stsd Bwrms", by M. 11. .4ltflliscl1; Tlirsis; Aug. 195%.

"Stress Distribution in Enpandml Strel Brand ' , by R. W. Lidwig; Tlrcsis: Jan. 1957.

"An Invrsiipntion of Wclilrrl Open Web lixpaiald Beams", by Altfilliscli, Cooke, and Toprac: AWS Jouiml, Feb. 1957, p 77-s.

DEFINITIONS OF SYMBOLS

d = Distancf: h~:twe~:n neutral axes of Tcc srction db -: Dcpth of original beam d, = Depth of cxpandt:d girder e = Lnrgth of Tee swtion, also lcngth of solid

web srction along nrntra! axis of girder. h -= Height of crlt, or distance of expansion

AT = CIOSS-s~ctionid area of TI:? section I, = Moment of inertia of open section of cx-

p:indrd girdw s - Section . modolns of flange of T m section

S , = Section modulns ol strm of Tcc stxction

X X

A36 steel C, = .40

Secondary bending stress In,) from applied shear, ksi

(AISC a,) Near t Neor support

(high moment) [high sheor)

FIGURE 12


the point of inflection of the Tee scction. This is convenient because it is the same section at which we assume the vertical shcar ( V ) is applicd for the secondary txnding stress. They also assume this force ( F ) is ~miformly distributed across the Tee scction.

This simplifies the calculations, since for a given unit panel only onc section must he considered for both the applied moment ( M ) and the applied shear ( V ) . This is Section @ at the point of inflection of the Tee section. Also, only one total bending stress is required for this sectinn-the maximum secondary bending stress at the stem added to the average main bending stress. It does not require calculating at two different points-the stem at Section @ and the flange at Section @

M since F =A and

d

The main bending stress (v,,) and secondary hmd- ing stress (my) may be considered according to AISG Interaction Formulas 6, 7a, and 7b. These are shown graphically in Figure 12. (Note that .41SC refers to main bending stress as u;, and to secondary bending stress as u,,.)

Buckling Due to Axiof Compression

The Tee section, because it is subjected to axial com- presiooli, also nnut bc checked against hnckling according to AISG Sec 1.9.1. See Figure 13, and see Table 1 of limiting ratios for steels of various yield strengths.

i FIGURE 13

Tee Section Stiffened by Tee Section Flange Welded Around Unstiffened Web Opening

< 3000 hi - - . ..~ -

< 3000 b, -- -

T - & - - r tf \ vr

Number of Poinfs to Check Along Girder's Length

It w11l hr dmrablc to chcck the proposed dcsign at only a limited number of points to determine initially whether it will work.

Total bending stress

t

Support '/i Span Midspon Point Along Length of Beom

FIGURE 14

eams and Girderr / 4.7-7

Total bending stress

Support '/a Span Midipan Pomt Along Lengih of Beam

FIGURE 15

Referring to Fignre 11; notice the bending stress (u,,) from the applied moment is assumed to be maxi- muin at the outer fibers of the flange. The bending stress (VT) from the applied shear is greatest at thc stem of the Teo because its section modnlns (S,) is less than the section inod~~lus at the outer flange ( S f ) For this reason, combinations of bending stresses must be ~.onsidr.red a t the outer fibers of the flange as \wil as the stem of the Tee.

In Figure 14, thc total trending strcsses at the outer fiber of the flarige as well us at the stem of the Tee section arc plotted along the length of thc beam. This data is from a typical &sign l>rohlcm. ln this case, the vertical shear :it the support is \' = 25 kips.

111 Fignre 15, tlic example has hren rcworkcd with cliffererit span lengths. and with diiferent applied nniform loading so that thr bcnding moment (and thc bending stress dnc to this moment) rtmains the same. Tho sliorter sixins reqnirt: an incrt:ased load, lierice increased shotir ( V ) . The longer spans require ;i lowcr load, hcner dncreawd sllear ( V ) .

Notice in Figure 15, tllat for short beams with higlrcr shcar form relativc to bending moment, this curve for tlir total hending stress (moment and s11t:ar) will rise on the left-hand sidc, a i d tlic point of maximrnn strcss will movr to the left. or ncar the, support. Of conrse there is a limit to how short and how high the vertical shrar ( V ) ma)- he, bocausc this type of open web construction docs weaken thc web for shear. For

TABLE I-limiting Ratios of Section Elements Under Compression

very high slit:ar loads, tllc opcwing in the exp;\nd(d web would dofcat its pnrpose, and a stantlard solid wch lmun 01- girder s l io~~ld he u s d For longer spans, with rd;itivdy lower sbrar force to bending moment, this c ~ ~ r v c \vill lower. shifting thr point of inaximum stress to tho right, or near the niidspm.

An altcmatc mctliod to finding the bending stress dircctly from the app l id momcnt ( M ) is to convert the moment ( M ) into a concentrated fnrct: ( F ) applied at the centcr of grxvity of the Tec scction and assume it to bc uniformly distribotcd across the section. See Figure 18.

FIGURE 16

Then:

This bending stress is the sa~ne at the outor flange of the Tce section 21s well as the inner stern. It is now only necessary to add the gru ter bmding stress from the applied shcar ( V ) of the Tee section. Therefore, the smaller section modulus at the stem of the Tee section will he nscd, and only one st:t of total stress values will be considered.

In Fignre 17, the applicd inomcnt ( M ) has been converted into a concentrated force ( F ) applicd a t the center of gravity of thc Tee section and assumed to he uniforndy distributed across the section.

This ilh~strates that the point of maximum combin-

ation of bending stresses due: to applied shear and ;litplied momcnt lirs sonitxhcrt. hchvccn I ) the support (region of high vcrtical shcar) and 2 ) the midsparr (rcgion of high hcnding moment). This point of maxinmrn stress is indicated in Figure 17 by an arrow.

Unless the hcarn is cxaniincd as in Figure 17 for t.he maximum stress all the way between the support arid micispan, it would he well to check a third point in addition to the support and midspan. A conveniont point wonld 11e at 'A span.

Thcre are threc mrthods of checking the horizontal shcar stress along the beam's neutral axis (N.A.):

1. Use: the n~nvcntional formula for shear stress,

Totol bending stress

I

I i

0 % a & % 6 X % a % % a %

Support % Span Midrpan

Point Along Length of Beom

FIGURE 17

pea-Web Expanded Beams and Girders /

assuming the web to be solid ( 7 = V - 9 ) . I t Then 1 - .

increase this stress by the ratio of overall web ;egment to net web scgment (s/e) to account for only a portion (e/s) of the web along the nentral 'axis being solid.

FIGURE I8

2. Treat a top segment of the beam as a free body acted upon by the bending moment forcc. The difference in this force from one end of the segment to the other is transferred out as horizontal shear along the neutral axis into the similar section below. This horizontal shear force is then divided by the net area of the solid portion of the web section along the neutral axis. See Figure 19.

By substitution:

V!, = Mz - MI d

which acts along distance (e) .

This horizoiltal shear force is then divided by the net area of the solid web section ( e tw) to give the shear stress:

3. Using the same free body, Figure 19, take momcnis about point ( y):

V, + V2 Assuming that = V,, the average vertical 2

shear at this point, this becomes-

and . . . . . . . . . . . . . . . . . . . . . . . . . t . e (6)

EB BUCKLING DUE TO HORIZONTAL SHEAR FORCE

The web of a conoentional plate girder may have to have transverse intermediate stiffeners to keep it from bnckling due to the diagonal compressive stresses resulting from the applied shear stresses. If stiffeners are used, the girder will have a higher carrying capacity. This is because the web, evrn though at the point of buckling, is still able to carry the diagonal tensile stresses, while the stiffener will transfer the compressive forces. The web of the girder then functions as the, web of a truss.

However, in the open-web expanded girder, treated as a Vierendeel trrrss, the opcn portion prevents any tension acting in the web. Therefore, a transverse stiffener on tho solid web section will not function as the vertical compression member for truss-like action.

Since this solid portion of the web is isolated to some extent, the horizontal shear force (V,) applied along the neutral axis of the honm will stress this web portion in bending.

The simplest method of analysis would be to consider a straight section ( I ? ) , Figure 20. However, the resulting bending stress acting vertically would somehow have to he rcsolved about an axis parallel to the

FIGURE 20

sloping ~ l g c of tliis tapervd web srction. Onc method by which tapered l~cams arid knees

are analyzed is the 'it'cdge hlethod, or-iginally pn~posed by W. R. Osgood arid iatcr modified '7y H. C. Olander (ASCE Transaction paper 2698, 1954). With this method, Figure 21, tlic non-parallel sides are extcnded out to where they intwscct; this becomes point 0. From this point as a rrnter, an arc is dr;iwn tlirough the wedge section reprmenting tlir scvtion ( a ) to be considered. Tlie section modnlus of this curved section is determined.

Thc actual forces and rnoments npplied to the member are then transferred old to point 0. The? horizontal force (V, , ) \vill cansc a moment at point 0.

It can l ~ o shown that these forces and moments acting at point 0 i~allse the bvnding stresses on t l ~ e curved section ( a ) of the wedge; sce Figurc 22.

Moment acting on curved section ( a ) :

FIGURE 21

where

Since:

ni + f p =--- or cos 0

Since:

= 2 p 0 and

t,v a2 S = - - . . .

Radial bending stress on this ct~rvtd section ( a ) : 6

FIGURE 22

eb Expanded Beams and Girders / 4.7-1 1

buckling

I + FIGURE 23

Thereforc, the radial bending strcss along cu~.ved section ( a ) :

It can b r shown that the curvt:d section ( a ) haviug the greatest bending strvss ( u ) occurs at a distance of:

This value of ( m ) will be Icss than ( h ) and may be used in the following Formula 12 if ( e ) docs not exceed these values-

1 for 0 = 30', e 5 1.58 11 1

For most drsigns, this wo~ild he true and Formula 12 could be rlscd directly witlmut first solving for ( m ) in For~nula 11.

This vahw of ( m ) for thc position of the greatest bending strcss may 11c inserted 1,ack into Fonnula 10, and tlre following will give the grratrst hending stress along ( a ) :

Tlir next step is to drterrnine the allowable cornpressive I~ending stress (d. If thc above bcnding strrss in the solid portiori of the web ( u ) is excessive, it might be possil~lc to incrrasc the distance ( e ) . IIow- ever, this will also increasc the length of the Tev

Moment applied to member

section, resulting iii ii~crcwc of the seco~iclary bending stress in the Tee st,cticin juT). -4s an alternative to incrmsing distanw ( e ) , it u-odd he possiblc to stiifen the outcr edge, of this wedge portion of the web by adding a flangt: around the edge of the hole in the well in the particular panel which is overstressed.

Allowable Compressive Bending

Tlicre ;m, two srrggt-stions for determining tht: allowable coinpressivt~ bending stress along the sloping edge of the wrrlgc scction of thr web:

I. Trmt this srv.?ion as a prismatic member and apply ALSG Scc. 1.5.1.4.5 Formula 4; sce Figure 23. ATSC Fonnula @ for allowable compressive stress:

when:

and

Scc additional 11otrs; Section 3.1. I I : - hi? i l l thc ahow formula, C , - 2.83;

I I I I ~ siiicc it carmot rxcwd 2.3 therefore C,, = 2.3 and AISC Formilla @ becomes-

Scc: Tal11c 2 for viiliirs of Form111:i 13 for various stecls.

2. As an alterl~ntc method, treat this as a canti-

4.7-12 / Girdea-Related

TABLE 2-Allowable Compressive Stress On Wedge Section of Qpen-Web Girder

For Various Steels

where:

Co~lsider the oriicr fibcr of this cmtilcver as an element in coinprt~ssion. Using the resrrlting (I&) ratio, determine the allon-ablc c<~nlpressive stress from the AISC tables.

or:

l e Shear Stress

From eithrr 1'ormol;i 13 or the ahovr. Mcthod 2; we obtain the allov-ablr compressive bmding stress ( u ) . Since V,, =: 7 t, c and holding the inaxiinum bending stress (u,) of Formula 1.2 to the allowable ( u ) , we - obtain the followitrg-

3 v,, t m 0 = - . - -. 4 t, e 0"

lever beam, and measure its unsupported length ( L ) from the point of inflection ( e ) to thc support; sec Figure 24.

Formrda 14 for nlloud>le shear stress (7 ) has b e ~ m simulifird for various anrrles of cut ( 0 ) : see Table 3. 6 hupport %, ~ ,,

If the allowablr: shaar stress ( I ) in this web scction - is hcld within the value shown in Formula 14, no f111.ther chock of web lxickling dut. to the comprtissive bending stress will have to 1)e made, nor 1\41 this ., edrre have to be reinforced with a flancrc.

"h

FIGURE 24

Reverse top holf end for end 1

., ., To kcrp the resulting shcar stress within this

allow;lble, either ( t , ) or (t.) may have to be increased; see Figurc 25.

Reverse top holf end far end - I

t +ie,it- -+lk 4 2 e , i C I YA point ez % point

Support 1

Support FIGURE 25

Open-Web Expanded Beoms and Girders /

Adjusting the Distance of Cut (el

The clistance ( e ) may be varied to providc the proper strength of the web, or the proper opening for duct work; sec Figure 8. Howevcr, as this distance (e) increases, the secondary brnding stress within the Tee section due to the applied shear force ( V ) also increases.

In otht,r words, ( c ) must he snfficiently large to provide proper strength in thc web section, pet must be small enough to provide proper Ixnding strength in the Tec scsction. In both cascs, these s t n s c s are eauscd directly by the applied vc:rtic:11 shrnr (\!) on the mon~her. This lxcom<~s nioro critical mar the, snpports whwe the shcar is thr: highest. Largcr trial W F beam sections arcp choscn rlntil the v:he of ( c ) will satisfy both conditions.

It would be possible to gradually wry the ske of the openinzs from the support to thc ceuterlinc; how- . . ever, this \vould be diiiicult to fabricate. If this is desired. it might he better to use t\vo dimcrisions of horizontal cut ( e l ) and (e,), altcrmating them and reversing their order at the '/s point. See Figure 25. This would allow a larger value of ( e l ) for the strength of the web and a smaller value of (e2) for the strength of the Tcc section, near the support in the region of high shear ( V ) . In the central region of the girder between the 'I4 points where the shear ( V ) is onc-half of this valrre or less, these values \viil reverse, resulting in the smaller value of ( e2 ) for the web and the larger value of ( e l ) for the Tee.

The top portion of the cut WF bexm would be cut in half and each half turned end for end. This will require a butt groove weld. However, this top section is in comp~-ession and the requirrment for the wald will not be as severe as though it were in the bottom tensile chord. It might be possible to make this compression butt joint by fillot welding splice bars on cach side of the Tee section. This lap joint would transfer the compressivc force; the splice bars u~ould apply additional stiffness and therefore a higlrcr allowable compressi\v strrss for this Tee section at midspan.

FIGURE 26

This cutting pat tcn~ results iii the hole at the wntcrlinc having twice the: lcngth as the othrrs. How- eve,-. this is the. ~rcgion of (mly high momont ( M ) ; there is almost no shear ( \ ' ) . This section should be snfficient if it car devclop the requirrd compn.ssion from the main btmding load.

TABLE 3-Allowable S h e w Stress For Various Angles of Cut

The edge of the wedge section of the weh may be strengthmed against buckling due to the horizontal shear force, by adding a flange aroiind the web opening. Set: Figure 26.

6 = 4 s

Here:

t , a' S .= At a +

6

Inscrling this into Formula 7, we gct-

n _ r s

It can he shown that the value of (in) for the position of thi~ gn3at<.st bending strrss is-

, ,8225 o.

FIGURE 27

This value of ( m ) could then he 1rst:d in Formula 12 for the bending stress. This \vould give the following formula for the greatest bending stress:

where:

Moment d i o g s V = 25k

EB BUCKLING DUE TO CO

Any dircct triursvt~rsi~ loiid :ippiied to the upper flangc of the open-weh girdcr is carried as vertical shear on t11c web. Sce I'igmo 27. Since this resisting shear is eqt~ally dividod b<,twet:n the top and hottonr Tee sectioli chords, half of this transverse load applied to a unit 17mel scginent of thc girdcr (distance s) must he trans- fi:rrtd as compr~ssiorr dou~n through thc solid portion ( < * ) ot' the web into the bottom chord.

If it is felt that this solid wet) section, acting as a column, cimnot handle this forw; it could he reinforced with a transvcrsc (vcrtical) stifl'cner. Usually this force, one-half of tho applied trnnsvcrse load with tbc segmcnt ( s ) , is small. Thus, the resulting cornpressivc stress within this web section ( e ) is low, and stiffwing is not usually required.

Compressivc stress in web section ( c ) :

The allow;~blr compressivc stress would he found in the AlSC tnblt~s; wing -

Shear diogrom --

FIGURE 28

eb Expatided Beams and Girders / 4.7-15

8. GENERAL OUTL1NE FOR DESIGN OF OPEN-WEB EXPANDED GIRDER

l)esib% of an open-web cxpandcd girder will be facili- iated by following the design outline bclow. Its application is dernonstratd by working a. typical design l r o h l ~ ~ m : l h i g n an opcn-web expanded girdcr with a span of 38 ft to support a nilifor~nly-distril~~~te(l load of 50 kip. Ilrsign on tlic basis or wing ,436 steel and Eli0 welds, and angle of cut d, = 15". Sre Figure 28.

STEP I . Determine the expanded girder's required 5ection snodulns (S,) at midspan for the main bending moment:

STEP 2. For the relationship of the cspanded girder'? depth to that of the original beam, let-

Assume it = about 1.5

STEP 3. Select a trial WF beam having a section modulus of-

1.30 Sh = ~- = 86.4 i n ? (use this as a guide) 1.5 Try an 18" W F 50#/f t h a m , liaving S , = 89.0 in."

Now, refigure K, using the S,, of the actual selcctect beam:

STEP 4. Determine the height of ct off to the nearest rnch or fraction of a

it ( h ) and rol n inch:

in order to keep tlw vertical shear stress in the stem of thc Tec swtion within the allowable:

h 5 d,, - 2 d,"

STEP 5. Then

STEP 6. Dctcr-mine the allowable compressive bending strws on wedge srction of web, using modified AISC SEC 1.5.1.4.5 liormula 0:

However, ( h ) cannot exceed the following value

" Could nsstimv shear ( V ) is :itmiit !IS% 01 nmximiinr shear (at the snpporl) liei.;iosc first panel will be away from tha point of SiippOrt. Howcwr, bcciiise wt. arc not ;at the support, thwc will l w some main hmdirrg s t i i sses lo hr nd&d lo thiw: sctondaiy hi,ndiiig s tnscs in thc 'Tec scc t im from applied slienr ( V ) , tlmce, it would be hr t t r r lo use i d 1 vaiuo of shear ( V ) .


Open-web expanded beam serves os longitudinal roof girder in the Tulsa Exposition Center. It provides the needed high moment of inertia, at minimum weight, and eliminates lateral wind bracing. Below, weldor is shown making connections of beam to the tapered box columns.

tlis shrar ( V ) at this ''i point is rcduccd to about lralf of that ;it thr slqiport, thc distancc ( e , ) may hc dor~ble thiit of (c,:) and still not inuxisc tlit rcsnlting secondary heiiding sticss (rr.,). Th<,ri,forrs, K:% =- c 2 / i s i sl~onld not t)l> Iws thas1 ?i.

Using the t\vo dirntnsions ( e , ) and ( ~ 2 ) ; the ;ihovc formulas btworne:

P 9. Now determirir. the properties of expanded girder:

. At the suppof t , cheek the secondary bending stress:

FIGURE 32 FIGURE 33

A , ~ = A, + A, - b t, + d,t,] = 5.861 in.'

( W ) (8) I M l = *, ( 4. + T LtB i n z i UT =- ~ - . ~ - - = 20,300 psi .1(2:16)

Tht. :illowahlo cornpi-t~ssivo hi~iiciing stress nxiy be found in ;i similar inaniicr to tliat of Step 6, exccpt the unsupportrd Icngth l i ~ r o is ( o ) .

-= 105.53 in.l At the support, thlw is no main bending mainexit,

TABLE 4 - 4 0 s Various Steels

a = 22.000 - 14.44 (~h) ' 1 c = 22.000 - 3.61 (.:;.I' t , ~

hence no axial coinpressive force acting on this Tee section. The allo\vablc stress here is-

or, fsosn Table 4 of vdue5 for dllrelent steels-

cr = 22,000 - 3.81 - = 20,200 psi

STEP I I . At midspan of girdel; check the main bending seess:

(as a compressiv(: or tensile stress)

"50"" a, ".. - U)200

(24.08) (5.861 ) -- , psi

or (as a bending stress)

STEP 12. If the main hellding stress ( m ) in Step 11 is excessive, it niay be redlicecl slightly with a higher

vdur of ( h ) ; howcvcr, this will greatly increase the sea,i~d:uy bending stress (Q) of Step 1.0, since it reduces the depth (d+) of the Tce section. In this case ~indoubtcdly, the WF hcam selected cannot be used and a larger WF Iimm must h r tried.

If tile miin Bmding stress (a , , ) is within thi?r. allo\\~ablc, hut thr sectmd:rry lwnding stress (m) in Step 10 excocds the allo\viihle, ( u , ~ ) may be greatly rednced by decri-asing ( h ) with jnst a slight increase in (u , , ) .

Strtwes (u,,) and (u.,.) may bc considered according to AlSC interaction formulas @ , @ and @, shown grap11ic:tlIy in Figurc 12.

As a matter oi interest: Table 5 shows that de- crmisiilg ( h ) rrsnits in a largc decrcase in the secondary bending strcss (u.,.) and n slight increase in the main bending stress (u , , )

If (11) cannot bc rcduccd bccaosc (u,,) is close to the nllo\val~le, m e two different size holes, (el) and ( e 2 ) . Pn~\.ide ;1 larger vnlne of distance ( e , ) for the compressive bending strcss in the \vcdge section of the woh, but a lower valw of (e l ) for the cantilevered Tee section.

TABLE 5

earns and Girders /

STEP 13. h/iake any adjustments necessary to facilitate fabrication. See the text immediately foilowing this design outline.

STEP 14. After the girder is detailed, the stresses may be rechecked in view of marc exact valrm of (V,) and (M,) since the cxact positions of the pancls are not known. .Also, i t may be well to check additioiial points between the point of support and midspan. SPC Figwe 34 and Tablc 6.

The practical aspects of structural fabrication may mean some adjustincut of original girder design is required.

ame Size Holes Are to be Used

If openings in the web are to be of uniform size for the full lcngth of the girder, that is c, = e2, and the open-web expanded girdrr is to he synzmetrical about its centerline, let n :I skumber d unit panek and use as a starting point in measuring a unit panel either:

( a ) Cmterline of wedge web section. Figure 35, or

( b ) Ceuterlinr of open Tee section, Figure 36

Divide the length of thc reqnired girder (L,) by the length of one unit panel ( s ) to get the number of units ( n ) . Then reduce ( n ) to the nearest whole

FIGURE 35

s .

FIGURE 36

number. The distance left over (z ) on each side is-

Since the length of the open-web expanded girder 1s-

L , = n s + 2 z

the length of thr W F beam to he cut is-

L ?, - -- (u + %) s -+ 2 z

The extra length of WF beam required is-

L, - L, = % s

FIGURE 34

Girder-Related

FIGURE 37

I n either case ( a ) or (h) , there probably will be a small hole left in the girder at the ends which must be filled. The simplest method is to add one or a pair of web doubling bars or plates at each end to cover and lap over the holes. See Figurc 38.

Web doubler plate Web doubler bar

It m~ght be po?cihle to adjust the value of (e ) so that the panels w l l fit exactly into the length of the girder (L,), See Figure 40.

Here:

L , = n s + e

= e ( 2 n i - I ) f 2 n h t a n 4

First, determme the number of holes ( n ) from the following formula and round off to the nearest whole number-

FIGURE 38

If the same size holes are to be used, that is c, - - e?; and the c i d e r is not to be symmetrical about its

centerline, then start a unit panel right at one end of the girder. The othcr end may have a partial hole in the web which will have to be ~vvered. The only advantage to this method is that just one end will have a bolo in the web to be covered. See Figure 39.

Second, find ihc required vairle of ( e ) from the iollowinlg formula-

f-, L, = (n + Y2)s + e - FIGURE 39

I>, - 2 n h tan + e = . .. 2 1 1 1 1

Hole in web on this / end must be covered

, . , , , , , , , . . , , , , , ( 2 0 )

eb Expanded Beams and Girders / 4.9-21

FIGURE 40 nsc/ L , = n s + e = e ( 2 n + 1 ) + 2 n h t o n +

This arljiistcd valiic of ( c ) xin not be less t h m I, - (11 - 1 ) h tan + that of S t q 8 in the dmign nirtiii~c, nor exceed the . . . . . . . (2%)

~ ; i l u c which wonld r twlt in ;iu extcssive secondary heridiug stress (w.,) i n Stcp 10.

Cn,w (1)). There artL an evcn number of holes in each I f Ditferent Size Holes Are to be Used half, therefore:

Adjnst ( n ) so i t is a multiple of 4, and rolvc for If distances ( e , ) and ( e 2 ) are riot to be the same, and (,,) fmin the fol1<,wing- the girder is symmetri<:nl ahout its cmteriine, then the following method may be employed. I, - (11 - 1) h tan

I13 ordcr to easily fabricate this type of opeu-web el . . . ~ . . . . . . . . . . ( 22b) n ( I -+- K:t)

zirder. it is necwsarv to be nhie to rotate each tow half 1 '2

about the % point. This prcsents two possibilitics- In both case ( a j ;md cast, ( I , ) this resulting value

case ( a ) rotation at the '4 point abmt the larger dirncn- of ( e l ) shonld not 131. less th;m tliat obtained in Step sion ( e , ) , and case ( I ) ) rotation at the ?k point aboiit

8 and that jl~st used in Poi-mula 11 to find (11). the sn~aller dimension [ c.. ). See Figure 41. . . -

Let ( n ) = number of holcs in thc web, counting the cvntc4ine hole as two holes.

. TAPERED BPEN-

Iktermine the approxilnate number of holes from- c~~~~~~~~ pattern axis at a slight

angle to the axis of tho heain results in a tapered girder.

. . . . . . . . . . (21) Sec Figiire 12. In ordcr to have ilie dcrper scction at the mid-

span, it is nwx!ssary to crit the top portion in half and Case (a). There are an odd number of holes in each revcrse these two top halvcs. The cut could be made half, therefore: in ihc lower portion; howc\:cr this is in tension, and a

Adjust ( n ) so it is a rnuitiple of 2 only, and solve simpl<,r \w4d a)iild be ni;idc in the compression or for (e,) from the foliowing- top portion,

/ Girder-Related

Reverse top half end for end Reverie top half end for end

Q - FIGURE 42

In iapercd open-web expanded girders, the axial forcc in the chord which slopes has a vcrtical component (F, =. F, tan a ) ; here (F, = M/d).

Whenever this chord changes direction, for example at the midspan of the girdcr, this vertical component must be considered. It will be carried as shear in the web members back to the suppol-t, and in this case has a sign opposite to that of the main shear ( V ) . Hence, its effect is to reduce the shear over most of the girder's length, but to increase it in the midspun region.

The modified shear bccomes-

This means there is a vcrtical shift of the initial shear diagram on each half of the gir-der, so that the central portion to be checked which initially had zero shear ( V = 0) now has a shear valuc (V' - F,) as

wcll as the maximnin hrnding moment. See Figrirt: 43. A transvcrsr stiffener at the point where the sloping

flange changes direction would transfer the vertical component of the flange efficim~tly into the wob. The greater the change in slope, the more important this would bccome.

If there is a panel opcning at this point, the Tee section must resist this vertical component in bending (in this cxample, the top Tec section). This is similar to the arlalysis of the secondaiy 1)cnding stress (ul.) due to the shear applied to the Tee section at midopening whrrre each half behaved as a cantilever beam. See Figure 44. However, in this ease, the cantilever beams have fixed ends (a t the centerline of the girdcr); rr- sdting in one-half the bending monient and stress. (This half length Tee section is treated ns a beam fixed at one end arid guidrd at the other end, with a concentrated load.)

. . . . . Girder with Iood - vertical componenl (F,] causes shear

I 11 in web

Shear diagram from applied load

Diagram of modified shear V' = v - F,

FIGURE 43

earns a n d Girders / 4.7-23

Q

FIGURE 44

The open-web expanded rolled beam is sometimes an economical substitute for o heavy built-up plate girder.

In the 21-story Washington Bldg., open-web expanded beams led to significant savings in construction costs.


Open-web expanded beam serves os longitudinal roof girder in the Tulsa Exposition Center. It provides the needed high moment of inertia, at minimum weight, and eliminates lateral wind bracing. Below, weldor is shown making connections of beam to the tapered box columns.

The concrete floor may be attached to the top flanges of the steel girders or beams by the use of suitable shear connectors. These allow the slab to act with the steel and form a composite heam having greater strength and rigidity.

The concrete slab lxcomes part of the compression flange of this composite element. As a result, the neut+al axis of the section will shift upward, making the bottom flange of the bcam more effective in tension. By such an arrangement, beam cross-sections and weight can he reduced. Since the concrete already serves as part of the floor, the the only additional cost will be the shear connectors.

The types of shear eounectors in use today take various shapes and sizes. Some typical ones are shown in Figure 1.

In addition to transmitting the horizoutal shear forces from the slab into the steel beam making both beam and slab act its a unit, the shear connector provides anchorage for the slab. This prevents any tendency for it to separate from the beam. While providing for these functions, conllector placement must not present difficulty in the subsequent placing of reinforcing rods for the concrete slab.

Because of lower shop costs and better conditions,

it is more economical to install t h e e connectors in the shop. However, this may be offset by thr possibility of damage to them during shipping, and by the difficulty presented to walkiug along the top flanges during er~vtion before the slab is poured. For the latter reasons, there is a growing bend toward geld installation of connectors.

The previous APSC Specifications had no infonna- tion on the use of shcar attachments for use in a m - posite construction. If shear attachments were to be used, AASIlO allowables were followed. These require the use of rather long fonnnla~ to detcnnine the in&- vidual factor of safety to be used on the connector. It also made a difference whether the beam was to be shored or not shored during the placing of the concrete floor.

Facsor of Safely The ncw AISC Specifications recognize the use of shear attachments and, as a result of recent research on this subjcct, has taken a more liberal stand on this. The design work has been greatly reduced, and no longer is it necessary to compute the factor of safety. A more liberal factor of safety is now included in the shear co~rnection foimulas. The use of shoring is no longer a factor in the design calculations of the connector, since it has heen found that the ultimate load carrying

FIG. 1 Representation nectors welded to top overlayer of concrete are sketched.

of five common types flange of steel girder

, Only short portions

of shear con- to anchor an of connectors

I t v

Steel beam

(a) Slab on both sides of beam

capacity of the composite beam is umffrcted whether shores have or have not been used.

hear Connector Spacing

AASHO requires the determination of shear connector spacing, which may vary along the length of the beam. Now AISC requires just one determination of spacing, and this value is used throughout the length of the beam, greatly simplifying the worli. This is because the allowables are such that at ultimate loading of the composite beam, some of the comlectors will yield before the others. This moverncnt provides a redisbi- bution of shear transfer so that all connections are ultimately loaded uniformly, hence uniform spacing is allowed.

Composile Section Properties

A further help is a series of tables listing properties of possible combinations of rolled beams with typical concrete slab sections, similar to tables in wide use for available rolled beam sections.

These new tables have been published in the AISC "Manual of Steel Constnzction,'' Sixth Edition, 1963, and in Bethlehem Steel Co.'s "Properties of Composite Sections for Bridges and Buildings."

The new tables eliminate the various calculations for composite sections. A simple calculation will indicate the required section modulus of the composite section, and a quick reference to the lablcs will in-

k Effective slab width (B) --i

i ~istdnce to outer fiber

_k of tension flange

FIGURE 3

(b) Slab on one side of beam

dicate possible combinations of rollcd beam and concrete slab.

In order to get the transfonned area of the concrete floor, it is necessary to decide how large a width of the concrete acts along with the steel beam to form the composite section. This is known as the effective width (B) of the slab. AISC (1.11.1) requires the foUowing:

shb on both sides of beam, Figure 2(aj

B 'h beam span

a 5 M distance to adjacent beam

a 5 8 times least thickness of slab (k)

slab on one side of beam, Figure 2jb)

B 5 4/12 beam span

B 5 '/z distance to adjacent beam

B 5 6 times ieast thickness of slab (t,)

This effective width of concrete is now transformed into an equivalent steel section, having the same thickness as the concrete (t,), but having a width equal to I/n that of the concrete. See Figure 3. Here n, the modular ratio, is the ratio of the moduh~s of elasticity of the stcel to that of the concrete.

From this transformed section, the various properties of the section may be determined.

I = moment of inertia of transfonned section, in.'

S = section modulus for thc extreme tension fibers of the steel beam (bottom flange), in.3

Beams may be totally encased within the floor slab as a Tee section in which the top of the beam is at least 1%" below the top and 2" above the bottom of the slab, and encased with at least 2" of concrete around the sides of the beam. With thcse conditions,

jmasuet

Nota

Rejected definida por jmasuet

ear Attachments -

shear attachments are not iised (AISC 1.11.1). if no temporary shores are used, the total bending

strass in thc telrsioil flange of tlre ciicnsed stcel hearn is figorod under two conditions:

1. The steel hcani acting alone for any dead loads applied prior to hardening of the concrete.

2. The steel beam acting with the concrete for any live loads and additional dead loads applied after hardening of the concrete.

The henin shall be so proportioned that. the above stress nnder either condition does not cxcecd .66 5,"

( M S G 1.11.2.1 j. If temporary shores are used, the tension steel

flange of thc enc;ised beam acting with thc concrete slab to folm the composite section shall be designed at u = .66 a;,* to carry all dead and livc loads applied

- ';If steel section is not compact: a = .60 c,.

-

With

Sharing

-

Withoul

Shoring

after hardening of tlrc concrete. If shcar attacl~mc~its are used, encasemcxt is not

needed and it ilocs not inntier in the design whcthi:r temporary shores are used or not used. in either casc, the steel tension Range acting with the concrnte s1;rb to f o m thc coml~osite s'~tion shall hc dcsigned at cr = .66 uJ" to carry all of tile lands (AISC 1.11.2.2). If no temporary shoring is used, the section modnlus of the cwnpositc section (S,) in rcgard to thc tension Range of the bcani shall not cxcced thr following:

I ( M S C Forniula 17) 1

where:

S, = section modulus of composite section (relative to its tcilsion steel flange)

esign of Section or Composite &onstructiora

Encored Beams (1.11.2.1) (no iheor ottach,nanti)

Section Modulus

-

and

Me M .,a = -- + 5 66 0, ( .60 a, s., s. - '

With Shew Attachments (I .I 1.2.2)

Section Modulus Used

I (AISC formulo 17) I

* o = .66 a, ior "compact" beams; otherwise a = 6 0 or

4.8-4 / Girder-Related Design 1

-4 n L k "r 4 Within elostic limit Uitimate iood condition

FIGURE 4

S, = section tnodnlus of steel beam (relative to beam, is equal to the total horizontal forces (F , ) from its tension flange) bending acting on either the slab or the beam. See

M, = dead-load moment prior to hardening of con- Figure 5.

crete

MI, = moment .due to live and additional dead Ioad alter hardening of concrete

where: Table 1 summarizes these requirements for encased

beams without shear attachments and for composite B = eifective width of slab

beams with shear attachments. t, = thickness of slab

Farces Carried by Connectors f t . - - compressive strengtl~ of concrete For elastic design, the horizontal unit shear force is A, == cross-soctional area of steel beam obtained from the well-known fonnula:

A, = cross-st:ctional area of effective concrete slab

V a y cr, = yield strength of steel f = ---- I

Figure 6 diagrams the bending inoment that results However in the new AISC Specification for build- in horizontal forces; compression in the concrete slab

ing applications, the cl(2sign is based on thc shear and tension in tlie steel beam. connectors allowing the composite beam to reach ulti- Thcse horizontal ultimate forces are then reduced mate Ioad. In the usual con~posite beam, the ultimate hy a factor of safcty of 3, and concrete is taken at 85% load is reachcd aftcr the full dapth of the steel beam of its strength. These formulas become: reaches yicld stress in tcnsion. This forcc is resisted by the ~mnpressive area of the concrete slab. See Figure 4. 3 5 f', A,

The total horizontal shear (V,,) at ultimate load v ,, = - . - . . . . . . . . . . . . . . * . . . . . .

to be transferred from concrete slab to steel beam ( 2 )

between section of maximum moment and ends of the (AISC For~nnla 18)

4 f: t=- rn

k-%-I F " y i

(a) Neutral axis lies within steel beam (b) Neutral axis lies within concrete slab

VI, = FJ, = b t, f', Vh = Fh = A. my

FIGURE 5

Shear Ateochments -

I

I Moment dmgm

I I

4- LLLL

+ } F, = f: b t (compresrioo)

7,- - 3 7 -- F, = A, o, (tension) i =I FIGURE 6

I (AISC Formula 19) 1

The smaller of the two values above (V, i ) is taken as the total horizontal shear force to be carried by all of the connectors betw-cen the point of maximum moment and the ends of the beam, or between the point of maximum moment and a point of contraflexure in continuous beams.

The number of shear connectors needed within this region is found by dividing the above force (Vh) by the allowable ( q ) for the type of connector used.

Allowable loads Formulas have been established to give the useful capacity of three types of shear connections. These are used hy AASHO in the bridge field with the proper values of ( K ) :

channel

q =: K2. ( h + % t ) w (Ibs/channel)

where:

w = channel length in inches

spiral

q = KB da GC (~bs / tum of spiral)

Later the Joint ASCE-ACT Committee on Com- posite Construction recommended these same basic

formulas, but applied a factor of safety of 2 and these became allowable loads for the conncctors.

In thc meantime additicmal testing has indicated the cvnnectors to have greater strength than previously thought. Although AISC did not pnblish these final formulas with their constants (10, they did produce Table 1.11.4 of values for allowable loads on some of the typical standard shear conncctors. See Table 2.

Working back from this table, the basic formulas for allowable loads on shear connectors would be the following:

TABLE 2-Allowable orizontol Shear Load (q), Kips (Applicable Only to Sfone Concrete)

Conneder If'. = 3,000 if', = 3,500 if', .= 4,000

%" diom. X 2'. hooked or

heoded stud i/B" diom. X 2%" hooked or

heoded stud

%" diam. X 3" hooked or headed stud

'/s" diom. X 31/2" hooked or

headed stud

3" channel, 4.1 lb. 4" choonel, 5.4 ib. S' channel, 6.7 lb. I/2" diom. spiral bar 1/8" diom, spiral boi

o = length of chonnei in inches.

FIGURE 7

live load momcnt

(6) WI. L ML = -- 8

- (240,000) (480) -

8

These will enable the engineer to compute the value for a shear cvnnector not covered in the AISC table.

The connectors may be spaced evenly along this region and shall have at least 1" of concrete cover in all directions.

pziL7-l Check the composite beam of Figure 7, and its shear connectors. The following art? given conditions:

36" WF 150-lb beams on 7' centers, with a 6" thick concrete slab

A36 steel, E70 welds, and 3000 psi cvncrete A nnifonnly distribnted live load of 240 kips Span of 40' between supports

E n = " = 10 (modular ratio)

E,

dead load moment

Steel beam = 6,000 lbs

Concrete slab = 20,160 Ibs

Total WD = 26,160 lbs

proiection of conmete slab

a S S t ,

5 8(6")

5 46"

a 5 'h distance to adjacent beam

5 %(84 - 12)

5 36" < 48'' OK

efjifectitic width of concrete flange acting with beam

B 5 - Y4 beam span

5 - %(40)

5 - 10' or 120"

B = 2a + hi

= 2(36) + (12)

= 84" < 120" OK

and width of transformed concrete area is 84"

B/n =- = 8.4" 10

properties of steel beam section

36" WF 150-lb beam

I = 9012.1 i n 4

S = 502.9 in.%

A. = 44.15 in."

db = 35.84"

bi = 11.972"

tg = ,940"

t, = ,625"

properties of compo.rite section

Tro~isformed k 8 4"4 / concrete a ieo

M N.A. = - A

( dirtmce from reference to iicutral axis)

axis

= 670 in."relative to bottom tension Range in steel beam)

, I 1 check bending stress in hcam -

Check the tensile be~lding st~ess in bottom flange of steel beam. From Table 1-

VB = M, + 5, S"

- - (1570 + (14,400) ( 670

= 23,800 psi < .GG uy

check secMon modulus

Since no shores are to be used, a further requirement is that the section modulus of the composite section shall not exceed-

1.35 + 0.35 s, I FIGURE 8

(14 400)] (5019) 5 [1,135 + 0.35 ( 1570 )

Taking reference section (y-y) through the beam's center of gravity:

5 2220 in3

SCc ,,., ,, = 670 inJ < 2290 in.3 OK

horizontal sheuli~

The horizontal shear to he transferred by connectors will be the smaller of the following two values:

T", II -. .- ' 85 f', A, 2

- -- .85 (3000)(6 x54) -.

2

= 642.6 kips

= 794.9 kips

So, w e Vh = 642.6 kips

Use %" x 4" studs. From Table 2, q = 11.5 kips per stud.

number of studs

or 60 studs from centerline to each end of beam. If using 2 rows of studs, use 28 lines on each end

of girder.

approximate spacing

S = 240" (half length) 28 (studs)

Place first line of studs at 'h of this space (or 4%") from end of beam; from there on give all studs full spacing (89/16").

hannel Connectars Use 4" 5.4-lb channel of 10" length. From Table 2,

q = 4.6 w

= 4.6 (10)

= 4.6 kips per channel

number of channels

Vh n = - q (642.6) -

- (4.6)

= 14 channels

from centerline to each end of beam, or 28 channels per beam.

approximate spacing

S = 24G" (half length) 14 (channels)

and use M of this or 8'k" for spacing first channel from end of beam.

To compute the required size of connecting weld:

F = 46 kips, each cl~annel

length of FUet weld

L = 2 x 1W'

= 20"

force on weld

leg size of weld (E70)

= ,205" or use %" h

Check: Welding lo .94" thick flange calls for minimum weld size of %6" , but the weld need not exceed thickness oi the thinner part joined, which is the

channel. Hence, use % 6"

Use %" diameter bar. From Table 2, q = 17.8 kips per t u n .

number of turns

v . = ! ! cl

= 36.1 from end to cnd or 37 turns from centerline to e a d ~ end of beam.

approximate pitch

240" (half length) S = -- - 37 (turirs)

= 6.49" or use 67/,,"

To compute the required connecting welds (E70), lcngth of uvld at each turn of spiral assume weld size is equivalent to a %" h fillet weld (has same throat). Force on the weld is-

9 L = - f

f = 11,200 o - - (17.8 kips) = 11,200 (%) we'd ( 4 2 0 lhs/iin.)

= 4200 lbs/in. = 3.18" or 1%'' on each sue -- OK

Application of one type of proprietary shear connector for composite construction, providing equivalent strength with less steel tonnage. Connectors welded to beams makes concrete slab integral with supporting member.

Lightweight stud welders permit shear connectors to be attached to girder flanges at high speed. Studs are the most papular form of attachment #or anchoring concrete floor slab to the steel girders, permitfing steel and concrete to act together for greater strength and rigidity.

Concrete roadway dccks may be attacl~ed to the top flanges of s t 4 girders or benms by the use of suitable shear connectors. Th tw coi~riectors allow the slabs to act with tlw steel and form a coinpositr heam having greater sbcngth and rigidity.

7% cont:rete slah becomes part of thc compression flangc of this composite dcmerrt. As a rcsnlt; the neutral axis of the section will shift upward, making the bottom flange of the beam more cfft4vi. in tcnsion. By such an anangcment, beam cross-scction and \veight can be reductd Since the concrete already serves as part of the floor, the only additional cost will he tho shear connectors.

The types of shcar connectors in use today take various shapcs and sizos. Sonrc typical ones arc shown in Figure 1.

In nddiijon to iransmitting t h ~ horizontal shear forces from the slab into thc steel heam making both beam arid slab act as a unit; the shear connrctor provides anchorage for the slab. This prevents any tendency for it to separate from the beam. While providing for these functions, connector placement must not present difiiculty in the subsequent placing of reinforcing rods for the conmete slab.

Because of lower shop costs and better conditions,

it is more cronomical to install thew connectors in the shop. Ilorvcver, this may be oiTsct by the possibility of damage to them t lu r i~~g shipping, arrd by the tiiffi- culty presented to walking along the top flanges durixg i.rection before the slab is poure(1. For the latter reasons, there is a growing trmd toward ficld ir~stallation of cori~rectors.

Erection procedures influenci. the de ign of the composite hwm. If thr girder or beam has proper tenrporasy support during construction, its d c s i p can be bastd on the dead loads plus live loads being carried by the composite section after the concrete has attained 75% of its %-day strength.

If the girdcr is not shored, then the steel alone must he designed to support the entire dead load during the curing period, and the composite section designed For ;my live, impact, and additional dead loads. This usually requires greater steel cross-section than is required for thr eoniposite design using temporary shoring. Howcvor, in bridge construction this savings in stoel usually cannot offst:t the high shoring costs for the long spans iiivolved. As a result, most bridges are designed withont shoring.

111 the negative moment regk~iis at the supports of continuous boams. the concrctc slah would hc stressed in tension a i d cannot be considered offodive in the design. Some bridge designers assume the reinforcing

FIG. 1 Representotion of five common types of shear connectors welded to top flange of steel girder to anchor an overlayer of concrete. Only short portions of conneciors are sketched.

1 Concrete slob/

Steel beam

(a) Slab on both sides of beam

FIGURE 2

steel in this area to be effective in tension when proper shear attaclments are continl~ed throughout the area. This approach slightly reduces the beam's cross- sectional area.

Shear connectors should have at least 1" of concrete cover in all directions. They should be designed for only the portion of the load carried by the composite section.

horizontal shear

where:

Vb = horizontal shear of steel flange, at junction of slab and beam, lbs/linear in.

V, = total external shear a&ing on composite section after concrete has attained 75% of its 28-day strength, ibs

m = statical moment of transformed concrete area about neutral axis of composite section, or the statical moment of the area of reinforcement embedded in slab for negative moment, in."

I, -. moment of inertia of transformed composite section

transformed area

In order to get the transformed area of the concrete deck, it is necessary to decide how large a width of the concrete acts along with the steel beam to form the composite section. This i~ known as the effective width (B) of the slab (AASHO 1.9.3).

Thus effective width of concrete is now transformed into an equivalent steel section, having the same thickness as the concrete (t,), but having a width equal to l /n that of the concrete. See Figure 3. Here n, the

(b) Slab on one side of beam

modular ratio, is the ratio of the modulus of elasticity of the steel to concrete.

From this transformed section, the various section properties may be determined:

m = statical moment = A, d, of concrete about neutral axis of composite section

I, = moment of inertia of transformed composite section, in.*

S = section modulus for the extreme tension fibers of the steel beam (bottom flange), in.3

The moment of inertia of the transformed concrete section (I,) may be read directly from Table 1, the section modulus ( S ) from Table 2, and the coefficient value of m/I, for horizontal shear (V,)) from Table 3. Tables 1, 2 and 3 are from "Composite Construction in Steel and Concrete" by Viest, Fountain and Smgleton, McGraw-H111.

where:

n =: E,/E, = 10, the modular ratio

B = effective slab width

t = slab thickness

design load (umking value) for one shear connector

Distance to outer fiber

1 of tenr~on flange

FIGURE 3

where:

Q = useful capacity of one shear connector, beyond which the connector permits an appreciable slip between concrete slab and steel beam, lbs

F.S. = factor of safety

useful capacity of one shear connector

omen(. 04 Inertia, Transformed Gomposih Seckion

Modular inlio n = lo, h = dfective slab width, t = slab thickness ........ ..... -.

1 a , I i - n , < b - l r t

From "comporite C ~ r f r v n i o n in Steel m d Concrete" by vier*, Fountoin & Sineleton. Copyright Q 1958. McGraw-Hill B w k company. Ured by permirrion.

Note: f', = 28-day compressive strength of concrete For most conditions, the uscful capacity ( Q ) of the

she.= connector may be read dii-ectlp from Table 4, 5, or 6 which makc it unnecessary to work the above formulas.

factor of safety The factor of safety to be used in coinputlng the

allowable design load for one shear corincctor, is obtained from the following formula*:

. . . . . . . . . . . . . . . . . . . . . . . . (7) " AASIIO (1.95) now allows as an alternnte, a factor safety of 4 in lieu of calculating it with the above formula.

TABLE 2-Section Modufus.

Modular ratio n = 1 1

st"?: I,r,<,"

. :,i W,.$,ii :,B wr ?Bi i t , W P ?d 80 W Y i l i I 6 WFZJ:

:so WF i O I 91, O F 18: I" WF ,,L :3<, W,? ,<a l 0 W I 110

:<I WT 220 WI i(10

Y 1 V F i i z a:, W,? 18"

30 Xi' i 2 i YO W i ' i l " SO WF i<i8

2: U P 101 2: WP Y<

2' Wi- ,Mi ?i WF 9, $4 W I U 9°F 1II

2% wi 7s Z i W P 68 2, W P ' 8

i 8 W F Ce 18 W* 56 i B W F 60

16 Wf ,m I8 WF 48 i i i WF I 0 16 WP 36

34 w i :<a 1.i W f 10 -

I Beam b = effective slob width, t = slob thiikners

?.,,.*,~," ,,%,,,,,>I,,. .Y,,. "I =,,,,, ,,,, ~ , $ = ,>*A ,I,, ,,,. 8

i I i - Fiom "Comporiie Conrtruction in Steei end Concrete" by Viest Fountain & Singleton. Copyright Q 1958. MiGraw-Hill Book corn: pmy. Ured by iiermiision.

where:

where:

MD, = max. moment caused by dead loads acting on composite section

MD, = max. moment caused by dead loads acting on steel beam alone

Mr. = max. moment caused by live load

S, = section moddus of composite beam for extreme tension fibers

S. = section modulus of steel beam for extreme tension fibers

3-Coefficient m/i, for Horizontal Shear

Modulor ratio n = 10, b = ciiective slob width, t = dab thichnesr

h a m "Comporiie Cons<nidian i n S k r l and Concrete" by Viert, Fountain & Singleton. Copyright @ 1958. kGiow-Hill Book Com- W " Y . Used by peimiriion.

TABLE 4.-Useful Capacity, Q, of One Stud Conneckw. Ibs. (h/d > 4.2)

S c m d o . CONCRETE S l k t h G T ~ . pr

6,500 1 7,100 1 7,600 r , 2 0 0 I 9,300 10,200 I 1,000 1 1,700 % 12,600 13.800 15.000 --- 1 6.000 - ~. ...

Note: A faitor of ioiety must be opplisd to the obove useful co- pacity, Q, to orrive at t h e working volue, q.

TABLE 5-Useful Capacity, Q, er Turn o( Spiral Connector

CONCRETE STRENGTH, f',, psi. Spiral wire p~-- - - ...-. . - . - .. . . . dia. in. 0 0 i--c0 r ... 7 4000

Note: A factor of safety must be applied to the above useful co- aacitv, Q. to oirivs at the war4ina volue. s.

VD --- vertical shcar caused by dead load acting on composite section

VL I= vertical shear causcd by live load

spacing of slzcer connectom

where:

s = spacing or pitch of shear connectors in the direction of beam axis, in.

n = number of shear connectors at one transverse beam cross-section

q = capacity of one connector, Ibs

Vh = horizontal shcar to be transferred, lbs

The spacing of shear connectors sllould not exceed 24".

ESlGN OF CONNECTING WELDS

Welds joining shear connectors to beams should be designed to the allowable fatigue force (f,?.), for the range (K) of shcar stress and the working load ( q ) of the connector. See Table 7.

where:

min. shear ( V ) K = max. shear ( V )

w = leg s i ~ e of fillet weld, in.

f, = allowable force on fillet weld, lbs/lin. in


1 Problem 1 I To determine the working load ( q ) , spacing (s) , and weld length ( L . ) for each of several typcs of shear connectors, for a typical composite section.

In the building field, the total horizontal shear force to be carried by the shear connectors is based on the total bending force in either the concrete or the steel section resulting from the maximum positive moment on the beam. It is assumed this force will be transferred from the concrete slab into the steel beam by the connectors along a distance from the point of maximum positive moment ont to the end of the beam, for simply supported beams; or from the point of maximum positive moment out to the point of contra- fiexure, for continuous beams.

In the bridge field, this shear transfer is based on the vertical shear applied to the beam. In most cases this value will vary along the beam's length. For this reason, more than one section may have to be checked when the size and number of shear connectors are determined.

This example considers just one point of application, the section near the pier supports, and assumes certain conditions:

Stud Connectors

Use W dia, x 4" studs. From Table 4, Q = 10.2 kips/stud.

working load

Q q =- F.S.

spacing of connectors (use 4 studs per transverse section)

weld length

Complete contact surface of stud is joined to beam. No calculation of weld length is necessary.

hannel Connectors

Use a 4" 5.4-lb channel of 10" length. From Table 6, Q L= 49.6 kips/channel.

working load

F.S. q .= - Q

FIGURE 4 L f,' = 3000 psi (concrete)

m - = 4 i n (See Table 3) 1,

F.S. = 3.81

V,,, = 49.6 kips

V,,, = 5.06 kips

calculating for horizontal shear

spacing of connectors

= 10.75" or use 10%''

allowable force on weld

Assume fillet leg size of w = 3/1$" and N = 600,000 cycles:

V,," I< = - Vm,,

- .- (+EL06 kips) (+46.6 kips)

= 1.4 kips/in. of weld

required ueld length

= 9.3" < 20" actually used OK -

This indicates most channels are overwelded.

Use %'' dia rod. From Table 5, Q = 21.31 kips/tum.

working load

Q q =- u S

4.61" or use 4K"/turn -

force on weld

Pissumc fillet leg size of w = %" and N = 600,000 cycles:

- - ( i 5 . 0 6 kips) ($49.6 kips)

7070 o f - W - K (From Table 7 )

= 2.8 kips/in. of weld

= 2.0" or I" each side in contact area .- - ... -. . . --

Studs are widely used in both building and bridge work as shear connectors for composite construction. Quickly attached by efficient orc- welding equipment, studs serve to anchor the concrete slab to the steel beams. The composite beam provides high strength at lower cost.

Typical scenes of modern bridge work featuring composite construction. Prior to pouring the concrete deck, studs are ot- tached to girder flanges by specialized arc-welding equipment. Connectors allow the concrete slob to act with the steel.

1. REINFORCED CONCRETE

Many hridge designs use reinforced concrete slabs for floors. These may be suppoited by stringers and floor beams of the bridge. When no iloor beams are present, the concrctc floor is supported directly on top of the primary longitudinal members.

On deck-type bridges, with the concrete floor resting on the top flange or top chord of the longitudinal member, the concrete slab may be anchored to the steel by means of shew attachmcnts. In this manner, the concretc floor becomes an integral part of the steel member in compression.

This composite construction is rccugnized by most structural authorities as an effective means of insuring economy (particularly in steel tonnage); of promoting shallow depth and more graceful shuchual lines, and of improving the rigidity of bridges. Typical savings produced with composite construction alone are in the range of 8 to 30% by weight of steel. To be effective, of course, the concrete must always be in compression to prevent cracks in the pavement.

Some types of shear attachments are shown in Figure 1. See Section 4.9 on Shear Attachments for

FIGURE 1

Steel grids may be used for floors for the following reasons:

1. Reduced dead weight of flooring. This reduces the required size of stringers, floor beams, and girders

arid results in a savings in the amount of steel and cost of the bridge.

2. Snow does not remain on the grid floor; hence, grids greatly lower snow rcmoval cost during the wintcr.

3. Since s11ow and rain do not remain on the grid floor, therc is no reason for a crown for drainage purpose"^ This si~nplifics construction costs.

4. For the same reason, scrlppers and drains are riot required.

5. Tlrr grid flooring a n be installed easily and quickly.

Sometimes a light concrete layer is applied to the steei grid.

FIGURE 2

3. STEEL PLATE

Steel plate welded to the hridge structure and properly stiffoned has been used for flooring. By welding a corn- parativcly thin steel plate to the top flange of longi-

FIGURE 3

tudinal members, a built-up section is produced which greatly increases the strength and stiffness of the member. This has sometimes been called "battledcclc flooring".

. TYPICAL FLOOR SYSTEMS

The design in Figure 4 ( a ) utilizes a steel grid floor in order to reduce the dead weight of the structure. The steel grid rests on the main girders and the longitudinal stringers. The floor beams are set lower so that the stringers, when placed on top, will be flush with the top of the girder. Brackets ,ue shop welded to the girders to receive the floor beams. The top bracket plate is slightly narrower than the flange of the floor beam, and the bottom bracket plate is slightly wider than the flange of the Boor beam. This is so that downhand fillet welds may be used in the field connection of the floor beams to the girders.

With a little extra care in shipping and creeting, it would be possible to shop weld the railing and like attachments to the girders and further reduce the field welding.

The floor system in Figure i ( b ) is made up of two longitudinal steel girdcrs with a concrete floor attached to the girders by means of shc'u connections. Althongh spiral shear cmncctiuos are shown here, this composite beam could be made by using any type of shear attachments. Shrar attachments can also be used on the floor beams.

in the design in Figure 5(a) , the top portion of the girders hclps to form the curb. For this reason, the floor bcams mnst be lowered, so as to get the bridge floor helow the top flange of the girders. To keep this floor level down, the stringers nnl Between the floor beams and their top flanges are flush with the top flanges of the floor beams. Although this produces a very compact and Acient design, it does involve a little more fitting and welding than the previous floor designs.

A vcry popular design today is the continuous girder deck bridge, Figure 5 (h) . Several plate girders are placed side-by-side with sufficient cross bracing. A composite concrete Boor is attached to the top of the girders by means of shear connectors. For short spans, rolled beams are used with cover plates added

FIGURE 4

FIGURE 5

F l o o ~ Systems for Bridges / 4.10-3

at points of high moment. For longer spans, deeper plate girders are fabricated. For a more efficient design, these girders are deeper at points of high moment. The outside girders usually have their intermediate stiffeners placed on one side only, the inboard side, so that they have a more pleasing appearance.

Box girders have been used for bridges; usually two or more are used. They may be joined by several metl~ods. The example in Figure 6 ( a ) uses floor heams flush with the top of the box girder, on which is placed a concrete floor attachcd with shear connectors.

with floor beams extending outward to support the bridge Boor. In Figure 6 (b ) , longitudinal stringers are sapported on the Woor beams, and the floor rests on tticse. It has evcn been suggested that a similar design could he made from a large diameter fabricated pipe section.

5. TORSIONAL RESISTANCE

Designers arr coming to realize the importance of designing bridge floors, etc.; with more inherent lateral stability and torsional resistance.

Box girder constrnction has sevcral :tdvantagcs. It presents a flat surface for otlicr r~tt;tch~ncnts; hmce, the floor b c a m do not havc to be copad whcn they are welded to the girder. Then, is irss of a c ~ l ~ o ~ i o n problem because of thl. flat srirfaces. Also, since tlie box girder ends may hc s c a l d off, the illside is protected. Perhaps the grmtcst advnntaga is the treman- dous incrcase in torsioi~iil rcsistanee offered by tlw closed box section. It ;tiso lias good lateral stability. These torsional and la t~ra l st;ihiliiy proper tit.^ nrc br- coining recognized advantagis. and morc bridge engineers are making use of tlrim

Some designs havr made use of a single box girder,

When a simple inernher is subjected to a torsional moment, shmr stresses occi.ir; one set being at right anglrs to the axis of the member and the other set ltmgthwise. In I'igr~rr. 7, shear forces ( b ) act at right angles to the lengthwise member and causc it to twist. A fiat scction 01- any opcn section offers vcry little rosistanec to twist. Thv cross membcrs are subjected to thr slicx forccs (;I) and. likewise, twist. If a diagonal mrmber is placcd in the: strncture, both shear forces ( a ) mid ( b ) act OII it. 'fowcver, the coinponents of thesr forws. acting at right angles to the diagonal

FIGURE 8

member, cancel each other out, so there is no twisting action applied to the member. These forccs do combine to place tension and compression in line with the member, thus placing the diagonal member in bending for which it is very rigid. Welding can be used to very good advantage in diagonal bracing.

Figure 8 is From a bridge designed by Camilo Piccone and ermteted over the Rio Blanco River in Mexico. It is based on an earlier design of Thomas C . Kavanagh. The floor makes use of diagonal members which procluce a grid type structure, extremely resistant to twisting and lateral movement.

Thermal chianges in temperature cause certain physical changes in the size and shape of all construction materials and in their completed strudures. The changes are in proportion to the dimensions of the structure, the coefficients of expansion for the materials, and the number of degrees of temperature change.

The structure contracts with the cold and expands with the heat, so a typical bridge might be approximately 1" longer per 100 linear feet in the summer than in the winter. It will also have daily and short- time changes of a lesser degree in proportion to every change in temperature and it will have additional movements from the elastic deflections of the structure.

These changes in lcngth can be compensated for hy corresponding drformations within the structure itself. This is because changing the stress in the stnic- ture will also cause it to change in length in proportion to its modulus of dasticity. However, it is usually more economical to u s e expansion joints since the forces that are required to deform a structure are very large.

Masonry materials such as stone and concrete compress elastically but will not stretch. Therefore, they are iilcely to crack when subjected to the stresses of temperature contraction.

For these reasons and others, most structures are dosigned with provision for expansion joints at intcr- vals to take care of the uormal movements of expansion and contraction and to relieve the thermal forces. Many types of joints in common use have been designed to do this, varying from open joints, simple planes of wealmess, 'md elastite joints such as are commonly used in pavements, to the long interlocking fingered castings and sliding bar joints used in bridge work.

One Example

The all-welded expansion joint shown in Figure 9 is similar to those in the deck of a large bridge built in recent years. This joint is made entirely kom rolled structural plates m d angles at a great saving in cost by welding.

It is typical of many cases wherein welding has

FIGURE 9

Door Systems for -5

not only simplified and improved bridge deck designs b ~ i t has also reduced the cost of the installation to corlsiderahly less than half the estimated cost of con- vrntional type of segmental cast steel fingered joints.

The joint as shown provides for 16" of movement computed at the rate of 1%'' per 100' for the 1200' length of stnicturc.

The joint (Fig. 9) is made in two halves, each half being symmetrical by rotating 1180" with respect to the other half. Thc joint integral with the curbs, extends the full width of the 24' roadway in one piece. This

teeth. The slight side taper of %" in the length of the tooth adds to the clearance as the teeth are pulled apart. The 18" length of iw ih is dctwmined by adding 1" ciearancr at extremc expansion movements, plus a minimum lap of I" whcn the bridge is fully contracted to the 16" of required movement.

The treth are spaced on 4" centers. This spacing is as small as practical in order to distribnte the loads from the roadway sm-fitce over as many treth as possible. It is also desirable in ordcr to avoid having large l~oles between the teeth when the joint is open. The

LAYOUT OF FLAME CUT TEETH

FIGURE 1 1

is fabricatcd to fit t l ~ curvature of the roadway crown. upper surfaces of the ends of the teeth are ground The intwlocking teeth which form the top surfaces down and rounded slightly to insure a smooth tran-

on both sides ol thc joint are flame-cut in a single op- sition of the loads from one side of the joint to (he eration from a common 28" x I" x 24' plate as shown other. in the layout of Figure 10. The cut is made just wide The joint shown in Figure 9 is designed to support enough to insure finish on both edges of the cut and 16,000-lb Ii-20 tmck wheel loads with 100% impact. to give proper clearance fur the final meshing of the This load is distributed equally to each of five adjacent


teeth and is assumed to be applied on a contact area 3" long, centered I.'?" from the end of the teeth. While in this extreme position, the teeth on only one side of the joint support the entire load. On this basis the depth of the web, the thickness of the plates, and other proportions are determined to support these load requirements.

The unusually long cantilevered projection of the teeth is reduced by snppolting the teeth directly on an auxiliary end cross beam. The cross beams in turn are supported from the end flwr beams at 10'-3" intervals by means of cantilevered stringer brackets. The floor beams span 35' center-to-center of busses, and the trusses are supported on expansion rocker or roller bridge shoes.

The strength of the tecth in this case is obtained by continuor~sly groove or fillet welding 5" x 'h" x 1'- 8%" vertical web plate ribs to the underside of each tooth, as shown in Figure 11. Thc rear ends of these ribs are anchored for uplift by groove welding to the back of the 7" x 4" x %" slab closure angle. This angle is continuously welded to the I" surface plate, and serves also as a latesai distribution beam between the plate anchors.

Plate anchors composed of 5'' x %" x 1'3" web plates are welded to the rear of the joint opposite the web of every fourth taoth. These plates are spaced at 16" centers, and each plate engages two Y4" jacking bolts to the flange of the floor beam. These bolts serve both as erection bolts for setting the joint to elevation and grade, and as anchor bolts to hold down the rear of the joint against uplift caused by traffic. The plate anchors lap with the main longitudinal reinforcement

bars in the slab for continuity, and the end of the concrete casts into the pocket formed by the surface plate and the 7" x 4" x %" angle.

The vertical leg of the 7" x 4" angle is flame cut to fit the curve of the roadway crown before welding to the 1" plate. This helps to hold the joint in proper shape. The ribs are all held together at the bottom by welding to the 5" x %" continuous plate bolted to the anxiliary cross beam.

The entire joint should be assembled in the shop with the cross brams :uid the field holes drilled to insure a proper fit in the field.

Field erection consists simply of setting the bridge shoes the proper distances apart, shimming the end cross beams to proper grade, and a final adjustment of the jacking bolts and the bolts to the cross beams. The concrete slab is then cast up to the joint around the anchors and cured, and the joint is ready for traffic.

One complete 24' joint as shown in Figure 9 weighs 6250 lhs. This compares to an estimated weight of 8500 lbs for a conventional cast stecl fingered joint.

This comparison indicates that the welded detail accomplishes a saving in metal weight of 26%, in addition to rpplacing expensive cast steel metal with rolled structural material. The relative cost of rolled metal is much less per pound.

A very important type of floor construction is the orthotropic deck, in which all elements of the structure work together. Having principal application in the bridge field, orthotropic constn~ction will be covered separately in the following Section 4.11.

1. THE ORTHOTROPlC DESIGN CONCEPT

There is a growing interest in this country in the use of orthotropic bridge design and construction, a system now commonly used in Europe.

With conventional bridge structures, the three main elc?ments-longitiidinal main girders, transverse floor beam, and lighter longitudinal stringers or stiffeners- all act indeperldently of each other. Usually an 8" thick concrete floor distributes the applied loads; see Figure 1(A).

In contrast, a11 elements of the orthotropic structure work together; see Figure 1(B). This new system uses a thin steel deck plate across the entire width and length of the bridge, and this serves as the top flange plate of the (1) longitudinal main girders, (2) transverse floor beams, and (3) lighter longitudinal stiffcners. The deck plate also contributes to the torsional resistance of the stiffeners when it forms a closed section.

I-Iaving a common top fiange member, all three elements act and load up together in the most efficient manner. The steel deck plate is topped with a light 1%" thick asphalt wearing surface for complete elimination of the heavy concrete floor.

The combined orthotropic deck st~ucture acts as a single plate or membrane with three separate sectional

properties: hending resistance about the x-x axis (transverse to the length of the bridge), bending resistance about the y-y axis (parallcl to the bridge), and torsional rcsisiance about the y-y axis. A corrcentrated load placed upon the deck plate is distributed over a wide area to several adjacent floor beams. The longitudir~al stiffeners below this load act as beams on elastic supports. With increasing load, the rather fiexible deck and stiffeners spread the load over a greater area. This action has been confirmed by many tests on modcls as well as actual bridges.

In the tests of the model of one bridge, the computed test load corresponding to maximum allowable design stress was 2.06 tons. The computed ultimate load was 5.6 tons. During testing, measurements indicated there was perfect dastic behavior up to an actual load of 4.1 tons. When loaded above the dastic limit, there was no rapid and unrestrained increase in deflection as is customary in the usual bending of beams; rather the deflections increased linearly just a little faster than the applied load. At a load of 48 tons, a crack started to appear in the stiffener region, and at 56 tons this had spread over the entire depth of the stiffener. This test hldicated an apparent factor of safety of 27 to 1.

With optimum use of welding, orthotropic construc-

/ $ " a ~ p h a i t surface

Conventiono 1 Brldyr Conventiono I Brldyr

, -. ' N o o r beam

FIGURE 1

tion rt-sults in the bridge superstruclur? ns~inilly weighing only half as rnrrch as woi~ld rmrlt froin any other design system. This weight :a\,ing is such a tremenclorrs advwtagr on lorig span bridges, that ortliotropic desig:r is rapidly replacing truss dcssign on a11 European bridgt.s having spans of 100' or more, and shoiild do thc same in this coiintry.

AISC hns piiidishcd ail cxccllcnt design i~xirrunl oil "Orthotropic S t rd Plate Deck Bridges" by Roman Wolcliirk (1963). It contains thcory, methods of design, and sr~ggcstcd details of orthotropic bridges.

This typo of hridge design ivor~ld be impractic;il without the i.xtensive usc of welding. The miles of welded joints afford a good opportimity to sub-

~ ~ s s o r h l e the sections (or anion~atic dobvnhand wilding and rnodrrn fabricating methods. Sincc riumi~rorss idm- tical dwk sections are rrquinrd, they may ix. set up in ;i jig and autorn:~tirnlly suhmrrged-:trc w e l d d with ~nir~imr~in time and cost.

. JOINING LONGITU lNAL STIFFENERS TO ECK PLATE

In Er~mpean orthotropic hridgt- design, longitudinal stiflcners :ire cominonl!. of trixprzoidal cmss-scction for torsional rigidity. .4mwican &%sign interest appears to favor this approach; sre Figure 2. -4ltho11gh riot too clear on the slwtrh of the Port hlann bridge, the edge

FIG. 2-Typical Hollow Trapezoidal Ribs and Connecting Welds

floor beam 1 Wesei Porta

rib

Web of 4" floor beom. 1 1

AiSC Standard (initial]

I (Feb 1960)

interrupted

Mannheim-Ludwigshafen

Continuous

floor beam - 1 I Port Monn -

L6%'4 They considered

Poplar Street both interrupted

St. Louis and continuous (proposed) trapezoidal ribs

FIGURE 3 ca

of the stiffener was cut square without any bevel. It was shown in tests by the f~lbricntor that a single pass madi. with the aut.om;itic srihrrrerged-arc wclder would prodilce a sound weld with tbroat grmter than stsener thickness; see Figure 3.

The torsional resistance of any closed tubular section, as indicated by Figure 4, is:

where:

[A] = area encloscd hy the: trapczoid t g = thickness of deck plate

t, - thickness of stiffrwcr

bR = width of deck p!:ite within region of stiffcner

b, = umlevoloped width of stiffener

In designing the Port Monn Bridge in British Columbia, Canada, engineers specified orthotropic deck construction for maximum weight reduction ond dollar economy. Deck plate is stiffened by longitudinal trough- shoped stringers formed by press-brake. Welding of stringers to tronsverse beams is done by a progressive ossembly technique . . . for near continuous-flow production.

FIGURE 4

l'hv &sign Manniil fur Orthotropic Sttel Plate Ihck liridgcs innlti~lics this torsional rc~sistairce ( R ) by a rcdnction factor ( p ) which lias Ivwr dciermincd hy trsting of varims shapes of stiffcm:rs. %is factor is afFcctrd by the shape. of thc stiffcncr.

Stiffcncrs can readily fomreri to the trqwmidal shape oil a prcss hr;rke. Recmse of the torrnagc re- (psired, it might hc more eco~iomical to pnrchase a spt.ciai irrill-rolled srvtion for the stiii'cnms; see Figure 5. T h ~ n thc outer portions of tlw platr w-kith which become webs of the lmilt-np trapmoid scction are rollcd thiimcr, m d tlic ccntral portion is left thicker for tho lowrr fiangc,. This places the inatcrial where required: f o r t h r(.ducing the bridge uvight and tonnage of stccl required. The plate conld bc rollcd to the final trapeztrid section, thiis ciiminating the braking operntion Imigths of this scction would nest and preseiit no problem in shipping.

Another rt+hment \vould bc to pnwicie slightly greater tliickness at web cxtreniities so as to give more hearing against the deck plate and greater throat to the connecting weld.

Thitker section

FIGURE 5

Back~ng bar,

Y Z 9r40ve welds

Two splices every /5'

FIGURE 6

3. FIELD SPLICE OF LONGITUDINAL STIFFENERS

There are two basic methods for detailing the intersection of longit~~dinal stiffeners and transverse floor beams; see Figure 6.

( A ) Following the common European practice, the floor beam webs run continuous and stiffeners are but to fit between the beams. The stiffeners are thus limited to about 15' ui length, and the main bending stresses of the structure in the stiffeners must be transferred trausversely through the w ~ h of each floor beam by means of groove welds ( T joint). There niight be a question of the possibility of a lamination in the web opening up because of the transverse force applied through it. This method requires a large nnmber of field groove welds to be made in the vertical and overhead position. There are 2 welds at each heam per stiffener.

( B ) An alternate method would be to have the trapezoid stiffeners run continuous throughout the length of the structure, with webs of the floor beams cut ont to fit around the stiffeners. This would clirninate any questions as to the safe transfer of main bending stresses.

This method wonld grcatly rcdnce the required field welding. For exaniple, the stiffcnrrs could be shop fabricated into 60' lengths; this would require just a single groove meld in the field every 60'. This would be a single groove butt joint in contrast to the 2 groove welds at each floor heam required by Alethod A. The critical field welding thus u~ould be only % of that required by Method A.

" - In a translation of a German paper, l'atigue Tests on Ilollow Rib C:onncctions" by FI. Hansch and C:. Mullcr, rcsnlts of fatigne testing three different dctails of longitndinal stiifeners were snmmarizcd:

1. The longitndinal stiffeners were internrpttd at the transverse floor beam wcbs and joined by fillet welds to the webs of t l ~ e floor boam.

2. The longitlldinnl stifl'mers cverc interrupted at the floor heam wehs, but \ \we \vrldcd with single bevel groove wclds to thc webs of tlif. floor beams.

3. The longitudinal stilfencrs ran continuously tln-ough the floor beam webs.

The results sholved the continuous stiffener (1) to have the highest fatigue strength, cr = 28,000 psi, when tested with a stress range of

'Thc shape of tllc closed t~ibiiliir k~ngi t \~dind stiffrnm- tcsted hail no appri.ciahlc rficct lipon the tcst I-csulls. Cold formirig of tlrta stiflcnrrs had no c i I t~ t . T h q rcconimend thxt thr dcsigncr place the firld splice of t lw stiilcncrs iri low-stressed regions.

4. SHOP FABRICATE SUBASSEMBLIES

l t is possihle to lal~ricate nrzirly the rmtir~. drck of the bridge, in sections. r~ndcr optimum shop nmditions and thcrchy miriimizp the amo~mt of fir.id w~icling. This includes dcck swtims lying 1xhw11 tlit. mnin box girders. and ;my swtiorls to h r c;intilrv<vd out from the hox girdcr.

Thr drck unit wliicli is to rrst hrt\r-wr~ tlic main box girdrrs can be in;idc initially in thrnc swtions. For ;In average bridge, each of thesr prciabricatd sections, 9' wide by 60' long, would weigh about 8% tuns; see Figure 7.

Three of these sections \vould he 1;tiil out, still upside down, and tack wclded together; see Figure 8 ( A ) . This work would preftmbly hc done on the

f ind means of transpoi-t. in some cases :I barge. 1':acii longittrdinal joint ol thc top d ~ k pink can he made \i,it!i a two-p:ws ivi~ld; o~ie pass on r d ~ sidc using x sr~hmergerl-arc :~utorii;itic wclder. This joint is a simple sq~~arc*-bistt joint witliout i~ny b;icLing bar, a ~ ~ d rcquircs rio l>r:vi:ling of plat[. edqm. : \ l t ~ ~ making the first pass, tllr fonr floor bcams 21re r i i i ~ n ~ ~ a l l ~ welded in place. Each bran1 consists of ;I hottom flmge p!atc and a a e h

having t r ; ipr~oi~ld <,litorlts ;ilong the top edge to fit :~rorn~d ewh stifk:rir:r.

With the, tr;~nsvrrsc. foor hc~im welded in pl:icc;

FIGURE 7

v2 l S e p e ~ s on deck E

FIGURE 8

4.1 1-6 / Girder-Related

the entire nnit can be turned over without undue strain on the incompleta butt weld. A second pass is taken to complete the automatic welding of the longitndinal joints, all in the dovvlihand position; see Figure S ( B ) . The result is a complete dock unit, 27' X 60', weighing abont 29 tons, to be hoisted from the barge into position between the two main box girders.

The Port Mann bridge d t ~ k panels were fabricated and wc4dcd in the shop as units 65' wide, the width of the drck lying in between the main longitudinal girders, and 25' long, the distance 1)etwt:en tlie imnsvmse floor beams. Thesc panels weighed bctwecn 32 and 36 tons, drperiding upon the deck plate thickness. In Europe, panels up to 58' X 18' have bccn Fabricated and trans- ported by barges to the site. The Save River bridge had prefabricated panels weighing 27.5 tons. The Mannheim-Lndwigshafen tiridge was erected in panels 18.5' wide and 60' long. The Severin bridge in Cologne was erected in panels 62.8' wide and 47 to 54' long.

. FIELD ERECT10

The ontire superstructure probably wo~ild he erected in units, starting from a pier support and cantilevering out. A travelirig crane coirld place tlic individual units. For any givm scgment of the span, the main longitudinal box girders would be put into position first. The field splice of tho top flange deck plate should be weidrd bec;rnse the l'h" thick asphalt floor to be applicd leaves little room [or splice plates and bolts. The erection bolts probably shoold bc on the girder webs. The girder's bottom flange may vary from %" to 3 or 4" thick platc, and could be spliced by field welding because field bolting of this thick plate would be costly.

Transverse shrinkage of the weld on the $5'' dack platc witliin this 1x1s girder is estimate1 at ahout .03", and shrinkage of the groovc wcld of 3 3" bottom flange plate at about .10". Under this condition, a suggested I~~-~~cedui -c is to weld the bottom flange to about ?* completiorr, thrw weld the top deck simultaneous with welding the remaining % of the bottom flange. In this maiinrr. bot l~ ilangcs shonld pull in togctller evenly.

T l ~ r nest stcp would be rrrction of the sohassem- bled dwk unit hctucen these two main box girders.

Wit11 a dcck unit raised into place, tlie ends of each floor beam would hc field w e l d d to the main box girdcrs. The two lor~gitudinal joints and one t ransvax joint of thc l /~ ' r deck platc siiould he weldrd in a single p s s with :I submcrgcd-arc tractor. Plates should be imrtially hrveled at the top and a backing bar i i s d so that iull-penetration u d d s can be made in the down-

FIGURE 9

hand position; see Figure 9. Longitudinal stiffn,crs would be field spliced by

n~anr~ally groove welding tlic hntt joint using a light hacking bar placed on the inside of the trapezoid, very similar to pipe welding. The upper edge of the stiffener could be notched at this joint so a backing bar can run contin~iously across the deck to facilitate automatic welding of the deck piate transverse joint. Under these conditions, tlic joints of deck plate and stiffeners shciild be offset at least 2", as shown in Figlire 10, so each deck unit can he lowered down u-ithout interference of the backing bars.

ckiny bar for ~t I ' f fener

e

Mew akcksection about t o be lowered inp/a.ce

FIGURE 10

If there is :my doubt ahont thr fit-up of multiple stilfcnm for field splicing, (wls of the stiffrncrs can br left un\veldc(I to the deck plate for about a foot. This will permit thrm to ho i~idividually aligned horizontally for welding.

If slxcific dimensions OF the stiffener indicates a possiblc prohlcm in accssihility for the wcldor in niak- ing the ficld splices, the deck plate can be left sliort by about 10" from cxch m d of tlir section; see Fignre 11. This worild also allow tlir back of the joints on the illside of tlic trapezoid stitrcner to bc root gonged and R mot or back p x s inadc. .4 20" wide deck platc section wolild thcn hc inserted, and two transvcrsc groove xelds made. This would doi~blc the icngth of translwsc welds for splicing the deck plates; ho\wver, all of this wclcli~~g would hc automatic, singlc pass work. Ends of the stiifenrrs \vonld then 11c overhcad welded to this deck insert; as shown in Fignrc 11.

An alterriate way to field splice the trapezoidal stiifenrrs is to place the 1x:vrl on the inside and a backing bar on the outsidc; tire weliior then makcs all the splices while working from the top of tlie deck.

ecks 1 4.11-7

transverse eutonktic weld \ o f deck F;eldsplicc of stiffener

Deck R + stiffemer v serving es the top Deck E + stiffener f l u y e , js in servioj as the t o p

comprcssioo f lmye , is in tension

FIGURE 12

This type of inspvction should he limited to critical joints \\hicli the Engineer should seli~ct. Fatigue conditions that reduce the allo\v:ible stress in design may indicate such a nwd; for rxample, groove wcldcd h t t joints snhject to tension, 3 \vide mngr of stress, ;I high stress, and a large ntirnher of cycles. As the factors that produce fatigue loadi~ig ;il-e reduced, the necessity for mdiographic inspection is likewise rcdoced.

If all of 1111. groove \vcicls in the deck plate are madt~ by the suhmergcd-arc antomatic proccss, proprr procedures car1 1)c cstahlishad to insure good mvlding. This should eliniinatc the ~ i t d lor costly radiographic inspection ol tllesr \velds, altho~igh linritrd spot chocks conld IF mad<>.

Any ficld spli~i. in the lower flanga of the main box girticrs in ;i rcgion of pwitivc moment, rnight be inspected by radiograph)-.

Fi,.ld splir:t!s in the longitudinal stiifcners must be considcrr.d from the type of loading:

1. The stilfecer si>rves along with the deck plate as the top f lang~ of thc main structure, and as such is subjected to tension in the negative rnornent region

near tlic pier supports. liowcver, this comes front the dred load of thr strvcturc and any live load sprt:;rd over ;t rather Izirge arm, thus the range of strtw varin- tion and the n ~ m ~ l w r of strcss c.yr1t.s would hc ri:lativcly small; S<Y. Figuri. 12.

2. l'hc stiifi,xlcr srrvcs along with the deck pl;ite ;is n short hiwn iwtwwn l h l - hc;ims, ; ~ n d :~ny 1oc;llizcd wheel load worild prndricc n wide range ir l s i res and thc i~iirr~hw of ;ippiic;iti(~ns <vrild hc vei-y high. Ilo\ir- wc,r, by using 4 l e t l d B to dotnil thc network of floor 1w;:rns and stiKrners the only critical wclds w o ~ ~ l d oct:nr ;it abont cwery 60' of hridgc h g t h . 'l'he influciicc lines, sfc I'ig~irc 13, show the sni~incrit dike to conc<~ntr.;ttcti \vliccl load at givc~i poii~ts as the load progrcssm along thc span bctwecn floor 11r;ims. Hy locati~ig the field splice of thc stiffcuw ;it :1 point ahout '/ro I, along the span Iwtwct:~~ s~~pporting Roor brrams, the hcndii?g strcss on thc n d d is rath1.r lmv m d ~vithmrt much Ructnation.

Spot checks of the stiifcner liald spliccs by gnmma ray irisliwtion, if rcqriircd, could he m:i& by rlrilling a small lido in the 12" deck piate and lowering thc capsiilc dowr~ li;~lf\v;iy into the interior of the [rape- zoidal area, with thc film wi-appcd arourid thc outside

. I 1 4 / Girder-Related Design

eld splice in siiffencr

I L -----------------A Deck @ in thsion ; bottom

Moment diaqram

Concentrated wheel load

Max. moment (due t o ?- concentrated l o u d ) on deck section

Infhence /;nes showing shift of maximum moment as the concentrated toed moves along span.

--

FIGURE 13

of the stiffrner. This hole can he filled later by- welding, or by tapping it and screwing a pipe plug into it.

. WELDOR QUALIFICATION

In addition to the standard .4\1'S u d d o r qualification test, it would he well for those men assigned to field weld the stiffeners to &st weld a test joint of this splice in position. This can be givcn a visnal inspection, including sawing of the joint at one or more points and etching to determine if proper fusion was obtained. It might bo well to consider weldors who have had some experience in pipe welding.

I Problem 1 I An orthotropic deck is to be fabricated in units 104" wide containing 4 trnPoidal stifleners cach 13" wide and on 11" centers. The stiffeners are weldcd to the 3 n /8 deck plate along their edges. If these nnits are 30' long, cstimate the amount of bending or camber due

to the shrin1r;lgc of the welds; see Figlire 14. To find the prnpcrties of this section, seiect refer-

ence axis (x -x ) along ~ ~ n t l t r ~ ~ c a t h sill-face of deck plate. This is almost through tlrc ciwtcr of gravity of the 2 welds, and tlw resr~lting distance to the ncritrxl nsis ( n ) will also hc the disiancc I~etwern the neutral axis aim1 the ccnter of gravity of wt.lds ( d ) .

(-3.5.412)2 = (279.87) -- ( a 7 9 j

- (Proin Table A )

- - -2.19" also = d

Orthotropic Bridge Decks / 4.1 1-

- L - - Neut ra l oxis

% (%") ('L") = 1/24

FIGURE 14

TABLE A

bending or camber I , = 30' = 360" I n orckr to find t l i ~ propi.rty of tlnis 111iilt-tip

005 A d L' section, it is newss:rry to lmrw tlit: properties of the A = ' " I i~rc of a cil& whicli fornns tlie roui~d huttom portion.

-1- ,585" ( r ~ i d s wonld go iip this ;Imolmt)

Tl~is 1~1e;ins when tlie 30' long unit is upside clown for \ w l d i ~ r ~ . the fixturt, should be curvcd suEcicntly to pull tlir. central section of thl. unit down by this arnouut ( ,585").

/ Problem 2 1 FIGURE 16

k t r t i i i I I I n I t .\lami bridge in British Cohirnhia coiisists of tr;n,c;.oiclal stillpni:rs 11 m ~ i Iw d ~ n v ~ i t l~at Ilic f(1l111wi11g is trii~.: with r o 1 1 1 1 bottoins spac(d OII 2-1" cpntcrs and n-eldtd to u 'r" to dcck plat<,. Tl~cs(. dtrck se<,tir~ns h 2 t r H artx shop \wldisd illto p;ii~ris ;~l~ori t 65' \\-id,. th<s M-idth of tlrt~ hridgr in bi,t\v<x~~i tlii. maill Iorigiti~di~~;il girders, dl

and 25' Itmg: as sliown in Fignrc 15. 1:stimate tint 2 \ i l , ~ ' 11

ainoirnt of htwiing or c;nribt~ dnc to tht: sIirii,k;igc of lg ~ t r t [ O ; I z s i ~ t ? ~ the welds.

8 k t n t r 0 1 r i i i i ty )

irder-Related Design

In this example:

0 = 72.45" or 1.263 radians

TABLE B

These values will now be used in finding the properties of the built-up section. To find these properties, select reference axis (x-x) along the w~derneath surface of the deck platc. This is almost through the center of gravity of the 2 welds, and the resulting distance to the nentral axis ( n ) mill also be the distancc between the neutral axis and the center of grnvity of welds (d) .

= (323.35) - -- (-38'76)2 (From Table B ) (19.27)

bentling or camber L = 25' = 30G"

0 0 5 A d U A = .: ~ .. 1-

= .48" (ends would go lip this amount)

This means when the 25' long unit is upside down for wclding, tiit. fixture shoi~ld be cnrved sufficiently to pnll the central section of the :mit down by this amount or about irY,

FIG. 1 Multiple burning torches cut heavy steel plaie to be used in fabricated bridge girders.

1. PLATE PREPARATION

Flange plates may be ordered as bars rolled to the proper width and thickness. No further prepamtion is rcquired excppt cntting to proper length and beveling the ends for thc butt joint.

Some fabricators will flame cut the flange plates from wide plates; Fignre 1. Since there is some shrink- ;tqe due to the &%me cntting opwation, the flalrge will have a swoep or bend if it i? cut along just one side. For this reason the flange is rnadc by cutting alorrg both sides, usually with a cutting unit having mnultiple torches which are cut at thc same time.

For girders with a horizontal curve, the flange plates arc flame cut to the proper cnrve.

2. FIT-UP AND ASSE

Fabricators having fnll-automatic, submerged-arc weld-

ing hc;rils usrx~lly fit thc flanges to the web ; ~ n d then cornplcte thc fillct wrlc1ii1g.

Platc gii-dcrs may be fitted a ~ d assembled by one of the follo~ving pl-occdures:

First, one flange is laid fiat on the floor. A chalk Un,: is markcd along tlrc wrrtrrlinc of the flangc and srndl right-angle clips tack weldt~i at intervals along the Inngth of the flangc w a r this ceutcrline. See Fignrc 2. Next, thc web is plaetd vertically on the flange and temporarily siipportd with :~ngl<is or bars tack welded hctwccn the web and the Range. The clips along the flange align the wcb along the ccnterline of the flangt:. Thc top flange plate may then ba placed on top of the wel). This rncthod may bi: nsed for straight girders if thry are not too deep

Thc plat(: girdcr r~iay be assembled hy placing the wcb down on a fixtrirc in the ho~izonral position: Figure 3. The fiangr platcs ar t p t in position and some

.?2-2 / Cirder-

FIGURE 3

FIGURE 4

clamping method (such as wedges, screws, jacks, or in some cases compressed air) is used to force the flangc tight against the edge of the web. Thcse fixtures automatically hold thc flange in propcr vertical alignlnent.

If thc wch is thin and very deep, caution must he used so that exccssive prcssllre is not used against the flanges because this may bow the web upward. See Fignre 4. Since the Ranges arc: vcrtical in the fixture, when the pressure is rcloascd and the web straightens out, the flange3 may rotate ;md not be parallel.

I-Iaunched or fishbelly girders are usually asscmhlcd with the web horizontal in this manner. However, some fishhclly girders that ,are not too deep have hem assembled upside down with the web vertical. Sec Figure 5. What would be the stmight top flange is placed on the bottom of the fixture, and the web is positioned vertically. What would he tho bottom flange is asscmhlcd on top, and its own weight is usually sufficient to pull it down against the cnrved edge of thr web with little additional force or heating.

FIGURE 6

3. CONTINUOUS

If ro l ld hams with cover plates, plate girders, and/or hox girdcrs arc symmetrical, the firnr fillet welds will be well balanccd about the neutral axis of the section. Rtwuse of this, there should ho very little distortion or bowing of the gil-der. Sre Figure 6. The seqilcnce for antomatic wcldi~rg to produc? the four fillet welds can he varicd without major dfcct on distortion.

In most cases the welding seqnence is hasetl on the type of fixturt used and the method of rnoving the girder from one welding position to another in the shop.

In Figurc 7, the fabricator has two fixhlres to hold the girder assembly at an inclined angle. Thcse fixtures lie on each side of the automatic weldrr which nxns lengthwise on a track. Since, it is more difficnlt to corn- pletely tnrn tho girdcr ovcr, the scqucnce must be designcd to do this as low times as possible.

In Fignre 7; the girder assembly is first placed

ricatiom of Plate ideas / 4.12-3

FIGURE 8

in the left fixturc and \veld a is made. The ncxt casiest stcp is to pick up the g i r h with the crane hook(:d to the upper and swing it over to the right fixture. Heris is made on thc samt: flailgr but opposite side of the veb. Now the girder rr~rist he picked up, laid down on the flor~r, turned over, and placid hack into one of the fixtures where weld @ is madc in thc flat position. Findly the girder is picked

and suvng over to the other fixture where weld 4 is made. b

In Figure 8, the fabricator uscs a set of trunnions on the cnd of the girder asstmbly, or places the girder within a serirs of eircdar hoops, so that the girdor may he revolved. After weld @ is com lctrd, the girder is turned complctely over and wcld & is made. Now the welding head must be moved over to the back

side of the girdi.r and wcld @ is m;&. Finally the girder is hmwd coinpk~tr~ly over 2nd wi:ld @ is made.

The dilfcrcncc in the above sripience of wrldhg pnsses dcpends twtirtily on thc fixtoring zind methods ustd rzither [hm any &ect on distortion.

4. ANGULAR DISTORT10 STIFFENERS

Usually thr flangr-to-w-eb fillet welds have been tomplmd; the trmsvcrse stiEoncrs ;,re fitted and wcldcd into the girder; Figure 9.

If the flanges arc? thin and wide, the girders may exhibit some angular distortion of thc flange platis. If this has occiirrcd, thl. Aangcs may have to be forced

FIGURE 9


apart before the stiffeners can be inserted between them.

The following formula will holp in estimating the amount of angular distortion of the flanges:

/=oa?:Yo_/ FIGURE 10

TABLE A

See Table A for value of 1) corresponding to actual leg of weld (a). --

,406 - -- ,543

.... .~ - - ,688

. .- .. 1.000

AASHO bridge specifications (2.10.32) state that these stiffeners shall fit sufficiently tight after painting that they will exclude water. In addition, no attachments should be welded to the tension flange if it is stressed ahove 73% of the allowable.

Some interpret the AASHO specikation to mean a force fit; this is costly and not necessary. The following procedure will comply with this:

1. Use a loose stifEener so it may be fitted easily. 2. Push this tight against the tension flange. 3. Weld this to the web of the girder. 4. Weld this to the compression flangc. Some states have not been concerned with this

tight fit and have cut the stiffeners short by about 1"; these have been pushed tight against the compression flange and welded to the web, If just a single stiffener is used, it is also welded to the compression flange. The recent plate girder research at Lehigh University found that the stiifenrrs do not have to be against the tension flange in order to develop the full capacity of the girder. The new AlSC specifications follow this in allowing transverse inte~mcdiate stiffeners to be cut sl~ort at the tension flange by a distance equal to 4 times the web thickness.

Fabricators having scmi-automatic welding equipment sometimes insert the transverse stiffeners into the

girder before welding the flanges to the web. This is easily done since the unwelded flanges are flat (not distorted). With the girder weh in the horizontal position, the semi-automatic welders are used to make the fillet welds between the flange and web as well as the stiifenen in the same set-up.

The corners of t l ~ c stiffeners are snipped so that the flange-to-web fillet weld may be continued in back of the stiffeners. Quite often all of this welding is completed in a single pnnel area before moving to the next. The girder is then turned over and the welding completed on the other side.

5. POSITION OF WELDING

The girder may he positioned with the web at an angle betwoen 30" and 45" with the horizon, pcrnlitting the welds to be deposited in the flat position. This position is desirable, since it makes welding easier and slightly faster. It also pelmits hctter control of bead shape and the production of larger welds in a single pass when necessary.

For example, the Iargcst single-pass fillet weld made in the horizontal position is about .X6'' with a single wire, and %" with tandem arc; whereas in the flat position this single-pass weld may be about 3/4" u-ith either process.

For a 1/4" or Gr' fillet weld, the position in which the weld is made, whether horizontal or flat, would not make mnch difference.

If a %'' or 1%'' fillet weld is required, the fabricator has several choices.

If the girder may be positioned with the web vertical, this will allow both welds on the same flange to be completed without moving the girder. See Figure l l ( a ) . If the fabricator has two welding heads, these two welds may be made simultaneously, thus reducing the overall welding time. However, this horizontal position does limit the maximum size of the weld which may be made in a single pass.

If the fabricator has a single-wire automatic head, he must make this fillet weld in two passes. If he has a tandem setup, this weld can be made in a single pass with less welding timr.

By tilting the girder at an angle, either a single wire or tandem heads can make this weld in a single pass; however, only one of the welds can be made a t one time. See Figure i l ( b ) . I t would be necessary to rotate the girder for each weld with increased handling time.

A fabricating shop with two automatic welding heads can make two fillct welds on the girder simultaneously. To do this, the shop must decide between two method^ of positioning the girder; Figure 12.

It might be argued that method ( a ) should he used

(a) Two welds-multiple posr (b) One weld-single pars

FIGURE 12 Y - - Y

lbl

becausr tlw girder is in~ich morr rigid about this axis (x-x) m d thrrcforr: would d d r c i less as a result of the first two welds on tlir hottom Aarigc.

However in method ( h ) tile weld is next to the neutral axis (y-y) of the girder. Its distance to this axis is rnr~ch less than that in ( a ) , and therefore it would have very little hending efi'ect on the girder.

Since this is a thick ffange, therc may be concern about gcttiilg a large cnongh fillct weld to provide enough welding licat for thc mass of flange plate. Tlier:rcfore, it might also he argued that method ( a ) would provide douhle the amount of heat input on the flange.

.4ctmlly then: should he little diffcrence between these rncthods in the efFect of wcld shrinkage after all of the welds have heen made

6. COVER PLATES FOR BEA

Many times, rolled bnams mnst have cover plates added to their flanges for increased sircngtl~. Usually two cover plates are added, keeping the section symmetrical a l~out the horizontal axis. For composite b e a m having shear attachments on the top flange so that the concrete floor x t s compositely with the bean, a cover plate may he added to the bottom ffange for increased strength. All of tiiesc hcams mnst have a certain amount of camber.

The u-clds conuecting thc cover plates to the beam Aange tend to shrink upon cooling. With a cover

plate on cadi flmgr, this shrinkage on top and bottom flimges of the beam will halnncc and ihe beam will not distort. liowcvm-, if there is a cover plate on just the bottom flange, the unbalanced shrinkage will cause the centcr of tlw beam to how upward; in other words, it will increase thc camber of the beam.

The cauihr~ing that resoits from this unbalanced welding can be estimated by the following formula:

where:

A -: total cross-sectional area of welds, sq. in.

~ & e r piote

Neutral axis of

of weid oteo

4.12-6 / Girder-Reloted Design

If more comber is needed

Position of beam Welded in this If less comber is needed in service position

(a) When cover plate is less than flange width

position If less camber i s needed in service

FIGURE 14

(b) When cover plare is greater than flange width

d = distrrnce from the center of gravity of welds to the neutral axis of the section, inches

L = length of the beam, inches

I = moment of inertia of the section,

This may be more or less than the final desired camber, Figure 14. If this camber due to welding is excessive, the beam must be snpported in such a manner that it tends to sag in the opposite direction before welding. If the camber due to welding is not enough, then the beam must sag in the same direction before welding.

A good experienced shop man will support the beam either near its ends or near its midpoint so as to control the direction and extent to which the beam bends before it is welded.

If the cover plate docs not extend to the full width of bottom fiange, it must be welded with the beam upside down, Figure 14(a). Supporting this beam near its ends will increase the final camber, and supporting the beam near its midpoint will decrease the final camber. If the cover plate extends beyond the bottom flange, it must be welded in this position and just the opposite technique must be used in supporting it; Figure 14(b).

The fillet welds holding this cover plate to the

beam should be intem~pted at the comer, if it is wider than the beam flange, as shown in Figure 15.

9. SHOP WELDING VS H E L D WELDING

It is practical to do as milch welding in the shop as possible and to makc only those weids in the field that can't be made in the shop. The following two sections on the Field Welding of Buildings (Sect. 4.13) and of Bridges (Sect. 4.14) include some recomrnendaiions on shop welding specific connection joints.

Cover plate 1 -

Don't hook weld round corner; will not

hove full throat

'~olled beam

FIGURE 15

Hardwood bloiks

FIGURE 2

. ERECTION HEL

Several methods of ieinporarily fastening these connrctions have heen used. Tack welding alone may br u~lsatisfactory l~ecause it does not malie :~llomvance for plnn~hing the hnilding before final welding.

Clamping the beams to the colnmn scat is not ahvays safe, althmgh this hiis h w n itscd for "sito erection" of lighter strncttirrs; see Figure 2.

The steel is ordered cut to length and delivered to the site of erection. Trmporary se;lt angles are clamped onto the colutnrr at the proper position, and a temporary lug clampc~l ot~to tlrr: top flange of thc btwn. The 11eam is hoisted into position and set npon

the. temporary seat angle of the coiornn. A tie bolt is thert s c r m d on to hold the beam in proper alignment with the colrnnn. Next, the hcam is weldcd directly to the colrmm, and any tcrnporary lugs then disconnccied and used over again.

Saxe rrwtion clips, which arc w ~ l d ~ d to the beam mds and the colrrmr~, have h c m ilsed with success; s w Figi1ri.s 3 and 4. Thcse rrnits mnsist of a forged steel clip and scat. The clip is shop wrldcd to the end of the bcnm, and tlit: scat is shop wrided at the propa position on the column During erwtion; the beam is placcd in position so tllat the clips drop down into the sent. An adjnstnble clip has h e m devclopcd to take care of possible poor fit-up between the beam

FIGURE 3 FIGURE 4

and t h cohimn. It is rt~comniriided that th:. wor1;ing lo;id on any

onc s u t sho~rld not c m w l 10.000 11,s. i f n gcatcr erection load is to h~ ciirriid. sucli iis a hoavy plat? girder or truss, it is r ~ ~ c ~ ~ m r n ~ ~ n i l e d that tw-o or mow swts be used, side by sidc.

The use of a feu. wcction l~olts lras 11cm found to br a satisfactory incoris of trrirlior;irily fastening b ~ f o r e \wldirig. fiolting nuy br: donr dire<:tly to main inc~~il~ei-s. It is I t s rostly to plmclr sinall attaclnnents for erection holts than to niovc hcavy main mr'ml~crs into the putich sliop for plriiching. Many tinios; holcs ;irv llatnc ciit i r i thc ends of lisams for r:rt:ction bolts.

In Figure 5 ( a ) , a sm:rll ronnt.ction plate is shop wel<lc:d to the bottom beam llnng~, at ill<, end. A scat is also shop \vddvd to tlic column fl;rngc. at the p n q w height. Illiring zrcctiorr, thc !xwrt is plact:d upon the. scat and two crcctiori holts nw rised to hold them in place.

III Figure 5 ( h j , thc I is conriectcd to the colnrnn \v& A scat angir is shop w c l d ~ I to the imiclc laces of thc column Aangcs and/or to the c * h n n wcb. -4 flat is shop ~ M e d at the orrd of thc lo\ver bcam flangr; sec Figurc 5 ( c ) . Ihr ing crcction, thc )warn is held in place by tu.0 erection holts. All pnnchirig has licen done on small attaching plates or angles. No

a n mctn- puitc,hing tias hem noccssnry on thc hcavy In, ' tiers. 4ny of several methods may bc used to tic in the top Loam Aangc.

I'igurc 5 ( d ) ilidicatrs that \vhm thc 1,rarn flangr is too wide for ty:isy access to Iiolts iipplicd as at Figlrrr j ( c ) , t h t~ anglc \velded b e h w w ~ the colmnn llanges may lrc revwsed. Isi t!tis castx, another angle of smne size is welded to thc underside of the lower hcam FIGURE 6

hrmn cnd into pmprr ulignrnmt with the connection. I-iowevt!r, \vith tlit. :iccurxy of placing the welding stilds arid laying oril t l ~ c corrrsponding slottcd Iiolcs so ;is to allow for sonrc horiz~~ntal ;tdjirstmcmt. tl~crt, should lic. little diificolty.

i'lrlrnl~ing of a 11dili1rg risrially stiirts amrrrd un rlevator shdt or srrvicr core. This is rrsoally centrally Iocatcd ;1nd has grt,atrr lirii~ii~g. The butt wtxlds of the hram ; i d girdcr fl:iiigc,s to t h ~ supportirrg column \\,ill haw sonr~. Iralisvrrsr siiriokirgr. It is ~ ~ ~ ~ c c s s ; i r y that this shrii1k;ige be mti~n;it(d and t h ~ , joint opmrd r ~ p b y this amount bnfor~, \w,l(iing. Otherwis(>, this shrinkage will accunir~liitc~ :dong the lcrlgth or width of the buildii~g a n d hiiild up to a s izal~k ;mount. Sce Figuw "1.

.A good r,stim:~te 01' this transwrsc shrinkage is-

whcrc:

A, -c cross-scction;il area of weld

'I'he a-oss-s~~cti~~i?:iI arm of tbc wcld may 11e corn- p i t d by hreaki~rg it (lo\r-rr into st;~r~dard arms; that is, rcctnnglrs for root opening. triariglt:~ for ilicludr~d imglo of !~rsvt+l, arid par:il,olas for wold I-einforeenre~it. This c:ilcdutio~i can he grmtly shortened hy making i ~ s c of starrtlard tal,lc giviiig thc wright oi weld mst:iI for v:irious joints; risc T:~blc 6 in Section 7.5. It is only necessary to divid~: t h ~ w values by 3.4 to arrive ;it the arca of the weld. This \dire is then placed into one of the above For~n~ilas for shrinkage.

I Problem 1 I To dctrrmin~~ thr shrinkage dFccts in making the welds indicat~d in Figilre 0. The ginlrr with a 1%" flange is to be \veld(d to :I colrirnn. The joint has a 'h" root olwning, an included angle of 45", and uses a backing bar.

From Table 6 in Scction 7.5, the weight of weld metal is 5.93 lbs/ft. m d has an are;? of-

Before welding, open up joints to increase distonce between faces of

columns to allow for weld rhrinkoge

Beam or girder

-~fter welding, welds will-j shrink and pull columns back to proper distonce

FIGURE 9

. I 3 4 / Girder-Related

FIGURE 10

The transverse shrinkage is-

Using 'A'' fillet wclds on the w& will result in vcry littlc transverse shrinkage. The average width of a '/4" fillet weld is ?'V, and 10% of this is .012" or about 10% of the shrinkage of the flange h t t welds.

In this example, thr joint of the girder Wangcs

FIGURE 11

would be opened up an cxtra '/a" on rach rnd of the girder so that the distance Letwecn the faces of the two n)lnmns is ?%" greater thiin the detail calls for. After w-c,lding. tllc two joints shonld shrink snificient to tiring the two columns back to the, dcsircd spacing. This shrinki~gc coiild he checked after w-elding and this vahc adjnstcd.

Thr box coh~mns in thc building shown in Figure

FIGURE 12

FIGURE 13

10, wcr? fai~ricatrd b y \wlding togt.ihcr four ailglcs. After they werc cn.ctcd; 21 short :niglc, scction was rrmovrd and a iong srciioii oE tlw girtltr- was slippic! into position within the colnmr~. Later the anglc swtion was put back.

Thr ends of the hcams were coped back so they coirid b(5 slippcd into plaw with their top Aangc rwi- ing on thc top flangr of the girdcrs; Fignre 11. 4 short seat angle shop wclded io the girder web supporicd t h r lower hcarn fi;~nge. This r(~srr1tcd in a very fast crectiot~ proccdurr without the rise of crection bolls. Latcr the hottom beam Bang<. was field w c l d d to the girder web, wing the seat angle as $1 backing strap.

FIGURE 14

-4 plate was placcd between the top bsam flangcs and tlir giudnr. Thc top Hangcs of tlir 1)cams w t w hntt groovc wclclc~I iogr~ther, nsing the plate as a hacking strap. The plirtc was then fillct welded to thc heum Bangcs. A long cover plate \rm them vdrird h, ilic 1)c~im 8angi:s l o tnkc care of the incrcnsed negatiue inonimlt of the. b w m at this support point. 1V1)ticc that this t y y . of w i ~ l d ~ l connection rn;ilir,s the 11t.am contin~ious, thmr l~y rrclncii~g its rcqnircd size. At the same time, it cloos no: tie the top ilangcs of the ),earn to the girder, which rniglit pridncc some l~iasial stressrs. All of the ficld w~ ld ing sho\vn lrerc was done in thr flat position, groatfy specding lip the crtbction \velding.

FIGURE 15


FIGURE 16

Welding is iised quite extensively on rigid frames. Figure 12 shows the sliop fabrication a r~d wclding of sectior~s of a large rigid fi-amc. For small structures, the entire frame is fabricated and erected in one piwe.

For larger strtictures, the frame may be divided into two or more sections and assemhlcd at the job site and eroctcd. Figun:s 13 and 14 show the construction of a rigid-frame freight ttmninal area, and the upright portions of the framc hcing ~infoaded from the railcar and hoisted into position by thc rail crane. Later tlie central portions of the arch were put into position. Welding macliincs, also on flat cars, were brought in and the field joints welded.

Frames for tile Long Beach Ihrhor Sired were

FIGURE 17

;rssemhlrd on the groin~d, E'igort 15. The scctions wcre Inid out on wood blocks and jacked u p to proper position arid cliccked with n transit. The field joints were tlicn mcl~icd. T h e crawler crmcs picked tlie elitire frame np and pl;ictd it in j~osition. Some of the Elcld welding which was in:rcccssihl(~ wherr on the ground, such as the back side of tlie web lxitt joint, was completed in the air.

4. WELDING OF JOISTS AND FLOORlNG

Welding is used univrrsally in tlrc attschmcnt of open- vr& joist to heams. This becomes a simple matter of laying the joist on the heam at the proper place and l;rtcr wclding in thc flat position. A considerable amount oi light-gai~gt, stecl roof dt&ing is used on top of joists or beams. This is easily and qnickly attached by means of wddirig in thr flat position. The use of both open- web joist a i d sterl decking is shown in Figure 16.

Flotx dccking of bravier gauge has been used as :I support for any of several iloor materials. Welding is used in the flat positio~l to fasten this steel deck to Imams of the steel strrlctorr. Many timcs this deck is designed to take the horizontal forces on the structure caused by wind or t:arthquakr.

5. WELDOR PLATFORMS

It does not take much in tha scaffolding to support a weldor and his equipment. Many of thr joints can bo reached without any platform; the weldor simply works off of the beam or works from a ladder.

For welds below the beam, it may be necessary to put up a platform. Figure 17 shows a rectangular wooden platform with four ropes att;lcbed to it. The platform is fastened to the steel structure at the proper

Icvx~l by tbc ropes. Altliorigli tliis type of platform is sclf-contained, it is reiher hmi,y; cspcciallp for onc mall.

Figrrrta IS slio\vs ;i sirnplr.r scafiold for a sin~ilar position in thr i d strii(.trirr. It is lighter 2nd easier Cor one mini lo set lip. Two wood pl:iiks have ropcs f;ist~wcd at tlicir ~ d s ; tlic miws art, tird to steel grab hcmks. Tho hooks, siipporting thc wood planks, are droppc~l owi- tlw ti111 flange, of' tlic h r m , and the other two plmks arc, put into pl;icc. This platform can hc irscd oil all h i r n s lr;lvi~~g approsim:ltcly the same dcptli \rithoi!t ;in?. fririhcr :!djiisln?~~nt in the rope length. It c;in hr. r i sd in nlmost any coiidition. L~snally a weldor's lieilwr or one fmm thr crcctirrg crew will set np thc necessary sc;~Roiding al~cod of time so there will he no delay in nelcli~ig.

On large structnrfr u&h liavc ronnections re- yniring quite a bit of w r l d i ~ ~ g ;..t the connections, it may help to rist: a woldor's cage \hphich hooks over the top flange of the bcanis and is pnt in place by the dcnick. This is SIIOWII in F i g u r ~ 19. I11ose cages can be c o v ~ w ~ l 011 tlircc sid1.s to f m n a windbrcok when used or, the ontsidr of t1i1. stwi strr~ctni-r. The weldor is not awnn, he is working :it 8 great height whon he is inside this shieltled cage.

FIGURE 19

FIGURE 18

Semi-automatic welding, using self- shieiding cored electrode, being employed in making beam-to- column connections on Wilshire- Ardmore Building in 10s Angeles.

Semi-ai erectio Towers Making in the use o f and coi cored e

~tomotic welding speeding n of 32-story Commerce in Kansas City, Missouri. weided girder connections open was facilitated by lightweight compact gun

ntinuously-fed, self-shielding dectrode.

1 . BUTT JQlNTS

111 butt groove weldir~g the cnds of Bang<, plates, some thoxght s l h ~ l d tx sivcn to thr kproper iype of joint. J and U joints require lh(: l r u t amolmt of weld metal; however, these joint typrs gmrrally require the plates to he preparcd by planing or milling which is impractical in most structtird fabricating shops. This limits the preparation to flame beveling, giving n V joint.

In the V joint, less wcid ~ r ~ e t a l is necessary as thc inclndcd angle is dwrc:~std. Howevcr, as this angle decrcascs, thc. root opciiing mnst he increased in order to get the clrctrode down into thta joint and producc a sou~id weld at the root of the joint. Obviously, the on(: tends to o i h t the other slightly in rtspect to the amount of weld m&l necded. On thicker plates, the joint with the smaller inc,lr~dd angle arid larger root opcning, rtquires the least weld metal.

If a hcking strap is usrd. any arnourit of root openiiig within rcason can he tolerated, and ail of the welding most he done on thc same side; in other words, a single-V joint. If a backing strap is not rmployed, this root oprning must bc held to nhout '/ar'. This enables the root pass to bridge tlir gap and not fd l t l~ ro~~g l i . The welding may be done on one side only, single-V; or it may be (lorre on both sides, double V. In cithor case, the joint is Imck-goug~xi from the opposite side to thc root bcfore depositing additional wcld metal on thc other side. This xi11 insure sound nictal throoghout tho rutire joint.

Single-V joints may be acceptable if the plates are riot too thick; for thicker plates. double-V joints ;ire prderred sincr they reqriire less wcld metal. Kcmernher thtrt ;i singlc-V joint will pl-oduce more ang~rlar distortion 'This incrcnses rapidly ;is the Range ttlickrress iricreases.

Shop Splicing

Shop splices in flange and web plates shoi~ld be rnade before tht: girder is fitted together and wolded, providing the resnlting scctiotrs are riot too long or hcavy to h:uidle. These shop splices do not have lo lie in a single plane, hut are pl;~ced where they arc most convenient, or where a transition in section is clcsired.

in the shop, flange plates can he turned over e;isily as woldir~g progresses, so that on thicker plate? double-V joints would be osed. They require the least

Fieid Splicing

t'i~sld splicrs u s ~ ~ : i l l ~ arr lomtnl on ;I siuglc>. plane. Slaggering the h t t iwlds 01 fiariges ;md wrbs will not irnl~rove perforru;irice of the giu~kr. It is much casier lo ~".c~pax: lhe joints ;uid maintain proper fit-up by flarnc-cntting :ind lxvrling whni a11 ure iocatrd in the snme plnnc. Sce Figure 2. Tlrcrr is :in advantage to haviiig estci~ded thr: fillet welds of l1:ii~gcs to the web d l the way to tlic wry crid of the girdcr. This provides h c t t ~ r support when thc flanges arc clamped togcther for temporary sl~pport di~riiig erection.

Most welding sqnonces for ficld splices of beams ard girders arc* hasvd on tbc iollowing general outline

I Manual-Flat

L w hwr I

r powdcr E-6024 .T?S emps d 40% OF #/.6.?/lb. rydmgrn iron p*dw E~6018

/80 ompr k 30% O f % 55/1b Sam; ;-Automatic -Rat 500 amps d 60% OP I. 05/16.

FIG. 1 Relative cost of flange butt welds.

FIG. 2 Three methods of preporing edges of girders for field welding. Placing the three welds in three different planes makes it difficult to get close fit. It is easier to lay out ai l three butt welds in same pione. Placing two flange welds in the some plane and slighdy offseeing the weld in the web offers o method of supporting one girder on the other during erection.

in which both Aanges and web are alternately welded to a portion of their depth, after secnring with sufficient tack welds; see Figure 3.

1. Weld a portion of the thickness of both fianges (about 'h to %), full width.

2. Weld a portion of the thickness of the n e b (about M ) , full width.

3. Complete the welding of the Aanges. 4. Complete thc welding of the web. For deep webs, the vertical welding is sometimes

divided into two or more sections, and a baekstep method is used; Figure 4. This will result in a more uniform trausverse shrinkage of this joint.

Most butt joints used in field splicing the webs are of the single-V type. For thicker webs, perhaps above M", a double-V joint is used in order to reduce the amount of welding required and to balance the welding about both sides to ciirninate any angular distortion.

Most flange butt joints to be field welded are

either the single-V or double-V type, depending on the flange thickness and the method of welding used. For higher welding speeds, such as when using iron powdered manual electrodes, or scmi-automatic, or fully- automatic bubrnerged-arc welding, more of the welding would be done in the flat position, with less in the overhead position.

It must be remembered that a single-V jcint will result in more angular distortion, and this increases

FIG. 3 &oth flanges and web are alternorely welded.

Direction o i welding: vertical up

FIG. 4 For deep webs, use back-step sequence.

rapidly as flange thickness increases. A double-V joint with half of the welding on both the top and bottom of the joint is best as far as distortion is concerned, but it may require a considerable amount of overhead welding. For this reason the AWS Prequalified Joints allow the double-V joint to be prepared so that a maximum weld of 3/a of the flange thickness is on top, and the remaining 'A on the bottom; Figure 5. This will give some reduction in the overall amount of weld metal, and yet reduce the amount of overhead welding.

Table 6 in Section 7.5 givcs the amount of weld metal required (lbs/ft of joint) for the various AWS Prequalified Joints. This wiil aid in making a better choice of the actual details for the best overall joint.

For the double-V butt joint for the flange, the State of Texas allows the field weldor to place the overhead pass in i l x bottom side of the joint first, and then after cleaning the top side to place the next pass in the flat position. Their thinking is that while some overhead weldillg is needed regardless of the sequence used, this procrdure eliminates a11 of the back chipping or back gouging in the overhead position. If the welding is done properly, there should be less clean-up required.

EB AT SPLICE

Considerable questioning has been directed toward whether the web should have coped holes to aid in field welding butt joints in the flange. The disadvantage of the cwped holes must be carefully weighed against the advantages of making a sounder weld in the flange.

Tcsts on 12" deep girders at the Unkwsity of lllinoisr have shown that the field splice having welds

* "Fatigue in Welded Beams and C,irdors", W. H. Miinre & J. E. Stallmeyer; Highway Research Board, Bulletin 315, 1962, p 45.

(0) Single-V groove joint. Simplest preporation. Tendency for ongulor distortion.

(b) Double-V groove joint. For thicker plate, reduces amount of weld metal. I$ welds alternote between top and bowom, there's no ongulor distortion. Unless plate is turned over, will require overhead welding on the bottom.

(c) When plates cannot be turned over, the amount of overhead welding con be reduced by extending the top portion of the double V to a moximum of 3/4 plate thickness.

FIGURE 5

FIG. 6 Results of ioiigue tests on welded beoms with splices.

in a single plane and wing coped holes has a fatigue strength of about 83% of the corresponding splice with no coped holes s t 100,000 cycles, and about 90% at 2,O(K),000 cycles. See Figure 6.

Knowing these figures represent the maximum reduction in fatigue strength because of the coped holes, it is felt these holes will do more good than harm since they insnrt. the best possible weld in the butt joint of the flanges, The reduetion in fatigue strength dne to coped holes on much deeper plate girders woirld seem to he less, since the reduction in section modulus ascribable to the coped hole would he mr~ch less. Of course, any notch effect of the coped hole wo111d still be present. If necessary, tbis bole can he filled by u&hg after the hutt joint of the flanges is comp1t:ted.

Good fit-up is essential to the development of efficient welding procedures. This means proper al ih~ment and correct root opening. Placement of flange and web butt spliccs in tire same plane greatly increases the ability to achieve correct root opening when the girder is pulled into alignment.

Figure 7 ilh~strates a misaligned double-V butt joint in a girder flange at the point of transition. Note the offset of the joint preparation makes it difficult to reach the root of the joint and deposit a sound weld

FIGURE 7

throrlghont the entire joint. The flange joints should be checked for alignment throughout their entire length before weiding.

This illustrated condition can exist at the ffange exiremitics even though perfect alignment exists in the web area. Accidental tilt of the Aanges during fabrication, mishandling during movement to the job site, or even a difference in warpage of the two flanges can cause this condition. The warpage problem increases with the size of web-to-flange fillet weld and decreases as the flange thickness increases.

Various methods exist for correcting this condition. Figure 8 illustrates one such method. When the p l a t ~ s are not too thick, small clips can be welded to the edgc of one plate. Driving a steel wedge hetwcen each clip and the other plntc will bring both edges into alignment. Welding the clips on just one side greatly simplifies their removal.

Figure 9 illnstrates still another method wlucb is used comn~only when problems develop in respect to misalibaed thicker flanges. Here (top sketch) a heavy

FIG. 8 Weld clip along one edge only, so it may be removed eosily with o hammer. Drive steel wedge below clip until piare edges are in alignment.

(a) Plates forced into alignment and held there by means of strongbocks. Pressure is opplied by means oC wedge driven between yoke and strongback.

(b) For heavier plates, pressure may be applied by means of bolts temporarily welded to the plate. Strongback is then pulled tightly against the plote.

bar or strongback is pulled up against the misaligned plates by driving steel. wedges between the bar and attached yokes. An alternate method (lower sketch) involves the welding of bolts to the misaligned plate ;ind then drawing the plate up against the strongback by tightening u p on the bolts.

4. RUN-OFF +A S OR EXTENSION

Rutt joints of stress carrying members should, where possible, be welded with some type of nm-off bar attadled to the ends of the joint to make it oasicr to obtain good quality weld metal at the ends.

In general the bar should have a similar joint prcpnration to that being welded: gonging or chipping may be osed to provide the depth of groove. For automatic: eldi ding, the bars should have s~lfieient width to support the flux osed during welding. These bars are {isu~ally removed after welding.

A flat run-off bar may not give proper support for weld metal to keep the top comers of the plate from melting b:ick at the mds; Figure lO(a), i f the bars were placed high moi~gh for this, they would be above the groovt: of the joint and \vould interfere with proper welding at the ends; the welding wire (if automatic welding) \v[.ould have to drop down into the groove at the start and climb out at the other end very quickly, undoul~tedly sticking; F i y r e 10 (b ) .

The flat run-off bar in Figure 10(c) for manual welding does not give proper support or maintain the

FIGURE 10

sides of the welded joint at the ends as welding progresses and requires special effort on the part of the welding operator to build these ends ilp.

The types of run-off bars illustrated in Fignre 11 wodd give the proper equivalent joint detail at the ends.

FIGURE l l

Steel sulky seat aids weldors on bridge construction. Float a t left lacks stability in windy weather, while sulky a t right enables operator to sit comfartably and safely.

Shop weld-fabricated girders of variable depth provided important economies and facilitated erection of Thompson'r Bridge near Gainesville, Georgia.

Determining Weld Size / 7.4-5

s 2 4 d

d 2 t* + < 2% tw

Spacing and Sire of SIof

L s 10 t,

w 2 t * + X8" 5 2% t, s , 2 4 w ST, 2 2 L

r 2 t*

4. PARTIAL-PENETRATION GROOVE

Partial-penetmtion groove welds are allowed in the building field. They have many applications; for example, field splices of cohimns, br~ilt-up box sections for trnss chords, etc.

For the V, J or U grooves made by manual welding, and all joints made by snhmcrged-arc welding, it is assirn~ctl the hottom of the joint can he rcached rasily. So. thc effective throat of the weld ( t , ) is equal to the ;ictlinI throat of the prepared groove ( t ) . See Figure 13.

If a hevcl groove is tvclded manually, it is assumed that the wcldor may not (p i t r reach the bottom of the groove. Thcrefore, AWS and AISC deduct 36" from the p rcp rcd groove. IIere the effective throat ( t , ) will q ~ a l the throat of the groove ( t ) minus %". See Figure 13(a) .

(a) Single bevel joint (b) Single J joint

FIGURE 13

Tension applied parallcl to the weld's nsis, or compression in any direction, has the same allowable stress as the plate.

Tension applied transverse to the weld's axis, or shear in any direct~on, has a reduced allowable stress, e q d to that for the throat of a corresponding fillet weld.

Jnst as fillet wolds have a minimnm size for thick plates because of fast cooling and greater restraint, so partial-penetration groove welds have a mininium cffective throat ( t , ) which should be used -

> t, =

where:

t, = thickness of thinner plate

a. Primary welds transmit the entire load at the particular point where they are located. If the weld fails, the member fails. The weld must have the same property as the member at this point. In brief, the weld becomes the member at this point.

b. Secondary welds simply hold the parts together, thus forming the member. In most cases, the forces on these welds are low.

c. Parallel welds have forces applied parallel to their axis. In the ,case of fillet welds, the throat is stressed only in shear. For an cqnal-legged fillet, the maximum shear stress occurs on the 45" throat.

d. Transverse welds ]lave forces applied transversely or at right angles to their axis. In the casc of fillet welds, the throat is strcssed both in shear and in tcl~sion or comprrwion. For an wpal-lcggcd fillet weld, the m;iximum shear stress occurs on the 67'h" throat, and the masin~um normal stress ocmrs on the 22%" throat.

Flexible connedlon No i e i t i o l n t , R = 0

Moment diogrnrn -

Full reitroint, R = 10096

Fully Rigid

(3 Moment dioqiom

Poitiol reitroint

Moment diogiam . -

Moment diogiam

FIGURE i

I,<, <~q~l:ll, 01- hl :~:: I < , : I'Y I>, This \ ~ l I ~ i l i l ~)ro(lli?<! the 1r;ist rcqnircrnciit for swliim n ~ o d d ~ r s , being '12 of that nwded for the origir~al sinipl!; siipported beam. This is true, but tlris idcd cod i t ion d c p n d s on two rt~quircmcnts:

1. l'lic supports to which tlic corinection joius tlie bra111 rnrist be iii~)-i(~lditig. i.c, ahsolutcly rigid.

2. Tlie beam must not lie ii~il~icliccd by adj;icent

earn-fa-Column Connections / 5.1-3

4. RIGID CONNECTIONS (Elortic Design)

5. PLASTIC-DESIGN CONNECTIONS

.l'hc nsc of \veld~!d crninc<.tions based on plastic design 11;is scvci-;:I ;~dvantages:

I. i\ more acwrat~ . in<Iiation of thc truc carr!-ing mrpacity of thc str~ictr~re.

2 . Rcq~tircs less stivl tli:tri wnventional simple I ~ m m construction. Jn riii~ny cases; there is a slight siivitig ovrr cot~vr~ntional el;istic dcsign of rigid frmxs.

3. Rrquires lcss &sign tinre than docs elastic desigli of rigid franws.

.1. Tcsted Iiy scv~:r;~l yrars of rrse:trcli on full-scde sti-uct~ircs. i. Hacked hy tlir .AISC. So for. plastic [lwign coni~cctions have hcm 1;lrgcly

rc.siricted to on<,-story strnetrrrcs, a i d to applications tvbcrr fatigue, or rrpwt loading is not a prohlrrn. Sec scpwatc Swt. 5.12 in lliis r~rnnrial for n frill disc~ission of \Veld4 Connections Sol- i'lastic Design

6. BEHAVIOR OF WELDED CONNECTIONS

Onc Ivay to lvttcr undcrstaiid tbc behavior of a Iirain-to-wliirrrlr cc~iir~cctio~i ~ n ~ d t ~ r load, and its load- c;trrying c;~p;~city, is to plot i t on n rnor~lcnt-rotntior~ chart; sce Figure 2.

The vertical ;tsis is tlw c t~d momci~t of thr bwm,

Beam Ice at working load

End rotation (0,). rodions

FIGURE 2

\vhii.Ii is ; i p p l i d to t l i i c.mlr~i.ction. The liori2o11t:il axis coinpicti,ly rcstl-ai11r4 (0,. -- 0 ) , in othcr is tile rcsiiltilli: rot:ition iii rndi;lns. kisically tilis is f ~ x l ~ & c ~ ~ d hKii11, ;llld is t Y ~ l l d to-

cqimtion cxpi-essiiig ihc rcsnltir~g eiid moii~cnt ( > I v ) alrd end r.ot;itio~i 1 0 , ) . inr a iiiiifor~iiiy l o a d d bciun and ;my cild r .cstr;~i~,l froiri ( ~ ~ m i p l c t r rigid to siniply s u p p t 1 ~ 1 , is:

This is a straiglil line, 1i:i~ilrg puints o and b on thc cliart.

Point a i s the e ~ l d moinci~t when t l ~ c wilncclio~i is

words ;i

I'oint h is thc tvrd rotalion whcll thc collrlcction has no ri,struint (.\I,. :- 0 ) . in other i r i~ rds a si~iiple beam. and is cqnal to-

\\' L'> ( b ) 0,. := -~ ,~ ~~- . 24 il I

For. inwe:iscd loads on the l m m ~ , the beam linr iiioYrs o ~ i t parallrl lo tlic first line. wit11 corri?qxmdii~gl) incrc:ised valncs of end ino~imrt ( ) and thc end rotation ( 0 , ) . This (d;ishrd) sccond 11cam linc or, the

Beam-to-Column Connections / 5.1-5

c,)l:~rt ~ q > r < ~ s m ~ t s tllc xldition of ii saft>ty f w t o - , ~! I~Ic I is ,,sll~lIly 1.67 t c 1 2 ti17it.s t1iat of ti , , , &st d t i d i is l>:ls<d C j ~ i thcb w1rki11g 10:~l.

'i'hi, poiiit at nlri(.li tlrr coi~ri:~ciion's curii. ii1ti.r- sc~cts tlw 1wm11 lint>. g iws [I t ( , riw~liii~ig t w l ~ n o i n ~ ~ n t mid r~jt ; i t io~i L I I I C ~ S t h givcw 1~1;id 1:rom this it is ~ W I I 111n\: tlie he;~in's l x ~ l i i i i i ~ ~ r ~ l q ~ c r ~ i l s on its con~irc t ior~.

It is ;issnni:~il. i r ~ illis w x , . ilic I X Y I I ~ I is sylnin<.lri~ i ,d ly l i ~ l c ~ c l m d the, t \ w end ~ T I I I ~ ~ ~ ~ I I S iw<, tllc S;III I<, .

113 this \ m y hilt11 < w l s will react si~nil;irly. CIII-vc 1 r ( , l~~- tw,nts a k x i l ~ l c ~ ~ ~ I I I I I K : ~ O I I . At >I \?t,ry

Imv I ~ I O I ~ I ( ~ I I ~ it safvly >,ic,lcls ( M I ) mid allo\vs t!~c> W ~ I ~

ti^ to rot;itiz ( 0 , 1 . This is typical of top :i~?glt, <:~l1lll~~ctiolls. \v1+1 fr~llllillg ; l l lgl~~s, slid ti)]) pI:1tt, <.i>lllll~c.. t i s r l l r g h I i c Notiw, N ~ > I I with tIr<~sc~ s ~ I - ~ I I I ~ ~ fkxihli~ eor~~~c~i:tions, SOIIIC. < ! I K ~ I I I < I I I I ~ , J I ~ & w s

Simply supported beam ' designed for R = 0

Fixed end heom designed for R = 100%

FIGURE 3

w d tlw h ; ; m I i r ~ t > ill 1%; lo;>d l-<,htivt~ to 1hc.i~ crossilig (11 ill<. I X Y U I I l in,~ at w o r k i ~ ~ q 10;id.

nit, Z ~ ~ . I L I C I I r t > s l l ~ t 5 ,I{ t t > ~ t i r l g ~ I ~ I - W ~ O I I ~ I X I P C O ~ I -

iic.ctions O:I :ill IS" \ii;F S'i* I K W I ~ I arc s1iou.n in Figtirr 4, 'i'\,r(! w ~ d i t i m s i ~ r < , w n s i i l c r d as S ~ I ( I \ W I I by the, h d di:igm~a~s, F i g t w :3.

Reiiin linr 11 ( I i s 4 ) is k);iscd oil a tl(:sign ~ I I ~ I I I ~ Y I ~ of \V I , at W I I ~ < Y I ~ I I < ~ . i.,,, si11q11y s t~ppo i - t t~ l . 1bi;m lint, ( 1 , is l'cx ;I 1~1:iiI 12:s tini<,s that of t!i<, workiug l<l:ld.

li(>;irn l i r ~ c , 11 is 11:isid oil a <l<,sign nioiniv! of 1;

\I' 1. :it tlw cwls, i .<c fiwil 1 ~ 1 s . i n ~ l will s ~ q ~ p o r t :I ,50V greiitcr 111x1. 1kx11a i i ~ ~ c , IJ, is [or a load 12:: k i~ r~<% t l~x t of tiic ~vork i~ ig l(tad, liotti of t l i : ~ . 1 \ ~ 1 b i w n li i~cs stop ;it ii .' ,50c,;. I I ~ Y ~ : I I I S P :it t l~ i s rc~st r~i i i~t th<> c t w t < ~ of the ~ W I I I I ~ V h ; ~ s this I I I O I I X W ~ of 1,; \Y I , m i l ;i rc4r:iint ~ v i r I I t i t i 1 s ~ s s I central portion ! ~ f the l ican~.

Top plat? ;I I is ;I 5,;'' t l ~ i r k platt:, 3" widi. :it the r l c c s~~c:timi, : I I I ~ has ;I i : rws-swt iwd nri.;~ of ii,, :~ .>J.$ ill.: It is \vid(,r~ecl to 6" :st tht, h1tt-\vc~1dcd ~ O I I I I W ~ ~ O I I . T11is i w ~ r ~ d i o n s1101!1d ~ w d i yield a! :11w11t f -= A,, I I , - ( 4 ) (:30.000) (18) r- ,553 i ~ ~ . - k i p T11c. :i:.tml WIII(, {mni tlic~ t<%t is :I!IIIII~ M -: MI iii..l<ip Abovr this inoii~iwt, the plati. yit,lds m i l (IIIC- to st]-iiin I~; i rd i~~i ing will havr inciw;ixi~cl ri~sist:niri~. 7lri. ~iitin~ntc: mmntwt s11011ld i i l x j ~ ~ t tlrict, t!~is yit,l(l ~ ~ I I I C . , or a l x ~ u t hl r 1200 iii.-kip. 7'hc~ rcstilting ri:str;~irrt is :about R I ~ , 3 4 5 7 ; . :I l i t tk too high fox t11c 11(mi1 to l~c, c l ~ s s e d :is simply s ~ i p l x ~ t d

Top plat<, #? 11;is t l~ i , siirnt, tl~ickncss, hiit !;as ;I ii" \vidtIi t l ~ r o ~ r g l ~ o ~ ~ t its Icrrgth. f t has dol~l)le the o-oss-sectioi1:11 :~rt.;i. A,, 1: 1.88 in.' .4s i , r p r c i d , it is twici. :is rigid, It sl~r~irld rr~aclt yic,ld at ; i l l o~~t h2 1110 I - k i p I I is t M = 1000 in.-kip. The rc3str;iint is :illoilt R := TiS';. Yotic? if tlie 11c;u11 h i d bmm cles iprd fil l- n rnon~i.nt of ' ; - 5Y L, i.c. :I ri>sti.;rint of I i - 100% thc ~ ~ I I I I I W ~ ~ O I I ' S c n s w \?oiild !MW inter- scct~>d the 11w1m I i w 1) illst shml of t11c R = 505 v a l ~ ~ ~ . ' l ' l i t~c \votild tlri.11 1w ;I slight m ~ ~ s t r - i ~ s of the bema at ct~i~tc~-Iin(, .

Top platr, %:3 is "d' tliid< ~ I I I ~ 7W' i\,ide, h:ivirig a cross-swtioi~d XI-ixn of 1,, =: (5.56 irr.' This grmtei- asva p~-odiii.<*s ;i nloi-c rigid c m ~ i ~ r c t i o n with greater ri.str;iint. I ~ c t i I I ~ I I (solid) s h o ~ s slightly more f i i i t tliali tlrir c a l c ~ ~ l a t c d c o r w (clotted). The mtra llr\\:ibility probat~ly conies fro111 sonic r n ~ ~ w i i i c ~ i ~ t t ~ i tii:, Itj\vcr portion of thc cinii~cction which has ~ ~ 1 s t short p ;~al l i , l fillct \velds joining tht: lower i imge of tile lmirn to t l ~ c scxt. A butt wrld pl;icrd d i r i d y :I~I-oss thc ciid of this lowtrr fialigc to the colnirur. i~ndoobtcdly woiilci lwing the rigidity of t!ic coii~ic~ciion c u r w up alii~ost t ( ~ t h t of the caloi- lated curve.

elded-Connection Design

.- A,: .34IN a

FIGURE 4

I Figure 5 illwtr;it~.s tlie additional rrstraining action provided by column flange stiffcncrs. Both connections I r e 'jl<,'' x 6 top plates.

Corinection # I has column stiffeners. In the case of the beam designed for a moment of '/;? \V L ( R =I 100%: down to R = 3%), it would sllpply a restraint of ahout R = 70.2%.

Connection li2 lias no column s t i f f e ~ ~ r s m d loses sufficicnt rigidity so that tire hram dcsigned for a moment of ' j W L, (1% = 100% do\\-n to 11 r= 50% ) will be overstressed. This is bcc;i~lse tli(, connection restraint wotdd hc only ;iborit 1% = 45%.

This sho\vs the i~nportmce of proper stiflrning.

7. FACTORS IN CONNECTION DESlG

Tbr following iterns grcittly :dFrct the cost of wrldcd st!-octt~rnl stccl and ~ a l i ~ l o t he overlooke(1. In order to takc f111l ad\,aiitngc of n-cldcd wnstri~rtion, they mnst he consid~wd.

oment Transfer

The hc~rdi l~g forws from thc r n d momcnt lie dmost entir-ely \vitI~ix t h ~ ~ I ~ I I I ~ I ' S of the 1)eiim. Tl ien~ost effec- tivc and diri,ct mrtliod to tralisfi~ ihcsc forces is solne t y p of flangc weld. The rrlativc n ~ ~ v i t s of thret: types are discussed llert~.

Beam-to-Column Connections / 5.1-7

BEnM FOR y#:* 8

.W1 .#04 .OOb 9 0 1 . D M .NI .OW .Or6 .Old .#LO

ROT4TION (6$, RADIANS

In iFiglire 6. tllc flai~gi.s ;:re dii-i.i.tly i ~ o n i i w t ~ l to Tlw h ~ ~ k i i i g strip illst ~ I P ~ O I V C Y I ( ~ of i11? f h ~ g v s th<. ro11111ii~ 1,) I I N ~ I S of gi-o(,v(~ xi-(;Ids. This is ilic inosl d lows t l i~ , \s<~l(l to lw m x l ~ ~ ~vilhin r ~ x s o i ~ ~ ~ l i l ~ ~ fi t-~ql. d i rwt 11i~tliii~1 01 iriiiisiwrii~g forws :uid rtqiiir(,s tlie 21s long :IS t l i c w is :I p r q w r root op(wirig. lmst : I I IKIWI~ of ~ I ~ \ ( I I I I ~ 'l'hr.ri. is littli, prnvisioi~ iiii- r )v r r - r r~~ i of ilir i.oIiiiiiir

di ir~~~iisirms is-11iih ~ri:~?: 11~. ;is iii~ich :is For <,xi.~.ssi\-i, ii\~c2r-n~ri. tlw i\:~irgi,s of ilw 11e:rrri in;iy h v t . to \I(. fImii(,-c~~t 11;idi. i l l t h ii<,ki, ill orc!<,r to pro- v i d ~ , the, r n i ~ ~ i r ~ i i ~ n i root o p i ~ ~ i ~ i g . o r I I I I ~ ~ I ~ I , tht2 c!sct,ssiw I I I I I ~ I I ~ ivill i~icrcose Ilic :unoiiilt of w(>Iilir~g r e q i ~ i r ~ d , 1n1t llw joiiit is still possil~l~:,

I t is iisii:rlly niorr costly lo i.111 tlw lic:un to mzct le11gI11: i l l :uI,liti~xi thvw is t 1 1 c ~ cost of 11mviiiig the f h ~ ~ g t s . hiillilig I h Iw:uri to ~1~11gIh is ~ ~ o s l l y and not ~ C ( , ( I I I I I ~ ~ I , I > I ~ < , ( ! ~ W : I I I S I ~ 1111~ ovt,r-rllll I I X I I I I ~ ( ~ I - ~ ! I S I of t1-c I I I 1 1 1 i 1 t l r ~ ~ i c I 4 ' 6 " ~ w i i l d reduce this

FIGURE 6 a r c ~ i r ~ c ~ y i!i fit-lip

FIGURE 7

FIGURE 8


FIGURE 19

The stiffcning of the latter connc:ction is mainly dependent on thc thickness of the stem of the Tee stiffener, tlie Ranges of the colnmn being too Ear away to offer much resistance.

The column wcb is ably assisted in preventing rotation at the connection by the flanges of the split- beam Tee stiffeners.

4. ANALYSIS OF STIFFENER REQUIREMENTS IN TENSION REGION OF CONNECTION (Elastic Design)

The following is adapted from "Welded Interior Beam- to-Column Connections", AISC 1959.

The colomn flange can be considered as acting as two plates, both of type ARCD; sec Figure 19. The beam flange is assnmrd to place a line load on each of these plates. The effective length of the plates ( p ) is assumed to be 12 t,. and the plates are assumed to be fixed at the ends of this length. The plate is also assumed to he fixed adjacent to the column web.

where:

m = w, + 2 ( K - t,)

~nalys is of this plate by incans of yield line theory leads to the, ultimate capacity of this plate being-

where:

Let:

For the wide-fiangr colrimns and beams used in pactical connections, it has h e n found that ci varies within the range of 3.5 to 5. A conservative figure would be-

P, = 3.5 u, t,'

The force carried by the central rigid portion of thc column in linc with the web is-

ekded-Connection Design

In Fig111-e 12, a shopwcldetl seat provides support fol- tllc dcad load oT the b~ ;nn . The 1re:rm is lit~ld i l l

place hy inwns of erection holts tlrrm~gh tl~r lmttoirr flangc.

In Figure 1:3, a slrop-\icldrd plate on the columii provides temporary support Tor thc be;irn. Erwtion holts

FIGURE 13

tl~rougli the beam wcb hold the heam in position. An anglo could be used i n s t t d of tlw platc. Altho~iglr tliis ~ o t ~ l d increase the matari:11 cost slightly, it would be easier to install and hold in proper alignment dnring welding. Sometimi:s a small seat is shop welded to the column, as sho~vn, to give support wliilc the ercction bolts are being installed.

If the beam is supported on a seat, the elevation at thc top of the beam may vary hccause of possible ovi:r-run or nnder-run of the beam. If thc beam is supported by a web connection, this may be laid out from t1r1. top of thr beam so as to eliminate this problem.

Saxe erection clips, Figarc 14, are made of forged stet31 and are readily \vel&aIrle. The clip is shop welded

FIGURE 14

to the nrder side of the beam Hitnge and the seat is sbop welded in tile proper position on the column.

Tl~is :illows t11e beam to slip easily into place during wcction. O11e typo of S:ise (,lip is adjnstaldc aild allows ;r movement of :i<e" as w-t:lI as sorniz rotation.

(,'onsider the use of \ \ ~ l d c d studs on mtin members in plat(: of erection holts; this will eliminate thc pouch- ing of main members. These 1m.e alrmdy been ac- i:eptcd in the br~ilding and bridge fielcls for me as shear attachments, and an increasing nrilnber of fabricating shops have this eqniprnent. Sce Fignres 15, 16 and 17.

FIGURE 15

FIGURE 16

earn-to-Column Connections / 5.1-1 1

FIGURE 17 FIGURE 18

General

Usc the neu-c.r 1 0 6 strcl for a 1 0 5 liighcr strtsss allow- :IIIIP and ahout 5 to ;?;- s;ivirrgs in stw1 ; ~ t little, additioir;tl rmit pricr3 iu s t t d EiO \i-clds 1 l : i i - ( 2 16%' highhtar allowal~le for fillot welds.

Use ;I 10% l~iglicr : i l l o ~ ~ a l ~ I e herrdi~lg stress for "compact ben~iis"; u == .66 ui irrstcad ol .CiO u,, and for ~ity,ativt: moment rrgior~ ;it srrpports use only 90% of tlic tm~rrriwt (-4ISC Scc 1.5.1.1.1).

Mnriy cmnwtiorrs prrrvid~, a dircct m d etFrctive transfr,r of iorct,s and yet arc too costly irr preparation, fitting ; ~ n d wt>ldiug.

'\I:trim~~nr r c o ~ ~ o m y is obtained wlreii a joint is

rlf.signcd for w<.lrling. It is not siiflicicnt to apply ~ ~ ' l d i t i g to a riv~'ted or b~rltcd design.

Us<, rigid, r,ontinrimis connectiotrs for a more ef& ('icnt structlrl-r,. This will rcdrrct. the beam weight nnd 1 s 1 1 y r td~ ices tlw overall weight of the completc strurtrtrc.

Use plastic design to r d u c e steel weigl~t hclow that o l simple f r a n h g . :irrri r e d w e tlrc design t i m : below that of conve~itional elastic rigid design.

Thc grratcst portior~ of wclding on a co~ineciion should 11c d w e in the shop and in tlie flat position. As much ;is possillle. rnisc~.l laneo~~s plates u s t ~ I in conri(:c- tions, soch as scat angles, stiffelrers on coiritnris, etc.. s l ~ o r ~ k l l x asscmhlcd. f i t t td ntrd weldcd in the sliop in the flat position.

Tlir ronncctiot~ t l ~ i ~ s t off~m proper n~~cessibility for welding; whetlrcr clo~rc in h o p or field. This is c s l w ci;rlly true of bc;rms fr:iming into the wcRs of coloinns.

I'roper fit-tip must hc obtained for l m t wel~lirip. Care must be i~sed in layout of tlie conncrtion, fl:rmi. vutting thc hc~im to the pnlpcr irngtll. preparation of thr joint, aiid crc,ctiilg t h rrlcnlber to tile propcr position a i d a l ig~~rncnt . Coo11 wwkmanslrip, resrilting in good fit-up pays on.

Weldor makes continuous beam-to-column connection on Inland Steel Co.'s office building in Chicago. At this level, the column cross-section is reduced, the upper column being stepped back. Spandrel beam is here joined to column by groove welds. The weldor, using low-hydrogen electrodes, welds into a backing bar. Run-off tabs are used to assure full throat size from side to side of flange.

For New York's 21-story 1180 Avenue of the Americas Building, welded construction offered important weight reductions and economy, quiet and fast ereciion. Maximum use of shop welding on connections minimized erection time.

When designing a flexible seat angle, it is important to understand how it is loaded, and how it reacts to its load. See Figure 1

FIGURE 1

The outstanding ( top) k g of the seat angle is snbject to bending stresses, and will deflect downward (1,a) . Tlre vertical reaction ( R ) on tha connecting weld of the angle results in direct shcar (1,b) arid in heirding forces ( 1,c).

If the seat angle is too thin, the top of the connecting weld tends to tear, because only this portion of the weld resists the hcnding action. Wit11 thicker angles, the whole lcngth of the conricciilig weld would carry this bending lo:~d (Fig. 1,d) .

The top leg of the seat angle is stressed in bending by tile rmction ( R ) on the end of the henm which it supports I t is necessary to determine the point at which this force is applied on the leg in order to get the moment arm of the force. See F~gure 2.

A simply snpported beam is pIacct1 on the seat angle (2,s). Because of the loading on tlie beam, thc bean] deflects and its ends rotate (2.b). Consequently the point of contact of the rcnction ( R ) tends to move outward. This increase in moment arm incrcases thr bending moment on the seat, causing the leg of the angle to dc5ect downward. As the deflected leg takes

tlic same s l o p as tlie loaded beam, the point of contact moves back ! 2.,c)

FIGURE 2

if tht: Icg of the angle were macle thicker, it woiild deflect less. Conseqircntly, the! point of cont:ict u~on1d extend farther o~i t along tire leg, i-lrns irlcrcasing the bending Inoment.

If the angle were made too thick, this hearing reaction would h e concentrated :ind might overstress the heam web in bearing.

If the angle \vex: nradc too thin, it would deilect too easily and the point of wntact would shift to the end of the beam, therehy not pmdncing snfficimt iengtltil of contact for proper srippt~st of the beam web.

Definitions of Symbols

w = k g sim of fillet wdd, inchcs a, = yield strrnpth of material u d , psi a = clearanve betwccn column and tnd of heam, usu-

ally 55" b =- width of sent angle, inthcs v -- rrrommt arm of reaction ( K ) to witical section

of iiorizo~ital k g of scat angb,, inrhc,s ee = distance of n:actim (N) to liack of fIexible sciit

noglc, inclrei t = thickiicss of mil mgli,, inches

t, = thicknrss of h.nm wrb, inches I( = vertical distancc from liottoin of bean flar~gc to lop

of fillet of beam web, ohtainei! f n m steel liand- book, irichcs

Lr = liorizuotal lrl: of sest an&., inches L, = vertical 1i.g of scat angle, also Icrigtl~ of vcitical

i.onnectirig wckl, i n c h N = miriinnim bcaring lcngth Ii s: vcrtical henring reaction :at mil r i i hcarn, kips

AISC (Sec. 1.10.10) specifics that the compressive stress at the web toe of the fillet ol a beam withoot hearing stiffcners shall riot exceed u = .75 us psi. This stress is located at distance K up from bottom face of flange. See Figure 3.

FIGURE 3

For mcl reactiom, the following formula is given:

R ........... == not over .75 rr, psi i t v ( N + K T

. . . . . (AlSC See 1.10.10) . ( l j

This means that the web scctioi~ ( N + K ) may bc stressed to u = .75 cr, psi. This planc lies at the top of the toe of the fillet of the beam web, or at height K. This can he projected down at 15" to the h u e of the hram flange to get the minimum bearing length ( N ) . l t is assnmed the hearing renction ( R ) may bt: centered midway ;dong this length ( N ) .

3. SEAT ANGLE

AlSC (Steel Constn~ction Manual), recommends the following method for finding the required size of the scat angle. Thc point of critical bending moment in the auglc k g is assr~med to he at the tangent of thc. fillet of the ontstandirlg leg of the angle. This is approxi-

t 1 - :!6" I c y in from the inside face of the vertical leg, for most angles rrscd as seat anglcs.

S t e p I : Determine the point where the beam

re;wtion is applied to the arrglr, so that the eccentricity or moment arm ( e j of the 1o;id may he known.

Nomograph No. 1 (Fig. 1 ) for A 36 steel will give the \ ,due of cr for Nesihlr seats or e, for stiffmid scats. (Stiffened scat brackets are discussed fnrther in the following section.) Known \dues needed for use of this nomograph are the cnd reaction ( R ) of tlre beam in kips, the thicliriess of thc beam web (k ) , and the distance frmn the hottom of the hearn flange to the top of the fillet ( K ) , obtained from any steel handbook.

S t e p 2: Dtstcrmirle thc required thickness of the angle ( t ) to provide sofficiait bending resistance for the giver1 heam reaction ( R ) .

Fmm this we gct-

0- b t' R e .I: 1 s t = rr S ~=: -- - . 6

Since the ontstarrding leg of the angle acts as a be:rm with partially restrainrrd ends, tlre AISC ;\I:inuai (1956, 11 263) allows a hending stress of u = 24,000 psi for A7 or A373 stacl. For A36 stecl, a value of u = 26,000 psi will br 11set1. Tliis thcn hctomes:

A7 or A373 Steel A36 Steel

Flexible Seat An

FIGURE %Thickness of Flexible Seat For A36 Steel

NOMOGRAPH NO. 2

Flexible Seat Angles /

To solve directly for ( t ) , the forlnula +9 may bc, prlt into the following form:

] A7 or A373 Steel I A36 Steel I

Knowing tlic values of A and e,, the tliickncss of the scat aiigle ( t ) may he found from the above formnla.

Ko~nograph No. 2 (Fig. 5 ) for A36 steel makes w e of Formiila $9 m d will give values of seat angle tlrickiicss ( t ) . Tlic width of thc svat :nigIc ( 1 1 ) is knowil sincr it is nsn;rlly made to estcnd at lcast %" on ench side of the beam Rango. -4 linc is dr:t\in from this valne ol ( h ) throrrgh the d r r e of ( R ) to the vt.rtical axis A-A. The rrqtiired thickness of the angle, ( t ) is foiind at thc intcwc.ction of a Irorizontal line through !-A and a vcrtifiil line through tlic givrn vaiw of ( ( 2 , ) . In case these 1inr.s intcrswt hetwcen t\vo values of angle thickncss; ilic lnrgcr value is wed as the answer.

'Tal~lc 1 will give \.;iht.s of Rjb in tcrms of smt angle tliickncss ( t ) and eccentricity ( r , ) . Table 1 is for 436 steel.

Step 3: 1)ctc~rrninr~ the horizontal length of the seat angle leg (I , , , ) . This mrrst bc srtiiicicnt to permit vasy ercrtion and pro\5da aniplc distance for the coil- uccting \velds and rrcction bolts on the hottoin flange of tlic heam.

This lniniinr~m lcngth is:

I ' : 1 - K 1 . . . . . . . . . . . . . . . . . . . . . . . . (12)

Step 4: I>rtcrminv the vmtical length (I,,) of tlir eoniiecting fillc~t \vdd7 for a givm leg size of weld (o) This will deii,rrninc the rqir i r(d lengtli of the seat

LE 1-Values of R/b For A36 Steel

THICKNESS OF SEAT ANGLE i t)

angle's vertirnl Icg, k i n g assumed equal.

horiron/ul forcc on weld

K Moment (each weld) - - ~ ( q ) == I' (31 LT)

9 -

FIGURE 6

also:

P = '"L ( f b ) ( % Li)

omneetion Design

From this:

2.25 R el f, = L,'

ljertical force on weld

rrsultant force on weld

leg sizc of fillct weld

actual force o =-- --

allowable force

A7, A373 Sreel; E60 Weld* 1 A36 Steel; E7O Weldr I

Since there are a Limited number of rolled angles available (for example, L = 9", S", 7", 6", 5", 4", etc.) it might be well to select a vcrtical leg length (L,) = vertical weld Iengt11, and solve for the required leg size of fillct weld (w).

Nomograph No. 3 is based on formula #14 and will give the required length of the vertical connecting wekl (L,) and its leg size (o) if the other vah~es ( R and el) are known. (The weld length is assrimed equal to the seat's leg length.) Nomograph No. 3 is for A36 steel and E'iO welds.

Table 2 will give values of R/o in terms of vertical leg length of the seat angle (L,) and ecccotricity (e,) Table 2 is for A36 steel, and E70 welds.

R - 19.2 L,' .- -~ -~

0 -

4. APPLYING CONNECTING

R 22.1 L," - ~- . . . . ( 1 4 ) 0 m-;~ 2 o . z es

The two vertical fillet welds should be "hooked around the top portion of the seat anglc for a distance of about twice the leg sizc of the fillet weld, or about K", provided the width of column flange exceeds the width of seat angle.

A horizontal 6llct meld across the top of the seat angle would greatly increase its strength; however, it might interfere with thc end of the beam during erwtion if the hcam were too long or the column too deep in section.

When width of the seat angle exceeds the width of the colunrn flange, coimecting fillet welds arc placed along the toes of tbc flange on the back side of thc

TABLE 2-Values or R / o Par A36 %eel & 270

R Reoction, kips - -. - - 22.4 L', w Leg r i m iillet weld L', + 20.25 exl

n~.. I VERTICAL LEG LENGTH OF SEAT ANGLE (Lr)

angle. These seats may line up on opposite sides of a

supporting web, either web of coliunn or w-t,h of girder, if the leg size of the fillet wcld is hcld to 3/4 of the web thickness when determining the lcngth (L,) of the weld. This will prevent the web within this length of coniwction from being stressed in s1it:ar in excess of a value equivalent to 3/4 of the allowable tension.

Don't hook w e d oround corner; Hook weld around will not have full throat corner of seat angle

Seat Angle Width Seat Angle Width Gieotei t h a n Column Flange Less tho" Column Flange

FIGURE 8

A fiexihie top angle is usually used to give sufiicient horizontal stabi1it)- to the bcim. It is not assumed to carry uny of the l~cam rc:ietio~-i. The most common is a 4" s 1" x %" arsglo, which will not restrain the beam end from rotating under load. Aftor the h t ~ i m is twcted, this top angle is field melded orsly alorsg its two tocs. For beam flanges 5" and less in \vidtli, the top angle is usually cot 4" long; for beam Hanges over 4" in width, the angle is usually cut 6" long.

In straight tmsion tests of top connecting angies at Leisigh University, the 4" s 4" x 'A" all& p~illed out as much 2:s 1.98" before failul-c, which is ahout 20 times

W C o l u m n flange

Greatest rotofion occurs

FIGURE 9

greater than us11al11. rep i rcd under noimal load conditions.

Notice in the following figure, that the greatest mo\~e~ncnt or rotation occurs in the fillet \veld cxmnect- ing the upper icg of the mgle to the column. It is important that this weld be made full size.

This trst ulsu inriicatnd that a return of the fillet weld around the: ends of the an& :it the column cqml to about '14 of thc log length rcsulted in the greatest strength askc1 mo\irJinelit hrfon: failure.

Hook oround

1 FIGURE 10

I Problem 1 / Design a ficrible seat angle to support a 12" WF 27# heam, having an end rcwtiou of R = 30 kips. Use A36 steel, ETO welds.

le Seat Angles / 5.2-

FIGURE 1 1

ihickncss of seat unglri

horizontal leg of scat nngle

( 1 j I , = 1 +- N - ( ? 4 ) + (3.82)

I~: 4.32'' or 4%" min. - ~~ - .

A 5" anglc. 1" thick, is not rollrd. The only 7" and CJ" iing1t.s n d l d haw a 1" liorizor~trrl leg which is not sufficient. 'This leaves just the 6" and 8" angles.

a ) Using a 6" r 6"x 1" srat m g l c I,, = 6"

.- ,461 or rise V2" -~ - .

b ) I'sirig a 8" i 6" x 1" scat mgle L, = 8"

Thc structural dcsigner might bc incliired to selrct the, 6" s li" r 1" angle himrisc of th(, obvioris saving in \veigl~t. The shop man knowing that tbc ?i,;" fillet weld in ( h ) is a single-pass wcld and can be made very fast, wlirrens the %" fillet weld in ( a ) is a three-pass

Don't hook weld more than fir' i'

Ploce top angle on

-4 Angle leilgth /-.-

FIGURE 12

weld, would select thc 8" x 6" x 1" angle ( b ). He knows From Table 2, using et = 2.4" that the cross-sectional area of a fillet weld, and there- a ) If L, = ti", R / o = 65.2 fore its wcighi, varies as the square of the leg size. He or leg size of fillet weld, figures the ratio of the leg sizes for ( a ) and for ( h ) to he 8 to 5. This ratio squared produces 64 to 25, or 30

- - 4 ~ ' or use W' 65.2 as far as he is concerned 2k times the amount of weld

metal. b ) If L, = 8", R / o = 107.0 or leg size of fillet weld,

From Table 1, K/b := 30/S = 3.75. Using ef = 2.4" 30 would give this value if t = I". (Here R/b = 4.22) o .= -~,-- = ,280 or use x6"

101.0 . ..

(From Anicncan In~titute of Sled Construction)

SEATED BEAM COMNECTIOMS Welded-EGOXX & E70XX electrodes

TABLE Vl l l

. . (o aitm:li bulm m ma* (optiundi.

Nnnunol b e m snthach is 'LA'. AUownbir londa in Table VIII-A ue &XI on 9,. x t b c k , r h i r l i pnvbdes for pssible miU undsmn b k m

S E C T I O N 5.3

ene e e

Ilihcn the r'action load ( K ) rcqnircs a tliiclacss of angle greater than tlie alailable sections, a stifferred seat bracket may be usvd. Thtw are t\vo alml>ws: ( A ) in uhich the scat stiffener is at riglit angles to the web of the heam, arid ( B ) in u-hie11 the seat stilfener is in line with the web of the beam.

For analysis, the stiEener of Type ( A ) is considered an eccentrically loadcd colnmn with the rmction load applicd at a f i x e d point. 'rli~. mtirin~im strcss is the sum of the direct load and brnding alfccts. The line of action of thc- comprt%ivc lo;rd is approxim;~trly parallel to thc outer edge of thc stiiFeni,r. Tlic criticd cross- scction of the stiffcirw ( to hc u s ~ l lor the area and section modillus) is at r-ight ;tnglrs to thr linc of action of the load.

The arca a i d sccti:io moduli~s i m -

A = t X = t L,, sin 4

X = Ll, sin tp

FIGURE 1

Sinci the inarirniiir~ strcss,

thc rcqiiireil thickncss of thc bracket web is-

The thickness of tlic imcket wrh car 1 x 7 c1cti:r- miircd qnicldy fnm Noniograpli No. .4 (Fig. 2) for 1\36 steel; tliis is h:wd on formnla +I. The v i ~ t i c d line at thr left is for v;iln~~s of load eccnrtricity (c,) and length of ontsianding braclict li'g (L,]). Tlie ~ l m t line is for thr angle 1)ctvwn the sidc of ilic brad&

PROBLFW FIND THICKNESJ Of ITIffENED SEA7 FOR THE FOLLObW6 CONDITNNS. L h ' 8 . e * 4.5- B . 90 ' P ; 58 KIPS (EN0 REACWON)

R E M t . v6 /NCH (STIFFENER ISNCI(NE;S)

2. S OF STIFFENE EB

If tlie beam rests in line with the bracket stiffener, Type B, Figure 3, the bearing length ( Y ) of tlie be;~m (AISC See 1.10.10) is-

and this would he tlie miniriium valuc allowed.

FIGURE 3

The eccentricity jc,) of the reaction load is-

e, = L,, - -

This value of load eccentricity (e,) can be quickly found by using Nomograph No. 1 (Fig. 4 in previous Sect. 5.2). Sonictimrs it is figured as 80% of tho bracket's outstandirlg leg length (I,,,).

The eccentrically loaded column forniula ( + I ) is seldom used in this case because it will result in an excessively thick bracket web or stiffener. This is be- catise the formula is based upon stress only and does not take into consideration some yielding of the bracket wliich will causc t11c point of application of the load to shift in toward the support, this n:dncing the moment arm arid t~ending stress.

AISC Maniml, page 4-39 recomnic~ids for A36 brnckct material that the bracket wcb's thichiess be at least equal to 1.33 tinics the requii-ed fillet weld size (E70 welds). Also it should not be lcss than the supported beam web thickness for 47, A373 and A36 beams, m d not less than 1.4 times the beam web thickness for A242 and A441 beams.

For stiffcncd seats in line on oppositc sides of the colnmn web, the fillet weld size should not esceed % the column web thickness when determining its length (L).

If the bracket is made up of plates, AISC rccnrnmcnds that thc wc4ds conncctiiig the top plate to the wcb of the stiffcnrr should lhave s t r e~~g th equivalent to tile horizol~tal n&ls between thc bracket and the column support.

The depth of the stiffener is determined by thc vertical lcngth of w.&l (L,) retpired to connect the bracket.

Thc lcilgth of the 1)rackct top plate (I,,,) s l io~ki hr sufficient for it to rxtcnd at loast beyond t l ~ c hearing Icmgth of the beam ( N ) .

The stiffened scat bracket is shop welilcd to the siipporting m(.mbcr in the flat or downhand position. IJsually the top portion of the bracket is welded on the underside only, and tllc useb of tlic stiiiemr is rvt:lded both sides, full Icngth. By placlng the weld on the underside of the bracket, it docs not interfere in any way with the beam which it supports.

Sorne rngineers do 11ot like the notch effect of this fillet weld's root to be at the outer fiber of the connection, and would prcfer to place this fillet wclcl on top of tlie bracket; this can be done.

The folIo\ving method is uscd to detennine the leg size of the connecting fillet weld ( w ) . For simplicity the length of the llorizo~ital top weld is assumed to be a certain prrccntage of the vertical weld lcngth (I,,). The top weld length is usoally less than the bracket width, and the vrrtical weld Icngth is assuinttd equal to the vertical length of the bracket.

This analysis uses the value of 0.4 I., for the top weld as it is a more i m n n o ~ ~ i y uscd value, although any reasonable value rniyiit be used, Figure 4.

'hus it can bo shown &at: rwutrul oris of connecting t ~ e l d

section 111odt~2t1.s of connerlzng weld

S, = 0.6 LT2 (top)

titfened Seat Brackets / 5.3-5

where: length of connccling zticld

A, -- 2.4 L,

bending force on wcld

1% K f = = .. ..

A , 2.4 I,,

resultant force on u.eld

leg size of fillct weld

actual force = .- .. .. -- or allo\z.able force

vertical weld length (L,.)

1 I

mwwer By knowing the value of R a d e,, the ( -'

may solve directly for I,,. The lcngth of connecting \vrticai weld (I,,) miy

he dctcrmined quickly from Nomograph No. 5 (Fig. 5 ) for A36 steel arid E7O welds; this is based on Eonnula gi. The wclded consiectioii is assmntxl to ewtrmd horizontally 0.2 1. on ctich side of the bracket web. The ~nasirnnm k g size of fillet weld ( w ) is held to % of the stiifener ttsickncss. Ilra\v n h e from \wid size (w) through thr re:iction ( R ) to the vertical line ( U ) . The rtqi~irecl lcngth of weld (I>,), - vcrtical length of stiffener (I,), is found at the intcrsectiols of a horizontal line through ( D ) and tt vertical lisle throligh the: given d r r e of (e,).

For stiffcner brackets which have a top width ( b ) other than 30% of the depth (L,), the Table I ionnulas may be isscd.

AT, A373 Steel; EEO Welds

R B = . - - 23.04 w

I Problem 1 I Design a bracket to support a beam with an end reaction of 58 kips. Tho beam lies at right angles to tile bracket. Use A36 strt%l and E70 welds. See Figure 6.

A36 Steel; ETO Welds

K 13 = - - - 26.88 w

Using Nomograph No. 4:

f, - 90"

R = 58 kips

TABLE I-Fillet

A36 Sfeel K E70 Welds

W = - ~ \ / ~ 1 6 . 0 ~ + e', 26.88

B m c b t Width ~ 7 , A373 Steel K E60 Weldr

~~ ~

ii = 0.4 L, &, fi.1-z 23.04 l',

~ ~~~ ~- ~~ ~ -~ ~ ~~ . ~ -

J ~ 2 ~ + ~ 4 . 0 6 ~ ~ r=Lm 28.00

i? = 0.6 Lr = . - JL', + 12.57 c2, w = JLzv + 12.57 + ex6 24.96 L'r 29.1

,.~-~ -~ I - R

J L ' - + 1 1 . 3 7 ~ 2 ~ W = . - R J ~ 2 v + i 1 . 3 7 + e P , b = 0.7 1, w = 11 01 $ 2 ~ . 30.24

FIGURE 6

read the required stiffener thickness as- t = y1 *''

Using Nomograph No. 5:

0 = X6" ( t = R = 58 kips

e, = 4.5"

FIGURE 7

Using Nomograph No 1 (Fig. 4, Sect. 5.2):

read the hearing Icngth and 1o:rd ecceiitriciky as-

N -. 1.54'' (if L,, = 4")

e, = 3.23"

Since t = 1 XG" , use t = Y4.' - plate.

read the required vertical length of the stiffener as- using Komogral;h xo, 5 : L - 13" v - - R - 58 kips

~ - x i C q e, = 3.37"

for o = %"; read L, = 10" Design a bracket to support a 2N', 65# I-beam with fi,r -- 3;o", read L, = 11" an end reaction of 55 kips. The beam lies in line with the brackct. Use A36 steel and E70 welds. Use tile qi/ ;O" fillrt \w111 wit11 a length of 11".

FIGURE 8

Stiffened Seat

(From Amcrican lrrstiti~te of Stcel Constniction)

STIFFENED SEATED BEAM CONNECTIONS Welded&E60XX or E70XX electrodes

TABU X

Aiiow;%ld<~ ioed* in 'i'&ir X i irr b i d iiu tile urr o f I!M)XX eintmdes. For 1170X'i ciiwLiinics. multi&y Labulri hndn i>y 1.16, or enter the U~t i le v i t i i M'?o of iliv aivae rwrfion. Note Advrntagc, may & t r k e n a f t h e higher nUownhle umlt dias of F:70XX rl .airodw onlv i f hih bracket md r u p ~ u r t i n g rnemkwz am &STM 3 6 . A242 or A441 m a k i r i .

1 1 1 '02. 235 ! 159. 191. 1223 X i ~11. i 1s 1 6 0 i o i 1 2% 168

~~~~~~ . " =pal *jldl m*nr *-lh i i o r x r i r c insus b y ! 16. a rnlrihr ,mnio *,,a 86% os

//lb/l 0",1 wnmn rmrx u=no<rr rrc vsra

I f the reaction values ola beam are not shorn on mnbrad draainm. the mn-

onnestion Design

Beam-to-coiumn connection being mode on the Colorado State Services Building in Denver. Operator i s anchoring the beam to o stiffened seat bracket by downhond welding, using iron powder electrode.

Extensive use of modern structural techniques and welding processes speeded erection of Detroit Bonk & Trust Co. Building. Stiffened seat bracket can be seen a t upper left. Angle clip to facilitate field splicing of column lengths shows immediately above.

1. GENERAL REQUIREMENTS

\Vrh framing angles are usually shop welded to tht: web of the beam. cstending abont S'' beyond the end uf the beam, m d field nv1dr.d to the supporting member.

Erection bolts are risually plactd near the bottom of the angle, so they do not restrain the beam end from rotating under load. For deeper girders, the erection bolts may he placed near the top of tlie angle for better stability during erection. If theri IS '. concern about any restraining action, the bolts may he removed after field welding.

The thickness of the framing angles must be limited to that which will allow snfficient flexibility, otherwise the connection wonld rcstrain the end of tho simply supported beam from rotating and thns would load up in end moment. AISC has a table of typical framing mgle corini~ctions. It lists 3" and 1" angles of '46 ' ' to - , , ,,;" thickness. Whcn thicker angles are used the leg against the supporting iix~mbrr must be iricreascd in ;ihout the same proportion as the thickness in order to maintain the same order of fit.xihility.

The analysis of this type of connection is divided into two parts: a ) the field weld of the angle to the supporting member and b ) the shop weld of the angle to the web of the beam.

2. ANALYSIS OF FIELD

When the reaction ( R ) is applicd, the franring ang1t.s tend to twist or rotate, pressing against each other at the top, and swinging away from rach other at the hottom.

It is assumed the two angles bear against each other for a vertical distance eqrlal to of their length. The remaining % of the lengtli is resisted by thr connecting welds. It is assunid dso that these forces on the x ~ l d s increase linearly, rcaching a masimiun (f,,) at tlie bottom of tlie conncctior~. Figure 1.

horizontal forcc on weld

Applid monient flom load =: Resisting moment of weld

R 2 " L,) = - P I,, - 3

where L,, = leg length ot angle

.75 R L,, o r p I>7

From force triangle, fin&

P = 95 ( f , , ) ( 3 & L,)

Hook weld around top; not to exceed % leg of angle, usually M"

I

FIGURE 1

PRO&EM. FIND TN£ 1fhG7fl( I~/ Of ThE P%AM/#6 AN6lt W :%,- (.VIE OF f/€U WfZD, R =IS KIPS (END .mcr/uN, in 3 - (LEG Jilt O i A N G l t )

RE40 1, ; /2" /i€rV67// OFRNGLE,

FIGURE 2-Framing Angles and Size of Field Welds For A36 Steel & E70 Weldr

NOMOGRAPH NO. 6

FIELD R

2 2; 3' 3;' 4 5 6 7' 5'

i I L, (LEG SIZE OF IINGLE)

Web Framing Angles / 5.4-3

From thme two equations, detcrmine-

f 9 R I,,, 1, -- 5 L,'

~~. . . ~ .. ~~ ~~~~~ .... .

f, flf,,' 4 f,' = "".) 5 112 i+ ( 2L, I< ) 2

or:

- - - f - ~ . Y I 2 + 12.96 I,,,? I I -

d,. 2LY2

I A7, A373 %eel; E60 welds] A36 Steel; E70 Welds I

Be sure thc supporting plate is thick enough for this resrilting weld size ( a )

Thc~ two vrrticnl \aelds comx'cting framing anglcs to supporting incnibrr should be "hookcd" around the top of the nnglcs for a dist;aice of about twice the leg size of the \r-eld, or about 'i". (Origi~ml tests indicated that a distance not to cxwrd 'A of thc ;iriglr's leg lcngth 11ciped thc carrying capxcity of thy connection.)

Nomograph So. 6 (Fig. 2 ) may be used for the f i l l l i n g This nomograph is for A36 steel and EiO \velds. In the chart on thc: right-hand siclc, from the point of intersection of the angle's leg size (LI,) and the length of the angle (L,), draw a horizontal lint! to the \~ r t i ca l axis 1.7.15. From this point, draw a line throng11 the rc;lction ( H ) to the left-hand axis. Read tht. leg sizc ( w ) of thc field weld on this axis.

Table 1, for A36 steel and EiO welds, gives valucs of R / o in terms of leg size of angle (L,7) and length of angle (L,).

AISC, Sect 1.17.5 specifies that the leg size of a fillet weld used in calculating its lcngth (L,) should not came the web of the snpporting member to be overstressed in shear.

For n single pair of framing angles on just one side of the supporting web, assume thc leg size of the

R 19.2 L;' -- _ ~ ~p~ - .. ~-

I" f~y-' + 12.96

TABLE t-Valuer of R/w For Field Weld of Framing Angle to Support

For A36 Steel & P70 Welds

R Reaction, kips - ~ - ~ ~~ ~~ ~~ ~~~~ . - w Leg sire of f i l let weld

R .- 20.1 LV2 - . . ~~ . (,)

L,;"IA72 ,? 12.96 L,,'

(I?)

fillct weld not to exceed 1.3 t , . For t ~ v o pairs of framing angles, o m on endl side

of the supporting wish. nssilme ihr leg size of the fillet weld not to escw%l ?!I t,v.

Ti~esc faciors of ('i) and !1.3 = 2 x %) mny be djusted lor the oxact type of steel used l ~ y referring to Table 2.

4'.

R Assume !h" set bock

FIGURE 3

Leg of Angle ( L i d ~. ~~ . ~~~

7" 8" ,. .~ ~~

2"

4 3 1 30 / 22 1 I 9 1 1 6 / I4 1 12

~ . . ~~~

3" 4" 5" ,~ ~~

6"


In Figure 3, analysis of the shop weld sho\vs- rcsultunt force on outer end of connecting weld

twisting (horizontal)

k

FIGURE 4 fk *

leg size of fll& weld ttristing (oertical)

actual forcc on melds = ~ ~ - -

f 2 - -1 . . . . . . . . . . . . . (4) allowable force

A7, A373 Steel; E60 W e l d r A36 %eel; E70 Weldr ..

shcur (oertical) ) 17) 0 = 9600

0 = -- 11,200

. . . . . . . . . . . . . . . . . . . . . . . . . ( 5 ) " b L , Unfortunately there is no way to simplify these

TABLE 2-Maximum Leg Size to Use in Calculating Vertical Lengrh of Weld

FOR VARIOUS C O M B I N A T I O N S OF WELD METALS A N D STEEL Given these condit ions:

Steel

thickness

I

Then: Moximvrn leg size of f i l le t weld to use in rolculoting vei t ico l length

A7 A373

36,000 ...........................

14,500

E70 or SAW9

11.200 w

.648

OY

T

w e l d - -

f

o / t 5

k g size *

33.000

13,000 --

E60 or SAW-I -

9,600 i o .

,667

Web thickness i t u ) over -

A36

42,000

17.000 ..............

E70 or SAW-2 ........

1 1.200 w

7 5 9

A242, A441

, - 46.000 ...

- 18.500

E70 or SAW-2

11,200 u

,826

O w , 1 % " To 4"

50,000 .

20,000 -

L70 or SAW-2 --

1 1.200 w -.

,893

Over j/," To , %" e r less


5.4-6 / Welded-Connection Design

Leis than % thick" / %'*.' thick or more I

FIGURE 6

formulas into one workahlr formula. It is necessary t11 work out eai.11 step l~trtil tlw final restilt is ohtair~od.

The leg size of this shop w&i nray h r dctcrmined quickly by rncans of Kornograph No. 7 (Fig. 5 ) , for 436 stcrl mil Ii70 wclds. In thc c11;rrt on t l ~ r right-hand side, from thc point of iuterstctim of the anglc's h i - zontal lrg length ( I ) and its vrrticnl length (L,) draw a l~orizontal iinc to thl, vrrtical x i s F-F. Fmm ttlis point, draw ;I liiic through the reaction ( R ) to the left-11:ind axis, Read ttlc leg size ( w ) of the shop wcld along thp left-11;nnd svalc of this axis.

I f the nomogr;iph is u s d f m n l~xft to right to i,stahlish ;in arrglr six,. be sill-<. that the leg size of tbt. fillct wcld docs not cxcc~xl a v;rloc which vould overstress the web of t / ~ ( ' hiwm in s11~:rr (AISC SCC 1.17.5) by producing ~ I I O short a lorgtl~ of connecting weld (I>,).

The follou.irrg limits apply to the fillet weld leg size (w) rclativc to thr thiclmess of the heam web (:IS usr:d in c;ilctll:tti~rg tlw wrticnl length of connecting weld ) :

A7, A373 Steel and E60 Weld

/T -- 10.000 , x i ) ( f , = 9600 w Ihs/in.)

A36 Steel ond E70 Weld I

l-lo\\:rve~-, tlir acti~al leg six: of the fillrt wcld used may exceed this value.

Tahlr 2 reflccts thr limiting \.aloe of w = Zi t,. AISC holds to this limit for shop weld of the ;rnglr to the beam (.4ISC M;rmlaf. pages 4-25).

Notice tlrc left-Iran11 :isis of Nomograph KO. 7 also gives the millill-urn \veb thickncss of tlrc h(mn in order to hold its sbcnr sti-css (7) within 14.500 psi. Illst 11c sure the ttctr~ai \ ? - ~ I I tl~ickness of t l ~ e supported hpain is

If edge is butit up to ensure full thioot of weld

-

e q t d to or csi,ct~is tl~is \ d r ~ c for~nd just opposite the resulting lrr: sizc of the wi:ld.

Somt: rnginwrs f i ~ l this limiting shmr v;ilire (.406 stt.c.1, r L. 14,500 psi) is to ins~~i-I, that thc wcb of thr hearrr dws not bllckli., and that a higlrcr allowable vdnr iniglrt 11e IISCYI hcrt., pcr11;ips 3/r of the allowable ttwsilc strength. In this rase thr ~n:rxim~im lcg sirc of thr weld would he Ireld to ?/r of thc web thick~rcss.

1 w := % t, 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 9 )

I S C (Scc 1.17.5) sp.rifics the m a s i m ~ ~ m k g size of fillct \wid rr1:itive to :rrrglc plate thickncss to be as shown in Figtirc 6,

l';rhlc 3 \\-ill give ~, ; i l l~cs of R/w in trrms of leg size of angle (L, , , ) ; x r d lmgtli of :rngle (I,,). Table 3 is for i t I S i t 3 6 stwl. and IT0 w~.lds.

TABLE 3-Values of R/w For Shop Weld of framing Angle To Beom W e b

For A36 Steel & E70 R Reaction, kips - .. - ................. . .

go Leg sire o i fillet weld


.4s india l td hv Firnrr~ 3 and the rolatcrl weld Shoo Weld of Fromins Anale to Beam Web , , ~ > - - ;m:rlysis, thc fillct welds con~i(vtirlg anglc to heam w d ~ Nomograph No, 7 shows tl lnt for a rwction ( K ) of should hi, Irookd aroriud tlir ends of tllr anglc. top 58 kips. ;rn alrgle leg (I, , ,) of 3" and l<>rlgth (I,,.) of mcl bottom, for the distance ( h ) to t l ~ c end of tlic l y , a fill(,t wrl(l ( w ) ~,,llllld hi, rt!(illireil, Ilellce bcam wcti. They sh011l11 not ire continned aronnd the llsc G". 3,r %,, fralning ar,gles, 94t;,, c i ~ d of the wrb, Fignrr 7. weld to crilunm and Sk" shop weld to boain web.

&,-- Don t hook weld I "round this edge Don t hook weld oiound th i i edge

Hook weld orovnd

4. STANDARD EB FRAMING ANGLE CONNECTIONS

FIGURE 9

FIGURE 7

To design ;i wch framing ;aiglc cnnrlrctioll to sl~pport a 70" 85,1 1 bcan~, Ira\-ing an rnd rt,action of R = 58 kips. Use A36 steel uiid J+:X) u & k .

Sct: Figlire 8.

Field Weld of Framing Angle to Column

Nornograpli No. fi s l ~ o \ x ~ that for a %" fillct wcld ( w ); a reaction j R ) of 58 kips and a11 mgle \uth a 1c.g (I,,,) of 3". its lciigtli ( I J , ) si-lonld br 101,L". How- ever, for a %i,i'' fillct weld ( w ) the angk l t ~ ~ g t h (I , . ) violrid only li;tvc to be ir~creased to 12".

Tnbie 3 giws tlw I S C allowil~le lo:~ds (kips) on n~f ih framing mglc conncctioris. rlsirig A%, r12.42 and A141 s t t ~ l s ; ~ n d i-70 \n.t,lcls. T111, talilc givcs the capacity ;und sizc of (Shop) \'(,Id -4 coi~ncciing the framing angle to the hcnm web. and of (Ficld) Weld I3 co11- neoting tlic framing arigle to the h a m slipport.

pzL-q To s?lcct a \wIi frmning ariglc roi?ncctioii for n

16'' H 263 Ir;rm (0.75" \vrh tlrickiirss and T =: 11") of h3.41 stwl, \\-it11 rmd rwciion of R 1: 05 kips. Usc I 3 0 wcl~ls. Allowal~lc s h r x is 20 ksi.

This h<vnm \r-cii~ld t;lhr ;III anglr xvitb length I,, =: 10'' ( r 12" I n T;ililt. 1, the (Shop) \Trcld 4 ~ ipac i ty \ ' .

FIGURE 8


TABLE L S t a n d a r d Web Framing Angle Connections From American lnstitutt of S t e e l Cotistruction

T1 FRAMED BEAM CONNECTIONS

' @ I . & WeIded~&E6OXX electrodes W e i d & ; . . ( ,

1 , , , I

FRAMED BEAM CONNECTIONS S t , , . - B J 07 Welded E 7 O X X electrodes

&i TABLE V!

1 , M I ,

hriir Llr" i

:*?*-51 : ?"

O,?X%,, i s I*?> -r 39 4 ~ i r ; ~ x

ixi i : , 4h 4XIY ' . 39 L X i * l , )i

!*iY %< 48 i . i l % # 3 9 3, i x i , ii

1 x 3 ~ : ~ ~ 68 i * i X b ~ I l X l X * 4 6 29

ir lr%+ dB 1 Y i X ' I ir 3 ' . '9

. i R I*?*% 19 irix;i l i

i>,!i k t d i 1Xir; 1) 3 , )1

A : , 4' i * !Y+ 39 i * i X ' i , ?Y

3 , !% I < , < % !V A , 1"

I,,. #,,A . t

- ,%,,"

- 7>,,

St '

> , L

)!I

'4,

)., i.,

i,

l , 6

+IS

>,,

>>, 3 ' "1 i

- ~ c ~ , . z %,,,, -

2-7 16:' i s

71, ! X L?:

19: LIB i!8

1 % 116 iar

ih7 l i 4 :00

cP'

I?? I41 ,,

i l l i!" 81 4

:,, n 0 i; i

!lil R i i : o

12 I ,: 3 $5 ;

!d i b l b t,' " ,,$ 0 il ; I& i

5,: ! ii 6 :r

," ? >,... a: , 40 I

:i 5 34 6 ?d i

! 0 "' " 7

a 7 .: 5 16 4

:a 6 1" l i 9 - ,&,,*,

'%*"-


nf 38.4 kips for a weld size of o = ?ip," and anglc length of L, :: 10" sliglitly excteds the rmction. The corrcsponding (Field) W d d R, nsing w : 'h", also is satisfactory. Sinct. the beanis rcqui rd wweh thickncss is 0.31'' while tlic actual ivcb thickncss is 0 . W , the indicatcd 3" x 3" x 5/,(1'' is d l right.

If the beam is rnade of A36 steel, this conncction's capacity will bc rcdueed in the ratio of 0.25/0.29 of actual to rcyrriml web thickness. The r t d t i n g capacity of 33.1 kips is less than the reaction. The nest larger connection with apparently sui6cient capacity sllows that (Shop) Weld A's capacity is -17 kips, using same angle section hut an angle lcngtl~ of L, = 12". Apply- ing the multiplier of O.2.5/0.!?9 redr~ccs tho capcity of the connection to 40.5 kips, which excw:ls the end reaction.

5. SINGLE-PLATE OR TEE CONNECTION O N BEAM WEB

In the previous dcsign of the field weld, connecting a pair of web framing angles to the supporting column or girdcr, it was assumrd that the reaction ( R ) applied eccentric to ench angle, r tsdted in a iendeocy for the angles to twist or rotate. In doing su, thcy would press togcthcr at thc top and swing :way from each other at the bottom, this bring rmis t~d by the welds. These forces arc in ;rddition to thc vertical fol-ces c a ~ ~ s e d by thc reaction ( R ) ; see Figure 10.

IIowrver, in both the single-pl;~te wcb connection and the Tce-st3ction tyl~i., this portion of thc conrrection welded to the col~nnn is solid. Thns, there is no tendmcy for this sprcding action which must be rcsisted by the welds. These vcrtical field welds to the

FIG. 10-Dauble-web framing angle

FIG. 11-Single plate or Tee

co111rnn \voold be designed then for just the vcrticd rcaction (11); see Figure 11.

In the shop ~ d d of the singlc plate to the web of the honm, Figrirc 13, this donlde vertical weld wonld be designcd for just tlic vrrtical reaction ( R ) . There is not enough rc~witrieity to considcr any bending action.

FIG. 12-Flat plate used for flexible connection on web of beam.


Tee section used far flexible

connecttaii on web of beam

FIG. 13-Tee section used for flexible connection on web of beom.

In the shop n r l d of thc T w connection to thc web of tlrc bram. Figure 13, the size and limgth of thr fillct .ivclti w o ~ k l be dt,tcrniinid inst as in the cast, of the doublr-ncl) fran~inz ;nrgirs. (:xct.pt thew is jnst a FIGURE 14 single fii1t.t weld in this casc rather than two; so, for n given cos~ncrtion, this wonk1 can-y just half of thc rcwtion of the corresponding donblt:-anglc connection.

fillct tcelrl in slzetir; portillel load 6. DIRECTLY-WELDED WEB CONNECTION 2(96(10w)l, := t, 13,000 I,

To sec how this typc of connection hch;ivcs, consider -1 the follo\ving 18" WF 85# beam, simply supported, 15' soan. with a unifonnlv distributcd load of 139 kios.

A '

the same hcnm and load u s d in the grricral discwsion on behavior of connt.ctions in Srct. 5.1, Topic 6.

If only thc wvl) is to he nvklrd to the cohn~rn, tho n~ns t h m c stifficit>nt length (L , ) so that the a&-

cent \vi,b of the hwim will not hc overstressed in s11o;tr. For A373 stecl

== 10.2", or U.SC 11" l.~ic~o;illy, tmnsvcrw fillct welds arc: ;ibout ?$ stron-ei than p;tr;iild fillet wclds; this can i>e pnn.ril by thmry as d l as

The leg size, of this fillrt weld rnrist hc t ~ p d to the twtiiig. 'This m a n s h,r trmsverst, h;rtis, tlri; 1i.g s i ic wodd bc thickness, ~ , ~ ~ ~ d uporl stanci:lrd ;lllcl,,.~t~,les, if i t is 3 of tlw platr tliirkn<,ss, iiist ;is in l);ti;i!Ii,l luaiis. Iiowevcr,

~, r Id ing codrs do not ;,s yct i-wognim tliir; :ind for code work, to matrh the :~liowahir strength of this web sectioii in f i 1 1 ~ ~ rvl,~ds for tr.ir,svcrsc io;,~is .jiri,,,id bc. ii,itrIi~ ccliiiil to ilic pl;itc shear as wcll as tcrrsion. tiiiclaiess.


I FIGURE 16

. - the k g size of this fillet weld is increased by this nmount.

The moment-rotation chart, Figwe 17, shows the beam line for this pnrtictilar bcmn lcngtli and load; and the actual connection curve taken from test data at 1,ehigh University.

In testing this co~meetion, thc heam \veh showed initial signs of yielding adjaccnt to the lo\ver mds of the weld at a monirnt of 3fi0 in.-kips. At a moment of 660 in.-kips, point ( a ) , thew wcrc indications that the beam ~ v e l ~ along the full length of the weld had yielded. At a moment of 870 in.-kips: 110th \velds cracked slightly

at the top; this point is ~narkecl with an "X" on the curvc. With furlhcr cracking of the weld and yielding in tho beam wch, thc lo\vm finngc of the beam roll- tadcd thc colurnn, point ( h ) , arid this resultrd in irlrreascd stiffness. Thr- inoment built tip to a ~ i ~ a x i m ~ n n of 1918 in.-kips, and t b e ~ ~ gr:idually fell off as tire \ d d continued to tear.

Notice in this partic~ular cminplr. the web wodd haw yicldrd the in11 Icngtli of the \wid at design lo;~d.

The \veld s t : ~ r t d to crwk whcn the corrnt.ction h:d rotatrri ;ihout ,011 r;idi:ins; this woold corrcspond to a horizo~~tal inovenncnl of .OV at t l ~ c top portion oi the wold. Cornpaw this s~n ;~ l l :inro~~nt of mov~:mcnt with that ol~tainrcl i r~ t l ~ c top conrn,ctiiiq plait: c~x:u~~ple of Figure 4 n-hicb 1i;irl thc zihility to pnll out 1.6" Iwforc failirrg.

This diicctly \velricd wrh conrieetion (Fig. 18)

FIGURE 17

eided-Construction Design

FIGURE 19

FIGURE 20

is not as dependable as a top connet:ting plate designed to picld at working load (Fig. 19) or aither flexible web framing angles (Fig. 20) or flexible top angle.

Also rcmember this highly y ie ldd web section, in the case of the directly welded wcb connection, must still snpport or carry the vertical reaction ( R ) of the beam, whereas in the top plate connection, the support of tire beam at the bottom seat is still sound no matter what happens to the top plate.

Figwe 17 ~vould indicate the directly welded web connection rosoits in an end moment of M, = 720 in: kips, or an end restraint of-

/ 'Field weld

This restraint is a little high to be classed as simply supported.

The same top plate connection is shown in dotted lines on Figure 17; it has about the same stiffness, hut many times the rotational ability.

The use of side platrs, Fignre 21, would allow a wide variation in fit-up, b.ut in general they are no better than the directly welded web connection. Unless the plates are as thick as tile beam web, the resulting connecting fillet welds will he smaller and will rednce the strength of the conncction

FIGURE 21

Fteld weld

shop weld

1 1 Field weld only on toe of ongle

FIGURE 22


In the tests at Leliigl~ University, the corresponding connection on the 18" WF 85# beam (S26"-thick web) nsed :$6" thick side plates with fillet welds. They failed at a lower load.

If 'htr thick side plates with %" fillet welds had been used, they undoubtedly- wonld have becn as strong as the directly welded wch connection.

7. ONE-SIDED WEB CONNECTlONS

A single web framing angle nsed by itself is not recommended; see Figure 22.

Use of only a single vertical fillet weld to join the angle to the supporting member imposes a greater eccentricity upon the connection. This resdts in a maximum force on the weld of about 4 times that of the double-angle connection; see Fignn:s 23 and 24.

It might be argued that in the conventional double- angle connection, the fieId weld is subject only to

FIGURE 23

FIGURE 24

vertical shear because the stiffness of the angles largely prevents any twisting action on the connection even though the analysis is based upon this twist as shown in Figure 23. However, there is no doubt that the single-angle connection has this twisting action which mould greatly decrease its strength.

Any additional welding on the single anglc, such as vertically along its heel or horizontally across the top and bottom edges, would make it rigid and prevent it from moving under load. This would cause the end moment to build up and greatly overstress the ccn- nection.

In the original resenrcb at 1,chigh University on welded connections, this single-angle connection wit11 a single vertical weld was never tested. Single angle connections welded both along the sides and along the ends were tested, but as already mentioned, they did not have enough flexibility, and the cnd moment built up above the strength of t l ~ c connection.


Web framing angles ore commonly shop welded to the supported beam. To facilitate erection, bolts are used in joining the other member until the web framing angle con be permanently welded to it. The erection bolts can be left in, or removed if there is any concern that they will offer restraint. Note the use of box section column, in this case it being hot rolled square structural tubing.

1. DESIGN PLATE TO BE STRESSED AT WELD

A top connecting plate if designed to be stressed at its yield will provide a flexible connection, suitable for a simple beam and easily adapted to carry the additional moment due to wind.

Since this flexibility is due to plastic yielding of the plate, the portion of its length which is to yield should be at least 1.2 times its width.

p Beam

b I ~

(length of beam)

FIGURE 1

The plate should be capable of plastically yielding a distance equivalent to the movement of the end of the top beam flange as it rotates under load if the connection were to offer no restraining action (AISC See. 1.15.4); see Figure 1. For a simply supported beam, uniformly loaded, this maximum movement ( e ) ~vo~ild be:

where:

e =: movement, in inches

L = length of beam, feet

The graph in Figure 2 illustrates what this movement would be as a function of beam length, under various load conditions.

There is no problem in detailing a top plate to safely yield this much, providing there are no notches which might act as stress risers and decrease the plate's strength. Any widening of the plate for the connecting welds must be done with a smooth transition in width.

( 2 loads @ % points 4 loods @ 1/, points

6 Uniformly distributed load

5 loods @ v6 points 5 3 loads @ % points

.4 1 load at Z

.3

.2

. I

10 20 30 40 50 60 70 80 90 100 Length of rimply supported beom (L), feet (orruming beam to be stressed to u = 20,000 at C )

FIGURE 2


E 6024 weld metal

6010 weld metal

80

I I I I I I I I 5 10 15 20 25 30 35 40

Elongation, % in 2"

FIG. 3 Stress-strain diagram for weld metal and beam plate.

ASTM specifies the following minimum percent of elongation as measured in an 8" gage length for structural steels:

This minimum value of 2m for A36 steel would represent a total elongation of 20% X 8" = 1.6" within the 8" length.

Notice in Figure 2 that a simply supported beam, uniformly loaded, with a span of 20 feet would rotate inward about .106", so that this particular beam would utilize only x5 of the capacity of this top plate to yield.

Figure 3, a stress-strain diagram, shows that a miid steel base plate will yield and reach maximum elongation before its welds reach this yield point.

The test specimen in Figure 4 shows that ample plastic elongation results from the steel tensile specin~en necking down and yklding. This is similar to the behavior of a top connecting plate which yields plastically under load.

2. TOP PLATE FOR S I

There is some question as to what value should be uscd for the end moment in the design of the top plate for simple beams. Any top plate will offer some restraint, and this will produce some end moment. Le- high researchers originally suggested assuming simple beam construction (AISC Type 2) to have an end restraint of about 20%. On this basis, the end moment for a uniformly loaded beam would be:

and this is 13.3% of the beam's resisting moment Heath Lawson ("Standard Details for Welded

Building Construction", AWS Journal, Oct. 1944, p. 916) suggests designing the top plate (simple beam construction) for an end moment of about 25% of the beam's resisting moment. This would correspond to an end restraint of about 37.5%, which approaches the range of "semi-rigid connections.

In Figure 5 the end of the top connecting plate is beveled and groove welded directly to the column, the groove weld and adjacent plate being designed to develop about 23% of the restraining moment of the

- - - - - FIGURE 4

Top PIaies gar Simple Beams ind / 5.5-3

beam using the standard allowable bending stress. The standard bending stress allowed here would be limited to u = .60 u,. (Type 2, simple framing).

Just beyond the groove weld section, the plate is reduced in width so that the same load will produce a localized yield stress (u7) . The length of this reduced section should be at least 1.2 times its width to assure ductile yielding.

This plate is attached to the beam flange by means of a continuous fillet weld across the end and retum- ing a sufficient distance on both sides of the plate to develop the strength of the groove weld at standard allowables:

A7, A373 Steels; E60 Welds -- ---- ~-

. . . ( 2 ) A36, A441 Sleek; E70 Weld

- ... .-

IND BRACING

Wind moments applied to simple beam c~nnections present an additional problem. Some means to transfer these wind moments must be provided in a connection which is designed to be Rexible. Any additional restraint in the connection will increase the end moment resulting from the gravity load. AISC Sec 1.2 provides for two approximate solutions, referred to hereafter as Method 1 and Method 2.

In tier buildings, designed in general as Type 2 construction, that is with beam-to-column connections (other than wind connections) flexible, the distribution of the wind moments between the several joints of the frame may be made by a recognized empirical method provided that either:

ethod I. The wind connections, designed to resist the assumed moments, are adequate to resist the moments induced by the gravity loading and the wind

at the increased unit stresses allowable, or fhod 2. The wind connections, if welded and

if design& to resist the assumed wind moments, are so designed that larger moments induced by the gravity loading under the actual condition of restraint will be relieved by deformation of the connection material without over-stress in the welds.

AISC Sec. 1.5.6 permits allowable stresses to be increased % above the values provided in Sec 1.5.1 (steel), and 1.5.3 (welds), when produced by wind or seismic loading acting alone or in combination with the design dead and live loads, on condition that the required section computed on this basis is not less than that required for the design dead and live load and impact, if any, computed without the % stress increase, nor less than that required by Sec. 1.7, (repeated Ioad- ing) if it is applicable. Since we are discussing Type 2 construction (simple framing) the initial basic allowable stress is 60 u,, not .66 u?

pz-tizq The top plate (Fig. 6 ) is designed to carry the force resulting from the end moment caused by the combination of the gravity and wind moments, and at a V3 increase in the standard stress allowable (or u = .80 u,). This 4; increase may also be applied to. the connecting welds (AISC See. 1.5.3, & 1.5.6). The fillet welds connecting the lower Range of the beam to the seat angle must be sufficient to transfer this same load.

The top plate must have the ability to yield plastically if overloaded (last paragraph of AISC Sec. 1.2).

FIGURE 5

At stondard ollowobler Minimum length of reduced

1" X W' backing bar

F = rtandord allowabl

MI (gravity)

d,


Fillet weld at 1'/3 M, (grovity)+M,(windl

stondord allowabl when loaded with F

In the alternate design of the top plate shown at upper right in Figure 6, the reduced section ( W ) is designed for the force resulting from the end moment caused by the combination of the gravity and wind moments at a 'h increase in the standard allowables. It will reach yield at a 25% increase in load ( F ) . The wider section at the groove weld (1% W ) will reach 1% 5- or .SO u, when the reduced section has reached this yield value.

I Method 2 1 The top plate (Fig. 7) is designed to carry the force resulting from the wind moment (M,) using a % increase in the standard allowables:

u = (1%) $0 up :: .80 up

The top plate must be capable of yielding plasti-

FIGURE 6

cally to relieve larger moments induced by gravity loading, figuring the connecting welds at standard allowable~.* This is the same method for figuring the connecting welds of top connecting plates for simply supported beams without wind loads.

The reduced section will reach yield stress (u,) at a 25% increase in load ( F ) . The wider section at the groove weld (1% W ) will reach standard allowables ( 8 0 u,) at this time.

In case there should be a reversal in wind moment, the top plate must be thick enough to safely withstand any compressive load without buckling.

It is recommended that the top plate's thickness be held to at least x 4 of its length ( L ) between welds. This will provide a slenderness ratio (L/r) of 83; and corresponds to about 80% of the allowable compressive strength for a short column (L/r ratio of 1 ) . - 'This weld altowable by AISC i s not clcar; AISC srmply says welds shall not be overstressed when plate is at yield.

At standard allowables M~n~murn lensth of reduced when reduced section is section between welds at yield in7)

1" X W' backing

At 1 % a when loaded with [F) ivind moment

Fillet weld at standard olloviobles when reduce

M, (wind)

db

FIGURE 7

Top Plates tor Simple Beams & Wind / 5.5-5

FIGURE 8

Where: Wt"

1 - -- x -- 12 and

raditw of gyration

slenc1erncss ratio

4. EXAMPLE OF TOP PLATE DESIGN- wltn WIND MOMENT

A 14" M7F 38# beam is simply supported and loaded urtiformly with 296 Ibs/in. on a 15-ft span. Based on these beam-load conditions, the masimum bending moment at center is M = 1200 in.-kips. Use A36 steel and E70 welds. Wind moment on each end is M,T = 600 in.-kips.

Beam conditions here: (See Figure 9.)

14" W F 38# beam

b = 6.776''

db = 14.12"

ti = ,513"

S = 54.6 in."

If there were no wind load, the above connection might hc designed for about 25% of the present

(gravity) moment as a simply supported beam:

= 300 in.-kips on connection at each end

= 21.3 kips

The rcduccd section of the top plate is designed to carry this force at yield stress (u,):

- - (21.3 kips) (36,000 psi)

- - .59 in."

or use a 1%'' x W' plate

Connecting Welds at Standard Allowables

For the groove weld to the cwlnmn flange, this plate is widened to 1%W, or-

width = 1% (1%)

= 2.V or use 3.0"

For the fillet welds to the beam flange, use 5/,," fillets at an allowable force of-

FIGURE 9

f, = 11,200 0

= 11,200 ( X e ) = 3500 lhs per linear inch

The length of this weld is-

- - ( 6 % in.2)(36,000 psi) (3500 lhs/in. )

This would he 13h" across the end, and 2%" along the sides.

efhod 1 for Additional

This connection will now he designed for the additional wind moment of M, = 600 in.-kips, using Method 1.

FIGURE 10

Beam conditions here:

14" WF 35# beam

b = 6.776'

db = 14.12"

tc = ,513"

S = 54.6 in.3

Total moment on the connection is-

M = M, + M,

= 300 in.-kips + 600 in.-kips

= 900 in.-kips

Force on top plate is- M F = - d b

= 63.8 lcips

The top plate is designed for this force at fS higher allowahles:

- - (63.8 kips) 1% (22,000 ps?K

= 2.18 in.2

or use a 3%" x %'' plate --

A, = 2.19 in." 22.8 i n . 0 K -.

The connecting welds are figured at % higher allowable~:

For the fillet welds at the beam flange, use M" fillets. The standard allowahle force is f, = 11,200 cd = 11,200 ( M ) = 5600 lhs per linear inch.


- (63.8 kips) - in (5600)

This weld length would be distributed 3%'' across the end, and 2%" along the side edges of the top plate.

The above connection may be cut from bar stock without the necessity of flame cutting any reduced section in it. This is a good connection and is in widespread use. The connecting groove weld and fillet welds are strong enough to develop the plate to yield plastically if necessary due to any accidental overload of the connection.

Some engineers prefer to widen this plate at the groove weld so that if the plate should have to reach - vield stress, the connecting welds would be stressed - only up to the wind allowable or % higher, hence u = 30 u,.

Accordingly, the plate is widened here to 1W =

(See Figure 11.)

The length of the fillet weld, using M" fillet welds and allowable of f, = 5600 lhs/in., would he-

Top Plates for Simple Beams &

FIGURE 11

F reduced section at yield

L,=- ( ) and fillet weld at 1% f,

'h higher allowable

- (2.19 im2) (36,000 psi) - -

1% (5600)

= 10.55" - This would he 3%" across the end, and 3%" along

the side edges of the plate.

Applying Method 2 for Additional

w FIGURE 12

Temporarily ignoring the gravity load, the top plate is designed to carry the wind load, M, = 600 h k i p on each end.

Compression Tensi top R on top

Wind moment

FIGURE 13

= 42.5 kips

The reduced section of the plate is designed to canr)- this at 44 higher allowable:

(42.5 kips) -- - 1% (22,000 j = 1.45 in.2

or use 3" by 36'' plate

The plate must now be modified so that larger moments induced by the gravity loading can be relieved by plastic yielding of tlre top plate, designing the connecting welds at standard allowablcs.

The plate is widened at the groove weld to 1% W = 1% (3) = 5.c".

For the connecting fillet weids to the beam flange, use %" fillets:

f, = 11,200 0

= 11,200 (%)

= 4200 lbs per linear inch


F 1.5 in.') (36,000 psi) L, =- =L f, (4200)


Beam 10,550 psi]

Connection (28.330)

& = + 600 it?-k

M, = - 600 in-k

FIGURE 14

FIGURE 15

This would be 3" of weld across the end, and 5" along each side.

5. EXAMINING THIS EXA

To better understand how this wind connection oper- ates, this example will be examined, using Method 2.

1. The cmm~ctioq~ is Erst designed for the wind moment of M, = 600 in.-kip at % increase in the standard allow-ables applied to each end of the beam.

The wind moment will cause a bending stress in the beam of-

= 10,990 psi

(See Figure 14.)

The corresponding stress in the top connecting plate is-

- (600 in-kips) - (14.12) (1.5)

= 28,330 psi

Note that the connection will not yield until a stress of 36,000 psi is reached.

2. Now the gravity load can be gradrially added, treating the beam as having fixed ends, until the right- hand connection reaches yield stress. This would be an additional stress in the connecting plate of: 36,000 - 28,330 = 7670 psi. This would corrcspond to a stress in the beam end of: (.388) (7670 psi) = 2980 psi.

(See Figure 15.)

Since the allowable moment on this end connection resulting froin gravity load is (hcated as a fixed end beam)-

w* L' Me, = --- -- also =cr, A, d 12

the portion of thc gravity load to be added here is-

The stress in this beam end due to gravity load is then added to the initial wind moment diagram:

(See Figure 16.)

Top Plates for Simple Beams & Wind / 5.5-9

- Mc2

,490 psi

FIGURE 16

3 FIGURE 17

8010 pri

M = - 517.6 in- ', Ma = - 762.8 in-k ,

9480 psi \

Connection 13,970 psi (24,430 psi)

FIGURE 18

At this point, the right-hand connection reaches or a bending stress of yield stress (u,. = 36,000 psi) even though the beam end is stressed to only u = 13,970 psi. Mez (955 in.-kips) ub2 = -- =

3. The remainder of the gravity load (w2 = w - Sb (54.6 in.3)

w, 296 - 60.2 = 235.8 lhs/in.) can now be applied, = 17,490 psi treating the beam as having one fixed end on the left and simply supported on the right. See Figure 17. w* L*

Also since M = - The resulting end moment here is- 16 -

ub at 9 = $5 (17,490) = 8750 psi wz L" Me* = - - (235.8) (180)2

8 8 'll~ese stresses are then added to the previous

955 in.-kip moment diagram; Figure 18.


FIGURE 19

2670 ps,

Beam Connection 3660 PSI

4650 psi (36,000 psi)

FIGURE 20 990 psi

4650 psi Connection Beom (36,000 psi) 4650 p

FIGURE 21 (36,000 psi)

The corresponding stress in the top plate is-

A lower design wind moment will not require as large a top connecting plate. The smaller plate will yield sooner and it is possible that the h a 1 gravity load would cause both end connections to yield.

Consider the same pl-obkm as previously but with the wind moment reduced to M, = 200 in.-kip, applied to each end of the beam.

The required top plate is designed for this wind moment:

= .48 in.'

or use a 1" x M" plate .- - -- - -. - -

(This very small top plate is used here only for illustrative purposes.)

A, = 5 0 in.' > .48 in.'

This moment will cause a bending stress in the beam of-

M, (200 in.-kips) ~~ -- - ~~ ---- ~~~

d A,, - (14.12) ( 5 0 )

= 28,330 psi

A portion of the gravity load is added, treating the bcarn as having fixed ends, until the riglit hand connection reaches yield stress. This would be an additional stress in the connection plate of: 36,000 - 28,330 = 7670 psi. This would correspond to :I stress in the beam of: (.l29) (7670 psi) = 990 psi. See Fignre 20.

Since the allowable moment on this end conncction resulting from gravity load is-

M, ub =- the portion of the gravity load to be addert here is- Sb

- - -. (200 in.-kips) (54.6 in.:')

= 3660 psi See Figure 19.

W, = 12 u,, A, d, .- - 12 (7670)(.50)(14.12)

L'" -

(180)'

Top Plates for Simple ind / 5.5-11

At this point, the right-hand connection reaches yield stress (u, = 36,000 psi) even though the end of the beam is stressed to only 5 = 4650 psi.

In this example, if the remainder of the gravity load were applied, the left-hand connection would go over the yield point. For this reason only enough of the gravity load will be added to bring the lcft-hand connection just to yield, treating the beam as having one fixed end on the left and simply supported on the right. See Figure 21.

To reach yield stress in the left connection, the stress in the beam must increase from 2670 psi compression in upper flange to 4650 psi tension, or 7320 psi.

This would correspond to an applied gravity load of:

- - 8(7320 psi) (54.6 i n 3 ) (180)"

so cr,= M(7320)

= 3660 psi

This now leaves a gravity load of ws to be applicd, treating the beam as having simply snpportcd ends since their connections have both reached yield stress.

The remaining gravity load:

Since:

= 13,150 psi

Ibis stress in the bcam is added to the preceding moment diagram; see Figure 22:

The total ue = 17,310 psi < 22,000 psi OK

7. AD APPLIED FIRST, THEN

In the preceding examination of the wind connection, the wind was applied &st and thcn the gravity load. This is the seqnence of design followed in Method 2. The cross-sectional area of the top plate is determined by wind only, and then the connecting welds are designed so that larger monlents induced by the gravity loading under actual conditions of restraint may cause the plate to yield plastically.

Of course in actual practice, the gravity load is applied first and thcn the wind may be encountered secondly. The same problem will now be examined in this order of loading.

The bean with the gravity load is considered as simply supported; however, the top plate which must resist the wind moment does restrain the end of the heam to some extent. ?he larger the plate, the greater the restraint, this will also increase the end moment rcstilting from the gravity load. It is necessary to get some indication of the restraining action of the connection so that the cnd moment from the gravity load may be known.

FIGURE 22


To do this, a simple moment-rotation diagram is constructed for both the loaded beam and the connection. The resulting conditions are represented by the point of intersection of these two lines or curves.

In the Lel~igh research of connections, the actual test results of moment-rotation of the connections were plotted on this type of diagram; in this example the properties of this top plate connection are computed, and will be fairly accurate since practically all of the movement will occur in the reduced portion of the top plate.

Connection l ine

FIGURE 23

I I bottom of beam

v-v--w

FIGURE 24

I I I mld-he~ght of beam

G-Q-VS

where L, = length of plate section between welds, inches

e Since 0 =-and e =: E Lp

db

also M, = up A, db

If the bottom of the beam is securely anchored and the top plate is relatively small, Figure 23, rotation map be assumed to occur about a point near the bottom of the beam. As the top plate becomes larger, offering more restraint, this point of rotation moves up. If the top plate has the same size as the beam flange, Figure 24, rotation may be assumed to be at mid-height of the beam.

Since movement ( e ) depends upon the over-all elastic elongation of the top plate, and for simplicity length (L,) is shown only as the length of the reduced portion, there is some elongation in the widened section as well as in the reduced section within the fillet welded zone. For this reason the value of the calculated rotation ( 8 ) in this example will be doubled.

Two points will determine the connection line. Since this line passes through the origin or zero load, it is only necessary to have a second point; for simplicity this second point will be a yield conditions.

At yield:

(36,000 psi) (4.5") - -- - (30 x 10') ((14.12")

= ,382 x radians

This value will be doubled because of elastic elongation of other portions of the plate:

0, =: ,764 x radians

and:

M, = a, A, db =r (36,000 psi) (1.5 in.2) ( 14.12")

= 762 in.-kips

Beam L i n ~ G r a v i t y load, uniformly loaded

It is necessary to have two points to detelmine this beam line on the moment-rotation chart:

( a ) the end moment ( M e ) if fully restrained

Top Plates for Simple Beams & Wind / 5.5-13

= 800 in.-kips

( b ) the end rotation ( 8 , ) if simply supported

where L = length of beam in inches

Connection a t yield in,)

moment, Me = 720 in-kips

Connection line

End rotation (OJ, X 10-3 radians 6.24

FIGURE 25

With the gravity load only on the beam, this would indicate that the end moment7 would be Me = 720 in.-kip. This would leave:

This would correspond to a bending stress at the end of the beam of-

= 13,200 psi See Figure 26.

The stress at centerline of the beam would be-

= 8800 psi

U b As before K =- = ,388 so that the stress U"

in the connecting plate would be--

up = 13,200 psi .388

= 34,020 psi

Now the wind load is gradually applied equally to both ends until the right-hand connection reaches yield. This would occur when the stress in the connecting plate is increased from 31,020 psi to 36,000 psi, or an increase of 1980 psi. This would correspond to a wind moment of-

13,200 ps i i 3,200 psi Connection

(34,020 psi) FIGURE 26


M, = 42 in-kips

Connection (1980 psij J "

FIGURE 27

.- 8800 psi

Beam 7 12,430 psi

L

FIGURE 28

FIGURE 29

- 19,020 psi

pea.. 13.970 psi

FIGURE 30

Connection (36,000 psij

Top Plates far Simple Beams & Wind / 5.5-15

And stress in the beam is-

= 770 psi See Figure 27

Adding this wind moment diagram to the initial gravity moment diagram gives I'ignrt: 28.

There now is left a wind mornent of 600 42 = 5% in.-kip to be applied to each end, but since the right-hand connection has reached yield stress, the remaining moment of 2 x 558 = 1116 in.-kip must he added to the left end of the beam.

= 20,440 psi

.= 52,680 psi (compressio~~) to be added to the 32,040 psi in tension already in the left-hand connecting plate

Adding this last wind moment diagram to the diagram in Figure 28 gives thc final diagram, Figure 30.

8. ALTERNATE GRAPHICAL SOLUTION

This same example can he illustrated in a slightly different manner. The right-hand connection and beam end is on the right of Fignre 31; the left-hand connection and its l~earn ond is on the left.

As b ih re , the beam line with gravity load only is constructed for both ends. This hcnm line represents the moment at the end caused by the gravity load, the actual value of the lnolnerrt depends on the effect of the connection.

A wind mornent would be represented by a horizontal line throngh the actual value of the moment. It would not he influenced by the connection iinless it exceeds the yield of the connection; then the portion of the wind moment carried would be limited by the yield of the coimection. 4ny wind moment superimposed on the gravity load will shift the beam line vertically up or down depending on the sign of the wind moment.

By observation, the right-hand connection can be

'Jb = - 13,970 p s ~ oe = - 36,000 psi

- I O O O l "3 a -- 900.-

[compression]

Left End

G M- = - 762 in-kips 1

i '6.24 x l o 3

End rototion [OJ, X 10-3 radians I

I

j. Add wind moment of negotive M, = 4 2 in-kips to right end of beom; connection reaches yield

%Add wind moment of positive M, = 1 I56 in-kips to left end of beam

Right End

FIGURE 31


increased another 42.0 in.-kip from wind, then it will reach yield and no further moment can be applied. Since the applied wind moment was 600 in.-kip on cach end, this will leave a balance of 2 x 800 in.-kip - 42 in.-kip = 1156 in.-kip to be carried entirely by the left-hand connection.

To do this, the beam line on the left of Figure 31 will be lowered vertically + 1158 in.-kip; see the dotted line. This will inkrsect the connection curve (extcnded into the positive moment region) at an end moment of Me = 320 in.-kip.

This will correspond to a bending stress in the beam end of 6050 psi, and in the connection plate of 15,600 psi. In this case, the connection curve h:~d to be extended downward into the positive moment region in order to intersect the new beam line. This indicates a $ moment and reverses the stress in the plate, now compression, arid the bottom of the beam connection is now in tension.

The previous examination of this problem indicated a bcnding stress in the left end of the beam of cri, = 8010 psi; this examination indicates a stress of ul, := 6050 psi. Why should there be a difference? The previous examination stopped after the first end momcnt due to gravity load was determined and then for simplicity from then on considered the connection as per- fcctly rigid, whereas this examination considered the elastic properties of the connecting plate all the way through the problem. This last approach would be a

little more accurate. This same prohlem was pi-eviously worked with a

reduced w i d moment of M , = 200 in.-kip applied to each end. Figure 32 shows how this can be worked graphically. This is an intrresting prohlcm since the lower wind lnorncnt reqnires a smaller top plate, with ?/3 the cross-sectional area, hence 'h the strength, and the gravity load ca~ised the plate to yield plastically at both rnds even before any wirid load is applied. This is represented by the black dot where the beam line (without wind) intersects with the connection curve.

When the wind moment is added, the right conncction is alrt:ady at yield and can carry no additio~ral moment, therefore the mtirc v.ind moment of 2 x 200 in.-kip = 400 in-kip must be carried by the left-hand connection. Accordingly the beam line is lowered vertically a distance of 400 in.-kip: see thc dashed line. As this is lowered. tbt. resulting moment (M,,) and rotation (0,) of the connection (black dot) slide down parallel to the clnstic portion of tlrc connection line until it intersocts with this new beam line (white dot).

In Figure 33 these final conditions representing the heam with gravity load and wind load are represented with black dots. If the wind were now removed, the left beam line moves npw-ard 200 in.-kip 2 n d the right beam line movt.s dou.11 200 in.-kip, tho new conditions being represented by the white dots. For a complete reversal of wind, this operation is again repeated and is represented by the broken lines.

? - 9004 + - r u u

.- Gravity iood; no wind - 800 2

Me = - 330 in-ktpr A- - 8. = - 3.8 x l o 3 iudionr \@'

400 in-kips-.. < 6 2 4 X 1 0 "

Right connectton 1s at yieid and con toke no odditionol moment; hence, odd wind moment of 21 + 2001 iwkiar =

Gravity load with wind + 400 in-kips to ieft end M. = + 30 in~kiar

Left End ~~ ... . .

Right End

FIGURE 32

Y

Top Plates (or Simple Beams &

4 Left End Right End

FIGURE 33

Typicol scene in structurol shop with weldors attaching stiffeners in place on curved knees. Proper use of welding results in significant savings in structural steel weight and in fabricating costs.


Welded continuous connections were used extensively in the Hartford Building in Son Francisco. Photo shows the use of short Tee sections welded in place under ends of girders to provide deeper section o t the point of moximum negative moment. Note thot columns ore weld fobricoted. The small ongle supports steel roof decking.

1. ANALYSIS OF CONNECTION --f H k -4 / i ,k M e ! - - 4 e +

-4 top connccting $ate designed to hc stressed only I

below its yicld point may he used as a semi-rigid connection. The reduced poltioil of the plate is detailed to have sufficient length ( L ) for elastic elongation of this section to provide the proper amount of joint rotation. See Figure 1.

Analysis of this type of connection reqriires locating the center of rotation. 'This depmds on the relative stiffness of the top hottom portions of the con- Rotation about bottom of beom Rotation about mid-height of beam

neetion. FIGURE 2 FIGURE 3 For the more flcxible type of semi-rigid connection,

rotation will occur closcr to thc bottom of the beam; The rmisting mornc,nt of the connection is- see Figire 2. For thc more rigid ccorir~cction, rotation will occur closer to the rnidhcight of the beam; see . . . . . . . . . . . . . . . . . . . . . . . . (1) Figure 3.

Alternote detail

iequi ied for joints of high reit ioint

Column flonge stdfenerr may be

1 FIGURE 1


My = A, or d; (top plate at yield)

I

t 8, 0,

[octuol) (flexible beam)

and the required cross-sectional area of the top plate is-

The rotation of the connection, assuming rotation about midheight of the beam is-

8, = -- mi and

The slope of this connection line is-

This connection line breaks at the yield point, or becomes horizontal at:

I M ~ = A,, u). db I . . . . . . . . . . . . . . . . . . . . . . . . ( 5 )

The actual conditions of moment (M,) and rotation (& ) are found at the intersection of the beam line and the connection line; see Figure 4.

Table 1 shows the moments ( M ) and end rotation (8) for various load and beam conditions.

The total centerline moment (ZMr ) and total end moment (ZM,.) of a beam with any combination of the Table 1 loads equals the sum of the individual values resulting from each type of load.

When designing a beam for a given end restraint ( R ) , the resulting maximnm moment at centerline for which the beam is designed (MI,) equals the difference between the maximum centerline moment ( M y ) when R = 0 and the actual end moment ( R M,) for the given value of R. See Figure 5.

This can also be found by totaling the individual

7- ZM*

Simply Supported i- Beom with desired R = O R = 100% end restraint (R)

FIG. 5 Moment diagrams for different restraints (R).

Top Plates for Semi-Rigid Connections

W @ Simply supported, w t h load

+ 1.- @ Apply negative moment at ends to

bring up to horizonto1 position

M* ( # W - c 1 ) 4 Final end moment for louded beom

@ $ 5 equal to oppiied moment in jb)

M, L /I = ~~ ~~~~

'' 2 E l

Me(#

W 4) Me @ Fixed end, ended beom

Me L 0 = .- . ... " 2 E l

W Simply supported, lauded beam

FIGURE 6

TABLE l-Moments and End Rotation for Various Load/Beam Conditions

End Mornen! M. W L ~~. -- i x e o €id

10

9.2-2 / Joint

In order to evaluate the weldability of steels, a limited kno\vledge of the basic arc welding process is advisable.

Welding consists of joining two pieces of metal by establishing a metnllurgical bond between them. Many different welding processes may be used to produce bonding through the application of pressure and/or through fnsion. Arc welding is a fusion process. The bond between the mptals is produced by reducing to a molten state the surfaces to be joined and then allowing the metal to solidify. When the molten metal solidifies, union is completed.

In the arc welding process, the intense heat required to reduce thr inetal to a liquid state is produced by an electric arc. The arc is formed between the work to be wt~lded and a metal wire or rod called the elcctrode. The arc, which produces a

Welding Machme AC or DC Power Source and Controls

Electrode Holder 7

\Ground Cable I

temperature of about 6500°F at the tip of the electrode, is formed by bringing the electrode close to the metal to he joined. The tremendous heat at the tip of the electrode melts filler metal and base metal, thus liquifying them in a common pool called ;I crater.* As the arens solidify, the metals are joined into one solid homogeneous piece. By moving the electrode along the scam or joint to be welded, the surfaces to be joined are welded together along their entire length.

The electric arc is the most widely used source of energy for the intense heat required for fusion

*For soinc applications, filler metal is deposited by a con- sumnblc we ld ing electrode; for others, a "nonmnsumable" elcctrode supplies the heat a n d s separate welding rod the filler metal.

wclding. The arc is an electrical discharge or spark sustziined in a gap in the electrical circuit. The resistance of the air or gas in the gap to the passage of thc current, transforms the electrical energy into heat at extremely high temprmtures. Electrical power consists of amperes and voltage. The amount of energy available is the product of the amperes and the voltage flowing through the circuit and is meastired in watts and kilowatts. The energy used is affected h y such variables as the constituents in &ctrode coatings, the typc of current (-46 or DC), the direction of cul-rent flow, and many others.

In all modern arc welding processes, the arc is shielded to control the complex arc phenomenon mid to improve the physical properties of the weld deposit. This shielding is accomplished through varions techniques: a chemical coating on the electrode wire, inert gases, granular flux compoi~nds, and metallic salts placed in thc core of the electrode. Arc shielding varies with the type of arc welding process used. In all cases, however, the shielding is intended: 1) to protect the molten metal from the air, oither with gas, vapor or slag; 2) to add alloying and fluxing ingredients; ,and 3) to control the melting of the rod for more effective use of the arc energy.

Gaseous Shield

The arc welding process requires ;I continuous supply of electric cnrrent suflicient in amperage :md voltage to maintain an wrc. 'l'his currcnt may be either altcmating (AC) or dircct (DC) , but it must be provirlecl through a source which can be controlled to satisfy the variables of the welding 11roces" :mmnerage and voltage.

Me L 6 -- ' - 2 E I

(762) (180) - - 2(30 x lO"(289.6)

= 7.9 x 10-Qadians -

Design top plate for an end moment of 75% M . = .75 (762 in.-kips) = 571 in.-kips.

Cross-sectional area of top plate:

M A -- - "-- u d,,

- (571,000) - (eo,ooo) ( m 8 6 j

= 2.06 in."

or use a ?k" x 5%'' plate, having A, = 2.06

Top Piales for Semi- igid Connections / 5.6-5

The length of the reduced portion of the top plate will be made I. = 7".

Thc slope of thc connection line:

A,, d,,? E M c - -- 8, 2 I,

This connfction line can also be constructed by solving for end momcot (M,.) and end rotation (8,) when stressed to yield, u. = 33,000 psi:

M, - A,, u> db

= (2.06) (33,000) ( 13.86)

FIGURE 9

WIDTH OF TOP CONNECTIN6 &?

0 16 IS I4 N 12 N 10

9 8

7

6

5

FIG. 10. Moment Capacity of Top Plate Connection. KIP - INCHES

PIVOT POINT IN

f THIS EXAMPLE

TDO 6 00

A ISC S K 1.5. I. 4.1 COO

IF COMPACT (SEC 2-61 AND AT 5 0 0 so0

NEGATIVE MO&E'IVl CAN USE 400

90% APPUED EffD MOMENT 400

Top Plates for Semi-Rigid Connections / 5.6-7

W L M, = -= 750 12

M = 410 in-kips

FIGURE 1 1

This calculated connection line is shown as a dotted line in Figure 9. It rises to a moment of M = 943 in.. kips at which time the top plate should reach yield stress. From tlicre on, this plate will yield plastically and build up a higher resistance as it work hardens. It would finally reach the ultimate tensile strength of the plate unless some other portion of the connection would fail first.

Superimposed upon this graph in soiid lines are the actual test results of this particular connection, from the paper "Weided Top Plate Ream-Column Con- nections" by Pray and Jcnsen, AWS Welding Journal, July 19.55, p 338-s.

The beam lines of the particular example are shown as broken lines in tbc figure. Notice that the beam line at working load intersects the connection curve (point a ) well within the capacity of the connection.

The second beam line at 1% working load also is well within the ultimate capacity of the connection (point b) .

Holding the length of the reduced portion of the top plate to L = 7" has resulted in an end moment of M = 680 in.-kips instead of the 75% value or M = 571 in.-kips as originally planned. This is a restraint of R = 89.3% instead of R = 75%.

A lower restraint coulcl he obtained by increasing the length of the reduced portion ( L ) of the top plate. However with the present conneetion the top plate has sufficient strength:

= 21,400 psi < 22,000 psi OK - (AISC Sec 1.5.1.4.1)

,y M 0' =---

A, db

Notice also that the connection curve lies quite a distance abovc the R = 50% point of the beam line. Since the beam is desigued on the basis of R = SO%, the connection could drop down to this valuc before the beam \i:onld be o\;erstressed.

The moment capacity of a proposed top plate connection can be readily obtained from the nomograph, Figure 10.

90% M used at negative moment; (AISC Sec 1.5.1.4.1)

2. CONNECTION BEHAVIOR UNDER ASYMMETRICAL CONDITIONS

In the usual analysis of a connection made by super- imposing a beam line on a connection curve, it is assumed that the beam is symmetrically loaded and has identical connectioris on both ends.

This is illustrated in Figure 11, where the member is a 14" W F 43# beam, and:

W = 50 kips

L = 15 ft

I = 429 in.*

When these conditions of symmetrical loading and identical connections do not exist, the following niethod may be used to better understand the behavior of the connection under a given load. The above beam and load value will be used.


Step I. Start at the left end ( a ) of the beam with the right end ( b ) held fixed. The left end ( a ) is first held fixed (0, = 0) and the end moment (M,) determined; the left end is then released and simply snpported (M, = 0) and the end rotation (0,) determined. See Figure 12.

released; @ fixed simply @ supported

0 - - 2.62 x 10.l " - 4 8 E l -

FIGURE 12

From these two points (M, = 750 in.-kips and 0. = 2.62 x 10-"radians), the bcam line for the left end ( a ) is drawn, Figure 13. Upon this is superimposed the connection line, and the point at which it intersccts the beam line represents the actual cnd moment and end rotation after the connection has allowed the bcam end to move.

750 in-k Beom line

Connection curve

750 in-k

l. - 2.62 x ~ i ~ h t end@ 1 - 1.6 X 70-3 held fixed

Left end @

FIGURE 14

Step 2. Thus with the right end held fixed (u, = O), the rcsulting moment at the right end ( h ) consisting of the initial momcnt and the additional moment d71e to moven~ent of the left end ( a ) , is-

Now the left end ( a ) of the beam is held fixed at 8, = -1.6 x 1 0 " while the right end ( b ) is released and simply supported (M, = 0) and the end rotation (Bb) determined. See Figure 15.

@ simply supported

[Leftm held fixed at R = - 1.6 x 107

FIGURE 13 FIGURE 15

This relaxing or movement of the left end ( a ) , From:

from 0, = 0 to 0, = 1.6 x radians, causes the fixed opposite end ( b ) to increase in end moment (M,,) . This 2 E I 4 E I Mb = .+ - - 0 + .- W L

L " O,, - - - --

increase may be found by the following: L 12

If a uniformly loaded beam is supported by fixed when: ends which have previously rotated (0, and O,), the two end moments (M, and Mb) are- Mb = 0 and @, = -1.6 x 10-8

Top Plates for Semi-Rigid Connections / 5.6-9

tlic rotatioti of the beam at the right end ( b ) , if simply supported a id no restraint from the connection, would be:

These two points ( M h = -979 and 0b = +3.42 x 10- " ) detcrmine tile beam line for the right end ( b ) ; Figure 16. Its intersection with the connection curve represents the actual end moment and end rotation after the comxction has allowed the end to move.

Left m d held fired of

due to niovemen!

Left end @

FIGURE 16

Step 3. As before, this movement of the right end ( b ) from B,, = O to Oh = +2.1 x causes an increase in the moment on the left end ( a ) ; Figure 16, left.

From :

when:

8, = -1.6 x 10 " and 0, = $2.1 s LOW3

the moment on the left ~ n d ( a ) is fomid to be

This ontirc procedure is repeated until the cor- rections bccomc very small, Figures 17 and 15.

FIGURE 17

Step 4. W l l r ~ ~ the left end ( a ) is simply supported (M, = 0 ) , tlic end rotation wonld be 0, = -3.67 s lo--:'. Releasing the left end ( a ) allows it to rotate to 8, = -2.25 x 10 " .

Step 5. This movement 8, from -1.6 x to -2.25 x 10-Qn the left end catrses the right moment to increase to Mi, = -472 in.-kips. When the right end ( b ) is simply supported (M. = O), the end rotation would be Bb = $3.74 x Releasing the right end ( b ) allows it to rotate to Ob = +2.3 x lo-'.

FIGURE 18

Step 6. This movement of BI, from 1-2.1 x 10Qo


+2.3 x 10-%n the right eud causes the left moment to increase to Ma = -43.5 in.-Mps. When the left end ( a ) is simply s~~pportctl (M, = 0), the cnd rotation would be H, = -3.76 x lo-". Releasing the left end ( a ) allows it to rotate to 0, = -2.40 x 10P3.

Step 7. This movement of 8, from --2.25 x 1O"o -2.40 x 10-%on the left end causes the right moment to incrcase to M,, = --428 in.-kips. When the right end ( b ) is simply supported (MI, = 0 ) , the end rotation would be HI, = +3.80 x 10 -:'. Releasing the right end ( b ) allows it to rotate to: B,, .= +2.40 x lP3.

Conclusion: The final end conditions resulting from this sequential handling of the givrn connection and beam loading a r e

Reference to Fignre 11 shows that thrse are the same values as obtained when thc beam was considered to be symtnetrically loaded with identical conditions on both ends.

3. BEHAVIOR OF CONNECTIONS STRESSED ABOVE YIELD

The same method wed prcvionsly may also be applied to connections that arc stressed above their yield points and thus yield plastically. See Figure 19, using same beam as before.

'4 Connection curve

tj,

FIGURE 19

To simplify this ar~alysis, two changes will be made.

First. In computing the two points of the beam line ( M , ) for fixed ends and (8,) for this end simply supportcd, it is noticed that these same values can be obtained by considering the beam as fixed at one end and sqqmrted at the other; with no gravity load. A

FIGURE 20

moment ( X I , . ) is applied at the snpported end and the resulting end rotation (H,.) is fonnd at this same end, Figure 20.

Here:

In this particular example:

With the particular scale used in the original construction of Figure 19,

1" = 4 x 10 :' radians

or 1 radian = % x lo1 inch

and 1" = 400 in-kips = 400,000 in.-lbs

or 1 in.-lb = % x inch

The slope of this beam line is-

or an angle of 70.7", Figure 21

750 in-k

Beom lhne determiried by Me and o

Me

y supported

He

FIGURE 21

Another method of constructing this slope is to use a convcnient valne of H,, for example, 0, = 5 x 10 '. The corresponding end moment would be-

Top Prates for Semi-Rigid Connections /

These two values are plotted on the figure and the slope determined by protractor, Figure 22.

Since the slope of the beam line remains constant, it won't he necessary to compute the value of 6, for the simply supported end for each step.

Second. Instead of computing the end moment after it has been increased by the angle movement on the other end of the beam, it is seen that the actual increase in moment is-

This may be drawn on the figure from any convenient value of 6, and Me. Any given increase in 6. is laid off horizontally on this line, and the increase in moment (M,) is measured off as the vertical distance and added to the moment on the opposite end of the beam. See Figure 23.

Application of Method This method is now used on the same 14" WF 43# beam, uniformly loaded with 50 kips on a 15-ft span; Figure 24. The connection is made with a top connecting plate, X6'' x 3", which is stressed to yield (cr =

FIGURE 23

Fixed end I /

I / rimply supported

/ ! 1 /

FIGURE 24

V Movement of left end (Ox)

Left end @

8, FIGURE 22

33,000 psi) at a moment of 423 in.-kips. With additional movement, the plate will strain

harden and its resisting moment will very gradually increase. This accounts for the slight rise in the connection line above the point of initial yield.

Increase in moment on opposite end

_I

Right end @

-k

1 2 3 4 5 6 7 Change in 0, 7 6 5 4 3 2 1

x 1p3 go x 10-3 8,

Left end @ Right end@


On the Ainsley Building in Miami, weldor is completing fillet weld on top connecting plate, leaving an unwelded length 1.2 times the plate width. PIote i s beveled and groove welded to the column.

Wcldirig is most effici~:ut in structures 11t.sipt.d tor full contiriiiity. This typr of dcrign builds ir~to the structure the inh(rmt strength w1iir.h comes from (ontinuous action of ;ill members. Lo;~(ls are easily rvdistrihuted when ovcrluading occurs oil wrtain mi-mbcrs.

Tliic type of desigri rr;ilizrs a weight swing in the beams sirrw a negativc mo~ncnt acts ;it the supports, thus redui:ilij: the positive moment at tlit: center of the span hy i11e same amount.

C;oiitiuuc~us couuc~ctioiw ;11so t ; i h ac1v:mtage of what i red fct h ~ : a 20% iucr-r,:!s(: in t l ~ ;illow.il?le i~ending str(,ss irk the negativ~, rnonwrit rr:giorr new the support. This is ;iccompli:,htd tlinn~gh ;I 10% iucreue irr bending ;111wwables for "crrrnp:~~'t" swtims. :md using a 10% reduction in the: ncg;~:ivc rnornt.nt. 'i'liis ridur- tion iu negrtive moment is :illuwcd iur 'coi~rpact" st,(:,- tions, provi<lrd the swtion m~~dulus Irwe is not 1t.s.: than that rquil.ed for tb(, positive r~~oments ill ttlc same beam and provided thi, comprtwion flange is regarded as unsupported from the point of suppurt to the point of contrdexure.

FIGURE 1 FIGURE 2

5.7-1

Alternate method of but t welding top flange connecting plate t o column flange using

placed between the conriocting plate and the beam flange to r~ r s~~rc : a complete-pcrit:tr:~tioll groove weld to the column. This eliminates b;rck gouging and welding an overlicad pass on the other side.

Reducing Welding Requirements

It is possiblc to design the seat stiffener to carry all of the end reaction, eliminating any vcrlical u ~ l d i n g in the field. This reduccs the ficld \I-ekling to just dowithand groove \vekiing of the heam flanges to tho column.

Where good fit-up can be assurtd, the beam fianges are beveled from the top side and groove welded in the field directly to the colurnn Aange. The beam web

is cut hack about 1" a r~d fillet welded to the wcb connecting platc.

Some fabricating shops have jigs so that colr~mns can be elcvnted into a vertical position. This allows muclr of t l ~ c shop welding on tho connecting plates to he made in the downhand position.

Cover Plates

When addcd at crids of beams to carry the extra negative momcnt; covcr plates must be welded to the column for continuity; Figure 4.

Shop wclding tllc cover platas to the beam, with the lower beam flange and the upper cover piatc left

FIGURE 3

FIGURE 4

Beam-$0-Column Continuous Connections / 5.7-3

nnbeveled, prodriccs a type of "J" groove for the weld corinecting them to the column flange.

If column-flangc stiKensr plates are needed in this case, they should be of about the same thickness as the beam Bange and cover plate combined. The ~ ~ s r ~ a l single thick stiffener in line with tach heam flange can be replaced with two platr:s, each having half tbe required thickness. This means working with lighter connecting matt:ri;~S and using two groove welds, each being half the size of the original singlc groove weld, which reduces the amonnt of welding on the stiffeners by half.

2. A N A L Y Z I N G NEED FOR COLUMN STIFFENERS

If the flange of the supporting column is too flexible, the forcrs transmitted by the connr,cting flanges will load the outstanding portion of the column Range as a cantilever beam and cause it to deflect slightly; Figure 5. As this ~Icflectiou takes place it reduces the stress in the outer ends of the hum-to-column connecting weld, thereby loading up the center portion of the weld in line with the column web.

It was previously thought that unless the column Aange is extremely rigid (thick), flange stiffeners must be added to the colr~mn in line with the beam's top

FIGURE 5

FIGURE 6

and bottom flanges (or their connecting plates). Snch stiffeners k w p thc column flange from deflecting and load the u d d uniformly.

However, recent resmrcl~ at Lehigh University indicates that iri most cases thc deciding factor is a crippling of the column web; Figure 6. If the column web is thick enough, stiffeners are not required.

Buckling of Column W e b Due t o Compressive force of Lower Beam FIange

A test was set up, Figure 7, to evaluate effects of the lower flange of the beam in compression against the column. Two bars, one on each side of the column, relx':sentt,d the cross-section of the beam flange. The test member was placed in a testing machine and loaded under compression.

In all cases, yielding began in the fillet of the

FIGURE 7


column just inside the column flange, and directly beneath the bars. Yielding progressed into the column web by means of lines radiating from this point to the column " K line, at a maximum slope of 1 to 2%. This progressed for some distance. I\ slight bending of the column Ranges was noticed at about 80% of the failure load. Figure 8 shows an analysis of this.

Column web

+ - / ~ / c

FIGURE 8

Overlooding of Column Flange Due to Tension Force of Upper Beom Flange

A test was set up, Figure 9, to evaluate effects of the upper flange of the beam in tension against the column. Two plates, one on each side of the column and welded to it, represented the cross-section of the beam flange. The member was pulled in a tensile testing machine,

FIGURE 10

Dimensions of both the column flange and the connecting plates were varied in order to study the effect of different combinations of colulnns and beams.

First yielding was noticed in the fillet of the column just inside the column flange, and directly beneath the attaching plates, at about 40% of the ultimate load. With fnrther loading, yielding proceeded into the column web, underneath the colnmn flange parallel to the attaching plate, and into the cohnnn flange from the center of the conrrecting welds, and parallel to the colnmn web. Aftcr ultimate loading, some members failed by cracking of the central portion of the connecting weld directly over the column web, some by cracking in the inside fi1lt.t of the column, and some by cracking in the inside fillet of the column, and some by a tearing out of material in the column flange.

FIGURE 9 FIGURE 11

earn-to-Column Continuous Connections / 5.7-5

FIGURE 12

Stondord Stitfeners

When some type of wrb stiffening is required, the standard horizontal flange stiffcners are an eiticicrit way to stiffen the column web. Figure 10 shows this type under test.

A Tee section flamo cot from a standard wide- flangr section may be lisnd for stiffening, Figure 11. The stem of the Tee section is welclcd to tire colrrmn web for a short distanw in from the m t l s . This could be entircly shop welded, all of it being clo~ic in thr flat position, pmsibly using a sc,mi-automatic wdder. This type stiffnrer would h a w nt~mcrous advantages in fom- way beam connections. The bmms rrormally framing into the columi~ web wonld now butt against this ilat surface with good :~cc<:ssil~ility, Tllc flnngcs of the beam coiild be beveled 45" and then easily groove welded in the field to tllis sltrface, using hacking straps. Thcre wonld be no 0 t h conrir:cting or attaching p1att.s to be used. In effect this part of tlie coriucctiu~~ would be identical to the connection used for beams framing to colnmn flanges.

See Figures 28, 29 and 30 and related text for speciiications of stiffeners applicable to clastic design.

Effect of Ecceni~ic Stiffeners

In a four-way beam-to-column colmection, the column

flanges may be stiffened by the connecting plates of the beam framing into the column web. It may be that the bcam framing to the column flange is of a different drpth. This in effect will provide eccentric stiffeners, Figure 12.

The lower part of Figure 12 shows how this was testcd. It was found that an eccentricity of 2" provided only al)out 65%: of the stiffening provided by concentric stiffont.rs, and an eccentricity of 4" provided less than 20%.

Three metliods of framing beains of different depths on opposilc flanges of columns are shown in Figure 13.

3. TEST COMPARISON OF STIFFENER TYP

The following is adapttxl from "We1dt:d Interior Beam- To-Columrr (:orinections", AISC 1959, wllicli summarized lcsls o11 various connections.

Figure 14 represents a dirwt beam-to-column connection. Iiero tllc column has no stiffening and is not as stiff against rotation as tllc 16'' W F 36# beams which frame to the colu~nn.

This arrattgeinent showed high stress conccntra- tio~is at thc ccnt~v of the bc:im tension flanges, and therefore at the celitcr of the connecting groovc weld.


FIGURE 13

However, it was noted that no weld failures occurred until after excessive rotation had taken place.

The stiffeners here in Figure 15 provide thc equivalent of beam flanges to the columns, and the columns become as stiff against rotation as the beams framing to the column.

The stress distribution on the compression flanges were uniform on the whole, while in the tension areas the stresses were somewhat higher in the center.

In Figure 16 the column is shown stiffened by a pair of wide-flange Tee sections. As a result the columns are as stiff against rotation as the beams framing into the columns.

From strain gage readings it was calculated that each of the vertical plate stifIencrs in the elastic range transmitted only ahout y/,, of the forces coming from the beam fangcs and the column web transmitted % of the forces.

Placing these stiffener plates closer to the column web might have improved the distribution. However, since the prime purpose of this type of connection is to afford a convenient four-way connection, the plate usually needs to be positioned flush with the edge of the column flange.

The stress distribution was uniform in both flanges at the working load. At 1.5 of the working load, high

Zero +

I d

I 4 20,000 psi w-

Stress distribution in tension flonge

FIGURE 14

Beam-to-Column Continuous Connections / 5.7-7

FIGURE 15 FIGURE 16

tensile stresses occumed at midflange. The con~lection in Figure 17 was stronger than its

two-way counterpart. This evidently shows that the stiffening action provided hy two beams framing into the column web strengthens the connection more than

it is weakened by the triasial stresses. The connections of Figure 18 involving (East-

West) beams weldcd dircctly to the column Ranges proved stiffer than (he com~ection of (Nori-11-South) beams to the Tee stiffeners.

FIGURE 17 FIGURE 18


FIGURE 19

The stiffcning of the latter connc:ction is mainly dependent on thc thickness of the stem of the Tee stiffener, tlie Ranges of the colnmn being too Ear away to offer much resistance.

The column wcb is ably assisted in preventing rotation at the connection by the flanges of the split- beam Tee stiffeners.

4. ANALYSIS OF STIFFENER REQUIREMENTS IN TENSION REGION OF CONNECTION (Elastic Design)

The following is adapted from "Welded Interior Beam- to-Column Connections", AISC 1959.

The colomn flange can be considered as acting as two plates, both of type ARCD; sec Figure 19. The beam flange is assnmrd to place a line load on each of these plates. The effective length of the plates ( p ) is assumed to be 12 t,. and the plates are assumed to be fixed at the ends of this length. The plate is also assumed to he fixed adjacent to the column web.

where:

m = w, + 2 ( K - t,)

~nalys is of this plate by incans of yield line theory leads to the, ultimate capacity of this plate being-

where:

Let:

For the wide-fiangr colrimns and beams used in pactical connections, it has h e n found that ci varies within the range of 3.5 to 5. A conservative figure would be-

P, = 3.5 u, t,'

The force carried by the central rigid portion of thc column in linc with the web is-

earn-to-Column Continuous Connections / 5.7-

Setting this total force equal to that of the beam's tension Hange:

FIGURE 20

Reducing the strength of this column region by 20% and making the conservative assumption that m/b, = .15, this reduces to the following:

If the thickness of the column flange (t,) meets the above requirement, colnmn s t i fhe r s are not needed in line with the tension Rangcs of the beam.

If the actud thickness of the column iiange (t,) is less than this valne, stiffeners are needed.

5. ANALYSIS OF STIFFENER RE I N COMPRESSION REGION OF CONNECTION (Elastic Design)

It is assrimed i11e coucentrated compression force from the beam flange spreads out into the column web at a slope of 1 in 2% m~til it reaches the K line or web toe of the fillet; see Figure 8.

Equating the resisting force of the column web to the applicd force of the beam flange, assuming yield stress-

If the tliickness of the colnmn web (w,,) meets the ;hove rrqnircmrnt. column stiiicners ;we not neoded in linc with the coniprcssion f la~~gcs of the 1)ram.

If the ;~ctuel ti~ickn(,ss of the column xvob (w,) is less than this value, tlie \veb must be stiffened in some manner.

. HORIZONTAL STIFFENERS

FIGURE 21

Equating the resisting force of the column web and a pair of horizontal plate stiffeners to the applied force of the beam flange at yield stress-

A, 2; A, - w,. (tb 4- 5 K,.) I where:

A, - total cross-scctioual area of pair of stiffeners

To prevent buckling of the stiffcner-

where:

b, = total width of pair of stifleners

If the stiflcner is displaced not more than 2" from alignment with the adjacent beam flange (as in Fig. 12), it may still be used if considered about 60% as


eBective as when in direct line. The stiffener thickness (t,) fourd from the above formula s l io~~ld than he mi~ltiplied by 1.70 to giw thc actual required value.

7. VERTICAL STIFFENERS

FIGURE 22

Becaust~ tlw vertical stiffelicrs (~lsually Tees) are placed at the outer d g c s ol the column ilnngc. they are as- sulncd to Be half as d f r ~ t i v e as tl~ougli p1:iccd noar the colurnli wch. It is :rssumcd the corlcc~~tr:it<d beam flangc force s p u d s out into ihc \~ r t i ca l stiffcnsr in the same manner as thc column w<lh.

Equating tlic ri,sistiug Some of tlw column web and a pair of vertic:ll Tee stiffmtc to the applied force of the beam flange at j-ield strms-

w, (tb $ 5 K,) ui + 2 x % tr (ti, + 5 Kc) u, - A* u, or

To prevent buckling of the stiffrner-

1 PraHem 1 1 As an example of applying the preceding analysis

of the tension region of a connection, we will analyze a connection which, wliel~ tested to failure, performed well; see Figure 23.

w W A O i t column

FIGURE 23

Beam-to-Column Continuous Connections / 5.7-1 1

where:

m = w, f 2 (K - t,)

= (.390) + 2 j (1 % e ) - (.606)]

Since:

h A = - (I

- (2.72) - (4.69) -- - .58

P p = - 9 (7.27) -

- (4.69)

= 1.55

and:

-

The total force which car] hc carried by the tcnsion

region of the colnmn stiffcncr's flange must eqnal or exceed the force of the beam's tension iiange, or:

Provided both column stiffener and beam have same yield strength:

4.28 2 3.00 O.K. I f w e nsed the conservativc formula:

but the initial design called for t, = ,606'' and the connection tested O.K.

8. CONNECTIONS THROUGH VERTICAL TEE STIFFENERS

Tests have shown that when thc beam flange extends the full width of the connecting plate, Figure 24, about 3~ of the flange force is carried by tho central portion of the plate. Each of the two outer edges carry about x, of this force.

Figure 25 comes from test data of Lehigh Uni- versity. Notice in the East-West beams, thc flange of which extends almost the full width of the colun~n

FIGURE 24


FIGURE 25 ~

flange, 44% of the force is transferred through the web of the connection even though it is only about half as thick as the stiffener plates. This corresponds well with the idea that the flange of the column in this region is similar to a two-span beam on three supports with a uniform load; in this case the center reaction is % of the total load, and the two outer supports each carry 3$, of the load.

The report "Welded Interior Beam-To-Column Connections", AISC 1959, mentiolis that "from strain gagc readings it was calculated that the vertical plate stiffeners in the elastic range each transmitted only about 3/1,ths of the forces coming from the beam

flanges and the web transmitted %ths." Of course, the same would not bc true in the Korth-

South beams becaose they do not extend the full width of the flange of the Tee stiffener. As a resitit, most of this force rniist be transfrrucd into the web or stem of the Tee stiffener since any portion of this force. reaching the outer edges of the column flange must be transferred as hcnding out along the flange of the Tee section.

Weld Size: Stiffener Stem t o Column W e b

On the basis of these tests at Lehigh University, on coniiectioris where the beam flange extends the full

FIGURE 26


width of the stifTener flange, we will assume that % of the beam flange force is carried by the stem portion of the connection. See Figorc 26.

Because of the stiffening effect of the beam web and the stem of the a~nnccting plate, tliis ccnlral (stem) portion of the connection will load up in bending. This assumes it rotates as a unit aboi~t a point at midheight. The bending force on the weld is zero at this neutral axis and increases linearly to a maximum value at the upper 3 r d lower edges of the connection.

Treating the weld group as a line, the section modulus is cqual t o -

The resulting maximum unit bending force at the top portion of the weld on the stem is-

M % M D 3 f b = - =

S, (D" - g") The leg size of this weld would be found by divid-

ing this value by the allowable for the particular weld metal.

h7, A373 Steel; E60 Weldr

f = 9600 o

A36, A441 Steel; E70 Welds 1 Here:

FIGURE 28

Weld Size: Stiffener Flange to Column Flange

The Tec stiffcwxs may be joined to the column flanges by a ) fillet welds, b ) groove welds, or c ) corncr welds. The groove welds ( b ) were used in the Lehigh Re- search of this connection.

(4 (bl (4 FIGURE 27

Since tests on full-width flanges showed that the two outer edges ol the connection carry about of the flange force, we will assume that each outer weld must carry 'h of the flange force. See Figure 28.

These welds will be pulled with an axial force of K F. We may assume the same distribution of force through the coniiecting plate at a slope of 1 to 2% into the connecting welds. This will provide an effective length of weld of tb + 5 t, to carry this force.

The unit force on this weld is-

The leg size of the fillet weld, or throat of groove weld, is detelmined by dividing this unit force by the suitable allowable.

The effect of the vertical shear load ( V ) on these


welds could Le checked by using the elktire length of the welds. Ilowever, this would represent little additional force on t ime wolds.

Proportioning the Tee Stiffener

Tho following will be helpful in selecting a Tee stiffener section for this type of connection, where the bcam flange equals the full width of the stiirener flange:

FIGURE 29

1. The thickness of the stiffener flange (t,) must be suificieut to transfer the tensile force of the beam flange. In this case 3/4 of the beam flange will be used.

2. The width of the stiffencr flange (b,) must be sufficient for it to reach to the column flanges.

3. The thickness of the stifiener stem (w,) should be about the same as the beam flange thickness (t,).

4. Tho depth of the stiffener (d,) , as measured through the stem portion, must be sufkient for it to extend from the face of the column web to the outer edge of the column flange.

5. As a guide, the stiffener should satisfy this condition:

or an approximation on the conservative side:

here Beam Flange idth < Stiffener Flange idth

Where the beam flange docs not extend the full width of the co~~necting plat(:, the stem portion oi the connection is assumed to carry the entire moment. There- fore thc maximum bending force on the top portion of this weld will be--

FIGURE 30

The same items as before are used to proportion thr Tee stiffener, except in items 1 and 5 where the full vzilue of thc: heam flange's section area is used instead of 3/4 of tbis value. These formulas bccome-

earn-to-Column Continuous Connectians / 52-25

I Problem 2 1 To dcsigrr a fiilly wcldtd bcnm-to-volnmn conncction for a 11" WF bram to all 8" WF coliimr~ to transfer an end moment of M -- 1lCU in.-kips anti a vertic:il shear of V == 20 kips. The solution of this problem will be considered with sevcn variations. Use A36 steel and E70 welds.

FIGURE 31

Hero:

M = 1100 in.-kips

V = 20 kips

Thc welding of both thc flailgrs and thc we11 along its full dvpth enahlcs thc lieam to d t v l o p its iull plastic moment, thus allowing the "compact" beam to be strcsscd 10% higher in brnding, or c . = .66 c,. This also allows the encl of the bcam, atid its welded con- nectioli, to be designrd for '30% of tlie elid snonwnt due to gravity 1o;iding. (AISC Sec l.5.1.4.1 and Sec 2.6)

= 23,700 psi < .66 u, < 24.000 psi OK -

The wcld on the 1je;rm's wcb niiist he able to stress the well in benLing to yicld (u,) tlirongho~~t its 'i~tirc dcptlr; see the bcndiiig strrss riistribntion in Fignre 5 The weld mnst also lic able to tr:insfer the vertical slrear.

leg size of fillct u e l d

actual force @ = ~ ~-~~~ ~ ~p

allowable force

I-lowever, since the beam web is welded to a ,433" thick flange of the column, the minimum size for this fillet wt.ld would be % G ' r ; see Section 7.4, Table 3.

WELD SIZE TO DEVELOP ULTIMATE LOAD

The next qi~estion is what size fillet wold would be required to develop the bcam web to yield stress. The forcc in question results from bending, so it is transverse to the weld.

The AWS allowables for fillet welds are based on parallel loading, AWS has not set up any allo\vable values for transverse loading.

(l~amllt~l load) (tr:insvi:rsc load-tension)

2(11,200 w ) 2 t, ( G O u s ) = t, 22,000

(transverse load) (transverse load-tcnsion)


For plastic design concepts, basrd on ultimate loading, the allowable for the fillet weld would be increased by the factor 1.67 (AISC Sec 2.7). This is the same increase used for the member ( 3 0 u, up to u y ) , hence the same relationship betwcen weld size and plate thickness will still hold.

Based on AWS Code allowables (for parallel loading), this fillet weld on the web of the beam would have to be equal to the web thickness.

t, = .27W or use o =: Ya"

However since it is known a fillet weld (o = j/4

t,") will outpull the web, a fillet weld will be used here.

FIGURE 32

M = 1100 in.-kips

V = 20 kips

Thc welding of the Ranges and full depth of the web enables the bcam to develop its full plastic moment, allowing the "compact" beam to be stressed 10% higher in bending, or u = .6G ui' In this casc the beam canti- levehs out from the support so that 110 10% redoction in the negative moment can be made.

- (1100 in-kips) -

(4S.5 in.")

= 22,700 psi < .G6 u, < 24,000 psi OK

The fillet weld on the web of the beam is figured as in met~Ioct@

FIGURE 33

Here:

M =. 1050 in.-kips

V = 20 kips

If this cant~lpver beam had an end moment of M -- 1050 in.-kips instead ol the previous 1100 in.-kips:

= 21,600 psi < .GO ur < 22,000 psi OK -

In this case the bending stress is within .GO u,, and the beam and connection must be able to develop a bending resistance q u a 1 to the product of the beam's section modulus and yield point stress (scc Fig. 27) rather than the full plastir moment. As a result it is not necessary to weld the web for its full depth.

For detormining the minimum length of the fillet weld on the web, assume the leg size to not exceed % tTV = ZiJ (287") = ,192". This will provide sufficient length of wcld so the bcam web at the connection will not he overstrossed in shear. (AISC Sec 1.17.5)

The minimum ler~gth of fillel weld on each side of the web is-

(20 kips) 20 kips - - -~ - 2(11,200 w ) - - 2(11,200) (.192)

If 3.: ," fillet welds are used (next size smaller than . l W r ) , their length wodd he-


v L, = - 2 f,"

.- (20 kips) --

2 ( 1 1 , 2 0 0 ) ( ~ , )

= 4.75"

Hence use Xe" 5" long on both sidcs < 4.65". -. OK

Since the size of this weld used in detcrmining its length was held to 24 of the wcb thickness, it is unnecessary to check the resulting shear stress in the web at this connection. Ho.rvever, to illustrate this, it will be checked here:

v 7web = -

AT"

(20 kips) = 5)(.2S7) = 14,000 psi < .40 u7 < 14,500 psi OK -

FIGURE 34

Here:

The wdding of the flanges and fnll depth of the web enables the l~eam to dcvclop its fn11 plastic moment, allowing the "conrp;lct" beam to be stressed 10% higher in bcnding, or - .66 u,. This also allows the end of thc beam, and its wcldcd connection, to be designed for '30% nf the end moment dne to gravity loading. (AISC Scc 1.5.1.4.1 and Scc 2.6)

bending stress in beam

- .9 (1100 in.-kips) - -.. . - . - - - - .

(41.8 in.a)

= 23,700 psi < .66 a, < 24,000 psi OK -

bending force on top connecting plate

- - .9 (1100 in-kips) -- - - .. 13.86'

= 71.5 kips

section area of top connecting plate

- (71.5 kips) -

(24,000 psi)

or use a 5%" x %" plate, the section area of which is-

If %" fillet welds are used to connect top plate to upper flange of beam:

f, = 11,200 ( % )


length of fillet weld

- (71.5 kips) - - - .

(4200 ibs/in.)

or use 5?'zr' of weld across the end, and return 6" along each side, fnr a total weld length of 17M".

Tho lower flange of the beam is groove butt welded dircctly to the colnrnn flange; and, since the wcb framing anglc carries thc shear reaction, n o fnrther work is reqnired on this lower portion of the connection. The seat angle simply serves to provide temporary snpport for the beam during erection and a hacking for the flange groove weld.

The fillet eld on the web of the beam is figured as in method 1 . 6

Top plate: 8%" x 3" x E"

Stiffener: 5" x 3" x %"

FIGURE 35

V = 20 kips

In this particular connection, the shear reaction is taken as bearing through the lower ilange of the beam.

There is no welding directly on the web. For this reason it cannot be assumed that the web can be stressed (in bending) to yield through its full depth. Since full plastic moment cannot be assumed, the bending stress allowable is hcld to u = .&I u, or u = 22.000 psi for A36 steel. (ATSC See 1.5.1.4.1)

bending stress in beam

= 20,200 psi < .60 a, < 22,000 pso

bending force in top connecting ph te

= 78.0 kips

section urca of top connecting plate

- - (78.0 kips) (22,000 psi)

= 3.54 i n 2

or use a 5" x 3'4'' plate, the section area of which is-

A, = 3.75 in.' > 3.54 in.' OK -

If M" fillet welds are used to connect the top plate to the upper flange of the beam:

f, = 11,200 (3h)


length of fillet weld

- (78.0 kips) - (4200 lbs/in.)

or use 5" of weld across the plate end and return 7" along each side, to give a total weld length of 19'' > 18.6" OK - DESIGN O F BOTTOM SEAT

FIGURE 36

The shcar reaction ( V ) by itself, applied to the bracket, produces a bending moment in the seat. This causes a tensile force in thc seat bracket's top plate and connecting welds.

In the usual simple bcam type construction, this moment must bc considered in addition to the shcar reaction when determining the required size of connecting weld on the seat.

In a continuous beam, the negative moment produces a compressive force in the lower flange which, in most cases, will offset the tensile force mentioned above.

Beam-to-Column Con@inuous Connections / 5.7-1

As a result, the welds connecting the seat bracket will be designed only to resist the vertical shear force (V).

web crippling from end reactions

R t g S 7 ~ )

=: 75 u, (AISC Sec 1.10.10)

or:

(20 kips) - ~ ~~ -

- .75[36,000 psi) (.313") 1 . 0

IIcnce the top plate of the seat must extend to at least M" gap 4- 1.37" = 1.87" and have a width at least 1" greater than the beam's flange width ( b ) = 1" -t 6.776 = 7.776"; or use an 8%" x 3" x 'h" plate. The 3" dimension would allow room for erection bolt.

seat stiffener

The thickness of the seat stiffener (t ,) should be slightly grcater than that of the bmm web (t, = .313"), or use a ?8" plate.

For determining the minimum length of the Blct weld on the stifrener, :lssunie the leg size to not exceed Y J t - -. .. ( ) 1 lh". This krcps the stiffener at the connection from being ovrrstr(:ssed in shear. (AISC Sec 1.17.5)

Thus, the niinimum lengtl~ oi fillet weld on cach side of the stiffener is-

(20 kips) = 2 7 T m o w

Because the column flange to which this weld is placed is ,433" thick, the miliimum fillet weld size would be $/16".

Hence, use:

- 20 kips -

2(11,200) ( :$;6)

or use welds of %," leg ~ i 7 c and 5" long, m d of course the stiffcner must be 5" deep.

In this case, the lower flange of the beam will not

FIGURE 37

be groove welded to the column flange. Instead, the top plate of the seat bracket will be extended to provide sufficient length of fillet weld.

If Ys" fillet welds are used along the edge of the ,513" thick beam flange:

- - (78.0 kips)

-- -- 2(11,200) (3/8)

= 9.3" or use 9%''

Therefore, allowing for 'h" fit-up gap, use a 10" x 8l/2" x 'W top plate for the seat.

FIGURE 38


In this case the connection is made through the Tee stiffeners of the column. Since the beam flange is nearly as wide as thc stifIen~r flange, the crntrd stem portion of the stiffener is designed for % of the moment and each outer edge of the stifiielrer flange for 'h of the moment.

The welding of the upper and lower portions of the stem to the column web is sufficient to stress the beam web up to yield (in bending) through its full depth. Thus, the beam may develop its full plastic moment. This allow,^ the "compact" beam to be stressed at u = .66 o;, and also to he designed for only 90% of the end moment. (AISC Sec 1.5.1.4.1 and Sec 2.6)

DETAIL THE TEE STIFFENER

x b,, tb 5.* w,K, 2 5

2 x(6.733) (.387)

- 5

2 .39 -

* w, (t, -+ 5 K,) = 314 beam flange area = x bb t,>

+lib -'-TI

For simplicity, use a conservative value:

011 this basis use Tee section cut from an 8" WF 48j: beam; see Figure 39.

t, = ,683'' -7 I- r - i

FIGURE 39

CHECK SIZE O F WELDS ON STIFFENER STEM

maximum bending force

At top of weld on stem. Use % of the moment (M ).



leg size of fillet ucld

~ctni i l force @ = . . .-

allowable force

CHECK WELDS AT OUTER EDGES OF STIFFENER

Use Ih of the moment ( M )

force on weld

6270 lbs/Iinear in.

if fillet welds, leg size

actnal Eorce = - allowable force

if partial-perwtratian single-bevel groove welds, throat size

actnal forcc t = - - allo\vable force

actual throat is-

t = t , + Y4"

= ,397" $ Yd'

= ,647" or use l%B"

CHECK EFFECT OF SHEAR

The vertical shear oi 20 kips was not considered on the welds bccausr of the great length of welding. This conld be cl~ecked out.

ossumcd total length of welding

L - 2 D i; 4 (t,, + 5 K , )

:= 2 (9 .18) + 4 ( 3 8 7 -+ 5 x I%,)

= 61.2"

unit shear force an zocld


For fillet welds. this would represent an additional leg size of-

For partial-penetration groove welds, this would represent an additional throat of-

These additional weld sizes are neglected in this exainple. If they had bccn appreciably larger, they would have been added to the weld sizes already obtained for bending.

9. LARGE HEAVILY LOADED BEAM-TO- COLUMN CONNECTlON

It might be wcll to consider the hasic transfer of forces through a beam-to-cohrmn connection.

A forcc applied transverse or at right angles to a member is transft:rrr:d almost wholly into the portions of that mi~mher wlricl~ lie piirallel to this fo rm See Figure 40.

In the design of some connections, the portion of this force ( F ) transfcrrcd into any given element of the built-np member has been assumed to be proportionate to the stiffness or moment of inertia of this element compared to thc total. Soe Figure 41.

An axial force in n member can transfer out at one end either as an axial forrc (norinal stress, either tensile or compressive) or orit sidcwnys into an adjacent member as shear.


FIGURE 41

Tensile Transfer

FIGURE 42

Tensile force from right-hand beam flange transfers directly as tension through the right-hand stiffener,

FIGURE 40

column web, left-hand s t i fhe r , and into flange of opposing beam.

~ e / d s lo column wch and flange must he designed for this force. Although the total length of welding on the stiffener would be figlwed for this force, actually most of the force would bc carried by the transverse weld hetwern the stiffener and the column web. Under ultimate loading, we can assume the transverse portion will have yielded and the force will he uniformly distributed.

Shear Transfer

FIGURE 43

Tensile force from beam flange transfers directly as tension into stiffener and then out as shear into the column flanges.

Parallel welds to column flanges must be designed for this force, unless another stiffener is placrd on the opposite sidc of the coluinn wob to back up this stiffener.


Tensile Transfer

FIGURE 44

Tensile force from hcain flallge ti-ansfm clirectly as tension throngh both stiffeners and web of colu~nn into otllcr 1)carn Aanga.

Transverse welds bet\rwn column flanges wid stiff- cnisrs intist be designed for tl~is form ( F ) less that which passm directly into the web f n ~ m the flange.

1'ar;illcl welds hetwccri stiffeilcrs and cohrmn web transfer no force. Comprrssion portion of beam connection wo1.11d keep stiifcner from buckling.

Shear Transfer

F = 2 F s + F w

FIGURE 45

Tensile force from beam flange transfers directly as tansion into s t i fhe r s nnd colnmn web. The tensile force in thc stiffeners thni transfers ont as shear thmugh the parallel welds intr; coluinii web.

Trmsversr welds l~etween u1111mn flanges on the beam side tmd stiffenrrs mint bc drsigned for this force (I?) less that wl~ich passes directly illto !he web from the flange. Pamilel welds to coluinn web must be designed for this same force.

Any unbalanced lnomciit ( M = MI - Ma) enter-

ing the colinnn nlust be transierrcd into the column flanges as a shear transfer. Assinne 211 > M2.

FIGURE 46

The tensile force F? of tlw flange of the left-hand beam will t r a ~ l s f ~ r as tension into the stiffener, then throngh the transverse welds along the column web into the other stiffenwj and into the flange of the other beam.

The unba1;ulced tensile force (F, - Fa) of the flange of the right-hand beam will tr8nsfi.r as tension into the right-lmid stiffener, and half of this through the transverse wi.lds of thc coluinn web into thc left- hand stilkner. This unbalanced tensile force in these stiffeners now transfers through the parallel welds as shown into the flanges of !lie u~lnmns.

Welds to column wcb must bc designed for the

2 FI + Fz balanced force, or 1% 17 + F = i- - ~ - ~ - .

Welds to column flange must be designed for the unbalanced force or F, - Fa.

Distribution of Tensile Force

There is some problem in estiiiiating the portion of the tensile force in the beam flange transferring directly into the web of the column and into thc colnmn stiffeners.

FIGURE 47

At first glance it \vonld swm reasonable to assnme this force wonlrl be divided according to tlle width of the stiffeners (b , j and thickness of column web (t,").


'column web

FIGURE 48

However, this column web scction is not limited to the thickness of the bcam flange since there is some spreading out of this force in the web. This might be assumed to occur at a slope of 1 to 2%.

FIGURE 49

The effective depth of the colun~n web through which force is distributed, is obtained as follows:

FIGURE 50 rolled column

d = t i , + 5 K ,

-4 K. /t

fabricated column

d = t b + 5 K ,

Since:

A, area i ~f colnrnn web over which force is tributed = d t,

A, = area of one stiffener (there is a pair)

(web) F, = F - (Aq. 2 2 As)

(stiffener) F, = F (A,%. :2 A )

Combined Stress in Stiffener (See Figure 51.)

dis-

On the left-hand figure, tho shear stress (T,,) results from the unbalanced East-West mumcrrts. This causes the diffcrence in tensile beam flange force (FI-F2) to be transferred as shear in the stiffeners into the colnmn flanges.

Although coi~servative in this particular analysis, it is assumed the small section in the stiffener to be checked lies outside of the path which the East-West tensile flange force will travel; hence us = 0. Actually some of this tensile force will spread out into this region, and this would result in lower principal stress. In eithcr case, it would be checked by the following formilla:

On thc right-hand figure, it is assumed the small section to be chrcked is not snbjected to any shear stress, just biaxial tensile stress. In this case, the use of the formula results in the principal stresses being e q d to the applied tensile stresses. This does not result in any higher stress.


Mohr'r Circle of Stress

FIGURE 51

To check beam-to-column connection shown in (9097 in-kips ) - - -~

Figure 52 (next page) for weld sizes. (23.59") = 3% kips

flange fo~.ce: 24" WF 160# beam flange force: 21" WF 73# beam

, 1.135''

M = u S

= (22,000 psi) (413.5 in.3)

= 9097 in.-kips

d -- 24.72" - 1.135"

= 23.59"

M = c S

(22,000 psi) ( 150.7 i x 3 )

:= 3315 in.-kips

d = 21.01" - .74"

= 20.50"


FIGURE 52

F = 386 kips

FIGURE 53


FIGURE 54

= 162, kips If I" ho~.izonlal plate stificners are uscd-

distvihution of ber~m force (See Figure 53.)

Depth of coli~rnll web though which beam force A, .- (10%) (1)

is transferred is- = 10.5 in.'


I I FIGURE 55

= 246 kips

= 70 kips

Figure 54 diagrams this distribution of beam force for four situ:%tiutls. Only onc need he considered for any one problem. Ilowever, in this example we will detail the welds so they can carry any combirration of forces from any of these four situations.

Figure 55 sl~ows thc forces on the various welds for \vhic11 size must be determined.

u:ckE size: stifienw to colunm flange; case@ and @

= ,344" or %" if shop weld, B but 3%" plate would need "z" B-

In the shop, fillet welds would he used, because they can be made on both sides of the stilTener.

For field welding, use 45" single bevel groove weld because it wonk1 be difficult to weld underside ovcr- head.

weld size: stifcncr to column web; case c and d

= ,605" or 5/arr$ if shop weld

(2" plate needs min. of %'' \ ) For field weld, use 45" single hevel groove weld.

weld size: heam flange to stiffener; case @and @

= .6Yr or %''

check combinmi stress in stiffener; cuse @

FIGURE 56

= G6GO psi

= 3860 psi

FIGURE 57

eom-to-Column Continuous Connections / 5.7-2

1 Problem 4 ) To cllrck tlrt. wi4d size joining the flange and web of the bnilt-up w e l d d column i i r Figures 57 arid 58.

@ weld on column bettoem floors

= 1310 lbs/in. lorrgitudinal shear on weld

= .1c"

but bccausc of 3%" plate, use .- V'&

@ ueld on column within, beam connection

L

Moment diagram


k - 9 3 / , . . 9 Y I, = 16.815 ind

FIGURE 58

The transverse force must he :~dded to this. A portion ol tlic beam Range forct, must he transferred through this ilal~ge-to-web weld witliiri thc distance d -- ti, + 5 K, = 18.64"; the rem;~i~idur of this force is transferred clirectly throilgh the horizontal stiffeners:

= 2-17 kips

This is a unit force on the weld of-

The resultant forcr on the weld is-

( a ) If fillet welds are used, tlre rerjoired leg size

( b ) If partial penetlxtiou J-groove welds are used, the requircd throat is-

10.460 t -- -A-

13,800

= ,622"

and the root face is-

( c ) If partial penetration bevel groove welds are used. the reauired t h r o ~ t is -

= ,662"

t = t,. -C %"

and the root face is-

10. ADDITIONAL STIFFENING OF WEB W I T H I N BEAM-TO-COLUMN CONNECTION

In wscs of mnisually h i g unb:~liince of applied inomelits l o a co lum~~, it iniglrt br well to check the rrsrilting sli<w stresses in the wcb within the con- ni~ctioir. Scc t:iqiri,s 59 a~ ld 60.

IIrw tlic mtl nmnrnts (34, and h4,) of the beam drlr to n coml~ii~ation o i the, gravity l o ; ~ l and wind, are rcsisted hy tlie moments (M:+ and M,) in the coli~rnn. .4 good csmiple of this occiirs in multi-story hriildiligs h n v i ~ ~ g iio interior columns.

Tllc forccs in the heam flanges (F,) resulting from tlic tmd rnonient ( M i j , are t~xnsferred into the web ol tlr? conliwtioi~ as shear.

The:-e are similar forces in the colunin flange (Fa and Pi) fro111 the samc resisting ii~oinei~t. These forces

Beom-to-Column Continuous Connections / 5.7-31

FIGURE 59

are tr;ilisIiwrd into tlw colu~nn wel) within the con- Analysis of Required Web Thickness nection rcgioo as shmr. The unit shear force applied to thc web of the con-

It c:m be assurni,d that xilost of tbib vertical shear nection is- force ( V , \ of thr beain weh is tra~~sferred diucctlv into - ~

\ ., the flange of the supportiilg cohim~i arid does not enter V F, - Vp Mi Vq =.-=--- - - the web of tile corin(,ctioi~. d d c dud, d,

The Iiorizontal shear force (V,) of the upper columr~ will he translrrred through the web of the The resulliilg unit shear stress in the web of the connection illto tlie luw.er column if caused by wind; comcction is- or out across the beam to the adjacent column if ca~rsed by gravity load. T = - - v 1 ME

wi - w ( d d.

FIGURE 60

Thcsr: rcsuiting vcrtical ;imI liorizontnl shear forces cause a diagonal coin]?uessive force to act on the web oi tlic co~inection; xnd, if the \vcb is too thin cornpared to its width or depth, it may suEer some buckling action. SFC Figlire 61.

Thc following a~lalysis, based on plastic design concepts, rmay be used to chwk iliis condition.

Using plastic design concepts, the applied moment (MI) will become tlic plastic moment. For this valuc, thc allowable shear stress ( 7 ) will be based on the yield streiigtli of the steel. The value for the shear

FIGURE 61


Resisting moment

at ollowoble [a] Reststing plastic moment

FIGURE 62

stress at yield (T, . ) may be found 11). usi~ig the Mises Or assuming that a conservative shape factor, yield criterion:

h'f Z f ; -2 = - = 1.12 0;. = J uX2 - ur uy + q2 4 Q rxy 1\1, s

M , = 1.12 M,, and My = o; S In this application of pure shmir, u, and o; = 0, and setting the critical value (rr,,.) q u a 1 to yield (cry), Formula 2 may bc reduced to- we obtain:

hence:

T i 7 =

I ,,I - ") 6 - \ d,,& d,:

The horizontal s h r forw ( V4) of the upper column acts in the oppuite dirwtion to ( F 1 ) and thus r e d r ~ u s t h : slirai- valili. in tilt: wr.h of t f ~ c connection; so this portiou <~oi~id be neglected for siinplieity. This formrtla thm bccomrs:

Tlw plastic mornmt ( h i l ) is obtainnd hy multiplying tiir plastic swtion rno~lriliis ( % ) of thc bmm by the yield slrt?ngtli (v,.) of the s t t~>l .

l'ha plastic si:ctio~i mo11olri.s for all rolled sections is availal~li~ in s e w d strr.1 malii~;~ls.

The plastic sectiori rn(~dii111s of a n~eided plate girder (Fig. 62) is obtained Slam the following formula:

If tbc actual thidmess of the web in the connection ( v ) is equal to or greater than this required valiie ( I Y I ) , 110 additional stiffening of the web would be necessary.

If t l ~ c web tl~iik~iess is less tiinn this value, it must be stiffened by some metllod.

Methods of Stiffening Web in Connection

A wch doubler ph te could be added to makc up this difkrcnce bt.twer~i actual aud rcqiiired v;ilucs of web thickness.

Web doubler

plate

FIGURE 63

W Z = b t ( d - t ) - 1 - ( d - 2 t y

4 . . . . . (3) 'I% most co~ninm soliitio~r is to usr: n pair of

diagonal stiffe~wrs. Thcir cross-swtional area would


FIGURE 64

depend on the comprr~ssive force they must carry, over and above that carried by thc web. See Figure 64.

The horizontal force applied to the connectiol~ is-

The horizontal shrar force resisted by the web is-

The rcsulting lioriLontal component applied to the diagonal stiffener is-

The force on the di;igonal stiffener is-

and the required total area of hoth stiifmers is-

also

also

\/ d,,"- d,' A . . ( d, ( \v , - w?) , - \ ) . . - .

a'--- 3

w, = miiiimoin reqiiircd web thickness, from Formula 2 or 4

w2 : nctiii~l \v1,1) thickness of connection

d, - length of diagonal of conncdiosi area

11. COPE HOLES

in other words going from a givm stress down to zero, etc. For a mow n;irron rmge of stress, for example K :z~ I/*, going from a givm strcss down to just one- I d , etc., tlierc was almost no diiference with or without copc holes.


Provides orcersibrlity ( for root govg~ng

\ L'

for welding

No backing bar used; joint must be back gouged

Bending stress ot

plostic moment (Mpj

FIGURE 65

Provides accesiibility

for welding

Bocking bar used; no

back gouging needed

Plastic dwig~n is not r isd rirrder fatigw loading conditions, so therc shonld he less concern here about thc need for cope holcs and tl~eir rcsnlting cffcct on tlie connectiori's stnmgth. Cope holes \voulcl prol)olily not result in any npj,rr,ii;ible loss in plastic strcngth. The additiond inomcmt brouglrt abont liy t rhving tlic \veh to be stressd to yicld strcngth uftcr the outer filxrs once reach yic*ld is ahont 105, and tlie cope liole represents 2% \ - e n srnall portion of tliis wch scction. Ifcnce, the rcd~rction in strmgth ca~r.scd by the cope liole should lic only n small fraction of the 10%.

Along the sariie liric of thought, any minor lack of weld pc~rictration dne to this lack of accessibility with no copt, hole \\-onld not be as critical.

111 going throrigli tlw original test rcports of wcldcd coirncctioiis for plastic ilcsign. thwc ;ire rinany boam-to- column connections or knccs in wlrich no cope holes were used. In the AISC report, "\17eldcd Interior Reann- To-Colnnin Connections" cope liolcs were nscd and a detail of these sliowi; s w Figure 66. Notice that back-

ing bars were rrscd a i d the holes were not later filled with n.cld metal.

111 plastic design_ cx>pe holrs we not rerlniri~d to prn\,idc the weld quality rr:qniueti, althongh t h y would make it easirr for tlic wc4ding opcrntor. And, if they arc osccl, they \von't Slaw a dctrimental effect on the strength of tlrr. connection if lelt ul~fi l id.

Thc cope hole hclps more for ;iccc.ssibility of the groove \veld on the lowcr flange if weldrd in position. In most cases tliis would be an amr of negatiw inomcnt and this \r-rsld would he un&,r compression, so this should not be as critical as the timion weld on the upper flangc.

IF the rnmihrr c:~ir~ld he tm-lied ow~r for shop welding, both fl:nigt~ coi~ld be hrwl td from tlie outside end copc holes nwild not he nredcd: sre Fignrr 67.

Flame-cut cope hole

FIGURE 66

%,"

Bocking bar

EAMS CONTINUOUS THROUGH COLUMN (COLUMN CUT OFF)

On orrc-story mnstrnction, it is qnitc common to nlitnin continnity of the hcam by allowing it to run continrioi~sly over tlic toil of thc colninn for two or more spans. Freqnently the splice in tlie hcnm is carried out to the point of coiitrailexure.

eom-to-Column Continuous Connections / 5.7-35

FIGURE 68

FIGURE 69

Figure 68 ( a ) shows the Iwam resting on a plate shop wckled t o the top of the column. In most cases fillet welds made in tho iIo\vnliarld or Hat position will be sufficient, since there is usrially very little moment which must be tmmisfcrrrd from tlic heam into the column.

Figriro 68 ( b ) sliows a similar connection made in the hcarn ;ind t11c girilcr which sripports it.

Figiircs 69 ( a ) and (1-1) s l ~ o w this mctliod c x t r n d d to multi-story constriiction. In hoth cascs, stiffming plates art, sliop m c l ~ l d ill betwwrl tiit. Rarlgcs of the beam, in liilo with the voliirnn fiangcs. so that the com- pressivt~ lo:id m;iy be t r ans fc r rd diret.tly from one colrlrnn flange to the other.

PLATES FOR CONTINUOUS FRA

Cover pliites nrl. sonwtimcs i ~ s e d in vonnrr.tio~r with rolltd helims in or&r to illwc;ise thc strcrigtlr ( S ) or stif%~iess ( I ) pn~pcr t ics of thc he;rm.

Uiiless nii i i in~r~m wcigl~t is ;I rcnl factor; t l ~ c usr of covcr p1:itc.s on simply siipporttd 11c~nnis might not 11c justified in l i ~ d d i n g vo~istri~ction since the savings in strcl inight riot o f h t the ad~l i t io i~al cost of fabricntirig and wclding the vovrr pl;it<. to tho hcam. 'I'his is becaust tilt, c o w r plate initst c x k n d quite a dist;incc to hot11 si11i.s of the beam centerline. Notice in the r ram- ple showr for uniform loacii~ig, Figure 70 ( a ) . that the covcr plat? must extend 70.7% of the beam's length ( c ) .

Becausi: of this grtmt Ic~igtli. the wcight reduction is only 8.79.

On contiii~~oiis g i r d w ;in11 tieams, however, there is a r t d ndvantagr in using covcr platcs since the iiicr<wt,d swtion p~-oOr~cid nerds to oxtciid only a very shi r t distance in from cmcli m d of the. 11rai~1, Figure 70 ( (1) . In tlir c~niirpli- s11own. tlw t o t d 11,ngtIi of cover pl;ite is j~tst 1h.:i'4. of t l i i . 1~11gth oi th? 1w;irn ( I ) . Ilore wcigl~t rcd~i(~tion i ~ i apl~lying covcr platrs to tlic continuous 1xvni is 29.8'3,.

A~lditioli;il n ~ ~ ~ i g l i t reduction is ;icl~icvrd in going Eroiii tlw simply siijqmrtcd Ixxm to the coiitiiritor~s Ironm \vitli fistd mds . 1 5 h 1 considwirig t l~ i s iii the ~ w m p k 1 1 l o v of i ~ g from 1 simply s~qqxxtr.d 1min1 to the, w i ~ t i r i ~ ~ i ~ n s twmn with covrzr p1att.s. the o\'i,r-all wt,iglit r~dr ic t io i~ i i i tiit, I)mm 'rwcr~nics 35.8';.

Constants to Help Colculote Finof Moments

Chi11-is h:iv<~ IXYW t l t~v~~1iq~c~t l 11y whicli tht, dc,sigiit>~- c:m I-i.ndily fiiid crnistiiirts to I I W ill <k,tci-minirig sti{fnt,ss fwtors, mrry-owr ~ X C ~ I I I - S ~ :i~id f i s ~ l - m i d r r i m i t ~ ~ ~ t s for bc;iiiis in \vliiclr tli(,rc ;XI-c ;il1riipt v1i;lngi~s in mi)mcnt oS ini.rtia i111i. to ni,lrlcd v i ~ v ~ r l h i t i ~

Soiiwrs incl~tdc: ( 1 ) tirill. 176. R . A. Caiigliy a i d 11. S. (: i~l~il ; i :

l o \ w Ei~ginwring Experimmt St:,., Imva S t ~ l t r Co l lqo , Aint.s, Iowi. :36 cli;iits S i n l m n ~ s with c o \ ~ ~ - 1,l:itcs at e ~ d . Also riyriiilcd as Stri~cturnl Stxidy 1102.150. The Lincoln Elcctric Co.

etded-Connection Design

Sjmply supported beam Continuous beom-fixed ends

uniform load uniform load

(a j

idi

Moment diagram

Moment diagram

weinht -- 100.096 weight = 100.0%

(c) ( f l

iengtli of cover ps = 70 7% L length of c o v e r k s = 18 3% L

weight = 91.0%

cover ies increase S by 1

weight = 70.246

cover ps increase S by 1

FIGURE 70

(2 ) "Moment I>istribulion", J . h l . Gmr:, 1963; D. Van Nostrand Co. 29 cl~;rrts for hcnrns with cover p1att:s at cnds; 42 i.1l;n.t~ for tapered hca~ns.

For methods of c;rlctrlnting t1it:se design factors, see Scct io~~ 6.1, on Dcsigrr of Rigid Frames.

Example I A frame is to he rlesigncd to support a nnifonn load ol 2.4 kip"/E Tlirtv spans of 20' c:lclr ;,st: s r~ppor td by fnur col~irnns, 12' Iiiglr. The beams arc 12" \VF 2 7 g beams, r r i n f o ~ c d n,itli .?6" s 5" coves plates for a distance of 2' on wclr si& of the intcrior srrpports. The colrimns arc S" \Z'F 31fi scctims. S w Figure 71.

* I urt! The section proprrtics of tht: rolled lbeani, I.'& 72, without and wit11 cowr plates are as follows:

= 56 in."


, %" X 5" cover Fks

12" WF 27# beams

8" WF 31# columns

I I

FIGURE 71

weight of this continuous beam with rover pleter= 1750 Ibl.

weight of equivdent simple beom

construction = 3480 lbr.

FIGURE 73

NTINUOUS CON

FIGURE 74 (a) FIGURE 74 (b) FIGURE 74 (c)


Shop rabvicated and welded Multi-Story Dormitory Buildinq con+inuous beam t w o in te r io r - - -

columns. Assembly e r e c t e d as single unit.

FIGURE 75

FIGURE 76

Beam-To-Column Cont inuous Connections / 5.7-39

Girder terminating at a column and not continuing through loads the column web in shear in the region of the beam connection. This couses high diagonal compressive stresses, and diagonal stiffeners ore used to resist the tendency of the web to buckle.

Typical column joint to develop continuity in both directions. The column is cut off at this point. The main girder (left to right) has 100% continuity, no joint; column stiffeners on girder webs are shop welded. The cross beams are provided continuity by the use of o welded top plote extending right across the upper girder flange. The column for the floor above is positioned on top of this connecting plate, temporarily held by angles shop-welded to the column web, and then permanently field welded along the flanges to the connecting plote.

elded-Conneciiion Design

Actual service conditions on beam-to-column continuous connections were simulated in this experimental setup at Lehigh University's Fritz Engineering Laboratories. Here, the column is subjected to compresrive axial lood by the main press ram while the beam stubs are loaded individually by means of hydraulic cylinders.

1. INTRODUCTION

Bcams may be made continuous through their girder supports by any of the methods illustrated in Figure 1.

In Figure 1 ( a ) , the beam flange and part of the web below are cut back so that this flange can he bntt welded directly to the edge of the girder flange, with top surfaces of both members on the same level.

In (h ) , ( c ) and ( d ) , the beam web is cut hack just below the top flange so that this top flange rests on the top flange of the girder. This allows a very easy method of erection.

Additional plates are used in ( c ) along the top after the top beam flanges have been welded to the girder. This gives the necessary increased area for the

negative moment over the support, and reduces the beam size for the reinainder of the span.

Sometimes a small seat is placed below the beam; as in ( e ) and ( f ) . This facilitates erection and also serves as a backing strip for tile groove weld on the lower beam flange.

Top connecting plates are used in ( e ) and ( f ) . These also serve 3s covcr plates to increasc the stiffness ( I ) or strength ( S ) properties at ends of the beam.

If beams are offset, Fignre 2, the top connecting plate can be adjusted to tie both together with the girder.

At exterior columns, Figure 3, the top connecting plate is cut in the shape of a Tee so as to tie in spandrel beams, girder and column.

FIGURE 1

5.8-2 / Welded-Connection

FIGURE 2

FIGURE 3

"4' TYPICAL BAY

TERSECTING FLANGES FIGURE 5

(1) For example, assume the girder to be simply Should the intersecting flanges of beams and girders be supported, and the beams welded for continuity to the isolated or may they be welded directly togeththa? girders.

FIGURE 6

Design the girder as simply supported. Use 14" WF 68# beam having S = 103.0 in.s

FIGURE 4

2oL 20X 20"

Consider the bay, Figure 5, with a dead - live w1 L Ma = --ij---

load of 200 lbs/ft2. On this basis each beam would have a 20-kip load uniformly distributed; each main girder - - (WL) (24C") would have three concentrated forces of 20 bps applied 6

at quarter points. = 2400 in.-kips

Beam-to-Girder Comtimuour Connections / 5.8-3

Here:

- - (2400 in.-kips) (103.0 in.")

= 23,300 psi compression

Since the girder in itself provides very little end restraint for the intersecting beams which it supports, the beams will be designed as simply supportcd even though their flanges are welded to the girder. Use a 10" WF 25jf hcam having S = 26.4 in."

However, if two beams framing on opposite sides of a girder are loaded, their ends will bc restrained and their end moments must be considered.

The resulting flange farces and stresses can be diagrammed as in Figure 7.

FIGURE 7

= 41.5 kips

= 15,900 psi

These two biaxial stresses, a, = - 23,300 psi and u, = $- 15,900 psi, will &ect the yield properties of the girder's top flange within the region where the beam flange is attached.

A plate subjected to uniaxial tensile stress, or stress in one direction only, will have a certain critical stress (uc,) above which the plate will yield plastically.

In this case, this stress point is referred to as the yield strength.

uniaxial stress

However, if in addition, there is a compressive stress applied at right angles, this will allow the plate to yield easier and at a lower load.

bioxiol stress

A convenient method to check the effect of the applied stresses upon the yielding of the plate is the Huber-Mises formula. If for a certain combination of normal stress ( u ) and ( ) and shear stress (T~,.), the resulting value of critical stress (u,,) is equal to the yield strength of the steel when tested in uniaxial tension, this combination of stresses is assumed to just produce yielding in the steel.

= 36,600 psi

This would indicate the top flange of the girder is on the verge of yielding, and the tensile flange of the beam should be isolated from the biaxial compressive


stress. This may he done by one of several methods, Figure 8.

( 2 ) Now assume the girder to be fixed at the ends and the beams welded for continuity to the girders.

FIGURE 9

Design the girder as having fixed ends. Use 14" WF 43# beam having S = 62.7 in."

6 Moment diagrom

9 0 M 0-1 = -

S .W (1500 in.-kips) - ~~~p -

(62.7 in.3)

= 21,500 psi

(Only need S = 56.2 in.3, but this is the lightest 14" WF section.)

M, L M2 = + 48

(60k) (24W') = + 48

= + 300 in.-kips

M 0-2 = 2

S

- - (300 in.-kips) (62.7 in."-

= 4780 psi

W L Ma=+- 16

(SOk) (240") = + 16

= + 900 in.-kips

M3 us = - S

- - (900 - -.. in.-kips) (62.7 in3)

= 14,350 psi

Beam-(a-Girder Continuaus Connections / 5.

a, = - 14,350 psi

a, = + 15,900 psi

a,,= J u x 2 - a , ~ , + a ~ 2 + 3 ~ x y - - / ( -14,350)'-( -14,350) (15,900) +15,9002

= 21,600 psi

The apparent factor of yielding is-

This seems reasonable, and under these conditions the beam flange could be butt welded directly to the edge of the girder flange without trying to isolate the two intersecting flanges.

FIGURE 10

ELDING OF TAPERED FLANGES

Figure 10 shows the method for butt welding wide- flange rolled beams which have a slightly tapered flange to the edge of a girder flange.

By using a light %" x 1" backing bar, it may be hammered as it is tack welded so that it will be tight against the joint.

Figure I1 shows the method for butt welding wide-flange rolled beams with a slightly tapered Bange to a flat plate.

By using a light YB" x 11' backing bar, it may be hammered as it is tack welded so that it will be tight against the joint.

If there is any criticism in doing this, the followi~tg should be remembered. This type of butt welded joint on the wide-flange beans with a slightly tapered flange presents a smoother transition in section and transfer of beam flange force, than the widely used type of (beam- to-columnj top connecting plate shown in Figure 12 which is accepted.

In this case (Fig. 12) the flange force must work

groove bun weld, ond oiro server or run-off tob ot outer edge


groove butt weid, ood olio server or run-off tab at outer edge

FIGURE I 1

! / ~ o p connecting plate

itself up through the connecting fillet welds into the top plate, and then out throngh the groove butt weld into the supporting member. Although there is a transverse Gllet weld across the end of the top plate, much of the flange force must spread out along the edge in order to enter the fillet welds along the side of the plate. These connections stood up very well under testing and showed they could develop the full plastic moment of the beam.

FIGURE 12

eom-to-Girder Continuous Connections /

LES OF CONTINUOUS CONNECTIONS

FIG. 13 Beomr framing to girder web.


Welded connections ore used throughout the Ainsley Building in Miomi. Here, the beams ore given continuity by connecting top flonges, using strop plotes reaching ocross the girder. Lower flanges ore butt welded to the web on both sides.

Continuous welded connections were used extensively in building the 7-story Horvey's Deportment Store in Nashville, Tenn. Here cross beoms ore given continuity through the moin floor girders by meons of a 1" thick cover plote ond a bottom support plote, wider thon the beom flange. This type of connection eliminotes any need for beveling plates and loying groove welds.

SECTION 5 . 9

1. INTRODUCTION

In trnsses of proper arc welded design, gusset plates are generally eliminated. Tensiorl members in the welded design are lighter bcwuse the entire cross- section is effective, and the amount of extraneous detail metal is reduced to a minimum.

Welded trusses may be designed in various ways, using T shapes, 13 and W F sections, etc. for chords. The diagonal members are t~snally angles. Various tll,es of welded truss designs are illustrated in the following:

1. Perhaps the simplest lype of truss construction .' is made of angle shapes and Tee's. In this example, the

bottom and top chords are made of T sections, with angle sections fur the diagonals. This is easy to fabricate and weld because the s t~ t ions lap each other and fillet welds are used, Fi y r e I .

FIGURE 1

2. For a heavier trnss, the vertical member can be an I 01 WF section. The web of this member, in the examplt~ illustrated, is slotted to fit over the stem of the T section. The T section is used for both the top and bottom chord members. The diagonal members are made of a double set of angles, Figure 2.

3. Some trusses make use of T sections for their diagonal members. The flanges of the diagonal members must be slotted to fit over the stem of the T section used for the top and bottom chords. The stem of the diagonal is also cut back and butt welded to the stem of the top and bottom chords, Figure 3.

4. Quite a few tn~sses arc made of WF sections completely: both top and bottom chords as well as


diagonal a id vertical members. This allows loads to be placed anywhere along the cop and bottom chords because of their high bending strength. (With the conventional truss design, loads must be placed only at points where diagonal or vertical members connect to the chord mcmbers.) Almost all of the \velds are on the flanges of the top and bottom chords, and since these are fiat surfaces, there is no difkvlt fitting of the members to make these connections, Figure 4.

5. Where longer lengths of connecting fillet welds are required, a simple flat plate may be butt welded directly to the stem of the horizontal T chord, without any joint preparation. This weld is then chipped or ground flush in the area where web members will connect, Figwe 5.

- FIGURE 5

6. Sometimes heavier trusses are made of WF sections with the web of the top and bottom chords in the horizontal position. The welding of these members would consist mainly of butt welding the, flanges together. Under severe loading, gusset plates may be added to strengthm~ the joint aud reduce the possibility of concentrated stresses, Figure 6.

7. It is now possible to obtain hot-rolled square and rectangular tubular sections in A36 steel at about the

same price as other hot-rc>lled sections. This type of section has many advantages. It has good resistance to bending, and has high moment of inertia and section modulus in both directions. It offers good streugth in compression because of high radius of gyration in both directions. It is very easy to join by welding to other similar swtions because of its flat sides. For lighter loads, fillet welds are sufficient. These sections offer good torsional resistance; this in tun1 provides greater lateral stability under compression, Figure 7.

8. Rormd tubular sections or pipe have certain advantages in truss construction: good bending resistance, good compressive strength, and good torsional resistance. There is no rusting problem on the inside if they are scaled at the ends by welding, hence only the outside must be painted. Although it is more difficult to cut, fit, and weld the pipe sections t o g ~ a e r , this is not a problem for fitters and weldors experienced in pipe fabrication and welding. Pipe is used extensively in Europe for trusses. In this country it has been used for some mill buildings, special trusses for material handling bridges, extremely large dragline booms, off-shore drilling rigs, etc., Figure 8.

Design of Trusses / 5.

TABLE 1-Effect of Eccentric Loading

f = 9,600 w A7, A373 iteel & E60 welds f = 11,200 w A36 steel R E70 welds

Welded connection If consider momeni MI = - Pe

There are many methods by which to join the various pipe sections together in a truss. In this case, the pipe is cut back and a gusset plate is used to tie them together. A gusset plate also provides additional stiffness to the pipe within the connection arra. How- ever, they tend to cause an unwen stress distribution within the pipe, with rather high strmses in line with the gusset plate. See Fignre 9.

These closed sections, with less surface area exposed to the elements, are less subject to corrosion than are open sections; in practically all cases they are left unpainted on the inside. I t is only necessary to see that the ends are scaled hy welding.

If neglect moment

2. EFFECT OF ECCENTRlC LOADING

It can be shown that, with mcrnhers hack to hack, or separated with a gusset plate, the connections will supply a restraining cnd moment: Since this moment is equal and opposite to the

moment due to thc eccentric loading [ M = P e ) , they will cancel. As a result there will he no moment through-

1 , .

FIGURE 10


FIGURE 1 1

out the length of the member and it will remain straight. However, this moment ( M , ) is carried by the

connecting welds in addition to thcir axial load (P). This moment is usually ncglected in the design of the welded connection, because of the difficulty in determining the length of weld ( L ) when it is considered. Further, there usually is not much clifferenee in the actual length of the required weld whether it is considered or not.

(a) if the moment ( M e ) is neglected:

(See Figure lo.)

Assuming A373 steel and E60 welds,

AT = 2.67 in.=

P = u A T

= (20,000) (2.67)

= 53.4 kips

leg size of fillet u:eld

@ = % t i

= ?4 (.425)

= ,3185" or %,Ir h total length of weld

P kips LT = -. -- X o ( 9 6 ) kips/in.

This would be distributed 4" across the end, returning 6.9' on the sides, or use 7" long on each side. This would give a total length of 18" of %B'' weld.

( b ) If the moment ( M e ) is considered:

(See Figure 11.)

Here:

e = y = .94"

d = 4"

w = g6" P = 53.4 kips

since:

F

and from this we find L = 8". (This value was found by plotting several valucs,of L on graph paper and selecting that L value which gave the closest value of P = 53.4 kips.) This would give a total length of 20" of % 6r' h weld.

In this case, the extra work involved in considering the moment did not pay for the very slight overstress in the weld when the moment was neglected.

If only one member is used, and the plate to which it is attached is not very rigid, this restraining end moment will not be sct up. The member will then have a moment due to the eccentric load ( M = P e) , in addition to its axial load ( P ) . See Figure 12.

uxiul tensile stress in member

P u = - A

bending stress

Since the distance to the outer tensile fiber (c) and the distance of the st-ction's center of gravity from the base line ( y ) are equal, and since the eccentricity of

Design of Trusser / 5.

Moment d i o g ~ m

of section (obtained m steel handbook)

FIGURE 12

loading ( e ) is nearly tqual to these, it is assumed for simplicity that c = e r y. Therefore, the total (maximum) stress is-

or the maximum axial load ( P ) for a given allowable stress (G-) is-

For the ST 4" 19.2# member used in the previous example, Figure 10, this additional moment due to eccentricity of loading would reduce the member's allowable axial tensile force to:

= 32 kips

In this particular case, the additional moment due to the eccentrically applied axial load reduces the mt:mber's allowable load carrying capacity by 40%. This far exceeds any reduction in the strength of the welded connection due to this moment. Thus, the connection will be on the conservative side.

Conclusions: ( a ) If the attaching plate is very flexible and

offcrs no restraining action at the end of the member, the full moment ( M = P e ) must be added to the member and no moment added to the connection. In other words, the connection is designed for the transfer of thc axial force only.

( b ) If the a t t a c h g plate is rigid cnougl~ so there is no end rotation of the member, this moment is not added to the member, but must be added to the connection.

Evcn in this example, if the moment were also figured to he added to the connection, at thc reduced load of P = 32 kips, it would not require as much weid as in the previous case:

e = .94" P = 32 kips

FIGURE 13

since: ( b ) calctdatcd allowable load:

p = f .

1 1 i($)' ( l d + L ) l + (diJ

= 32 kips

From this we find L = 4.4" or = 4%". (This value was found by plotting several values of 1, on graph paper and selecting that which gave the closest value of P = 32 kips.) This would give a total length of 13" of %/,," h weld.

This is another case where theory would indicate a much higher reduction in the carrying capacity of a connection than actual testing shours. The following lap joints wcre welded and pulled to failure.

( a ) calculatcd allouable load:

= 7500 lbs

Theory would indicate that, in the above samples, increasing the eccentricity ( e ) from '/a" up to 1" would dccrcase the strength of the welds by 60%.

Yet, the actual test results showed:

( a ) f = 11,260 Ibs/in.

( b ) f = 10,380 ibs/in.

or that this large increase in ecxentricity (e) , from V4"

to l", only decreased the strength by 8.7%. The reasons for neglecting this eccentricity in the

detailing of most connections may be summarized as folIows:

1. In the usual welded connection, the eccentricity is not vely large, and in these cases the thcoretical reduction in strength due to the additional moment in- duccd by the eccentricity is not very much.

2. Actual test results indicate a much smaller decrease in strength due to this eccentricity than theory would indicate. Also these test pieces were very short; the nsnal member would be much longer and, if any-

FIGURE 14

Design of Trusses / 5.9-9

FIGURE 15

FIGURE 16

FIGURE 17

thing, would minimize this problem. 3. The eccentric loading would effect a reduction

in strength of the member several times greater than any reduction in the strength of the welded connection.

4. It is very time-consuming to include this moment in consideration of the connection.

AISC Sec 1.15.3 requires that welds at the ends of any member transmitting axial force into that member shall have their center of gravity line up with the gravity axis of the member unless provision is made for the effect of the resulting eccentricity. However, except for fatigue loading conditions, fillet welds connecting the ends of single angles, double angles, and similar types of members (i.e. having low center of gravity or neutral ixis, relative to attaching surface) need not be balanced about the neutral axis of the member.

3. DISTRIBUTION A N D TRANSFER OF FORCES

It is assumed that the axial forces in a member are uniformly distributed throughout the various elements of the cross-section.

See Figure 15, where:

A, = area of web

AT = total arca of section

If the force in some element of a member cannot be transferred directly through the connection, this portion of the force must work its way around into another element of the member which can provide this transfer. See Figure 16.

This decrease in axial force ( F ) of one element of a member is accomplished through a transfer in shear ( V ) into another element. See Figure 17.

The length of this shear transfer (I,) must be sufficient so that the resulting shear stress ( 7 ) within thk area does not exceed the allou,able. This area may also have to be reinforced with doubler plates so it call safely carry this increased axial force.

If we assume uniform distribution of axial stress through the cross-section of the following member, then the web arca has a force of P,.

(See Figure 18.)

Shear transfer from web:

A* = area of flange V, = P, = u A, and


t, = ,270'' T - 2.67 in2

( A, = 0.99 in2 J Web

3/8/1V

FIGURE 18

P, = 5 A,

= (20,000) (.99)

= 19.8 kips

This force in the web area (P, = 19.8 kips) must be transferred down into the flange by shear (V,), and out into the conncction.

Theoretically, if the section is not to be stressed above its allowable, this shear transfer (V,) must take place within a length bounded by the connecting welds.

If this is true, then this 19.8-kip force in the web, transferred as shear through a length of 5%" where the flange joins the web, causes a shear stress in the section (a-a) of:

- - (19.8 kips) (.%'0) (5%)

= 13,330 psi > 13,000 psi (A373 steel)

This is close cnough. However, if it were higher, it would indicate that one of the following conditions exists:

a. The shear transfer takes place over a greater distance and, beyond the welds, must travel this short distance in the flange as additional tension until the weld is reached. It thus slightly overstresses the section (b-b) in tension.

8"W 31 .#

t , = F = 125 kcpr

+ W' doubler plater

FIGURE 19

esign of Trusses / 5.9-9

FIGURE 20

b. The shear transfer does take place within this 5%" length, and slightly ovcrstresses this section (a-a) in shear.

In most cases the welded conntdon will provide sufficient length (a-a) for the proper transfer of thme forces from one portion of the member to another.

I Problem 1 ] To detail an attachment to the tension member shown in Figure 19.

If wc assume the total axial tensile force ( F = 125 kips) is divided among the two flanges and web of the beam by the ratio of their areas to the total area, then the force in the flange which must be transferred out is-

= 47.5 kips

( a ) If the doubler plates are 6" wide, this flange force (F, = 47.5 kips) must first transfer into the beam web along the length ( L ) as shear, V = 47.5 kips.

This length ( L ) must be-

The k g size of these parallel welds would be based upon the force on the weld:

actual force = - allowable force

= ,194'' or use Y4" (A373 steel; E60 weld)

( b ) If the doubler plates are 7" wide and are welded directly to the inside of the flanges of the WF section, the flange force (F* = 47.5 kips) will transfer directly through the parallel welds. See Figure 21.

If the leg size of these parallel fillet welds is o = %", the length of these welds would be-

(17.5 kips) - ... - 2(Y600) ('h)

= 4.95" or use 5"

v L = (See Figure 20.) Transverse Forces t," T Any transmme component of a force applied to a mem-

(47.5 kips) - - her is carried by those dements of the member which (288) (13,000) lie parallel to this force. In other words, a vertical force

= 12.7" or 12%" applied to an I beam with the web vertical is camed as

h- 5,. -4

FIGURE 21


shear almost entirely by the web. If the web is horizontal, this force is carried as shear almost cntirely by the two flanges. See Figure 22.

In a truss connection subject to a moment (for example, a Vierendeel Trnss), the applied moments, if unbalanced, cause shear forces ( V ) around the periphery of the connection web. The resulting diagonal compression from these shear forces can buckle the web if it is not thick enough. See Figure B.

The Law of Force and Reaction states that in a member constrained by its supports, an applied force at any point sets up at this point an equal, collinear. opposite reaction. This of course assumes the memher to be a rigid body, that is one which does not change its shape or dimensions.

In the following member which is supported, the FIGURE 22 applied force ( F ) has two components: horizontal (F,,) and vertical (F,). The result is two reactions in the member: vertical (R,) in the web stiffener, and horizontal ( R , , ) for the most part in the lower flange. See Figure 24. because therc is no stiffener), there will be little or no

In order for one of thcse components of the applied transfer of the other component (hcrt: F,,) even though force to bc transferred into another member, it is nw- there is a member or slemmt present to do this. In essary for the othcl- cwmponcnt to be transfmed also. other words the amount of a force component (here

Figure 25 illustrates this. If either one of the form F,,) which may be transferred into the member de- components cannot be carried (F, in this example, pends on the ability of the connection to transfer the

Diagonal compression on web o f connection due to shear forces from

unbolonced moment

FIGURE 23

FIGURE 24


FIGURE 25

FIGURE 26

other component (here F ) . Of cor~rse the applied force (17) will bc reduced also_ and under thcse conditions some other portion of this member must transfer it. In this case the web of member A will transfer thi? halancc of the force (F) .

Determining Need for Stiffeners No~mally stiffeners woold be 21dded to a mcmber in which largc concentrated transvrrse forces are applied.

IIowrver, for smaller mcmbers with lower forces, thesc stiffeners are sometimes left off in truss ronncc- tions. It is difficult to know under what conditions this might have to bc stifiened.

In n:cent research at 1,rhigh liniversity or1 "Welded lntcrior Ream-to-Column Connections", short scctiolis were tested imder trarrsversc comprrssion as uell as tension, with 2nd without stiffoners. See Figure 37.

It was foond that the compressive force applied over a narrow section ( t r ) of inemher's flange spread out over a wide section of the wc11 by the time the net web thickness was reached. A conservative valw for this distar~ce is given as:

(te + 5 K )

- Stiffeners

ud~ere K = the distancr from the outer face of the flange to thc web toe of the fillet. This value for all rolled scctions may bo found in any steel handbook.

tt = thickness of the flange of the cor~necting member which supplies the compressive fo1-cc.

Although thcre usas no axial compression applied to the member in this test, on subsequent work involving actual beam-to-colr~mn connections, axial compression was sin~ultanronsly applied. See Figure 28.

It was found that an axial compressive stress of ahout l.fi5 times the working stress (14,500 psi), or u -- 24,000 psi, had little effect on the strength of the connection. At the end of each test with the final loads left on the beams, this axial compressive strcss was increased to twice the working stress or u = 29000 psi with no indicalion of trouble in the conncction.

From this, they concluded that the minimum web thickness of thc c o h ~ ~ n n for which stiffeners are not required is found from the following:


Toe of

of web

$9 Bar represents connecting flange

I

(0) Test to determine Compression region criterion

(b) Test to determine Tension region criterion

FIGURE 27

t* bb w 2 --- t, + 5K

This research, concrmed with the application of . . concentrntcd flange forces applied to flanges of W F members, was directed toward beam-to-column conncc- tions. However, it does seem reasonable to use this as a guide for the distribution of Range forccs in tnrss connertions. This will then provide an indication of the stresses in the chord resulting from the flange force of the connecting member.

In the test of the tension area, they found that the thicknrss of the column flange ( t , ) determined whether stiffeners were required. On the basis of their tests, they made the following analysis.

Analysis of Tension Region of Connection

The following is adaptrd from "Welded Interior Beam- to-Column Connections", AlSC 1959. FIGURE 28


FIGURE 29

The column flange can be considered as acting as two plates, both of type ABCD; see Figure 19. The beam flange is assumed to place a line load on each of these platcs. The effective lmgth of the plates ( p ) is assumed to be 12 t, and the plates are assumed to be fixed a t the ends of this leugth. The plate is also assumcd to be fixed adjacent to the column web.

See Figure 29. where:

m = wTC + 2(K - tc)

Analysis of this plate by means of yield line theory leads to the uitima<e capacity of this plate being-

where:

For the wide-flange columns and beams used in practical connections, it has been found that cl varies within the range of 3.5 to 5. A conservative figure would bc-

The force carricd by the central rigid portion of the column in line with the web is-

Setting this total force equal to that of the beam's tension flange:

Reducing the strength of this column region by 20% and making the conservative assumption that m/bl, = .15, this reduces to the following:


- bb tb - .12 b,, tb t, - -

5.6

If the column flange has this thickness, stiffeners are not required as far as the tension area is concerned.

We might cany this thought one step further and apply it to a tension flange which connmts to the member at an angle other than 9O0, such as in a truss connection. See Figure 30.

resistance of supporting flange (t,)

P = (.SO) us tb (.15 bb) + (.180) 7 uY h2

pull of tension flange (tb)

PI = b, t , ITy

.'. (.go) U, t,, ( . I5 bb) - + (.SO) 7 IT^ tC2 = bb tb us sin a

bb tb (sin a - .12) . . . . . . . . . . . . . (4)

Application to Truss Connections

This Lchigh work for beam-to-column connections will now be applied as a guide for determining the distribution of compressive forces in a truss connection.

I t is assumed that this transfer of the flange force of @occurs in the web of membc@within distance of ( t + 5K). See Figure 31.

Here:

tb t = -;--. sin d,

The vertical component of the web force of member @ transfers directly into the web of member @ within the distance of d

sin d,

Within the region b-c, these compressive stresses in the web of member @ overlap and would be added.

+ F , sin d,

+ 5.)- (&)w

FIGURE 31


FIGURE 32

I where:

or sin' (h F The vertical component of the web force of member

n = 1 - ! + - Fw]! ( 5 ) @ t~ansfers directly into the web of member @ t,, + 5K sm (h d ' . . ' ' '

If the thickness of the web (w) of member @ satisfies this fonnula, stiffeners are not req~~ired . Nor- mally, member @ will not be stressed up to its allowable in compn:ssion, so that this shorter method of checking stiffener requirements is on the conservative side.

within the distance d - . Another method would be to assume ultimate load sin 4

conditions, with all pzrts involved, stressed to yield. Using the previous formula ( 5 ) : The compressive stress within this section would b~

or

4. VERTICAL STIFFENERS

w 2 sin2 d, b,, tb rt,, + 5K sin 4 + ] ( 6 )

force F, sin d, (T:,=-- -

d area sin 4

Within the re ion (b-c), these compressive stresses in the member 6 overlap and would be added:

Now if ultirnatc load conditions are assumed, that is all parts involved are stressed to yield:

I where:

F, = h, t, o; F, = d WD u,

(r = .. ~~

Ff sin d, F, sin2 d,

(--,ti-+ 5K ) w + h, t, + a;.-- sm r6

If Formula 8 should indicate that stiffeners are required, bt tr, UY sin 4 - the same method of analysis may he extended to get an expression for the cross-sectional area of the vertical ' - ( & + s K stiffeners. S c e Figme 32. + d w, ur sinP 4

It is assumed the transfer of the flange force of d w member @ occurs in the web of member @ within the distance ( t + 5K) as well as in the flange stseners. and the required cross.sectionaj area of a pair of stiffen- The compressive stress within this section would be-- ,,, becomes:

( 7 )

force Ff sin 4) Ul = = 'uea h, ts ', _W bb tli sin 6 - - ( 5 w - wb sin2 4 sin d,


5. LONGfTUDlNAL STIFFENERS

The type of connection shown here may be reinforced with two stiffeners placed parallel to the web, and welded to the flanges of member @. See Figure 33.

In the Lehigh test of this type of stiffening for beam-to-column connections, these plates were added along the outer edges of the flange so that beams framing in the other direction could be attached directly to them without extending within the column section. It was found that thcse plates each carried about x0 of the applied compression, while the central web section loaded up and carried the remaining %. For this reason the recommendation was made to assume these plates to be about half as effective.

It is interesting to remember that when a beam is sopported a t three points, the two ends and the center, the hvo outer supports each will carry only x o of the load and at center 56 of the load. If the outer supports are pushed in for 3; of the beam length toward the center, all three reactions will be equal.

By setting the stiffening plates about 5 bb in from the edge of the flange of member @, as shown above, it seems reasonable to assume they will carry a greater load and can be considered as effective as the web.

Although the K value a lies only to the distribution in the web of member @ and has nothing to do with these side plates, the Lehigh researchers for sim. plicity assumed the same distribution in the plates. The compressive stress in the web @ and the two side stiffeners due to the vertical component of the flange force of member @ is:

force 0-1 =

area

FIGURE 33

The compressive stress in the weh of member @ due to the vertical component of the web force of member @ is:

force F , sin d, 0-2 = - -. .-

area d .-. w sin d,

T h e s stresses are added together.

Now if ultimate load conditions are assumed, that is all parts involved are stressed to yield:

where:

F, = bb tb as F, = d wb u,

and the required thickness of the two vertical plate stiffeners becomes:


@

FIGURE 35

These plates must have sufficient welds connecting them to the lower Bange because the compressive force of member A enters here. Since fillet welds cannot be placed on Q t e inside, this would incan a rather large fillet weld on the outside. It may be more economical to bevel the plate and use a groove weld. In this example, the vertical compressive force is transferred from the plate down into the vertical member @; thus a silnple fillet weld along the top edge of thc plate to the upper flange would bc sufficient.

This discussion and resulting formulas will allow the connection to be d~atailed without computing the actual stresses. It is based on providing a connection as strong as the members.

Since member @ will normally not be stressed to its full allowable ~n~npression, a more efiicient connection would probably result if the actual stresses were computed, using these guides on distribution. Instead of providing full-strength welds, their size would then bc determined from thesc computed forces.

These ideas will now be applied to various parts of a truss connection.

6. STIFFENING ACTUAL TRUSS CONNECTIONS

The vertical cnmponent (F,) from the flange enters the stiffener and passes into the web of shear, V = F,, along section a-a. The horizontal com-

from the flange of @ enters the lower . The weld bet \veu stiffener and web

would be designed to transfer this shear form ((V, Figure 34.

The force ( F ) from the flange of @ transfers directly into the stiffener, leaving no horizontal com-

ponent to entpr the lowcr flange of @ . This forcc: ( F ) , now in the stiffener, gradually transfers into the web of @ as shear, from section a-a to section b-h. -

p7 This unit shear force is equivalent to v = -- The weld

bctween stiffeners and web of memb$@ would bc designed to transfer this shwr force ( V ) , F i y r e 35.

The force ( F ) from the flange of @ enters thc stiffcner, and is transferred through to the opposite end. The vertical component (F,) miters the flange of

, and the horizontal component (F,,) enters the


upper flange of @ . No shear force is transferred throu h the weld between stiffener and web of member 6 . Only enough weld is required near mid- section of stiffener to keep it from buckling, Figure 36.

FIGURE 37

The force ( F ) from the flange of @ enters the stiffener, and is transferred through to the opposite end. The vertical component (F,) is taken by the second stiffener as (F,), and the horizontal component (F,,) is taken by the upper flange of @ , Figure 37.

In these last two eases, it is assumed that no portion of the force ( F ) in the stiffener is transferred into the web of @) . The welding of the stiffener would be similar to the previons case, that is Figure 37.

concentrated force into the web is to he taken, then the conservative method may be used. Thus, it is assumed that the flange force must first be transferred as shear into the web of the same member before it is transferred through the connecting weld into member @) . This weld may have to be made larger because

of this additional force, Figure 38. If this flange force ( F ) is high, a web doubler

plate might have to be used so that these forees can be effectively distributed into the web of @ without overstressing it.

( Problem 2A I Consider the connection of Figure 39, using A373 steel and E60 welds.

In this case a portion of the vertical component of @ is transferred directly into @ . It will be assumed that the vertical component d the left flange

and the vertical force in the right flange of be transferred around through the web of

of two vertical stiffeners. See Figure 40. ( a ) Cheek the size of the connecting welds on

the flanges of @ .

unit force on fmge fillet welds

- - (138 kips) 2(10)

= 6.9 kips/linear inch

leg size of flange fillet welds

= .72" or use 3/'' (or use a groove weld)

( b ) Check the size of the connecting welds on the web of @ , which has a force of 74 kips.

unit force on web fillet welds

F f" = t;

- - (74 kips) Z(17.5)


FIGURE 38 leg size of web fillet welds

2.11 OR = -

If there are no flange stiffeners on member A 9.6 and no advantage of the precceding distribution of the = .22"

Design cf Trusses / 5.9-19

FIGURE 39

FIGURE 40

However, the minimum fillet weld to be attached to the 1.063"-thick flange would be - w, = %u". (AISC Set 1.17.4)

( c ) Determine required sectional area of vertical stiffeners.

- -. (97 kips) (29.7 ksi)

(AISC Sec 1.5.1.5.2)

=: 3.27 ia2, or use two %" x - 5" stiffeners

Their A, = 3.75 in.2 > 3.27 OK - (d ) Check the size of connecting welds to trans-

fer this force (F,) as shear into the web of B .

unit force on stiffener-to-web fillet we&

97 kips f = -- 4(12.6)


leg size of fiUet welds

( e ) Check the vertical shear stress along a-a. v

T = - See Figure 41 A,

- - (97 kips) (.660) (12.62)

= 11,650 psi < 13,000 psi < .40 ur OK (AISC See 1.5.1.2)-

5.9-20 / Welded-Connection

FIGURE 41

( f ) Check the horizontal shear stress along b-b in the web of @ arallel to the welded connection betwen @ and &) . Thk length is about 20".

The total horizontal mmponent from transferred into @ is 248 kips. The @ ha5 a compressive force of 215 kips on the right

end and 118 kips on the left end. This means it will pick up 215 - 118 = 97 kips from @ .

Hence, a force of 248 - 97 = 151 kips is to be transferred into the web of @ over a distance of ?OM.

(151 kips) = y m 2 q = 11,430 psi < 13,000 psi < .40 u, OK

(AISC Sec 1.5.1.2)-

As a result no stiffening of the web of @! is required as far as shear is cunce~ned. If these shcar stresses exceed the allowable, the web of the connection could be reinforced with a doubler plate, eithcr on the web itself, or separated slightly and welded to the

edges of the upper and lower flanges of @ . ( g There is one more item to check; consider

point b x in the figure below. It is necessary that the vertical component of the right flange of @ be transferred into the left flange of @ , and yet its horizontal componmt be transferred into the lower flange of @

FIGURE 43

Theoretically, the flange of can only transmit an axial force ( F ) bcttween point and @ . There would be no problem if these 3 flanges met at a common point.

FIGURE 44

In order for the flangc of @ to take the vertical component (F,) from the flange of @ at @ , it is necessary that the horizontal component (F,,) also

FIGURE 42

Design of Trusses / 5.

FIGURE 45

be taken a t this point and somehow carricd up into the If the shcar transfer ( V ) hetwcen thcse two stiff- lower flange of @ . enws exceeds the allowable of the web of @ , a

Likewise, in order for the fan e of @ to take doublcr plate may hc added to the web; or a plate the horizontal component (F.) at ($ , it is neccsrrry 1~my he set out on each side to box in this area. that the vertical component (FY) also be takcn at this point and carried into the flange of @. There are .--. several methods by which this may be done. .. % --:.,.

(5,) of the flange of @ into the web of @ so that the horizontal cam onent (F,,) could be transferred into the Range of 6 .

FIGURE 46

In this substructure for an offshore drilling rig, the truss connections carry iorge concentrated transverse forces. Vertical flange stiffeners are required to prevent web buckling. The triangular "gusset" is welded in to enclose the ores for greater protection against corrosion i n addition to stiffening.


Another solution of the same problem would be to check the stiffener requirements using the Lehigh research for beam-to-column connections as a guide for the distribution of the forces through the connection,

( a ) See if the web thickness ( w ) of @ is sufficient for stiffeners not to be required; Figure 47.

w 2 1.18" required > ,660" actual

On this basis some stiffeners would be required.

Ka"

FIGURE 47

( b ) Check the tension flange of @ where it joins the flange of @ , as to the necessity of stiifcners to transfer the flange force; Figure 48.

t , = . 4 0 a x -

= .40 J (10.075) (.as) = 1.05" < 1.063" OK - .-

On this basis. stiffeners would not be needed on- posite this flange of @ where it joins the bottom flange of (@

(c ) Check the tension flange of @ where it joins the flange of member @, Figme 49.

h, t, (sin a - .12) t" = 4 G :


FIGURE 50

FIGURE 51

On this basis, stiffeners would not h e required on longiturlinul flange stifcners @ opposite this flangc of member @ .

Either tical flange stiffeners or longihidinal flange stiffeners can be used to provide added stilhl-ness for the compressive force of @ .

oertical flange stifiencrs

w h,,t,, sin + -~ ,663 w - w,, sin" --

2 (.660) (10.345) (1.118)(.707)

'r .. ~~~~ 2 53'' - (.go)-(.6% j (.707 )" .-

1.118 + 5 x 1 % ~ or use a pair of 35" x 12%" x 36" stiffeners.

2 - 7.03 in.'

so use two pairs of 3/4" x 5" stiffeners. ~ . . -~~ - -


7. TYPICAL TRUSS PROBLE

FIGURE 52

Properties of Members Used in Problem 3

- 168'

Check the details of this connection, using A373 steel and E60 welds.

( a ) Consider the moment and vertical shear on section a-a.

M = F d = (16SV - 14L)(1(Y') = 1540 in-kips

V = 154 kips

bending

shear

resulting maximum normal stress (See Figure 53.)

= 10,980 psi

The resulting bending stress of u = 8,000 psi at the outer fiber is for a horizontal edge. If this edge slopes ($), the resulting fiber stress along this edge may be found from the following:

(See Figure 54.)


= 5730 psi n = 8000 psi

FIGURE 53

at top edge of gusset plate

Q, = 12. cos 12" = 977

8 000 u = -2-- = 8,390 psi (compression)

,977"

FIGURE 54

at bottom edge of gusset plate

@ = 30" cos 30" = ,865

8 000 u = 2;--- = 10,700 psi (tension) ,865'

( b ) Consider the transfix of the vortical component (I.',) of the truss members @ and @ duough gusset plate @ and into the web of column @ within the connection length of 43" as shear. From this vertical component (F,), deduct the portion to be carried by the right flange of A . (This does not have to enter the web of column .) This portion carried 8 by the right flange can be determined by the ratio of the flange area to the total section area.

The forcc taken by this flange is-

= 55.5 kips

This leaves 154 - 55.5 = 98.5 kips to pass into the web (some of which will enter into the left Range). The resulting shear stress within this 43" length of web is:

- 5,490 psi < 15,000 psi < .40 u, OK (AISC See 1.5.1.zj--

This transfcr can ho made while still keeping the flangc compressive stress within the unifonn stress of-

( 168 kips) = = 8400 psi (20.00 in.')

( c Consider the vertical weld between connection plate b C and member @ . The forces applied on the left side of this weld are-

FIGURE 55 ] '\\

f, = 1.76k/in \\ fr

M = (168" - 14")(7.03") = 1082-in.-kips

V = 154 kips

section morlwlz~s of ucld connection

bending forcc on weld

shcar force on zccld

rcwrltant forcc on weld

f, = d v = (1.76)' -+ (1.79)2

= 2.51 kips/in.

lcg size of fillet weld

(2.51) = . - "1" (9.6)

. or use X6''

( d ) Flange plates, %" by 4%", are welded onto @ to extend the flange of @ back a sufficient dis-

tance. The cornpressivc force in the flange of @ is-


On this basis, the stress in each of these flange plates is:

(78 kips) LT = - - . . -. (2") (%") (4%')

= 13,100 psi OK -

The force from an adjacent pair of these plates is transferred into @ as double shear.

FIGURE 56

This shear stress in @ is-

(78.0 kips) = q i T 7 ) v )

= 2600 psi < 13,000 psi OK - size of connecting zcelds

( 1 5 6 k/in. ) &, = - - .IW or use x6,,h

(9.6 k/in.)

However, tho .4WS as well as the AtSC would require a %" fillet .. wald bccause of the %" plate.

( e ) At section 1,-b at the termination of the flange plates, wc will assume the 200-kip compressive forcc

must be taken by @ alone. The cross-sectional area of @ is A = 15.B in2.

For the same stresy in 0 , this would require - the same cross-sectional area, or 15.88 in." and a net width of

There is sufficient width; see Figure 52. ( f ) At swtion c-c halfway along the flange lates,

it is assumed that half of the flange force of 6 has been transferred out into @ :

For the two Range plates, this reduction would Ieave-

(200") - 2 (39.1") - 122.0 kips to be taken by

0. For the same stress, this would require an area

of-

and a net width of-

There is sufficient width; see Figure 52. (g ) Another section which might be checked is

along d-d. The ioads on this section are the direct com- prcssiivr load of the colnmn @ , a shearin? force from the tension in the lowcr chord mcmber , and a bmding moment from the eccentricity of both the colun~rr A and the hottomchord h o d @ . This critical section ( 9 - d ) is placed as high as possible above the lomcr chord (@ without intrwxpting the stiffening elements of the conneciion. In this case it is placed Y' ahove the ce~nterline of mcmber @ .

The propcrtics of this built-up cross-section are

FIGURE 57


computed and the eccentricities determined. For simplicity in this compntation, the reference axis (x-x) is placed along the conterline of the column A 0.

From this:

c = (14.06 + 17) - (7.03 + 5.36) = 18.67"

Applbd Loads

Member

FIGURE 58

14" WF 68# 1 20.00 1 0 1 0 1 0 / 724.1

A d

compression

F, = 16Sk - 14k = 154 kips

FT cr - - = 5050 psi (compression) A

shear

F,, = 126&

M = : A d l = : M d

bending

I,

G- = --- (233'0.3.0) = a% psi (compression) ( 127.5)

This is a total compressive stress of 3050 + %%I = 7470 psi, and a shear stress of 7 6 4 psi at the outer edge of the connection plate @ .

The resultant maximum normal (compressive) stress at the edge of the plate is-

= 12:800 psi

Check the outer edge of this plate @ as a colnmn.

radius of gyration

r = ,289 t t= (.289)(%) = ,181"

The unbraccd length of this edge is L = IS", and

and the corresponding allowable compressive stress is-

u = 14,130 psi > 12,285 psi OK ( A I S C ~ ~ C 1.5.1.3.1)

If the calculated compressive stress had exceeded this allo\vahle, a flange could have been added along this one outer adge to give it sufficient stiffness against lx~ckling.

Plate @ will have i/lBt' b 4'' flange plates to extend the flanges of member 6 along a distance of 12". W' fillct wclds will ire sufficient to attach these plates, tl~is size being n q o i l d because of the %" plate. No further checking is necessary because, by observation, the lB-kip force is much less than the 200-kip force of mrlnber @ and the same amount of plate @ is available.

Determine the leg sizs of the four fillet welds connecting the two %'' gusset plates to the vertical leg of a tower. A373 steel, $360 \velds. See Figme 59.

The horizontal component of the 350-kip force of the diagonal mcmhrr (10" WF 100#) is transferred back to the horizontal member (248 kips) through the


3.87" I

-4 k- Weld group

gusset plate. The only force transferred through this connecting weid to the vertical memhcr (14" WF 136#) connecting weld to the vertical member (14" TVF 136+) is the 248-kip vertical force acting 3l/2"

away from thc crnter of gravity of the welded connection.

Trcot the weld group as a line:

tuisting nction

vcrticnl force:

FIGURE 59

horizontal force

vertical sllear

resultant

actud force (,, -- allowable force

l:iowcvcr, .\\.I5 and becanse of 1:; ,".ilqge.

A373 steel

A, = 1.83 in2

SAa" X 6%" X 12" R

FIGURE 60

I Problem 5 1 Determine the weld sizes on this connection. A373 steel, I160 welds.

( a ) Find the reqnired size of fillet weld hchvren member @ and connecting platcs @ The total length of connrcting weld is-

L = 1 ( W ) + 2(6.08") = 36.0"

force of weld

F (95 kips) f - = = 2,641' L (36")

upsjiri

(2.64 k/in.) = - 07-" - J or use x6" (9.6 kjin.)

Check the length of web @ within the conncction along section x-x, requirrd to transfer the force of the web @ ont into the flanges of as shear.

force i n wck

F, '351, = 23.6 kips (7.37)

( b ) Find tha reqnired s k e of fillet weld between flanges of @ and platcs @. The total length of connecting wrld is-

L = 1(3'/2") + 2(12") == 38.0"

jorcc on u&l



Trusses were essential to the all welded froming of the steel and gloss Phillis Wheotley Elementary School in New Orleans. The school was erected off the ground on two rows of concrete piers, plus exposed steel supporting columns under end trusses of the contilevered classroom wings. This provides both open and sheltered play area beneath the structure.

The roof supporting space frame that tops the Upjohn Co.'s Kolomozoo office building is of welded angle construction. A system of subassembly jigs focilitated the holding of alignment during fabricotion of the giant frome sections. Nearly all joints are welded downhand.


Main load-carrying element in the world's largest ore reclaimer, at Kaiser's Eagle Mountain mine in California, is a 170' long welded truss of triangular cross-section. Tu- bular construction is used where practical for extra strength and torsional resistance, and in order to keep weight to a minimum. Closeup below shows welded cluster where vertical and diagonal members meet the top chord.

1. INTRODUCTION

Tubular construction is bcginning to be used to a greater extent in this country, although for many years it has been an accepted method in Europe where it is used extensively. Although the advantages of thc tube have been known for a long time, it was the introduction of welding to the connections which made its extensive use possible.

The tube represents an efficient section, having good properties in all directions. There is no problem in maintaining the inside of the tube against corrosion and in most cases this is loft unpainted. The welded connections seal the tube against any moisture entering and prcvents the circulation of air, hence any rusting very soon stops and equilibrium is reached.

The joints represent the intersections of curved surfaces, and therefore extra care and time is involved in cntting the pipe to prepare the joints. Usually these are flame-cut, although there are abrasive cut-off saws which make a series of straight cuts and provide good fit-up and there arc shears with special tools which allow the end of the tube to be sheared. Fully automatic flame-cutting machines have been built which may be preset for the inner diameter of the tube to be cut, the outside diameter of the tube which it intersects, and the angle of intersection. This will very quickly provide the proper cut, at the proper bevel, and results in close fit-up of the joint.

Recently steel mills have introduccd square and rectangular tubing; these of course, are much easier to connect because of their flat surfaces.

2. GUSSET PLATES

Gusset plates have been used in pipe connections for at least 3 reasons:

(1) Provides additional length of fillet weldii~g to the pipe Most pipe is not very thick. For example, 4" standard pipe Bas a V4" thick wall. Unless extra care is used in cutting, beveling, and fitting, it is easier to use fillet wclds rather than try to make 100% penetration groove welds on thin-wall pipe.

Weld @ does not

hove io be made os

carefully becoure fillet weld @ provides addition01 strength

FIGURE 1

(2) Allows the inttmecting pipe members to be cut short and the gusset platc caries the cntire load back to the main member.

In some cases, the web membcrs are shop fabricatcd and welded into assrmhlies. This facilitates field erection and wrlding hecause only vertical wclds between the main pipe member and gusset plate are still reqnired.

weld Man pipe

FIGURE 2

( 3 ) Providcs a dirtzt transf(:r of force through a main p i p member when othtr members connect on nppositr. sides of thc ni~mber. This may hc done if it is felt that the maill menrhcr has too low a thicktiess ( t ) to diameter ( d ) ratio and would need additional stiffness.


FIGURE 3

Anothm solution to this problem would he to add a "slwve" or "collar" around the main rncinher u'itlrin this cr)nrwction mnc so that it ~ v o i ~ l d have the required thichrws. Tt a;onld ljc possible to insert hy welding, a short lcngtli of thicker tiibing within this zone. Ustially the inain pipe members must be butt welded together somewl~cre to provide the required irngth, and this weld could be located at tliis position. See Figure 4.

If the wail thicknrss, bevel, and fit-up of thc pipr: arc sufficient for 100% pcnctxation groovr \velds to be made, there should hc no rtaason lor gusset platss. In most cases, with proper care, groovc welds could be made easily.

Although gi~ssct plates arc used in pipe connections, they tend to stiffcn the pipe and, as a resiilt, concentratr the stress in thc pipo at the end of the plate. See Figure 5.

Ii has been si~ggested that, if gusset plates are to be nscd, tlwy he t:rperrd at their ends so as to have less stincning effect on the pipe and thus provide a more even distribution of stTess within the pipe at this connection.

Under static loads, any reasonable stress concentration in the pipe near thc termination of the gusset plate woi~ld probably bo reduced by some localized plastic yielding; so, this \vould not be a prohlem. How- ever, grisset plates should be avoidcd for connrctions subject to fatigue loading.

3. ORDER OF ASSEMBLY

When web mtambers intersect at a connt7ction, normally the tensile member is first welded completely all the wny aroimd to the maill niemhcr. Then the compression member is cut back to overlap the tensile member, and

Gieoie i stress concentration More uniform stress

FIGURE 4

FIGURE 5

Connections for Tubular Condruction / 5.10-3

1 Tensile member

FIGURE 6

this is wi.ld~xl to hoth of thesc mt~mbel-s. Evmy effort is i r d e to obtain tlic hest tcnsile connection; Figure 6.

This is not quite as important as it first sounds sirm most of the vertical co~nponent in the tension member is tr:msfrrred directly into tho compression memho. through thp \velds of this overlapping portion ( b ) witlro~rt w e r passing throngh the wcld connecting t h ~ ~ tension irmnhcr to ihr main horizontal member (a ) .

Thc portion of the x ~ l d ( a ) in the overlapped area connecting the tcnsion m(,mhcr to the main member is snhjcctd to two Sorces: tension from the tensile, rnernbw, and r:ompression fmrn the cornpression memher sincc it pushes agitilist this overlapped portion of thc tensile member. One forcc offsets the othrr, so that vt:ry little of any vcrtical force mrlst he casried by this portion of the weld at (a) . jwt the horizontal force into thc top rnoml~er.

Fignrvs 7 :tnd 8 descrihc a trst condncted at the Vniwrsity of Chlifon~ia, "~ic~scarch on Tubular Con- rirctions in St]-uctnrd LVork" ]. C;. Uouwkamp, WRC ji.71, .hog. 1961. This test shows the effect that overlapping the intwsocting web members has on the strength of the joint.

It is seen that a more negative rccentrieity of the connection ( c ) resnlts in more overlapping of the web ~ncmbers and greater stifl'ness of the main member. With this grcat ovcriapping of thc ueb members, the tr:tnsfr.r of the vertird component 01 the diagonal web mmnhrr into thc vertical iwh momber will occur before it miters thc main horizontal chord inember. The above

test shows this connection to have the highest strength, actually slightly higher than the tube itself, which in a separate test pulled a t an average of 260 kips. Eotice all three of the above tests failed in the tube wall adjacent to the connecting weld.

4. APPLICABLE BRITISH SPECIFICATIONS

The following is taken from Addition No. 1 (Nov 1953) to H.S. 449 (l.948), British Standards Institution:

Sealed tubes or sealed box sections, for exposed structures shall not be thilmer than ,160"; for non- exposed structures this limit is .128", and not less than-

D = outside diameter of pipe t = . l o VE-

t = thickrms of pipe

The angle betwwn intersecting pipe shall not be less tharr 30"; otherwise the strength of the connection shall be demonstrated.

A cmnplete ptw:tration goove weld may be used regardless of the ratio of the diameters of the intersecting pipes.

If the ratio of the diameter of the pipes is less than 'h, fillet welds may ho used.

If this ratio is '/A or greater, a combination of fillct welds for a portion of the joint and groove welds for the remainder may br. nssd.

Pipes eonrrected end to and shall be groove u-alded. In a fillct u ~ l d or a combination of fillet and groove

eided-Connection Design

FIG. 80 This pipe connection (Fig. 7a) hod o positive eccentricity of v4 the diameter of the lorger pipe. Its ultimote lood was 137 kips.

FIG. 8b This pipe connection (Fig. 7b) had no eccentricity. There's o slight overlopping of the connection. Its ultimote lood was 209 kips.

FIG. 8c This pipe connection (Fig. 7c) hod o negotive eccentricity of $f4 the diorneter of the lorger pipe. Because of larger ornount of overlapping, its ultimate load was 277 kips.

Connections for Tubular Construction / 5.10-5

weld, the allowable stress on the t11ro:lt shall not exceed the allowable shear stress of the pipe.

In a groove weld, the allownblc tensile, compressive, or shear strcss on the throat shall not exceed that of the pipe.

5. DESIGN OF TUBULAR TRUSS CONNECTIONS

The application of tuitular construction to a truss arrangement is typified by the following problem. Here the loading is similar to that on the connection which was the snbject of Problem 3, in the preceding Section 5.9.

To design an eEcirnt connection on this tubular truss, Figure 9.

( a ) First c h c k the allowable loads on the various selectcd pipe sections against thc actual loading.

Member @ L (432) -. - r (4.38)

= 98.7

and the allowable is rr = 12,520 psi

P = u A

= (12,520 ) (14.58)

= 182 kips > 168 kips OK - Member @

and the allowable is IT = 16,660 psi

P Z U A

= (16,660) (14.58)

= 243 kips > 200 kips OK

= (20,000) (7.165)

= 145.3 kips > 126 kips OK --

-12" Std pipe t = l/s"

A = 14.58 in2 r = 4.38" (rodius of gyrotion)

FIGURE 9

( b ) Use a W gusset plate on this connection, resulting in Figure 10.

moment applied to pipe

M,, = (1Bk)(7 .8W)

= 990 in.-kip

also

M, = (154") (6%")

= 982 in.-kips

assumed oalue of e

e = 1 2 t

= 12 (%)

= 4%"


maximum unit force jrudial) applied to 1" ring section of pipe @

= 1.98 kips

FIGURE 11

Althonglt there is just a single radial force ( f ) acting on tlw p i p shell, assume there is an equal force on the oppositr side of the shell, resisting this force.

FIGURE 10

This represents a worse condition than actually exists.

t? s = -

6

- - (36)' - 6

= .0Z3 in."

M,,, (a t force f ) = k f r

= (.318)(1.98(6)

= 3.78 in.-kips

M ( r = -

S

- ( 3.78) -- (.023)

= 164,000 psi Excessive .

Heca~ise of t h<w excessive bending stresses within the pipe shell resdting from the moment applied by


thc connecting pl:rtc, somc mcans of stiffcning the pipe \tithin this arra must lie ~ ~ s c d . T11<w arc several pos- sibilit im.

( 1 ) O n e pmsi l~k solution is to pr~t a casing around thc pipe so as to iricrtmc its wall thickn(~s. This will provide suilicient st-ction modulns so that the rcsnlting bending strcss is rrduced to ; ~ r i allowable value. (hs- sum? u = 18,000 psi.)

= ,210 in."

Do not nerd cirrurnferent~ol fillet welds oround either

I- end of %" liner unless to ieol the ends

60" oroove weld on %" liner - also j p n s pipe member. Weld lies dong neutral ox i i of plpe, so this becomes built-up section to resist bending

%"

3/l"-thi~k stiffening lhner around p,pe

FIGURE 12

Since 1.17" - %" (present thickness of @ ) = ,745" requirrd additkina1 thicla~css. or add :I %'-thick wrap-arorind shcet around this pipc @ in the arcit of tht. connwtion. See Figllrc 12.

( 2 ) :\notht~r possiblr solntion \tould hr to add to the wall thickness at top and bottom of the eonnt:etion.

.. , ,, X 10" wrap-oround R

FIGURE 13


= 2.77 in.:'

:== l.29" rqnircd, and since i.29" - 3h'' = .915", sldd a 1" x 10" plat? &-rapped aromd tlle pipe @ at t h ~ top and bottom of the coirncction.

m t' s =: ~

6

( c ) I)etcrmii~c the amonnt of required am~cc t ing wtrld between pipc @ and gnsset plate @

where: w = width of stiffening ring

For dotermining the minimum length of connec- ti011 ( 1 .) to hold slrtw strcss (r) within the sillowablt~, use the following lr~avimnrn leg size of weld:

plate

4 I, 9600 w = 4 t, 1. r

FIGURE 14

An alt(m~atr mt,thod woi~ld 11e to rise %'' fillet weld all the way aroimd the m d of the pipe @ :

FIGURE 15

Connections $or Tubular Construction / 5.10-9

-.: ,i.5.6", or 17.8'' o~r cadi sidc of the $6'' giisset plate.

If thc transvrrsc \veld is 12" long, this leavcs 27.8 - 12 = 15.8". or 8" on cach sidn.

6. TEMPLATES FOR PlPE CONNECTIONS

Althougli pipc f;ibricatitrg shops have shop nwn who an. cxpt~rimctd in laying out m d prrprirrg th iw joints hy making thvir O\VII tcmplntw this is somt.thing new for most strl~ot:ir;il shops. It may hc, m w x a r y to supply templates for th? morc critical pipe joillts w11cre a jiussct plat? is riot spccifietl.

Thwt: arc t;~I,los of ordirratrs amilahlc for most standard pipe sizt,s ;ind given angk,s of intersection (ED, 30' , 45", 6O", and $10" ) . tIou;cvt.r, t h ( w may hc of little, vdue btcause otlicr rormd tubi~lar s(:ctions ma); be ustd which are ilot standard pipe sizes, : i r d in structur;d work thc arlgl? of itltcrs~~ctiorl \<%I1 not iitw's- sarily be one of the ahovc.

For good fit-rip. i t is nt,cessary that the inirnr radius (1 , ) of the snrallvr pi ,tz @ and the outer radius ( rz ) of the larger pipe irrtersc.ct along a curve which forms the root of the joint.

Followitig is a suggcstrd metlmd for making templates which will cover a11 possible connections at any angfr of intwscction, any :irnount of offset, and any possiblt combin;rtion of pipe sizes. This template will allow the c t d of the srndlcr pipe to he cnt for proper fit-lip against thr surface of the larger pipe. 111 structurd work, it is not ncccssary lo cut a hole into the side of thc 1;irgcr pipe at the conn?ctionl as is done in prcss~re piping so a srcor~d tr~nplatc is not needed for this cut.

The inner radius ( r , ) of thc~ sinallcr p i x .\ and 6 0 the outer radius (r , ) of thc largcu pipe H .me med to makr the template. This is done gr;ipliicnlly or ;~rr;~lyti~~;rlly, as explained a in\: lx~ragrapfrs further.

Tlrc tcniplatc is mad? of soiue type of iiravy p;ipcr. It is nirapp(d arorlnd ih t pipe to he cut, at the propcr location. The c?ntc,r of tlris tcnrl)l:rtc rdg? is transfcrrcd onto the pipe with chdk. Thr: rhalkcd curvi. on the pipeis tlien marked with a st:rics of c:~ntcrpmch marks. Tht: pipe is thrn flainr-cut along this cl~rve, krrping the torch tip trorni;rl or at right mglcs to the surface of the pipe. This \vill prtid~ice the p r o p ~ r curve for the joi~rt as far as tho inside of tlrc pip(. is <,or~cerncd.

It is then necessary to brvt,l the edgo of this pipe back from the outsidr, jnst torrclring tliis inside cut to pro\.ide the raquirrd inclrldd angle, for the groove weld. A good expcrie~rcrd flamc-cutting operator will

ilo tliis witliout any difhdty. If fillct \wlds are to be irsed instead of groove

iwlds, t b i secmid cut or i~cvcl is only needcd at rc- twtrant corrlcrs of th(, joint or whew the nnglc 11rtwec11 the siirf:iccs of tha iirtcrstbctirrg pipes is less than 90".

TABLE 1-Properties of Polar Angles

12 POSITIONS or (8) mrif ion 1 a I r i n a I sin2 a I I-cor a

TABLE 2-Properties of Polar Angles

5.10-10 / Wetded-Connection Design

0 @ 0 @ 0 @ 0 @ 4 3 ~ ~ ~ @ @ @ @ @ ~

FIGURE c TEMPLA76 DEVELOPMENT OF PIPE A

FIGURE 16

Graphical Method of Making Template

Refercnct>s at-? to vir\\.s ( a ) , ( h ) , arrd ( c ) of Figrrrr 16. 1. Ilraw a sidc vie\v of the cormcction. figure ( a ) .

Drnw an end v i tv of the i,onnection. fig~rrc (11). 2. l a y off pipe @ into a g i \ w ti~~mhc,r of q r a l

swtions, for (~x;inrplc 16, ;ind nitmlwr these 1 ; " 3, ctc. tlrrr~rlgh to 1G. llraw iitlrm throiigh thcsc points p;rrallcl to thc axis of pipc @ in Imth f ig~i r~s .

3. \Vhere tllrse prirrilld liiics of pipc @ intcmcct pip? @ , in figrlrc ( b ) , rnnkc points ( D ) .

5. II'hcr~, th~sc* p;lrnll<,l liu<,s of pipe @ intersect ci~rr iqm~dilrg p;~r,illi.! lini3s of pis" @ , in figiirc ( i i ) , m i l - k points ( I : ) . Krirnlwr thrsr points in accord- alrce \rith the origirinl divisiiw of t111. pipe @ .

6. 111 ~ ; ~ J I I T ( c ) , lay ofr l i111~ x-x , m1t1;d to t11c ortt<,~ circrimfrrrtiw of pip<, @ , and d i ~ i d o into 113 q u a 1 scgm(x~~ts.

Connections tor Tubular Construction / 5.10-1 1

FIGURE 17

7 . In fignrc [ a ) , dr:iw refermcts line %-Z at right aoglos to tht: itxis of pipc @ and thnil~gli tlw vertex of the coni~c~ction angle. From this line Z-Z mtSasure thc 01-dinatr c1istam.c (11) to thc various intrrsccting points ( E ) . I.ay thtw distattcr:~ (h ) off v(zrtically {I-om linc Z-Z in figrise ( c ) . Do this for all the points and draw a curw through thc upper cxtrcmitii~s of ilicss vt,rtical h e s . This Becornrs the tcmplatc for cutting pipe @ , figure ( c ) .

Analytical Method

Thc follon-ing f~xtni~ln will give thr value of the ordi- ~ ~ a t r ( 1 1 j tor ;my polar position ( m ) dong tlw s~riallrr pip? This mcthrid of finding d t fly formda c~Iirnin;rti~s thr mapping of f i g ~ ~ r ~ s ( a ) and ( b ) in the 'grapliic:il 1nclI1~1 of 1:igum lfi.

I'ri~cticdly all s t r ~ ~ c t ~ ~ r d pip, c o ~ ~ ~ ~ e c t i o n s u-ill 11avc no offs~t, :I = 0; :ind this ljrcomcs-

or:

< .-..r7-...-- r 2 - r . , - - , -2 '2 m ll = - .. ~ ~~ ~ ~- I ( 1 - cos a )

tan 4

r., r h = [A] i- -- . ~ ' [R] . . . . . . . . . . . ( 3 )

stn 4 tan 4

-;-I

[ R ] = 1 - cos rn

r, = inner radios of s m d r r intrrsccfing pipe

6 =- irnglc of interswtion h<>twcc~i ases of pipes

11 z ordiiinte of thc trmplate for the smallt:r pipe for any 1)osition ( m )

Tahlrss 1 and 2 will give the rlcwssary valrrcs for sin U-. sill' o , a 1 ~ 1 1 - cos m for the viirio~~s pt~lar mgles ( a ) for r i t h 12 ~ ~~ positions or 16 positions of the pipr.

I f Formula 3 is h) be ~ c d , tile followiirg nornograph, Figr~re IS, will give vollies of [ A ] . Valurs of / 13 1 may I J ~ fo1111d in Tables 1 and 2.

I Problem 2 I Foa thts tuhnlar coiinwtion wpnwnted in Figure 16, the sn~;rllt.r pipc A , inside ri?clius r, =-: Y, iiitersrets thc 1;trgw pipe R . rmlsirk r;idi~is r2 3", at an 8 a~rgtc of is'', and ~ . i t l l :in oifset of a = 2".



Following are the ordinates ( h ) for the various positions figured both graphically (see Figure 16) and analytically (with Formula 1 ) . This tahle shows close agreement between the two sets of values.

porltion 1 graphical / onolyticd

A sheet of paper is laid out. A straight line X-X is drawn across the paper, parallel to the long edge and %" or 3" from this edge. Starting from the left edge of the paper, measure off a distance on this line equal to the outer circumference of the smaller pipe A and mark this on the line. This can be done in two ways; the circumference of the pipe may be figured by knowing the outside diameter of the pipe, or this paper may be wrapped around the outside of the pipe and marked where this edge of the paper overlaps.

The easiest way to divide this line (which represents the circumference) into equal segments is to fold the left edge of the paper back toward the right until it lies directly on top of this mark, then fold this flat upon itself. This divides the circumference into two equal parts. Now fold this edge hack toward the left until it lies directly over this fold, and fold down. Do the same for the similar portion on the bottom. This now divides the circumference into four equal parts. Open the paper and divide each of these quarter sections into three equal parts and number each of these vertical lines from 1 to 12. If 16 positions are to be used, divide each of these quarter sections into four equal parts and number from 1 to 16.

Lay off the comesponding ordinates ( h ) on these lines. Draw a curve through these points and cut along this curve; the lower portion of the paper is the template.

I Problem 3 1 in the connection represented in Figure 19, the axes of these three intersecting pipes lie on a common plane; there is no offset ( a = 0).

A template is re uired to cut pipe @ which intersects both pipes &) and @ . The inner radius of pipe @ is 2", the outer radius of pipe @ is 3", and the outer radius of pipe @ is 21%". The graphical work is shown in Figure 19.

Notice that the finished template is made of two portions, that due to the intersection with pipe @ , and that due to intersecting p i p @ .

I Problem 4 1 In this example, the nomogaph (Fig. 18) will be used to find the ordinates ( h ) for a template to he used in cutting the smaller pipe of a two-pipe ~xmnection. The smaller pipe A has an inside radius of rn = 2", the larger pipe 8 B has an outside radius of r2 = 3", and the angle of their intcrscction is $ = 60'.

sin 60' = .8660

tan 60' = 1.7321

Formula (3)

The results are shown below in table form. As o matter of interest, the values computed by Formula (2) are listed on the extreme right and indicate the reasonable accuracy of the nomograph.


FIGURE 19

FIGURE c TEMPI ATE : D€YElOPM€NI OF PIPE A

7. BOX SECTlONS

The squara and rwtangiilar hox sections, in which tubing has more recently hecome available at competitive prices, eliminate the, prohlcm of fit-up that is associated with the i r ~ i ~ n d st:ctions. With box sections, the tnd of the sm:~Iler tuhc can be simply sawed with a single cut at the reqnired angle.

Field erection of box sections is easily siiiqMied by the use of Saxe clips, Figure 20. The clip and its seat are shop u-elded to the two intersecting members. Usually t l ~ c clip is welded to tlie inside of the box Ixam whm: it is loss \wlnorahle l o damage during shipment to the projrct site. The clip also furrctions as 2% seat to help in support of the beam. Tliis allows the joint to be made without any attachments on the ontside, and produces a pleasing appearance.

Square and rectangulor structurol tubing, now ovoiloble in many standard sizes, tends to simplify desigv and focilitote erection. Both shop and field connections a r e genera l l y more easily mode thon when using round tubing.

ConnecPions for Tubular ansfruction / 5.1

Soxe seat ihop Sone clip shop welded to face welded to inside of columri of box beam

I of tubular box beom, oliowing

, use of simple fillet weld "round \ , outside, Ideal for exposed steel

L FIGURE 20

5.10-16 / Welded-Connect ion

Space frame roof on the combined worehovse ond mochine shop in Bethlehem Steel Co.'s reseorch complex offers on interesting silhouette (ot top). Roof frome is formed by eleven 96'-span welded pipe trusses braced aport by inclined pipe struts ond orched structural members. The result is a very rigid structure, olthough temporary stiffening with steel chonnels wor required during erection.

Conneceionr for Tubular Construction / 5.1

Typical connections to facilitate erection of structure using square tubing for columns. Columns hove equally high strength in both x and y directions, plus excellent torsional resistance. Connections combine welding ond erection bolting.


Unique roof suspension system com- biner with "tubular" design of members and weld fabrication to provide vast unobstructed area and light oiry atmosphere to the Tulsa (Oklahoma) Exposition Center. In photo above, slag is being chipped from root pass on splice of built up box-section roof girder, prepora- tory to making main f i l l passes.

1. GENERAL REQUIREMENTS

The knee is an irnport;~nt part of a rigid frame and some thought should be given to its design.

The knee of any rigid frame must be capabl~a of- 1 . Transfining the end nmnent from the beam

into the colomn. 2. Transftming thc vertical shear at the end of the

beam into the colurnn. 3. Transferring the horizontal shcar of the column

A kner differs from the usual straight beam in these rqxx!ts:

1. The l ic~~tral axis shifts toward the inrrt.r flange, causing nn incrcnse in the i l s d l x d i n g Forces at this point.

2. Axial Range forws must change dircction, causing radial forces to he set 11p.

2. EVALUATlON OF KNEE TYPES

IQuro 1 illustratt~s thc fin. principlil types of knees into the beam. for rigid frames.

(a] Squoie corner [b) Square coiner w ~ t h bracket (c) Topered haunch

(d ) Tapered hclutich je) Curved homch

FIGURE 1


,0002 ,0004 ,0006 .0008 0010 ,0012 ,001 4 .a016 .[

Unit ongulor rotation (+). rodiondin.

FIGURE 2

I t might he thought that the simple square type of knee connection would naturally he as rigid as the connc.:cting members, since it is a continuation of the same section. In many cases, this is true. However, stress causes strain, and the accumulation of strain over a distance results in a movement of some kind: deuection, angular movement, etc. This means that the sharp comer of this joint increases the stress in this region by several times. This stress concentration resdts in a higher strain and, therefore, grcater movement in this local region.

With the square type of knee in which just Uange stiffeners are addcd, it is difficult to cxcccd the stiffness of the member. In most cases it will just equal the

member, and in some cases it will he less. Figure 2 shours moment-rotation curves of various

knee connections.* The vcrtical axis is the applied moment; the horizontal axis is the rcstsolting rotation of the connection. The vertical height of the curve represents the maximwn or ultimate strength of the connection. The slope of the straight portion of the curve represents the stiffness of the connection, with the more nearly vertical con7es being the stiffer. The right-hand extremity of the curve represents the rota- - *Figure 2 adapted from "Connections for Wolded Continuous Portal Frames", Sccdle, Tripractsoglon, and Johnston; AWS Journal; Part I July 1951, Part 11 August 1951, and Part I11 November 1952.

igid-Frame Knees (Elastic) / 5.1 1-3

l l i l i l i l l l i i l l i i i i l l l l i l l l i l i i

Frame under load

v v

Point of inflection; zero moment

Moment diagE

points of reflection; , no moment opplied

v

Portion of knee in testlng machine, subject to compressive force (F) to duplicate actual load conditions in frame

v F

FIGURE 3

increase slightly, with slightly lower rotational capacity. tional capacity of the connection.

Notice that the square-comer knee is the most flexible. It falls slightly short of the beam itself, but it does have the greatest rotational capacity. Tapered haunch knees (not shown here) and those with the additional bracket have greater stiffness and higher mornent capacity, but less rotational capacity. The curved knees are the most rigid, have the highest moment capacity, and have a rotational capacity somewhere between the simple square corner and the haunched knee. As the radius of curvature of this inner flange is increased, the stiffness and moment capacity

Another purpose of the hannched and curved knees is to rnovr the connection to the beam back into a region of lower mon~ent so that the beam will not be overstressed in bending.

The dimensions of the test knm are so chosen that they ~ x t e n d out to the point of inflection (zero moment) of an a c t ~ ~ a l framc; Figurc 3.

In this manner, the ttxting machine applies a compressive force ( F ) which becomes the component of the two forces V (vrrtical) and H (horizontal) which would actually he applied to the knee at the frame's point of infl~ction.

5.1 1-4 / Welded-Connection Design

3. SHEAR IN CONNECTION shear into the connection web within the distance equal to the depth of the connecting member, the resulting

An axial force (tensile or compressive) can transfer shear stress within this counection web is- sideways out of one elemcnt of a ~nember as shear. For example, the tensile force from the beam flange will transfer down through the connection web as shear -1 . . . . , . , , . . . . . . , . . . . (1)

into the supporting column; Figure 4.

If this shear stress exceeds the allowable for the - e F b A web, it must be rcdnced by increasing the web thickness

within the connection area. Or, a pair of diagonal stiffeners must be added to transfer some of this flange form as a diagonal component.

One method of detailing this connection is to cal- ... culatc the imrtion of the flangr force which may be

I I

FIGURE 4

where the flange force in the beam is-

and the flange force in the column is-

transferred as shear within the web by stressing it to the allowable. Then, diagonal stiffeners are detailed to transfer whatever flange force remains.

Anotlicr method is to assume that the shortening of the diagonal stiffener under the compression component is equal to the diagonal shortening of the web due to tire shear strrss. From this, the resulting shear stress ( r w ) in the web and thc compressive stress (US)

in the diagonal stiffener may be found for any given set of conditions.

Derivation of Stress Values

The final diagonal dimension (d l ) of the web, due to shear action on the web, will be-

d 2 = d" + dC2 - 2 db d, cos (90' - y )

but

cos (90" - y ) = cos 90" cos ( y ) + sin 90" sin ( y )

Assuming this flange force (F ) is transferred as - - sin y

. .

--- Initial conditions of y = T/G = E Finol conditions of

stiffener and web Final conditions of web stiffener

FIGURE 5

Rigid-Frame Knees (Elastic) / 5.1 1-5

For small strains (t,) and angles ( y ) -

sin (7) = tan ( y ) - - 6

Hence:

7 d12 = c$ 2 I d L 2 <I,, d , h i c and E,

7 d, = 4 d 2 d,% - 2 dh d" - hut

E,

sin 0 db == dC tan 0 -- &-- cos 0

sin2 0 T sin 0 dl = d"-- 4. &'- " 2 --

e cos? 0 C E, cos 0

d, - T - 1 - 2 sin 0 cos 0 cos 0 ER

Thc final dimension of the diagonal stiffener (dz), due to compression, will be-

Since the movemeot-

A =.: E d,

Since diagonal stiffener and web are attached, the final diroension of diagonals in each case must be equal:

Squaring both sides:

T 1 - 2 =- sin 0 cos 0 =

or I Since for steel:

7 -- sin 0 cos 0 = E = 30,000,000 psi E, E, - 12,000,000 psi

.'. E = 2.5 E.

and the compressive stress in the diagonal 3tiEener is-

Now we go back to the flange force (F) since it causes this load on the connection region.

The flange force of the beam is equal to the shear force carried by the web plus the horizontal component of the compressive force carried by the diagonal stiffener.

u. = 2.5 T sin 0 cos 0

Subytih~ting ( 2 ) into ( 3 ) gives-

F = 7 t, d, + (2.5 T sin 0 cos 0) A, cos 0

= T [tW dc + 2.5 A, sin 0 cos2 01

. . . . . . . . . . . . . . . . . . ( 2 )

or, the shear stress in the connection web is-

F 7 = I t, d,. + 2.5 A, sin 0 cosY 0

Also, from (2)-

ux T = 2.5 sill 0 cos 0

Substituting this into (3)-

i t w 6 + rs As cos 0 2.5 sin 0 cos 0

tw d, .

= - ( 2.5 sin 0 nu 0 -t 4, cos 0

or; the compressivr. stress in the diagonal stiffener is-

Some knees are more complex than those described here and analysis most consider factors that are covered more adequately in Section 2.12, Buckling of Plates.

0, = - t, d" -- - . i A, cos 0

2.5 sin 0 cos 0

To check stiffener requiremcnts on the square knee connection shown in Fignrc 6, for the loads indicated. A36 steel and Ei0 welds are used.

. . . , , . . . . (5)


-L 14" UZ 84+ column

I tw = 451"

FIGURE 6

Here:

14.18 cos 0 = :-- = ,561 25.33

20.99 tan 0 = - = 1.480

14.18

flange force on the beam

- 117.6 kips

ethod 1

hor i z~n td component carried by u e b in shear

F, = T t, d,

= (14,500) (.45l)(14.18)

= 92.8 kips

This leaves (117.6 - 92.8 =) 1.4.8 kips to he carried hy the horizontal component of the comprcssivc force on the diagonal stiffener.

compresrice force on stiffcrm

required ~ec t ioml area of stiffeners

- - (26.4) -- ( 22.0)

= 1.2 in.' (pair)

Also required:

b,/t, = 17

Hence, nse a pair of ?*it' x 3" diagonal stiffcners. - - - .

Checking this size against the requirements:

A, = 2 x %" x 3"

= 3.0 in.' > 1.2 in.' OK -

ethod 2 Plastic Design (See Sect. 5.12)

required thicknrss of connection web

This exceeds the actual web thickness of t, = ,451". so stiffening is required.

= 5.64 in.' (pair)

Use a pair of V4" x 4" diagonal stiffeners. -~ ---- ~~~ ~. ~ .. .

Checking this size against the requirements:

A s - . - - 9 3/21 1"

= 6.0 in.? > 5.64 i n . 0 K

= 26.4 kips


ethod 3 Start with a pair of 'A'' x 3" diagonal stiffeners and, assuming both diagonals contract the same amount urrdrr load, check stresses in web and stiffener.

shear stress in web

7 = F -- t, d, + 2.5 A, sin 0 cos2 0

compressiue stress in diagonal

u. = F t, d, -- + A, cos 0

2.5 sin 0 cos 0

= 14,200 psi

As a matter of interest, increasing the size of the diagonal stiffener to 3/" x 4" would decrease these stresses to-

T = 11,400 psi

06 = 13,250 psi

4. COMPRESSIVE FORCES IN CONNECT1 WEB

An axial force is able to change its direction if suitable resisting components of force are available.

In the square or tapered haunch, this abrupt change

A F, Rodiol cornpresslve

in direction of the compressive Range force is accomplished by means of a diagonal stifleuer; Figure i ( b )

In the curved haunch, this change in direction of the axial force is uniform along the curved edge of the flange and resnlts from radial con~pressive forces in thc web; Fignre 7 ( a ) .

The force in the inner flangc of the knee is greater than the force in the outer fiangc because: it has a smaller radius of curvature. Iisually this inner flange is the compression flange; therefore, this is the region to be checked for stiffening requiremonts using the following formula for radial compressive forces in the web.

In this case, the unit radial force (f , ) is a function of the compressive force (F,) in the flange and the radius of curvature ( r , ) of the flange.

This action is similar to the radial pressure applied to the rim of a pulley by the tensile forces in the belt.

As the radius of curvature decreases, these forces increase.

As this change in direction of the flange becomes more abrupt, as in a square or tapered haunch, these radial forces are concentrated into a single force. And, they must be resisted by a diagonal stiffener; Figure 5@).

The axial force in the flange is assumed to be uniformly distributed across the width, therefore the radial pressure or stress is-

F f, = 2 lbs/linear in. of web

ri

Diagonal resisting

F< = a A,

. . . . . . . . . . . . (6)

FIGURE 7


When applied to the flange, this radial stress will Also: load any cross-section as a cantilever beam, since it i s M = u t S Where: supported only along its centerline by the web; Figure 1" tf2

ut t12 S=-- 8. - - 6 - or

h

ut t f 2 0- ti b12 6 -

and & inner flange 8 r,

3 u bf2 F T X

b - b + 4 From this relationship, it is seen that in order to hold the transverse tensile stress (u,) to a value not exceeding the axial compressive stress of the flange (u),

FIG. 8 Cross-section of lower flange and web. the following must be held:

The bending moment along the centerline of 1 beam flallge due tn th;. ~~ai .1 lnla Y ~ ~ I I he.

the . . . . . . . . . . . . . . . . . . . . . . v ... *" .-.*.-a ."-- (81

YX bi2 - -- - - \ - I 8 If this value is exceeded, stiffeners would be used between the inner compressive curved flange and web.

- G- tf hr2 - .-

ri 8 bl = width of flange

tf = thickness of flange

ri = radios of curvature of inner flange

ut = transverse tensile stress in flange

a = axial compressive stress in flange

Radiai compressive force exerted

by web ,

/ \ Tionweire tensile

stress due to bending I I J of fl..,.

FIGURE 9


FIGURE 10

This analysis assumes a uniform distribution of stress across the cross-section of the flange.

If this is based on plastic design, the plastic section modulus ( 2 ) is used instead of section modulus (S), where

Then (7) becomes the following:

Bleich has carried this analysis a little further; see Figure 9.*

Because of the slight yielding of the flange's outer edge, there is a non-uniform distribution of flange stress (u ) . This compressive stress is maximum in line with the web. In the following formula, the value of a

comes from the graph, Figure 10.

The transverse tensile bending stress (u,) in the curved flange is found in the following formula; the value of p comes from the graph, Figure 10.

If this value is too high, stiffeners should be welded between this flange and the web. These keep the flange from bending. These stiffeners usually need not extend all the way between flanges, but may be a serics of short triangular plates connecting with the curved flange.

The unit radial compressive force (f,) which acts transverse to the connecting fillet welds between the curved flange and the web is found irom- - * Fmm "Design of Rigid Frame Knees" F. Bleich, AISC

curvature

' """' Sirerr on inner flange

2

Inner face of Ronge

(b/

1 FIGURE 11


F f, = - Ibs/linear in. I ( 2 welds)

F RADlUS OF CURVATURE ON STRESS IN INNER CORNER

A straight beam has an infinite radius of curvature ( r = m ). As the b e d becomes curved, this radius decreases, and thc 11eutral.axis -na longer coincides with the center of gravity, but shifts toward the inner face. See Figure 11 (a) .

Because of the shift of the neutral axis, the bending stress in the inner flange increases greatly while the bending stress in the outer flange decreases. This increase at the inner flange becomes more severe as the radius of curvature decreases.

In a squarsknee connection, this radius of curvature is provided by only the reinforcement of the bevel groove weld or fillet weld on this inside comer; Figure 11 ( b ) . For this reason, the square knee may not quite develop the full plaqtic moment of the connecting member unless it is somehow reinforced.

If for some reason a reversal in moment should be applied to the knee and the inner face of the lnee is subjected to tension instead of the usual compression, it is important that this be a good sound weld. This is especially true at the surface of the weld. If the knee is loaded up to its plastic moment, the metal within the section below the weld is stressed up to its yield strength. During this time, the weld undergoes a considerable amount of plastic yielding and some strain hardening. The weld metal does have the ability to elongate about 28% as measured in 2" before failure. However, this zone in which the yielding is confined is very narrow, being the width of the weld. Consc- quently, the overall movement of the connection due to plastic yielding of the weld is very low, although s&~cient.

In this case almost all of the weld's ability to elongate may be used in developing the plastic moment of the connection. Any defect in the weld which would lower its ductility would probably prevent the connection from reaching its plastic moment. The knee could have greater strength and rotational capacity if this inner face were changed to a haunched or curved knee section. In testing these square knees in tension, plastic moment was reached when this weld was of good quality. Fortunately most knees are stressed in compression at this inner comer, without any tendency for this weld to fail.

6. LOCATING SECTION OF HAU CHECK

Most theories concerning the strength of knees differ only in the placing of the neutral axis, and in locating the resul~ing section for determining the section modulus.

FIGURE 12

One method, Figure 12, uses straight sections normal to the axis of either the beam or column. The section modulus is dctcrmined about an axis through the center of gravity of the section. The resulting stress in the inner flange is increased by the factor

where 4 is the slope of the flange. Although this method is easy, it might indicate excessively high stresses when the flange has a rather steep slope.

FIGURE 13

Another method, Figure 13, is to extend the centerlines of the beam and column to intersed in the knee. Straight sections are used, and the section modulus is determined about an axis lying on this centerline. This will give conservative values for the stress in the sloping flange. Because of this, no factor is used for the stress on the sloping flange.

A more accurate but longer method, Figure 14, is based on a curved section forming a wedge beam by

Rigid-Frame Knees (Elastic) 5.1 1-1 1

FIGURE 14

W. R. Osgood* and aodified by H. C. Olander.** - * "Theory of Flexure for Beams with Nonparallel Extreme Fibers'' by W. R. Osgood, ASME Vol. 61, 1939. **"Stresses in the Comers of Rigid Frames" by H. 0. Olander, ASCE Transactions Paper 2698, 1953.

Method of Using a Straight Cross-Section

Dimension of Straight Section The dimensions of a straight sec%ion (A-B) of the haunch may be found from the following:

Here:

Bending Stress in Curved Flange (See Figure 16.)

v = r sin ( 2 a;)

Here:

b = a cos d,

. . . . . . . . . . . . . . . . . . . . . (13)

fa fa = ------- cos d,

fb a,, = - b x I"

- fa -- 1 x -- cos d, a cos d,

FIGURE 16

FIGURE 15


P'

H

(a) Curved knee (b) Tapered knee

FIGURE 17

FIGURE 18

Here: \,

. . . . . . . . . . . . . . . . . . . . . . . . . . (15)

. . . . . (16)

. . . . . (17)

Wedge Method of Determining Section

The wedge method may be used on any beam section whose flanges are not parallel.

A curved section (A-R) is constructed where the stresses are to be checked. This is normal to both gauges and has a radius ( p ) the center of which lies

. . . . . . . . . . . . . . . . . . . . . . . . on the straight flange. See Figure 17. 1- (18) The transverse force (P i ) , axial force (P,'), and

moment (M') acting at the apex ( C ) of the wedge are . . . . . . . . . . . . . . . . . . . . . . . . found. See Figure 18. ( d , l (19)

d - + r[l-cos ( 2 a ) ] P = s i n T 2 a ) sm ( 2 a )

d = - r[l-cos ( 2 cc ) ] tan (2 a ) sin ( 2 a )


transuerse force applied to wedge at point C

(P{ = pi cos a - Pa sin cc 1 . . . . . . . .

axial force applied to wedge a t point C

moment about point C

M' = 3- P t m + Pa- -,"I . . . . . . .

the curved haunch section, as described in following paragraphs.

. (20) M a m e o t (M') Applied to Wedge M e m b e r

The horizontal bending stresses (u,,) resulting from the applied rnommt ( M ' ) , Figure 19(a), may be replaced

. (21) with its two components: radial bmtiing stress (a,) and tangential shcar stress ( T ) , Figure 1Y(b). In Figure lY(c) arc shown the resulting stresses.

It is seen in taking moments about the apex (C)

. (22) of the wedge that all of the radial bending stresses pass throngh this point and cannot contribute to any moment. The tangential shear stresses along the curved

These applied forces result in various stresses on section (A-B) acting normal to, and at a distance ( p )

(a) Resisting horizontal bending stress

(b) Components of (c) Resisting radial bending stress (a,) bending stress normal to curved section (A-8);

also tangenfiol shear stress (7)

FIGURE 19

(a) Resisting horizontal (b) Components of these (c) Resisting rodial bending bending stress and two stresses stress (u,) normal to curved vertical shear stress section (A-B)

FIGURE 20


u ~ i l produce an eqnal and oppo~ite moment. The value of this tangentla1 shear force ( V ) acting on this cr~rved section (A-B) may he found from the following:

Transverse Force IP,') Applied t o Wedge Member

The applied transverse force (P,') results in horizontal bending stresses (cr,,) as well as vertical shear stresses; Figure 20(a).

These two stresses may he completely replaced with a single component, radial bending stress (err); Figure 20 (b ) . The results are shown in Figure 20(c). Notice that no tangential shear stresses are present.

Axial Force (Pi) Applied to Wedge Member

The axial force (P,') applied a t the apex of the wedge member, causes radial stresses to occur along the curved section (A-B); Figure 21. There are no tangential shear stresses from this force, because they cancel out.

Summary

The effects of all these forces applied to the wedge member may he summarized as follows:

shear stress on section A-B

(a) Resulting axial stress

moment applied to section A-B

normal stress on inner flange

normal stress on outer flange

I Problem 2 1 To check stresses and stiffener requirements on the knee connection shown in Figure 22, for the loads indicated. A36 steel and E70 welds are used.

STEP I : Check Lower Curved Flange (Figure 23)

properties of haunch section (1-1)

Use reference axis (y-y) through centcrline of web plate.

(b) Components of axial stress (c) Resisting radial stresses (crJ

FIGURE 21


FIGURE 22

FIGURE 23

Ided-Connection

average stress in lower curved flange at (1-1)

P M ct Uf = -

A '-1-

(150 kips) (100" x 100 kips) (!Z3.1%") -- -- -- - (41.6%) +- (15,153 in.")

= 18,870 psi (compression)

force in flange

F, = ur At

= (18,870) (10)

= 188.7 kip?

radial pressure of flange againsi web

radial compressive stress in web

- - (1887 Ibs/in. ) ( W ' )

= 3774 psi

The outer edges of the lower curved flange will tend to bend away from the center of curvature under this radial pressure, and will cause an uneven &hi- hution of flange stress.

The maximum flange stress will be-

and the transverse bending stress in the flange will h e

-t = p Urn,,

The values of a and /3 are obtained from Figure 10. In this case,

and we find- - = .96 p = .70

Hence:

maximum flange stress

transverse bending stress in flange

0-t = p u r n a x

= (.70) (19,600)

= 13,760 psi

These stresses are a little high, so radial stiffeners will be added between the lower curved flange and the web.

STEP 2: Check Nounch Section tor Bending Stress Using Olander i wedge method and curved section (A-B) (See Figure 24.)

Here:

sin 1.8" = ,30902

cos 18" = .95106

tan 18" = ,32492

sin 9" = .I5643

cos 9" = ,98769

18" = ,31417 radians

dimensions of wedge section (ABC)

I Haunch I I section

= 19,660 psi Wedge section (ABC)


, 8 e ~ 8 c ' ~ Point of inflection in beom (M = 0)

Point of inflection

, in column [M = 0)

M' = + 14,456 in-kips

d r = .:.-- +-;- (1 - cos 2 = ) sm 2 a sm 2-

= 161.79 + 15.84

= 177.63"

d, = p 2 a

= (177.63) (.31417 radians)

= 55.81''

Hounch section (A-8)

FIGURE 24

d r n ( I - c o s 2 a )

tan 2 a sin 2-


m = u - n

= 25" - 138.04" - - - 113.04"

properties of haunch section (A-BJ

Use reference axis (y-y) through centerline of web plate.

Total

Find forces applied at apex ( C ) of wedge section (ABC) :

transverse force at C

Ptf = Pt cos a - P, sin a

= (150) (.98769) - (100) (.15643)

= 132.5 kips

axial force at C

Pa' = P, cos a + Pt sin a

= (100)(.98769) + (150)(.15643)

= 123.5 kips

moment about C

These forces result in the following stresses on the haunch section (A-B) o£ the wedge (see Figure 26):

FIGURE 26

shear stresses in section (A-B)

M ' v = - P

- ( 14,456) - (177.63)

= 81.35 kips

V Q - V[Atyr + Awywl 7 = -- -

1 tw I tw

- (81.35) (7.5 x 28.975 + 14.3 x 14.3) - .- -

(19,686) (35)

= 1800 psi

moment applied to section (A-B)

M = M' - Ptr p

= (114,456) - (132.5) (177.6) - - -9082 in.-kips

nonnal stress on inner flange

- (123.5) (-9082) (26.46) - - - + (44.53) ( 19,686)

- - - 15,000 psi

normal stress on outer flung?

.- - (123.5) (-9082) (29.35) - - (44.53) (19,686) --

= -+ 10,300 psi -

As an alternate method Clzeck Haunch Section for Bending Stress Using Conventional Struigllt Section (A-B)

(See Figure 27.)


v = 3(

U = -

Here:

v = r sin ( 2 a )

= ( 100) ( ,30402)

= 30.902"

FIGURE 27

c, = 28.872" c, = 26.008"

moment applied to section

M = (150) (55.902) = 8385.3 in.-kips

d, = d +r (1 - cos 2 a )

=: (50) --I- (100) (.O488)

= 54.88"

properties of hnrrnch section (A-B) o = - 13,800 o' = 15,280

Use reference asis (y -y ) through cmtcrlirre of web.

tensile bending nnrl axial stress in outw flange

-+ 10,550 psi, tension

I FiGURE 28

compressii;e bending and uxiol stress normal to section

Plate

in inner flange

M = A - y

- - 13,800 psi, corriprcssion

I, z Mey A y


(a) Bending stresses in haunch using curved wedge sections, bored on Olander method

stress nom~nl to axis of czmed flange

LT u' =

cos' 2 a

-. 13,800 -

(.95106)?

= 15,260 psi, compression ~

(b) Bending stresses in haunch using conventional straight sections

FIGURE 29

STEP 4: Summary

Fignre 19 summarizes the stresscs at several sections of the haunch for botlr the \vetlge mt:tliod and the conventional method using straight sections.

Tho \vedga inetliod gives results that check close with experirriental results, although it does require more time. The conventional rnctliod nsing straight sections in which the stress oil the inward c~inved flange is increased to acconnt for the sloping flange is easier. No\vever, rrotc that it does give lriglier values for the steeper S I O ~ R .

1. INTRODUCTION TO PLASTIC DESIGN

Thc allowabli. stress used on steel structnres in hendiug is .GO rr,. a percantage of the steel's yield strength (AISC Scc 1.5.1.4). A steel structure desigued on this basis may carry an overload as great as 1.67 times the designed load before the most stressrd fiber reaches the yield point. Katurally, this does not represent the maximum lond-carrying capacity of the structure, nor does it indicate. the reserve strength still in the structure.

Plastic design does not make use of the conventional allowable stresses, but rather thc calculated ultimate load-carrying capacity of the structure.

With this method, the given load is increased by 1.70 times the given live and dead load for simple and continuous beams, 1.83 times the given live and dead load for continuous frames, and 1.40 times these loads when acting in conjunction with 1.40 times any specified wind or earthquake forces. Then the members are designed to ccary this load at their ultimate or plastic strength. Some yielding must take place before this ultimate load L reached; however, under normal working loads, yielding will seldom occur.

For the past 25 years, a considerable amount of research, both in Europe aud the United States, has been devoted to the ultimate load-carrying capacity of steel structures.

For about 15 years, extensive work on fiill-scale structures has beerr going on at Lehigh University under the joint sponsorship of the Structural Committee of the Welding Research Council and the American Insti- tute of Steel Construction. Much has been learned as a result of this work.

ojor Conclusions

The ultimate load-carrying capacity of a beam section is much greater than the load at yield point. For many years, it has been known that a beam stressed at its outer fibers to thc yield point still had a considerable amount of reserve strength before final rupture or collapse. Consider Figure 1.

In this graph for A36 steel, the vertical axis is the applied moment ( M ) , the horizontal axis is the resulting angle of rotation (+). Within the elastic limit ( B ) ,

thew is a strzrigllt-line relationship. It is assu~ncd that the I~ending stresses arc zero along the ntwtral axis of the bram and incrcase linearly until thry are maximum at the outrr fihcrs. This is illustrated at the top of the figure. At poiirt ( A ) , the maximum outer fiber bending stress has reached 23,000 psi. .4t point ( B ) , this stress has reached the yield point, or 36,000 psi, and yielding at the outer fiber starts to take place. In couventional design, this point is assuined to be the ultimatc load on the member; however, this mrve shows there is still son~e more vcserve strength left in the beam. As the beam is still further loaded, as at ( C ) , the outer fibers are not stressed higher, but thc fibers down inside the beam start to load to the yield point, as in (D) . At this point, tlie beam becomes a plastic hinge; in other words, it will undergo a considerable amount of angle change with very little further increase in load.

M, is the moment yield point (B) , and M, is the

4 36 Sfeei

8 ---

?L $6 iangla of rotation)

FIGURE 1


no load

!st plastic Mr * hrnga formed

0 a t center

r-+-l becomes arch

h i nge

plaastic hinge

hinge

FIGURE 2

plastic moment which causes the beam at point ( D ) to act as a plastic hinge. For a rectangular cross-section, the plastic moment (M,,) is 1.5 times the moment at yield point (M,). For the standard rolled W F sections, this plastic moment (M,,) is usually taken as 1.12 times the moment at yicld point (M,) . The multiplier varies for other sectional configurations.

Redistribution of moments causes other plastic hinges to form. In Figure 2, a rigid frame with pinned ends is loaded with 21 concentrated load at midspan. The frame w-ith no load is shown in ( a ) . The frame is loaded in ( b ) so that its maximum bending stress is 22,000 psi, the albwnble. Notict: from the bending diagram that the moment at n~idspan is grratcr than thc momcnts at the ends or knees of the frame. The three marks at midspan show the moment M where u = 22,000 psi, or allou-able; My where u = 36,000 psi, or yield point; and M,, at plastic hinge. Notice at the left knee how much more the moment can be increased before a plastic hinge is formed.

In ( c ) the load has hem increased until a plastic hinge has becn formed at midspan. The knees of the frame in this example have only reached about half of this value. Even though, with conventional thinking,

this heam has scrvcd its us(~fnlness, it still will not fail hecnusc the txvo krwcs an- still intact and the frame now 1 ) ~ ~ ) m e s a thrt-r-hinged arch, the other two hinges bcing the original pinrrcd rnds.

Further loadirig of the frame may he continued, as in ( d ) , with the kners loading up ~rntil they become plastic hingcs, as in ( e ) . Orlly when this point is rc;ichrd would the whole frarnc fail. This condition is rt.fcrrd to as mcchaiiism; that is, the structure would dcforni app~~~$a l : l y with only the slightest increase in load.

This entire hin~c, adion takrs place in u small portion of the uoai1ol)L: clnngution of the membcr. In the lo\\-er portion of Figure 3 is a stress-strain curve showing the amouut of movement which may be used in the plastic range. This may seem large, but it is a very small portion of the u h d e cnrvt., as shown in the upper portion of tha figure, which is carried out to 25% d o n g t ' lon.

The working load is nzultiplicd by a factor of safety (1.85) to give thr? ultimate load. The dcsign of the structurc is bused on this ultimate load. In order to establish a proper factor of safety to use in connection with thr ultimate, load, as found in the plastic method of design, it worrld bc w d l to consider the loading of a simply supported beam with a concentrated load applied at its midpoint. This is shown in Figure 4. The moment diagrams for this beam are shown for the three loads: the inomcnt M causing a bending stress of 22,000 psi; thc moment My causing 36,000 psi or yield point; and the moment M, causing a plastic hinge. Here, for A36 stcel:

Allowable hending stress = 22,000 psi Yield stress = 36,000 psi = 67% above @ Plastic hinge occurs 12% above @

*) 2 , k---Plastic Ranye-- - - 3 2 1.30 I t i

I ZC G. I I , 1 I I

t :I , 2; o.,.,o-a P i b rio-2 0 - zo./oQ

Strain E /"/in

FIGURE 3

elded Connections for Plastic Design / 5.12-3

Momant Diagram

FIGURE 4

Hence:

@ ( . 6 7 ) ( 1 . 2 ) = 1.88 of @ Thus. the true load factor of safct\, of thn simide

beam is 1.88. -. In convei~tional design, it is assumed that thc ulti-

mate load is the value which causes the lxam to he stressed to its yield point at the point of maximum stress. This would bc represented in the figure by the moment at @.

In conventional design, if the allowable bending stress is 22;000 psi and thr yicld point of the (A3G) steel is assumed to bc 36,000 psi, the designer is actually using a factor of safety of 1.67.

l3y means of plastic design, the ultimate load is approximately 12% higher (in the case of a WF beam) than the load which causes the yield point to be reached. Therefore, the factor of safrty for plastic design on the same basis would be (1.67) (1.12) = 1.88.

Example m To illustrate plastic design, a hcam will be designed using thrcc difftarent mcthods: ( a ) simple beam, ( b ) elastic dcsign, rigid frame, and ( c ) plastic design, rigid frame Thc bcarn will have a span of 80' and carry a conctmtratd load of 55 kips at midspan. For simplicity the d w d load \vill hr rit$ectcd.

( a ) The siml~ly sripportcd beam is shown in Figure 5 with its monicnt diagmm. The mnxirnum momcnt for~nula is found in any beam table. From this, the reqnired srction modulns ( S ) is found to bc 600.0 in.3, using an a1lownl)le load of 22.000 psi in bendi~~g. This beam may be made of a 36" WF b r a n which woighs 182 Ibs/ft.

l Simpla Beam

moment diagram

FIGURE 5

= GOO in."

So, use 36" W F 18% beam with S = 621 in."

( b ) The elastic design, rigid frame is shown in Figrire 6. Its span is 80' end its height is 20'. Tllcre are several ways to s o h for the bending moments on this frame.

FIGURE 6

In this exn~nplc thc momrnt at midspan would be-

-- (,iS.O00) (SO x 12) -

7 (22,OW)

= 343 in.:'

So, use a 30" WF 124# beam with S = 354.6 in.3

The redundant or unknown horizontal force at the pinned end of the frame is first found. Then, froin this, the moment diagram is drawn and the maximum moment found. The required section ~nodulus (S ) of the frame is determined from this maximum moment.


This is foiind to be 343 in." wliich is 55% of that required for the single beam. This hfam could be made of a 30" WF beam having a weight of 124 lhs/ft.

( c ) The plastic design, rigid framc is shown in Figure 7. With this method, the possible plastic hinges are found which could caust: a mcchanis~n or the condition whcrrby the strocti~re beyond a certain stress point wonld deform appreciably with only the slightest increase in load. These points of plastic hinge, in this example, are at the midpoint and the two ttiids, and are assigned the \.due of M,,. An expression is needed from which this value hl, can be found.

Plastic dasign PL /-M= 7

FIGURE 7

Here:

= 1017.5 ft-kips

So, use a 27" W F 114# beam, with plastic moment (M,) of 1029 ft-kips. (See AISC Manual of Steel Con- struction, Plastic Section Modulus Table.)

In this case, it is noticrd that the altitude of the overall triangle in the moment diagram, which is M,, plus M,,, is also thc same as that of the moment diagram of a simply supported beam with a concentrated load at its midspan, Figure 5. This can be fount1 in any

P L beam table. Hence, M, plus M , is set equal to - 4 . using for P the ultimate load which is the working load times 1.85. This works out to M,, = 1017.5 ft-kips as the ultiinnte load plastic momcut, at centrriine and at the two beam cnds.

* * *

Summary of Advantages

As a summary, here are some of the advantages of plastic desibm:

1. More accurately indicates the true carrying capacity of the structure.

2. Reqnires less steel than conventional simple beam constri~rtion and, in most cases, results in a saving over tlie use of conventional elastic design of rigid frames.

3. Requires lvss design time tlian does elastic design of rigid framing.

4. Result of years of research and testing of full- scale structures.

5. Has the backing of the American Institute of Steel Construction.

2. D E S I G N R E Q U I R E M E N T S OF T H E M E M B E R

Loads (AISC Src. 2.1) The applied loads shall be increased by the follow-

ing factor: 1.70 livc and dcad loads on simple and continuous

beams 1.85 live and dead loads on continuous frames 1.40 loads acting in conjunction with 1.40 times

any wind and earthqualie forces

Columns (AISC Sec. 2.3) Columns in continnous frames where side-sway is

not prevented shall he proportioned so that: I I

(AISC formula 20)

where:

I, = unbr;~ced lmgtli of column in the plane nornral to tliat of tlie ~nntin11011s frame

r = radins of gyration of coluinn about an axis n o r ~ n d to the p1;ine of the continuous frame

Stte the nomograph, Fignro 8, lor convenience in reading thc limiting value of L/r directly from the vnl~scs of P and P,.

The AISC fominlas (21) , (221, and (23) give tlie effective moment (M,,) , which a giviw sllape is capable of resisting in terms of its full plastic moment (M,,) when it snpports an axial force (1') in addition to its moment. See Table 1.

The maximum axial load (1') shall not csveed .60 P, or .60 u, A,, where A, = cross-sectional area of the column.

FIGURE 8-Limiting Slenderness Ratio of Columns in Continuous Fromes (Plastic Design), Sideswoy Permitted

LIMIT OF(%) FOR COLUMNS IN CONTINUOUS FRAMES WHERE JIDE SWff Y 15 NOT PREVENTED

EXAMPLE :

P = 1000 lC

Py = 4000'

READ jk = 35


TABLE 1-Allowable End Moments Relative To Full Plastic Moment of Axially-Loaded Members

case?

when P/Py 5 0.15

pz-=-q when P/P, > 0.15 AISC iormula 0

L when - < 60 and

- < .I5 then

Notes: See Tcbler 2-33. 3-33. 2-36 ond 1-36 for volvei o i B, G, K ond J

TABLE 2-33 (AISC Table 4-33) TABLE 3-33 (AISC Table 5-33) FOX sa XSI SrEcir lr" rirLo miai srrxr


TABLE 2-36 (AISC Table 4-36) TABLE 3-36 (AISC Table 5-36)

run 36 rsi mi.<,P,lo riais ixrxxr nFi, .

.A,. Dl. dl . .M.

M,

.M . .$I. ill. M.

- l ,

.' , 11 (3 44 6.3

16 4: i n 43 50

61 6 2 Sii 54 66

!>C 17 i x 10 611

6 , 62 Ci 61 Ui

F*, 67 ti* 69 70

71 72 73 71 75

76 77 78 79 80 -

- X

i.0:iB 1 019 1 070 1 ""I: 1 106

1 122 l i 4 l i 1 138 i 176 1 is:>

i ('13 1 132 1 211 1 271 1 290

1 310 1 310 1 :XI l 371 1 892

1 418 1 416 I (56 l '7" i 601

1 623 1 b46 i s 7 0 1 143 1 (117

i 64, 1 6,;s 1 591 i.716 1.742

1.mw 1 "94 1 S21 1 848 1 R76 -

91 92 Y:, 94 95

96 Y i 9" '9

100

in* 102 103 104 10s

106 107 108 ice t i 0

i l l ,I2 i i i i l l Lii

118 $17 i i 6 i i 9 i z i i -

If L/r > 120, the ratio of axial load ( P ) to plastic load (P,) shall be-

I (AISC formula 24) 1 Assuming depth of web = 9 5 d (depth of mem- h r r ) , the shear on web section at ultimate load is-

V" = t,(.95 d ) m, Shear (AISC Sec. 2.4)

Webs of columns, beams, and girders not reinforced by a web doubler plate or diagonal stiffeners shall be so proportioned that:

inimum Width-to-Thickness Rufios (AISC Scc. 2.6) When subjected to cornpression involving plastic

hinge rotation under ultimate loading, section clcments shall be so proportioned that: FIGURE 9


FIGURE 10

and when beam or g~rd r r is s~~hjected to axial force ( P ) and plastic bending moment (P, ) at ultimate load,

See nomograph, Figure 11, for convenient direct reading of d,,/t,\, ratio from values of P and P,.

Lateral Bracing (AISC Sec. 2.8)

Plastic hinge locations associated with all but the last failure mrchanism shall be adequately braced to resist lateral and torsiold displacement.

Laterally unsupported distance ( L ) from such braced hinged locations to the nmrest adjacent point on the frame similarly braced shall b~-

(AISC formula 26)

but nerd not be 1 t . s than 1- where:

r, = radius of gyration of meniher about its weak axis

M = the lesser of the moments at the ends of the rrnbraced segment

M -- - - the end momcnt ratio, positive when the

segment is brnt in single curvature and negative when bcnt in double curvature

In the usual square frame. plastic hinges would ultimately form at maximum negative moments at the coiners, and at thc maximum positive moment near the center of the span. However, a tapered haunch may develop a plastic liingc at the comer and also at the point wliere tlie Iraunch connects to the straight portions of the rafter or colunm because of the reduced depth of the momber. These also become points where lateral bracing must he provided.

3. BASIC REQUIREMENTS OF WELDED CONNECTIONS

Coilr~ections are an important part of any steel structure desihpcd according to plastic &:sign concepts. The connection must allow the members to reach their full plastic moments with sufficient strength, adeqrratc rotational ability, and proper stiffness. Thcy must be capable of resisting momcnts, shear forces, and axial loads to which tb(~y would he sul~jwted by the ultimate loading. Stiffcncrs may be rcquiretl to preserve the flange continuity of intcrrupted mmnhcrs at their junction with othcr mm1hrrs in :I continuous frame.

A basic reqiiiremtwt is that the web of the resulting cor~nectioo mirst provide adtynate resistance against blickling from ( a ) Shear-the diagonal compressive force resulting fl-om shear forces applied to the u ~ b from thc colrr~ccting flangt,~, which in turn are stressed by the end moment of the member, and ( b ) Thrust-any conceiitratrd compressive force applied at the rdge of the web from a11 intersecting flange of a member, this force rcsl~lting from the end moment of that member. See Figure 12.

In addition to mveting the above requirements, the connection should be so designed that it may be economically fabricated and w~h lcd .

Groove welds and fillet welds shall be proportioned

Welded Connections (or Plastic Design / 5.12-9


( 0 ) Web resisting shear

FIGURE 12

FIGURE 13

elded Connections for Plastic Design / 5.12-1 1

to rrsist thc forces produced at ultimate load, using an increase of 1.67 ovcr tiic standard a1low:lblcs (AISC Sec. 2.7).

Followiiig p;~g~:s cover first thr (itssign of simple two-way r(x:tangillar corr1t.r conn(~ctions, tapered lrarrr~clti:s, and cnrvtd I~aurrcht~s. Kext, tlrr design of beam-to-colrirnn <,mtncctions, wI~i,ther tlirce-way or four-way, is d c d t with.

r\nalysis mcl dcsign oi a particirl;~r conntsction may not always br as simple as those ill~islrat(d 011 tlicsc pages. Figure 13 slrows some other typical welded connections.

4. STRAIGHT CORNER C

The forces in the flanges of' both rnornbcrs at the connection resulting from the moment (hl,) are transferred into the contirction .iwh as shc:tr (V) .

Some of the vertical shear in thc hoam (V,) :md the horizontal shear in the column (V,) will also be transferred into the cotincction web. IIowr\er, in most cases these values are small compared to those resulting from the applied moment. Also, in a simple comer connection, these are of opposite sign and tend to reduce the actual shear valiio in the connection.

111 this analysis, only the shear resulting from the applied rnomcnt is considered in the web of the connection.

Diagonal compression

Fc = v

connecilon

FIGURE 14

The miitimiirn wi,h thickness rtqriir-1.d to assuro that the web of thc mniitr~i~liorr clots not huckle from the shear forces set "1' 1)) llw rnrimcltt applied to thc corinection (M, , ) , inay hi. fo~irrd froin the following:

unit shear force applied to mn~rer:fion n:eh

FIGURE 15

resulting shear stress in connection web

The values for the shear stress at yield (7,) may be found by using the Mises criterion for yielding-

uCr = J u? - u, my + uY2 + 3 rri2

In this application of pure shear, u, and u, = 0 and setting the critic;rl value (u,,) equal to yield (u , ) , we obtain-

Hence,

The nornograph, Figure 16, will facilitate finding this reqnired wcb thickness.

In ihc above:

M,, =: phstii. rnontc.nt at connection, in-lbs d ,, . . , .I t ptli of lwam, in.

d,. ..: d<q)tIi of c~~lt~irrri, in.-llx

w ;rctii:rl \ye11 tllickness in coirii<vtiorr arm, in.

w, = rcijtiircd web thicktress in connection area, in.

uF = yic,lcl str<.nglh or s t d , psi


Welded Connections for Plastic Design / 5.12-13

AISC uses an effective depth of the heam and column as 9.5% of their actual drpths to allow for the presence of plastic strain in thr flanges. due to con- current bending. .Applying this reduction to both the depth of the beam ( I ) and the col~imn (d,) , and also expressing the applic:d plastic moment (M,) in ft- Ibs rather than in.-lbs, this formula hccomes:

Here M,, = plastic moment, f t : h

For most wide flange ( W F ) stxctions, the web thickness ( w ) will he less than the required value (w,) above, and some form of stiffening will be required.

Web Doubler Plate

A web doubler plate, or a pair, may be used to bring the total web thickness up to the minimum (w,) obtained above.

Welds should be arranged at the edges of doubler plates so as to transfer the shear forces directly to the boundary stiffeners and flanges.

11_Ji plate

FIGURE 17

Diogonol Stiffeners

A sy~lin~ctl-icd pair of diagonal stiffeners may be addcd to this comcction to pirwmt the. wr,h imm hi~ckling. These stiffeners rr.sist cnoogh of the flangc forw ( F ) that the l-esdtirrg shcar ( ) xl~p1ird to this wrh is rechlccd sufficiently to prevcnt hnckling.

Stiffen~rs having a thickr~ess cqod to that of the rolled section flange of the heam or column nonually will be adequate, although this thickness will he greater than required. Thc minimum thickness of ilks stifrcner may be f o ~ m d frorn the following:

Thn horizontal flange iorce ( of the hearn is resisted by the combined effect of tlla web shear ( V ) and thc horizontal component of the mrnpressive force ( P ) in the stiffener.

where

and since

1 M w d & = - [ cos e --L dl, u,. - -&I I . . . . ( 1 2 )

where

e = angle of diagonal stiffener with horizon,

FIGURE 18


A. 7.: area of a pair of diagonal stifhers,

A, = b, t,

In t h~ : usnal detailing of the corlrrtxtion, the re- qtiirtvl wcb thickness (u,,) is first fonntl. The actual wab tlrirknrss ( w ) of course is known, therefore it would he simpler to change this fotmula into the following so that the reqriircd area of thc tiiagonal stiffener may be found from these two values (w,) and ( w ) :

From Formula 10,

and substituting this into Formula 12,

1 M, A, = -- .. - cos B [[dl o, fl

and since

d, cos B = d,

or could use

t, = t*

also in all cases

For full strength, stiffeners should be welded across their ends wit11 either fillet welds or groove welds, and to the connection web with continuous fillet welds.

To design a 90" connection for a 21" M7F 62# roof girder to a 14" WF 8411; column. Use A36 steel and E70 welds. Load from girder: M, ultimatc plastic moment = 432 ft-kips.

14" W 84#

column

Column Girder 14" WF841f 21" WF62#

dr -- 14.18'' 1 di1 = 20.99..

FIGURE 19

The required web reinforcement is determined as follows:

-

- c ( 4 3 2 ft-kips x 12) > ( i.

.- 20.99 ) (14.18") (36 ksi) 2 0.837"

web furnished by the 14" W F 84# col~l~nm = 0.451" --

effective web to be furnished by stiffeners 2 0.386"

This reinforcement may be provided by one of two possible types of stiffcners as noted below.

( a ) Web Doubler P la te

The additional web plate must be suflicient to develop the required web thickness. The welds should be arranged at the edges so as to transmit the shear forces directly to the boundary stiffeners and Ranges. Plate must be ,386" thick, or use a 5<n" thick 13late.

'- Web Plate Doubler

FIGURE 20

elded Connections for Plastic Design /

---l-T 21" W 6 2 2 432 X 12 F =

14.18 = 4 4 1 k 1

I I stiffeners 4" X '!4/ia" 1 20.99"

\ I L - - - - - - - Y

FIGURE 21

fbj Diagonol Stiffener

The diagonal stiffener will resist the diagonal component of the flange load as a compression strut. The flange force to be carrind by the stiffener is the portion that exceeds the amount carried by thc web. Assuming the bending moment to be carried entirely by the flanges, the compressive force in the diagonal stiffener is compnted as in Fignre 21.

Multiply this diagonal compressive force of 441 kips by the ratio of the additional thickness needed to that already in the web:

441 (g) = 204 kips h r a on diagonal stiffener

- - 204 kips 36 ksi

= 5.65 in.%eeded in the stiffener

or use a pair of %" x 4" stiffeners, As = 6.0 > 5.65 OK

Now solve this portion of the problem by using Formula 3:

db 8 = tan-' - dc

= tan-' 1.48

and

cos 55.03" = ,560

= 5.65 in.%eedcd in the stiffener

If b. = 8", thcn

= ,707" or use 3/4"

Or use two plates, 3/4" x 4", for the diagonal stiffeners. Check their width-to-thickness ratio:


Welds for Stiffener

Only nominal fillct welding is required between stitf- ener and connection web to rcsist buckling. These welds are rised simply to hold thc stiffeners in position. Welding at terminations of the stiffener should be sufficient to transfer forces.

To dt:velop the full capacity of the stiffener, it may be butt welded to the comers, or full-strength fillet welds niay be used.

Thp required leg size of fillet weld to match the ultimate capacity of the stiffener would be-

EGO Welds & A7, A373 Plate

2(9600 w j 1.67 = t, 33,000

o = 1.03 t,

E70 We1d.s & An6 Plate

Hence, use %" leg fillet welds acmss the cnds of the stiffener.

It may bc simplcr to make the cross-sectional area of these diagonal stifIenrrs equal to that of the flange of the member whose web they reinforce.

5. HAUNCHED CONNECTIONS

Haunched connections, Figure 23, are sometimes used in order to nlore nearly match the moment requirements of a frame. This produccs a deecpr section in the region of maximum momcnt, extending back until the moment is rcduced to a value which the rolled section is capable of carrying. In this manlier a smaller rolled section may be used for the remainder of the frame. This has been a rather standard practice in the conventional elastic rigid frame.

Haunched knecs may exhibit poor rotational ability if the knee buckles laterally before the desired design conditions have b'en reached.

The haunch connection should be proportioned with si~fficient strength and buckling resistance so that a plastic hinge may be formed at the end of the haunch where it joins the rolled member.

I

FIGURE 23


Lehigh University's extensive research in plastic design included the testlng to destruction of full-scale structures such as this 40' gabled frome

Plastic design of this 8-acre rubber plant simplified mathematical analysis of the structure ond moment distribution. Two results: a uniform factor of safety and a saving of 140 tons of structural steel.


FIGURE 24

Lower flange of beam

FIGURE 25


(See Figures 24 ;md 25, facing page)

Thickness of Top Flange and W e b of Haunch flangc'sthiicknms. Silrcl, this is the tc~rrsion flange, it will be same or thiinrer than the lower (co~npression) flange.

The thickness of the top flange nrrd the web of the It can he siionii that the pl;~stic swtion mo~iolos [ Z ) haunch slmild be> at least equal to the tl~ickness of the of an 1. section is: rolled beam to which it connects.

tension

Thickness of Lower Flange of Haunch

The lower flangc of the haunch must be increased in thickness so that when it is stressed to the yield point (u,), its horizontal component will be equal to the force in the lowcr beam flange stressed to yield.

The force in the sloping lowcr flange of the haunch a t the plastic moment (M,,) is-

Tc = u, hh ti,

The component of this force (T,) in line with and against the force in the beam Aange is-

T = T, cos p = u, b,, t,, cos p

and this must match the force ( T ) in the lower Aange

of the rolled beam, or:

T = u, bl, ti, cos p must equal T = u, bn tb

4ssuming the same flange width for the haunch as the beam, i.e. h , = bbr gives-

Transverse Stiff cners

T, = T, sin p

or us b, t,, = cr, bl, ti, sin p

Assuming the same flange width for the stiffener as the beam, i.e, h,, = b,,, gives-

AlSC suggests making the total area of these stiffeners not less than % of the haunch flange area (AISC Commenta~y p 37, item 4 )

Reguird h u n c h Section

Section (1-1 j, in the region of high moment, should be checked. The two flanges may vary in thickness, so for simplicity and a conservative value use the upper

Stress distribution at plastic moment (M,]

FIGURE 26

resisting plastic moment of section

dl, - 2 t d,, - 2 t + 2 I ( )(--i-) since

This increased plastic section modulus may be obtained by:

1. Increasing the dtyth (d, , ) and holding the Aange area constant, or

2, Increasing the iia~ige thickness ( t ) and holding the depth (d l , ) constant.

By assuming that (d, , - t ) is equal to ( d , - 2 t ) , and solving for the expression (d,, - 2 t ) , it is found from the above formula that:


Fmm this, the requind depth (d, , ) of the 1l:imich may brt io~inrl for any vehie of pl:tstic s < , c h n niodulus

(Z) . Thc 1i;iiinch s~,ctiori miist h? :rhlc to dcvt~lop the

plastic inor~icilt at any lmint ;rloiig its imgth:

, z u J . . . . . . . . . . . . . . . . . . . . . . . . . . (22)

or at any scctiou (x-x)-

Usuall\- just tlw two ends of thr: haunch must he checked. This would l x scction (1-1) at ille haunch point ( H ) , and scctioli (2-2) ;it the connection to the rolled beam. The latter finding will also dictnte the required section moriirlus of the straiglht beam, since its highest moment will occur at section (9-2).

Heedlr~' points orit that. if the moment is assumed to incrrnsr linerally Srorn the point of inAi:ction (0) to the haunch point ( H ) , and the distance ( 0 - R ) from the point of inflection to the end of the rolled beam is 3 d, then the critical section will always be along (2-2) if the angle P of the txpcr is greater than 12 ,; if this angle is less than 12", then section (1-1) must also be checked.

Laterol Stability

Bracing should be placed at the extremities and the common intersecting points of the compression flange. - *"Plastic Design of Steel Frames" Lynn S. Ueedle; John S. Wiley & Sons, publishers.

The cornniwtary of the AISC specifications scts the following lirnils for latvral I~racing.

The taper of' tli<, hau~jcli may br snch that the resrilhig hei~ding strcss 21t plnstic Ionding, wheu corn- p ~ i t ( d b y using thc plastic inodiil~is (%) , is approximately a t yield (q) at Ilotll cnds @ & @. If this is the caw, then Ii~nit ihr ur~l~r;rccd l~~rigth (Li,):

If thc bcntiing strcss :it orrc rnd is approsiinately at yield (cry), using the pl;isiic modulus ( Z ) _ and at the other end is I t s than yicld (my c: us ) when using the secton ~nodulus S , limit the ~inhraced length (LJ:

. . . . . . . . . . . . . * (26)

but

If the bending stress colnputed on the basis of section modulirs ( S ) is less than yield (us < IT,) at all transverse sections of the haunch from @ to 0, then check to sce that greatest co~nputed strrss:

Resisting shear forces in web of section ABCD

CD = - dh

tan (a + yj

FIGURE 27

Welded Connections Cor Plostic Design / 5.12-21

I

F& = A', q

FIGURE 28

Diagonal Stiffeners

Tlra tapered liamch has an extra-large web in the bend of the knee. This is subject to buckling, and should he strengthmi,d by di:~gonal stiff(m.rs. The required stiffener scction arca sho~ild be figtrrcd from tbr compressive force on the web diagonal r ( d t i n g fronr tllc larger of two forces: ( a ) the itmsilc forces on the outer ilange of the I~aumh at point @, and ( b ) the compressive forces on the inner flange of the haunch at point f& - ( 1 ) Based on tensile forces at @ The comprcssive force in the diagonal stiffcrier is fouird by taking thc sum of the horizontal components of the Forces in tllc outer Aanges nlid setting them equal to zero. Sce Figure 27.

+ At u, cos y - n.,, dt,

c O S y - A, a; cos a = 0 or

cos y A - 4

w,, ill, cos y

- t ( G ; ) - (n-tiirli <x -+ .; )z;;-

\vhero:

At : area of top (temion) flange of haunch

A, =- total area of a pail- of diagonal stiffeners

(2) Based on compressive forces at A 0 The compressive force in the diagonal stiffener is

found in a similar mnnncr as before; the horizontal components of the forces in tho inner flanges are set in cqrlilihriurn. See Figure 28.

4- A, r, cos u 4- A,? us sin P2 - A,, us cos (PI + y ) = 0

A,, cos (6 , 4- y ) - A,,? sin PL 4 -- - -- - . E - . . . . (29)

If .4, = !I,, = A,.,, tlris hecomes-

(31 When outer (tensile) flanges form right ongfe

If the beam and colrirnn are at right mgles to each other, y = 0. See Figme 29.

and ,O = Pi = P2 a z 15"

A, r: A,, = .4e2


Thc modifird formulas above may also be used for cor~venience in finding the stiffener requirement of gablo frames, bu t will provide a more conservative value.

Summary of Tapered Haunch

Wr 2 W L , ~ ~

t th 2 - cos p

Based on load from ttwsion flange-

FIGURE 29 A, f i ~ , - 0.82 \v,,d, Rased on load from vomprcssion flange-

A, 2 JT A, (cos p - sin p ) also b, , -

t. = 17

Then the preceding two formulas reduce to the following: b, t, 2 ti, sin p = -

17 based on tensile forces in outer flanges

tt, b', 2 3/s tbhb and shear reststance of web

WI, M I A, 2 O A , - 0 . 8 2 w,, d , , ] . . . . . . . . . . . (31) 4 Zl, = b t [dl, - t ) + - (d,, - 2 t)" 2 rr,

based on comprcssivc forces in inner flange Check laferal stability of compression flange

LA, 2 0 . 4 , (cos p -- sin /3)]

also

( a ) ii both ends of haunch @ or @ are stressed to (32) yield (c,) using Z

Here:


NNECTIONS

,8 = angle between tangents of given section and beam flange

r = radius of curvature of inner flange

d, = depth of curved haunch at any section (x-x)

= d2 -1 '(1 - cos PA) x = r sin p,

It is seen in F i p r e 331 that thc moment resdting from ultimatr: loading gradn:dly incrrvxrs ont to the corner of thc 1i:iurrch. IIowever, tlle dcpth of the ha~inch and therefore its hi~nding stress also increases toward tlie corner, so that the critical scction (x-x) witliin tho h;nmih will occ~ir at some distancc ( x ) or some angle (P.) El-om section 2-2. For most curvod h;runclics, this angle (p,) will he about 12".

Thickness of Top Flange and Web of Haunch

The thickness of the top fiatige arid of thc web of the hatinch should be at lenst cijn;iI to t ime fmtiires of the rolled beam to which it ronnrds. If bcniline stress .,

\I; at @, u? =- < c,, then the onter flange thickness S of tlie hnnncl~ ( t ) does not have to (weed the bram flange thickness (ti,) (AISC Commentary).

Thickness of Lower Flange ot Haunch

Tlic lower flange of tlie ht~uncli must b r increased in thickness so that when it is stirssed to yield (u,), its component along the bcem axis is equal to the force in the lower beam flange when stressed to yield.

FIGURE 32

5.12-24 / W e l d e d - C o n n e c t i o n Design

For any givcn depth (d,), the pkistic section moclu- lus (Z,) may be increased by increasing the flange thickness ( t,,) .

Assuming the web thickucss aud ilange width of tlie curved llaunch is at least equal to that of the beam, the required thiclcness of the lower flaugc would be:

As in tlie tapcred haunch, the phstic st,ction motl~i- lus ( 2 ) at m y given point ( X ) is:

W Z, = bl, ti, (d, -- t,) + -' (d, - 2 t,,)2 4

W Z, = b,, ti, (d, - ti,) + " i d , - 2 4

The l I S C Cominentary (Sec. 2.7) recommends that thc thickuess of this inner flange of the curved halnich should be-

. ( 3 5 )

where values Tor ( m ) come from the graph, Figure 33.

. l

3 4 5 6 7 n = a/d

FIGURE 33

Here:

a = distance from point of inflection ( M = 0 ) of the column to the point of plastic moment (M,,) in the haunch

d = depth of coh~mli section

In order to prevent local buckling of the curved inner flange, limit the radius of curvature t o -

FIGURE 34

This is based on a '30" knee (outer flanges fonn a right angle), which is the most conservative.

Thc radiiis of curvature may be increased above this limit if additional poiuts of snpport are added to decrease the critical arc length ( C ) .

The unbraccd length between uoints of lateral u

support must be held to-

where

C = r $

4 = radian measure

this lirr .. . lit, the tliidness of thc m w d iuucr ilauge nus t he iucrc:xsed hy-

or the final tlriikrcss will bc-

An ;iltern;it<. metliod wol~ld he to increase the width of the iiilwr fl;tilgc (h i , ) to a minimurn of C/6 -- -

* ASCli Commmt:iry on Plmtic Design in Steel, p. 116

Welded Connections for Plastic esign / 5.12-25

FIGURE 35

without decreasing the original Hange thickness (t , , ): A, u, = 2 A, u, sin (20.5" - y / 4 )

u

Diagonal Stiffeners

(1) Based on compressive forces at @ (2) Based on tensile forces a t @ An approximate value of the comprcsive force . .

appliod to the diagonal stiEener as a rcsult of the The compressive force in tile diagonal stiflener compressive forces in the ciirvcd inner Ransc may be is forrild taking tlIc llouizontal cornpo~ients of these made by treating the curved hauncli as a tapercd telisilc aarlSe forces, and settirig them equal to zero. haunch. Sec Figure 35. Sen Figure 36.

FIGURE 36

ws ds cos - -- uy co$ y tan( + y ) fl

- A, u, cos a: = 0

Resisting sheor forces in web of section ABCD


Radial compressive force exerted

Transverse tensile

> cos y A A, - W, di, I I . . . (43) COS a

where:

At = area of top (tension) flange of haunch

A. = total area of a pair of diagonal stiffeners

Radiol Support of Lower Flange

The radial components of force in the curved inner flange tcnd to lxsh tlre flange in toward the web, and to bend the flange as shown in Fignre 37(h). Because of the slight yielding of the outer edge of the flange, there is a non-uniform distribntion of ihc flange strcss ( r ) , Figure 37(a) . This stress is maximum in line wit11 the web. There is also a tl.a~~sversc tensile stress across the onter face of this flange, Figure 37(b) .

The unit radial form ( f , ) acting on the curved inner flange from the axial coinprcssive force (F,) within the flange, Figure 38, is-

F f, = 2 (Ibs/cir inch) r

Trcating a 1" slice of this flange supported by the web of the haunch as a cantilever beam and uniformly loaded with this unit radial force (f,), Figure 39:

FIGURE 37

stress due to bending of flange

FIGURE 38

or unit load ( p ) on section:

r, th p = 7--


FIGURE 39

ness (h,/t,) of thp mrved inner flange to the following, wlrichcver is thc sm;iller:

P~~ovicic s:ifimers : ~ t :ind midway bctween the two points of talqpicy. Make the total cross-sectional area of the pair of diagoiial stiffcncrs at their midpoint not less than % of the inner curved flange area.

Summary of Curved Haunch Requirements

thicklness of outer flange ( t ) ) ti,

web of lraunch (w,,) 2 wb

tb thickness of curved inner flange ( is) 2; - - cos p = (1 -t m ) t

(based on tcnsile fiange)

. cos y A, g WI, di, A, - -- cos " I

(based on compressive flange)

90 - y 2 2~~ sin (&-I and

. .

M ,> Therefor(. limit the ratio of flange width to thick- I i bending stress at @ u2 =- S < cr,, then


outer flange tliickni+ss ( t ) does not have to exceed beam flang~: (ti>).

Othrnvist~, usc additional lateral support to decrease arc length ( C ) .

Asswr~e ci-itical section (x-S) at-

p, = 1 2 O

then

and

x - M z 2 -=.

C 5 6 b , wliere:

C = r +

+ = radian measure

Otherwisc, increase the thickness of the curved flange to-

or increase the width of the curved inner flange to-

without decreasing the flange thickness.

. BEAM-TO-COLUMN CONNECTIONS (Multiple Span)

Web Resisting Shear

When the moments in two beams franring into an intcrior coliimri iliiier by a larger amormt, this difference in mommt d l c ; i~~sc largc shear forces to act on the conrrc,ction \veh. Tile \vvb must be cliccked to see if it has sutficiiwt thickness; if not, it must be reinforcrd with either a wi,h doublcr plate or diagonal stiffeners.

(See Figure 41.)

hori~omtul d ~ e u r applied on connection web

aloi~g top portion

= F, - PI - V,

shear resisted by connection web

along top portion

= w d, r y

where:

V, = horizontal h e a r force in the column above the connection, lbs

FIGURE 41


FIGURE 42

M, and M2 = moinrmts in bt::~ms (1) and ( 2 ) , in.-lbs.

d, - depth of coliiuin, in.

dl and d? = dcpth of beams ( I . ) and ( 2 )

w = tliickness CIE connection w b , i n

If it is assumcd that: 1. tlrc column li(:igiit (11) has a point of inflectioi~

at mid-hlbight, 2. the d q ~ t h of the larger beam (d2) is %r, of the

column bight ( I I ) , or less, 3, tlic yield strength of the stcel is u, = 33,000

psi, and 4, the unbalancrd morncnt ( h l ) is expressed in

fooi-kips, tiris for~nula will rcdwe to t11:: folloiving:

The method of detcrininirig the value of M is illustxatcd in Figrire 42,

eb Resisting Thrust

Stiffencis are qriitc ofiw required on members in line with the coniixessiorr ilii~qes which act against them, to ixeveni crippling of the web where the concentrated coinpressivc force is al~plied.

Wliera a heam sripportsa column, or a column slipports a beam, on just one fiange, the stiffeners on its web net:d only estmd inst bcyoncl its neutral axis.

'nie following formii1;is will indicate w1x:n stiilen- ers are required, and also the oecesswy sim of t ime stiffei~ors:

1. \Z't,l~ still(mws arc required adjacent to the beam

2. Wr.1, stificlri.rs ;ir(, rcqnirrd adjaccnt to the beam co~npmssio~~ ILiiig~ if-----

. . . . . . . . . . . . . . . . . . . . . . . . . . . . (49)

where:

A, = .. FIGURE 43 * t 1 , + 5 K c


also

FIGURE 45

If horizontal flalige platc stiffeners are uscd, F i g ~ ~ r e 45, their dimensions are found I'rorn the following:

where : A, = l l b X ti,

AI - \,I (ti, -+- 5 Kc) t > . s b.

w,. = reqiiircd tltickness of connection wch

. . . . . . . . . . . . (50)

(S r r Swtion 5.7 on (h t i i l uo r~s Coi~ncciions for fut-tlrrr cxpl;~tintion )

If vertical plate stiiieners are used, Figure -46: they s l i d r l he proportioned to carry tlic excess of beam flaiigc force ovcr that wllich the column web is able to can-y. It is assti~lied the beam iiange estends alniost thc fnli width of the co111mn Ranges, and that the stif-

frncrs arc only I r d i as effrctive, since they lie at the (Inter edge of tlic flange.

FIGURE 46

(See S<,ction 5.7 on Continrious Coiinections for hrtlicr exp1:ui:rtion.)

The niimngi-apli, Figrirt: 47, inn) bc riscd to find the dist:riice ( t , , -4- 5 K,) ovcr whicli the corrw~itr:~ted foi-c:e f n m tlic beait~ fiairg~ sp~-c.:tds nut into tllc c o l ~ ~ m n web, In tllc case of ;I h i l t -ui , colntnn, use the flangc iliickncss (t , .) and find the distance (t , + 5 t,) from thc ~iomogrnpli.

'I'his value of (t , , - 1 5 K,) or (t,, - 5 t,.) can then be used in fitiding [he required wc11 tliickncss (w,) from the nomogr;ipli, Figure 46.

Welded Connections for Plastic es%n / 5.12-31

FIGURE 4GThickness of Connection Web To Resist Thrust of Compression Flange.

If COLUMN FLANGE THICKNEJS z.7 EXCEEDS THIS VALUE OF (tc )- L?6 STIFFENERS ARE NOT REQUIRED 2,5 OPPOSITE TENSION BEAM FL4NGE

IF WEB THICKNESS OF COLUMN ( w c ) EXCEEDS THIS REQUIRED YALUE( +)- STIFFENERS ARE NOT REQUIRED 7 OPPOSITE COMPRESSION BEAM FLANGE wr

I

. . <

.' .

, , .

14" W34 *BEAM TO 8'' W35* COLUMN Af = 6.75 x.453 = 3.058 INz

HENCE NEED STIFFENERRS TENSON FLANGE

bb 45%) = 4.8 (FROM PREVIOUS NOMOGRAPH) I READ wr = .64 ACTUAL /5 ,315 " HENCE NEED STIFFENERS COMPRESSION FLANGE

Is r<.inforum~r,i?i nwcssnrv at this interior connection? h/fornet~ts at iiltiliiat<> load arc, sllovr-n t,clo\v. A36 steel

-

FIGURE 49

beam dimcrwioru

d, = 21.13" b b - 8.27"

Wb = ,430''

tb = ,685"

column clirnensioru

d, = 13.81"

w, = ,339"

b, = 8.031"

Kc := 1X6"

diagonal of cairncr.tioil web

dB == m -- = a - 1 3 ' T- 13.812

= 23.18"

The necessary web thickness will be determined by the AISC requirements for webs irr the connection region, The algebraic sums of thc clockwise and counter-clockwise moments on opposite sides of the coinlcction are:

ed Connections for Plastic Design /

M r-:- 460 ft-kips - 250 ft-kips

:= 210 ft-kips

and

M I - 0 l i p s + - 50 ft-kips

= 210 ft-kips

required thickness of conncction u:eb

f i ( 2 1 0 it-kips x 12) - ~ ~ ~. - (21.13) (i3.81 j(36 ksi) .

= ,416"

onclusions (Fig. 50)

( a ) This req~lil-cd n e b thickness would be satisfied if the beam were ;illowed to lun through the column. This would give :i web thickness of ,430". OK

( b ) If tlw column were to run continuons through the beam, as illustrated above, then a l/4" doubler plate would be required in this conncction area to make up the difference in thickness.

( c ) Another choice v.ould be to use a pair of diagonal stiffeners having thc following cross-sectional a r w

Or use a pair of 3" by 36'' stifhers, the area of which checks out as-

A, = %" ( 2 x 3" + ,339")

= 2.38 in." 1.03 iu." OK - .41so, thc required thickness is-

In adrtitiou to this, the web of the column must be checked against buckling from the conceutrated compressive forces applied by the beam flanges.

If the web thickness exceeds the following value, stiffeners are not needed opposite beam compression flange :


(a) Run beam through column (b) A Y4" doubler plate Add plate stiffeners across beam, (dl A pair of 4" x 1Y2" horizontal in line with column flanges to flange plate stiffeners transfer column load

(c) A pair of 3" x 3/8" diagonal stiffeners (e) A pair of Tee vertical stiffeners (d) A pair of 4" x Y2" horizontal cut from 21" WF 1 1 2 g or 5/8" plote

flange plate stiffeners Tee section also provides the necessary additional web material fol this connection.

FIGURE 50


Since w, = .339", some additional stiffening is required. There are two solutions.

( d ) Horizontal flange plufr stiffeners, the required thickness of which is found from the following formula:

but the following is called for-

IIencc, use a pair of 4" x K" horizontal plate stiffeners.

( e ) Vertical stiffeners, the required thickness of

which is found from the following formula:

and this checks against the following requirement-

This T section ro111d be name cut from a 12" WF 112# section, which has a flange thickness of ,865" ( w t need ,517") and a flange width of 13.00" (we need a t least 13.635"). Othemdse, it could be fabricated from %" thick plate welded together.

Summary

There are four possible methods of making this connection, Figure 50. E;rch uses a combination of the preceding solutions to stiifm the connection weh so it may safely transmit thr s l ~ r ~ ~ r forces rcsnlting from the unbalarrced monicnt as well as to prevent buckling from the concentrated comprt:ssive forces applied by the beam.

/ Welded-Connection Design

Shop-fabricated Vierendeel trusses lowered steel requirements and reduced time for erection of Hamburgers clothing store in Baltimore. Here a weldor is connecting a corner bracket between web member and bottom chord of the truss, using low-hydrogen electrode for root passes.

1. ADVANTAGES OF VlERENDEEL TRUSSES

A Vicrendeel truss is in effect a rigid frame. It differs from the simple truss (Sect. 5.9), but it also differs in some respects from the usual rigid frame (Sect. 5.11).

Although the Vierendeel truss has been used widely in European bridge design, the relatively high cost of riveted construction precluded its early popularity in this country. Modem welding processes have changed the economics and several structures using the welded Vierendeel truss have been built here in recent years.

Currently the major field for welded Vierendeel trusses is in building design; Figure 1. For example, they have been used as roof supports to carry the extra load of a superstructure, as exterior floor-high members for rigid support of heavy masonry walls, and in exterior wall grid systems for aesthetic value as well as construction advantages.

In exterior use, the large panel areas provide adequate window area to be 6lled in by glass or translu- cent materials; chord and web members arc sometimes faced with masonry. When used as interior members,

the web openings permit savings in space since piping, conduits, and duds may be fed through them.

Some Vierendeel trusses are fabricated from wide- fiange beams, as shown at the top in Figure 2. Here the top and bottom chord members, as well as the verticals, are standard rolled beams. Additional plates are used to join these members.

At the center in Figure 2, the vertical rolled sections are extended ail the way to the top and bottom members. A triangular gusset section or bracket is in- sected on each side of the connection. These gussets are flame cut from standard rolled sections, usually having the same flange width as the other members. This is a simpler method and therefore is widely used. However, it does not result in as smooth stress distribution at points of high bending moment as does a design with crwed comers.

Another method of achieving these curved comers is illustrated at the bottom in Figure 2. Here the truss is Aame cut from flat plate with flanges welded to it around the web openings and across top and bottom edges. Also see Open-Web Expanded Beams, Sec- tion 4.7.


FIGURE 2

2. BASIC C O N N E C T I O N REQUIREMENTS

In the usual rigid-frame design certain assumptions are made: the beams and columns deflect, and the connections rotate; but within the connection itself, there is no appreciable movement. Of course the connection does undergo some movement (not to be confused with rotation). However, the distances over which this movement takes place are small mmpared with the lengths of the beams and ~wlurnns. Consequently the movement

within the joint has little effect on the h a 1 moment distribution in the frame.

The Vierendeel truss on the other hand is more compact; for example, the lengths of the vertical members often are relatively shorter. See Figure 3. The more massive ~~nnect ions thus occupy a larger portion of this frame than most others. Any angular movement of vertical members due to yielding within the connection itself will greatly increase the moments in horizontal members. There is no method of computing or pre- dicting how much the connection will yield; therefore, every effort must be made to provide a connection at least as rigid as the adjoining members.

It might be thought that the simple square type of connection would naturally be as rigid as the members, since it is a continuation of the same section. In many cases this is true. However, it might be well to remember that stress causes strain, and the accumulation of strain over a distance resulb in appreciable movement of some kind: deflection, angular movement, etc. The sharp comer of this connection increases the stress in this area by several times. This stress concentration results in a higher strain 2nd therefore greater movement in this small area. Since only flange stiffeners are added to this square-comered connection, it is difficult to exceed the stiffness of the member. In most cases, it will just equal the member, and in some cases it will be less.

3. PLASTIC D A T A H A S A P P L I C A T I O N

There is little test data on the connections used in the Vierelldeel truss. However, data available on the plastic design of comer connections or knees will be helpful.

FIG. 3-In this building addition, use of Vierendeel trusses will provide a column- free orea of about 30' x 60' for large trucks and trailers to load and unload communicotions equipment.

elded Connections for Vierendeel Trusses / 5.13-3

FIGURE 4

1

,0002 ,0004 .0006 ,0008 ,0010 ,0012 .0014 ,0016 .C Unit angular rotation (4); rodions/in.

Figure 4 shows moment-rotation curves of various comer connections.* The vertical axis is the applied moment; the horizontal axis is the resulting rotation of the connection. The vertical height of the curve represents the maximum or ultimate strength moment of the connection. The slope of the straight portion of the cuwe represents the stiffness of the connection, with the more nearly vertical curves representing the stiffer connections. The right-hand extremity of the curve represents the rotational capacity of the connection.

In plastic design, it is necessary that the connection - *Figure 1 adapted from "Connections for Welded Continuous Portal Frames", Beedle, Topractsoglou and Johnston; AWS Jour- nal; Part I July 1951, Part I1 August 1951, and Part 111 November 1952.

havc high rotational capacity in addition to exceeding the moment capacity of the member. In Vierendeel trusses, it is more important that the connection have a stiffness equal to or exceeding that of the member, and a high moment capacity in order to safely carry accidental overloads. Here the extra rotational capacity would not be as important because it is an elastic design rather than a plastic design.

In Figure 4 notice that the square-comer conoec- tion is the most flexible. It falls slightly short of the beam itself, but does have the greatest rotational capacity. The comer with the bracket has greater stiffness and higher moment capacity, hut less rotational capacity. Tapered haunch knees, not shown here, were found


FIGURE 4

to behave similarly. The curved knees are the most rigid, have the highest moment capacity, and have a rotational capacity somewhere in between the simple square corner and the haunched knee. As the radius of curvature of this inner flange is increased, the stiffness and moment capacity increase slightly, with slightly lower rotational capacity.

UARE CONNECTIONS

When the flanges of one member intersect the flange of another, stiffeners should be added in line with the intersecting flanges. The stiffeners transfer the forces of the flange back into the web of the other membcr. See Figure 5. These flange forces are distributed as shear into the web along the full web depth. This will prevent the web from buckling due to the concentrated Bange forces.

The unbalanced moment about a connection will cause shear forces around the periphery of the conneo tion web. Fignre 6. The vertical shear force and the horizontal shear force will result in a diagonal compressive force applied to the mmection web. Unless the web has sufficient thickness or iri re~nforced, it may buckle. According to plastic design (and this may be used in elastic des ip ) , the required thickness of the joint web must b e -

and:

FIGURE 6

Connections for Vierendeel Trusses / 5.13-5

FIGURE 7

t, = thickness of connection web, inches

f, = unit shear force, lbs/Iinear inch = T t,

dh = depth of horizontal member, inches

d, = depth of vertical nmnber, inches

FIG. 8 Methods of obtaining web thickness to meet requirement of Formula #2.

M = algebraic sum of clockwise and counterclock- wise moments applied by members framing to opposite sides of the joint web boundary at ultimate load, inch-pounds

For a panel subjected to shear forces and having a ratio of width to thickness up to about 70 (the connection webs will almost always be within this value), the critical shear stress equals the yield shear stress (Tp), or-

?;r = 7,. and

Web doubler

plate

(a) Web of connection reinforced with web doubling plate

Diagonal stiffener

(b) Web of conneaion reinforced with diagonal stiffeners

(c) Web of connection reinforced with longitudinal stiffeners


If the thickness of the connection web should be less than this required value, AISC in their work on Plastic Design (which may also be used in Elastic De- sign) recommends adding either ( a ) a doubler plate to the web to get this required thickness, see Figure 8, or ( b ) a pair of diagonal stiffeners to carry this diagonal compression, the area of these stiffeners to be sufficient for just the additional requirements.

It seems reasonable that ( c ) a pair of longitudinal stiffeners extending through the connection area would be sufficient to resist this web shear. These stiffeners would be flat plates standing vertically h&ween flanges of the chord member and welded to the flanges near their outer edges.

5. CURVED-KNEE CONNECTIONS

Tensile stress (urn,.,) in the inner flange of a curved knee tends to pull the flange away from the web, and to bend the curved flange as shown at the lower right

of Figure 9. Because of the slight yielding of the flange's outer edge, there is a non-uniform distribution of flange stress ( u ) . This stress is maximum in line with the web.

In addition there is a transverse tensile bending stress (u , ) in the curved flange. If this value is too high, stiffeners should be welded between this flange and the web. These keep the flange from bending and pulling away from the web. These stiffeners usually need not extend all the way between flanges, but may be a series of short triangular plates connecting with the curved flange.

In the following formulas, the values of factors o:

and p come from the graph, Figure lo.*

longitudinal tensile stress in flange

. . . . . . . . ."" . . " '"" (3)

transuerse tensile bending stress in fhnge

......................... M radial force

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . (5 )

The radial force (f,) acts transverse to the m e t welds connecting the flange and the web.

*From "Design of Rigid Frame Knees", by F. Bleicb, AISC.

Rad~oi tensk force (f,j

FIGURE 9

elded Connections for Vierendeel Trusses / 5.1

FIGURE 10

Values

Valuer

ARY OF REQUIREMENTS

Here is a summary of the general requirements for these Vierendeel truss connections:

1. The bottom chord is in tension and the connections here must provide continuity of the member for this tensile force; the top chord is in compression and the connections here must provide continuity of the member for this compressive force. For these reasons, the inside flanges of the horizontal chords should be made continuous throughout the connection.

2. There may be some axial tension or compression in the vertical member, but this is usually of a smaller magnitnde.

3. Large moments are applied by the horizontal and vertical legs to each connection.

4. A pair of connections, one above the other, tend to he restrained from rotation by the vertical member which connects them. The rotation of these connections

due to deflection of horizontal and vertical members is taken into consideration when the truss is designed. However, yielding within the connection itself is not considered in the design and this could alter the moment distribution of the truss, therefore it is important tlrat the connection have equal or greater s@ness than the members connecting to it.

5. The web of the connection must be stiffened against buckling due to the high shear stress resulting from the unbalanced moment of the two horizontal members connecting at the joint. This difference in moment is equal to the moment applied by the vertical member also connected there. This web must either have sufficient thickness or be reinforced with a doubler plate or some type of stiffeners.

6. Flange stiffeners should be used whenever there is an abrupt change in direction or curvature of the flange.

Vierendeel trusses in this addition to the New England Life Insurance CO. home office building permined orchi- teci to match window openings in original buildings, yet accomplish significant savings in steel ond in floor spoce. Design also provided stiffer construction, reducing d a n g e r of cracked masonry.


Use of Vierendeel trusses here provided a column-free area of about 30' x MY for lorge trucks ond trailers to load and unload communications equipment.

1. METHODS OF A

There is no single best method to analyze statically indi~tcrminatc stni~.tiircs. l'lirre arc- many mcthods, and muny comhirintions and adaptations of these methods. One mc~tliod map h r siinpli~ and (pick, h i t can only be used to a lirnitcd cxtt:rrt. :'mother mcthod may have wide applicatioir, h t I>(: so lai~orious that it is not used inuch.

Most tcxts on stritically indctcnniriate structures start ont witli the various m(*tliotls of dctcrmi~iing deflections of thr s t r i~c t~~rc . Thcy them corrsider the analysis of thesr strnctnrixs. Thc nicthoc1s of finding deffoctions arc siniple tools which may he usad in tho analysis of ihc strr~ctni-c.

1Prvrc arc nctunlly ahout five basic, mrll uscd methods for the :tn:ilysis of sieticnlly inclrtrrnrinate structures tmcorrnt~nd in rigid frame designing:

I. Least Work Mt:thod 2. Central Mctliod 3. SIopv I>~.flrction hlctliod 4. hlo~nent and Shcar Ilistribution Mrthod 5. Column Analogy hlcthod All of these mrthods. when applied to continuous

beams and frames, give the resulting bending me- ments at various points along tlw structure. In order to proct:cd this far to get the n,sulting niornents 011

thc stnictorc, it is first ncwssary to assum? thc moments of inertia of the rn~mhcrs. This is 11sually a good guess or appn~xiinatioir, Tlren, from th<w resr~lting bcnding mornmts, the rncmt>er is built up. If the find reqiiirctl mo~nci~t of ir~crti;~ is more than that which u-as started with, thc work mlrst be repcatcd; or adjusted, using this niwcr v:llne. I11 sonrc tnetlmds orily the ratios of the mrious rnorncrits of incrtia rrctd he wed.

ethod of Least Work

The nictlrocl of least work dqmids on tlrc follow-ing. It is coi~sidcrcd that a strncti~rr. will deform under the nppliattion of n lo:ld, i r i such a inanncr that the intrrri:d \\-ork of drforin;itii~n will hi. held to a minimum. This inethod may be oiitlini~l as follows:

1. Cut tile strutiuro so that it hcconrc~s statically det~mniiiatr.

2. 1 '11~ uuknown monic~lts or forces become the reduridar~ts or unknown qnantities.

3. Set up an equation for the internal work of the

stri~ct~rre in tt,rms of these redidants . 4. A derivative of this is then set tyn:rl to zcro, and

this will give thr minimum vdue of this redundant forct,.

General Method

The gmrral mcthud consists of the following: 1. Cut the stniehire at the reduildnnt or urrlmown

forcr. 2. Di:ter~nine the oprning of this gap caused by

tho givm h a d (while cut) . Several methods may be usad to find this dr&ction.

3. Apply a rcdondat~t forw to close this gap. 4 Fmm th~ . given 1 1 d s m d this redundant force,

makc np a momc.nt diagr;m and design thc sirncture from this.

For more thm one rt&uidant force, cut a11 members at thew rednndar~t forccs arid close the gaps simulii~nrously.

To usr the general method, the designer must be able to find d14Irctions in Step 2. Sorne of the methods for finding deflections are as follows:

( a ) Rcd Work ( b ) Castigliano's Theorem (c) Virtual Work ( d ) Arca Moment ( c ) Conjugat~t Dearn ( f ) ilngle Wc,ights ( g ) Willot-Mohr Diagram Scvcral of these int~thods an. described in Section

2.5 or) Dt.i3rction by liendir~g and will not he discussed h ~ w .

Slope Deflecfion Method

In the general mcthod jnst outlined; the redundant or i~nknoa-n forccs : i d moments are fonnd. In a similar rnimnor, it is possiblr to solve for thc onknown joint rot;ltions and dcflrctions. As soon as these are found, tho end moments may he dctrnnintd and these corn- h i n d mith the original niomcnts from the applied load.

oment and Shear Distribution Method

The moment distrihntiorr or 1I:irdy Cross method consists of lrolding thc joints in a frame fxed so that they cannot rot:ite. Tlrr: m d moments of cach loaded membcr are forind f ~ m n standard hram diagrams in handbooks. Thcn, onc ;it a timc, a joint is rcltvscd, allowed


(a) Actual Frame (b) Elastic area of analo~aur column

FIGURE 1

to rotate, and the11 fixed again. This relcase causes a new distribution of the moment about this point, and somc of this change is carried over into the next joint. This proccdmc is followed for each joint in the entire frame, and then the whole process is repeated over all the joints as often as required rmtil these cor- rections become very small.

This method is outlined as follows: I . Fix the joints from rotation and find the mo-

ments, trcating the member as a simple structure. 2. Remove thr joint restraints one at a time, and

balance moments about the joint. This unbalanced moment is then distributed about the joint.

3. Some of this distributed moment is then canied over into the other end of the member.

4. This is repeated until the unbalanced moments become very small. The final moments are then used to design the structure.

Column Analogy M e t h o d

The outline or over-all shape of the given frame is considered as a column cross-section, called an elastic area. Thc length of each portion of this elastic area is equal to the actual length of the corresponding member of the frame. The width of each portion of this elastic area is equal to the 1/EI of the corresponding member of the frame.

The properties of this elastic area are determined: area, center of gravity or elastic center, and moments of inertia about the two axcs (x-x and y-y).

The statically indeterminate frame must be cut, usually at one of the supports, so that it becomes statically determinate. Under this condition, the moment diagram caused by the applied loads is constructed and then treated as a load (M/EI) applied to the elastic area of the analogous column.

Just as an eccentrically loaded column has an axial compressive strcss and bending stresses about the two axes (x-x and y-y), so the analogous column has "stresses" at any point equal to the axial compressive "stress" and the two bending "stresses". These resulting "stfesscs" of the analogous column are the

corrective moments which must be added to the statically determinate moments of the "cut" frame in order to bring the frame back to its original shape and condition before it was "cut".

This is outlined as follows: 1. Determine properties of the elastic area: area,

center of gravity or elastic center, and moments of inertia about the two axcs (x-x and y-y).

2. Cut the frame to make it statically determinatc. Use moment diagram from applied loads as a load ( M / E I ) on thc clastic arca of the analogous column.

3. Determine axial "stress" and the two bending "stresses" of the analogous column. These become corrective moments which must bc added to the statically deternminatc moment of Step 2 to give the final moments of the statically indeterminate frame.

4. From these moments, find the redundant forces at the cut portion of the frame.

2. COLUMN ANALOGY METHOD

The outline of the givol frame is considered to be a column cross-section, called an elastic area; Figure 1.

The length of each member in the elastic area is considered cqual to the actual length of the corresponding member of the actual frame.

The width of each member in the elastic area is equal to 1/EI of the corresponding member of the frame.

It is seen by Figure 1 that for a pinned-end frame the moment of inertia of the flexible pin is zero. Hence the width of the elastic area at this point is

and the elastic area at this pinned end would equal m . For a fixed end, the moment of inertia at this

rigid support is assumed to be m. The resulting width oE the elastic area at this point is-

Design of Rigid Frames / 6.1-3

and thc v1:rstic : Ira at this fixed end would he zero. The, ('1astic area, with its dinwnsions riow known

I,mgth : L

111,ight =: 11

is now t rc~~tcd Iikc any other cross-stxction, and its propertics d~~termirird.

h this cx;r~nrile of i i i ~ ~ ~ i i d encis: I

Area

( 2 coluinns) (beam) (pinned ends)

Elastic Center

The elastic center is fo~ind as though it were the center of gravity of the elastic area.

axis x-x

Taking moments aliout the base line, it is seen that the. i,l;~stic axis s-x of the c1:rstic area must pass through the frame basc since, in the nrialogoos column, thc. p inod ends h a w irifi~ritc ( x ) mea.

This may be proved by mathcmatically determining tiit, elastic cmtcr of gravity:

axis y-y

By ohscr~viiorr, i t is sccn that thc y-y axis wo~rld pass thmugh the wnter of this elastic art:;^ h~.causc of section symmetry.

oment of inertia

I,, = 2 ( -b (- I<: I[ ) 1. 19 + 2 (i) 0

( 2 coluinns) (beams) (pinned ends)

Since the infinite ekistic arcn a t thr pin lics along the clnstic axis x-x, it will hnvc no effwt upon I,.,.

I p ~ > = V-, since there is ;in i n h i t c elirstic sea at

ill<, t\vo pitintd ends isrid thcst. lir :ri the, extreme ends of 1111, svction ;~lrout axis x-x.

Apply Load to Elastic dreo

T l ~ c statimlly intlct~~miirrate frarrrr, I'igl~re 2 ( a ) , lnlrst h a w sonic portiorr cut, r~srially ;it orrc of the stipports, so t11;1t i t tiwornr:s st;itifi~lIy dt,tr:rrnin;rtc, Figrrl-c 2(1)) . ITiliicr this eoirditiori, the. f,r,~iding momcnt diagram c ; i r ~ s ~ ~ t by I npi11ii.d 1o:irls is coristruct~~d, i;igur<, 2 j c ) . 'I'his is tlwn tr(.nttd ;rs ;I 1o:rd (hl , jCT) applied to tht ixl;~stie arm of ilrc :rnaIogous column, Figur(. 3 (a ) .

J I I S ~ ;is an ccc~mlric;rlly loaded iollnnn has an axial load mri tilting mom~iils (kt , = I-' y, and M, = P x),

[ o ) Statically indeterminate frame

(b) One support rut to make frame itotically determinate

li) Moment clioijrom for the

stoticnlly delertninote frome

FIGURE 2


M (a) Analogous column loaded with -

E l (b) Actual column with eccentric lood (P)

FIGURE 3

so the analogons column has an axial load and tilting moments. Consider the moment diagram dividcd by EI as the load about the two axes (x-x and y-y) through thc elastic center:

axial loud on anologous column

- P a b - -. -. 2 E IL

moment about axis x-x on analogous column

- P a b h - -- 2 E I,,

moment about axis y-y on unalogous column

- P a b - ( b - a ) (4b + 4a - 3L)

12 E I, L

Just as the eccentrically loaded column has stresses at any point equal to the axial compressive stress plus the two bending stresses-

u = ua (axial) t IT, (bending,.,) i o;. (bending,.,)

so thc analogons column has "stresses" at any point equal to thr axial "stress" (ma) plus the two bcnding "strcsscs" (us & u,). Thrse are the correspouding corrective momonts (M,, M,, & M,.) which must be ap- p l i d to the statically determinate moments of the "cut" franic in Figurc 2 ( b ) lo bring thc frame back to its original shape and condition, Figure 2 ( a ) .

= 0 (See Figure 4.)

Design of Rigid Frames /

Y

FIG. 4 No corrective moment to be added here. FIG. 6 No corrective moment to be added here.

when c, = 0

M, = 0 (See Figure 5.)

. . . . . . . . . . . . . . . ( 3 )

Since I,., = oo

M, = 0 (See Figure 6.)

Thc final moincnt on thc frame will be as given in Figure 7.

FIG. 5 Corrective moment to be added here.

FIGURE 7


- 48' ________PI

FIGURE 8

I - 48' -------q I Y

FIGURE 9

Find the moments ( M ) and the other rt!dunttant forces (I3 and V ) of the following frame, having fixed ends, by mcans of the Column Analogy hlethod; Figure 8.

This frame must he transformed into the analogous column, and the properties of this eq~iivalcnt elastic area determined; Figure 9.

Member

Calumnr

Rafters +5.0 +260 433

Total + 147.5 2856

= $ 2.2' measured from reference axis (x'-x' )

Use a reference axis (x'-x') through the top of = 2856 - 325 the column. = 2531 i n 4


FIGURE 10

distance from elastic center (x-x) to outer fiber

(bottom) c, = -15 - 2.2 = -17.2'

(top) c, = +I0 - 2.2 = + 7.8'

axis y-y of 'Iristic centcr (Sce Figure 11.)

H" observation it is seen that this passes through thc cmtwlinc of the frame:

I ,~ , - 2(7.5)(24)' + 2(26)(1Z2) + 2(1248)

( 2 cohlmns) ( 2 rafters)

= 18.624 i n 4

- - Moment of inertis

of rafter about its

- lo ' own center of gravity

distance from elastic ccntrr (y-y) to outer fiber

(right side) c, = +24

(left side) c, = -24

Cutting Frame So I t Becomes Statically Determinate

Thc frame is now crlt so that it becomes st:itically determinate. The resulti~rg moment diagram, divided hy the real momt,nt of irwrtia ( I ) , is trratcd 3s a load upon thc nnalogous coh~rrrri or elastic nrca. (We don't divide by E here bcc;ruse E is constant; for stecl, E = 30 x 10") This may be done in several ways, princi- pally:

FIGURE 11


A. Cut thc right fixed end support at @. The My., = (-450,000)(-9.7) + (--390,000) (--.53) portion of the rafter to the left of the applied load = + 4,571,700 becomes a statically determinate cantilever beam.

B. Release the ends of the rafters at @ and 0. My., = ( -- 450,000) ( -- 24) - (-390,000) (-20) This becomes a statically determinate simply supported haunched beam. = i 18,600,000

Method A: Cut the frame at @. With the load correction moment at @ applied at 0, the raftcr cantilevers out from @. The end moment at @, M = -60,000 ft-lbs, is also applied to the left column 0-0. (Sec Figure 15.) c - P M 7 . x c ! F Mr., c, -- - - . I . " -

+ - - the three loads on elastic area .4 LX 1.w

- - -840,000 - - - 67,570 ft-lbs

W TO DETERMINE C RRECTIVE MOMENTS (Diagrams Apply to Option A)

The moment diagram divided by the moment of inertia These loads, in turn, result in 3 types of resisting of the statically doterminant frame is considered to he " stresses": the load on the elastic area of the analogous column. P M... c7 cx = M,., c, ( E is constant.) O" = a o r = ----- LX 1Y.Y

The resultant "stress" at any point of the elastic area may he found from the conventional stress in an eccentrically-loaded column:

P = - ; M F . 7 CY Mx-x cx a 1,- $7

These "stresses" are the correcting moments, which must be applied to the original moments of the statically determinate frame to produce the final moments of the statically indeterminate frame.

FIGURE 12

This total load on the clastic area may be broken down into 3 loads:

X

a. Axial load, P

b. Moment, M, ., about axis x-x

c. Moment, M,.,, about axis y-y FIG. 14 Correcting moments


FIGURE 15

final moment = original moment - correction moment corrcciion moment at @

MI = - 60,000 $- 67,620 . =: + 7.8' P . M c M,, c, = --1- 7570 ft-lbs - - + -'"L + - ~.

- A Lx L, -

-840,000 (+4,571,700) (4-7.8) - - . + ~ . . . . -.

correction moment at @ 67 2531 (+18,600,000) (0)

c = - 2.2' + .. ..

P My., r, 18,624 - + ?.E~~ (2 +. cx - 24, - A 1 , ~ ~ L I- = + 1550 ft-lbs .- - ---840,000 ( +4,571,700) (-2.2) + final moment -

67 2,531P-.- Mh = - 1550 ft-lbs ( 4-18,800,000) ( -24) + -. .- . ---

18,624 correction moment at @ - - - 40,480 ft-lbs c, = - 2.2'

P Ms., c, h , I , , c, - - 4.. 1~ . - A : final moment - original moment - corrtvtion moment I,~, I,%y

correction moment at @ = + 7460 ft-lbs

( + 18,600 000) (,!?A) + - 7 8 , 6 2 4

= - 19,640 ft-lbs

I' +

+ hl, ,. c, A I x ~ , 1,,

c - - 1 - r- 3.8' final moment

c, 7- - 1.7' ME = -- 7460 ft-lbs


+ 19,460' '

FIGURE 16

final momcnt .MI H = ..

M6 = + 19,640 ft-lbs h

-. 7570 ft-lhs

The final moments of the statically indeterminate 4.191 -- ~~ -

frame are di;rgramn~ed in Fignre 16. = 1806 lbs

Horizontal Redundant Force

To find the horizontal rednndant force ( H ) at the base of the column, first find the point of inflection (zero moment) in thc column. Then find the horizontal force required at this point to equal the end moment at the base of the column.

FIGURE 17

Vertical Rmciion

To find the vertical reaction (V) at the base of the column, take the inomcnts about the base of the opposite column and set them equal to zero. (See Figure 18.)

Method 8: Relcase ends of the rafters at @ and @, so that the rafter hecomes simply snpportcd and statically indeterminate. (See Figure 19.)

the three loads on elastic area

Design of Rigid Frclmes / 6.1-1 1

FIGURE 18

M,., = ( j-292,500) (+1.13) + (97,500) (-k4.47) final moment r original moment - correction moment + (390,000) (+5.3) + (300,000) (+4.47) MI = 0 + 7600

= + 4,576,650 = + 7600 ft-lbs

M,., = (+292,%0) (-16) (97,500) (-8) + (390,000)(-6) + (390,000)(+6)

correction moment at @

- c, = - 2.2' - - 4,680,000

- P -. M,.,c, M ,., c, - * + - correction moment at @

Ix.x + 7,; c, = - 17.2' .-

67 2531 +1,170,000 (+4.576,650) (-2.2) - - - L - '

P M,~, c M,~, c, - - + --2 + -- - A (-4,680,000) ( -24)

L X 17-s + - ... ~-

18,624

- +1,170,000 (+4,576,650) ( --17.2) -- + ~~~~-~~~

m 2531 = + 19,520 ft-lbs

(-4 680 000) (-24) + --'---!... ;, -- 18,621 final moment

- - - 7600 ft-lbs MI. = - 19,520 ft-lbs

FIGURE 19


correction moment at @ c, = + 2.8'

P M,., c, = - + - A Is.x

( ---4,680,000) (-12) + - - 18,624

= + 25,540 ft-lbs

final moment

Ma = + 45,000 - 25,540

= + 19,4% ft-lbs

corrcction moment at @ c, = + 7.8'

P M,~, c, . M,., c, ---+: - A

+- LX 17.y

final moment

Mg = + 30,000 - 31,560

= - 1560 ft-lbs

correction moment at @ c, = - 2.2'

P + M;" CY + My-,, ~2 - - c, = 24' - A x-I 17.1

= i 7450 ft-lbs

final moment

Mg = - 7450 ft-lbs

correction moment at @ c, = - 17.2'

P M c M,., c, - - + 2>xA + -:.~

- A Ix.x Ir.y

- 67

+1,170,000 (+4,576,630) (-17.2) - + 2531

(-4,680.000) (+N) + - - SS,6%

- - - 19,670 ft-lbs

final moment

Me = 0 + 19,670

= + 19,670 ft-lhs

Alternate Method

It is possible to work this problem in a slightly different manner. As heforc-

1. Determine the properties of the elastic area. 2. Cut the frame to make it statically determinate,

as before. 3. Dividing the moment diagram of this cut frame

by the moment of inertia of the corresponcling members of the frame, treat it as the load on the elastic area. ( E is constant.)

4. Find the resulting three parts of this load on the elastic area; that is,

a. Load, P b. Moment, M,., c. Moment, My.,

Then find the three corrective actioi~s-fixed end moment (MI,), liorizontal force ( A ) , and vertical force (V)-which must bc applied at the base of the frame to bring it back to the original shape and condition of the statically indeterminate frame. Find these from the following formulas:

Figure 20 shows their application to solution of the immediate problems.

The resulting moments ahout the frame for each of these mrrective actioxs are dctermincd and placed for cnnvenicnce in tahlr form. This facilitates totaling then1 to produce the final moments at any point of the statically indeterminate framc. See Figure 21.

3. FIXED END MOMENTS, STIFFNESS FACTORS, AND CARRY-OVER FACT0

When some type of moment distribution is used for the analysis of continuous frames, it is necessary to know the following:

I. Fixed end moments (Mi,) of the beam. 2. Stiffness factor ( K ) for each end of the beam

so the distribution factors may be determined. 3. Carry-over factor ( C ) of a moment from one

end of the beam to the other end. These items may he found from already-developed

charts, or by use of the column analogy method which


/ " + - - - -

X - compression

H =

1806

M,=t i c l= [ -1806) [ -17 .2 )=+31 ,062 ' t i M = -

i..A~ M, = Vc,:

FIGURE 20


is applicable to any type of beam, Figure 22. The cover-plated beam is representative of any

beam in which there is an abrupt change of scction . . . and of mome,nt of inertia. The other two common conditions in which there is an abrupt change of scction are 1) where plate of heavier thickness is used for the flanges for a short distance nt the ends of the beam, and 2) where short lengths of smaller beams are used below the regular beams to reinforce them a t and near the points of support.

FIGURE 21

Constants to Help Cwlculwte Finwf Moments

0 0 M,

Charts have been developed by which the designer can readily find constants to use in determining stiffness factors, carry-over factors, and fixed-end moments for beams.

Sources include: I. Bull. 176, R. .4. Caughy and R. S. Cebula; Iowa

Engineering Experiment Station, Iowa State College, .4mes, Iowa. 36 charts for beams with cover platcs at ends.

0 0

~

0 0

~~~

Prismatic -

@ 0

~ ----

0 -60.000

P Mrr = - +12,537 1-12.537 +12,537

A

0 -60.000

..~

M, = - 7458' 8

+12,537 +12.537

Topered beam

i 1 2 . 5 3 7 ~- -- + 3,974 i +31.062

-23.969 ' 23,969 ~ , g f i ~ . -- ..

- -

H a y -

- Cover plated beam

@=+ / \

+31.062 .+ 3,974 -~ .. .

FIGURE 22

Hounched beom

M3 = + 19,465'*

- 5.057 / -14,008 -~ V . x - . +---. . .

Total + 7,SM -19,520 +19,465 1 - 1,551

123,969 + 2 3 , 9 6 9 - 1 1 . ~ 4 - ~ - - ~ 1


2. "hloment l)istrih~rtion," J. M. r I ; D. Van Nostrnnd Co.. 378 pages; 29 clixts for braox \vith covcr plates at ends; -12 chal-ts lor tapwcd hmrns.

4. F I N D I N G FIXED END MOMENTS BY C O L U M N ANALOGY

Roftving hack to Topic 2, Thc Coliiml~ Analogy h4ethod. the outlinc of tlie hem1 is ronsidercd to be the cross-section of ;I colmnn (or elastic zrrcn). See I'igurc 23.

k-

--

Real beam "

Y Elostic area

FIGURE 23

The length of the clastic area is equal to the length of the veal beam, and the ~ i d t h at any point of the elastic awa is equal to tht: l /EI of the r r d beam at the corresponding point. Since \vex arc: draling with steel, the modulus of elasticity ( I ? ) is constant and will drop out of tlrc calculations. As the depth and moment of inertia of the real beam increases, the i.lastic area decreases.

Thc following dcs~gn procedure may then he followc d.

1. Detcmmi~re the propcrtics of thc clastic area: a. Area of the cl;~stic arm (A) h. Iacation of axis y-y through the elastic

center of thc elastic ;area. c. Distanct. iron1 the elastic center ( y -1 - ) to

the outer fiber-s of thc cltistic nrca (c. , ) tmd (c, , ) . d. Momcnt of inertia of the elastic area (I,.,).

2. Kelexse both ends @ and @ of the fixtdcnd beam and draw the moment diagram of this "simply- supportcd" hcam. Use this moment diagram, divided by El, as thc load upon tht: elastic area (analogous column).

3. The rtwiltirig "strcssts" at thc ends @ :rnd @

I~i,comc thc correction momrnts which n111st he added ti? ilia mommt of the "simply-s~rppol-[rd" hemr to trans- form it back to the original fixed-wd, statically indeterminate bcarn. Sinw i n this case \VI. started o r~ t with zcro cnd mnm~nts for thc "si1nply-srrplx1rt~~d" hcam, these corri.ction ~iioinrwts tbcr~ 1)rcornc thc fixed m d moments of t l ~ e final I-igid hram:

M,,, at c.nd @ hir,, at cnd @

Stiffness Factor by Column Analogy

The stiffness factor ( K ) is a measurt? of tlw resistance of the mrmbrr against t ~ l d rotation. i t map be defined as the moment necrassary to produce a irnit end rotation at the same end, wl~ile the opposite end is held fixed:

K* = MA

Carry-Over Factor by Column Analogy

For any applied moment ( M A ) at A , the resulting moment ( M A ) at the other rnd 8 is determined. The carry-over factor is the ratio of thcse two moments:

MAIJ C* = - -- MA

In both of these two c;lscs, Stifl'ness Factor and Carry-Over Factor, the fixed-end beam is rr.leased at one end @ :md rotatrd througli a unit angle chango (4 ) . The restilting end moments ( M A ) at @ and (M,,,*) at @ are found.

FIGURE 24

This unit ;iilqIc rotation is app l i~d as a single load at thc nutcr edgy of the clastic :rrm (analogous column), just as ;in <vwntri<. load might he applied to a real column. S w Tahle 1.

For a unifi~rrnly 1o:ldcd; simply supporiod h a m , the hcnding niommt 11as tlic shiipe of a parabola. It will he helpful to know t l i ~ , loads ( t ' ) and clistxnces ( e ) at the center of gravity of these areas. See Table 2.


5. COLUMN ANALOGY METHOD APPLIED TO BEAMS HAVING ABRUPT CHANGE OF SECTiON

The Columtr Analogy Method will now bc uscd to find the Iixcd end moments, stiffness factor, and thc carry- over factors for a fixed-end beam with cover plates at one end, supporting a uniform load (us). The technique would bc applicd similarly to any beam having abrupt change of section.

Figure 25 diagrams the rcal loaded beam, at top, and the elastic area of an analogous column, below. On this dastic area,

TABLE l-Column Ana

Load of the "nil mgle ihonge = 1

- x

@

elortic aieo jonalogous

Unit m g I e chonge i!oodl ploced at A 0 M,., = I c*

at @

y: Unit Angle Rotation

Load F placed ot A

M,., = F a* 0

ot @ F M,-, ca - F c Z F + * "* = -- + - -- A 3-7 A 17.7

tood F placed at @ M, , = F ca

O t @


length = actual length of beam

STEP 1: Dcterrnnre Properties of thi5 Ela \ t r~ Area

area

elastic center (y-yj

Take momwts about @

moment of inertia jl ,~,j

STEP 2: Iktermine the Fixed End Moments

the bcain are releascd so snpported. This moment

diagram now becon~es the load on the elastic area, Figure 26.

TABLE 2-Loads and Their Eccentricity

Load (Pal or (Pi1 o f portion of marner! diagram

Distance t o c q of this load

L = a + b w = u n i t uni form laud (Ibr/in.!

Distance to CG of this ood

8

w = unit uni form load lIbi/in.!


Moment d i a g m

M, = = (L - x ) 2

Load diagmm jM,/l,)

on elortic a im

FIGURE 26

"uxiuP' load (P)

P = P, + PI,

fixed end moments

This load ( P ) and (M,..,,) on the elastic arca causes "stresses" similar to those on an eccentrically loaded column. These "stresses" become the correction moments, or in this case the end moments of the fixed- end beam.

STEP 3: Determine Stiffness and Cnrry-Over Factors

A load of a unit angle change (+) is applicd to the elastic area at the outer edge , and the resulting

found. end moments (MA) at @ (Mar,) at @ are

Now the load of a unit angle change ( 4 ) ) is a plied to the elastic area at the other outer edge and thc resulting end moment (M,*) at n is found. Notice that the end mommt (Mu,) at A is equal

MY.? = 1 ci3

8 to (M~L,,) at @ which is already found.

at @ 1 . 1 cn2

Mn -- -- * -- A L - Y

From thcse three values ( M A ) , (MAB) and (M"), the iollowing may he found:

stiffness juctor at

K, = M, 8

stiffness factor at @ K, = M,

curry-over fucto~, @ to @

M,., = 1 c* FIGURE 27


TABLE 3-Design Summary: Beam Cover Plated At One End

C,, Cu, e , + eb are conridered to be I + )

Fixed End Mamentr

End Momentz Resulting from Treating Angulor Ratotion or o Load

Stiffness Foctoir

Carryover Foctois

6. COLUMN ANALOGY METHOD APPLIED TO BEAMS HAVING GRADUALLY VARYING SECTION

Summary The lollowing method may hc rised to find the fixed

cxnll.,ple of tilt: uIlifor,ll~y.~o~I~jc~C~, fixt.&e,l(i ljeam end monicnts. stiffncss riictors, and carry-over factors Lvith l,latc.s at one t , l ,d , l lny slsnril ,ar~ed as of 1jc~a1n~\r.hicIi 11avt~ constantly varying moments of in T a l k 3. incrtin, s~iclr 21s 1 ~ 1 1 n c h r d ;ind taprred bmnts, Figurt:

"" 21.

Modified E x a r n p h A hcanr tvbich tapws along a straight line ( in Althonglr the woi-k is not shown, the s:nnc3 fixcxl-cnd otlwr woi-(Is. its clvpth inwxs< ,s 1inr;rrly don:: t l ~ : tmnn n.it11 coucr pl;ttcs at both r d s , uniformly loatled, letigth of tlw brarn; se? Fig. 25, top) will liavc a may bc sommarizcd as in Table 1. (Sce lrcrt page) ~nomcnt of iiwrtia ( I ) ulrich docs not increase linearly


TABLE 4--Design Summary: Beam Cover Ploted At Both Ends

iiiiiiiiii

M,, at A 6 LI 2 3 a 1 M,,o~B

End Moment. Resulting from Treoting Angulor Rotation an o Load

Stiffness Factors

Carry-Over Factors

but will have a slight curve (see Fig. 28, center, solid area of elastic area line). This curve approaches a straight line as the a beam becomes less tapered. x -

1, A - log Although a slight error will be introduced, it will I" - IA I*

greatly simplify the analysis if we assume this moment z -

b 10 A - log - of inertia distribution to be a straight (dotted) linc. Ic - In In However, this slight error may be reduced by breaking the beam into two parts (see Fig. 28, bottom) and moment of elnstic area *, about axis A-A assumii~g a stsaight line variation of the moment of

M*./ = ( ) ( - - - a inertia between the thrce points @, @, and 0. /&A D - This is represented by the dashed line in Figure 28, center. moment of ehstic area A, about axis B-B

I, - I~ - I,% log, - STEP I : Determine Properties of the Elastic Area /B-B

Design of Rigid Fromes / 6.1-21

FIGURE 28

distance from C.G. of elastic area A, to axis A-A

MaJ

distance from C.G, of elastic area A, to axis B-B

Ma./

monzent of elastic urea A, about axis A-A

total moment of ekstic area about axis A-A

MA.* M A z / -4- MA^/ /*-A /A-A

elastic center ( y - y )

moment of inertia of elastic urea A, about axis A-A

moment of incrtda of elastic area A, ubout axis B-B

Since thrsc moments of inertia can't be added, not being taken about tho same axis, it will be necessary to shift axis 13-Ii and axis A-A to the elastic center y-y. If axis A-A is always taken at thc shallow end of the tapered beam, negative sigrrs will be avoided in the calculations.

6.1-22 / Mircelloneous Structure Design

momcnt of inertia of clustic area A, ubout axis y-y

Using the parallel axis theorem:

I = I -I- A, c," /A.A /x.x

Tax/ = IAJ - A, Q~ . . /x-x /A-A

Now we wish moments of inertia of A, about the elastic axis y-y, and again using parallel axis iheorem-

I*J = TAX/ -f AX(CA - /Y-Y Ix.=

or I&/ = IAx/ - A, cX2 + AI(cb - c,)" /m /A-A

a n d L J = I * = / + A , c ~ ( c A - ~ ~ , ) /F.F /&A

moment of inertia of elastic area A, about axis y-y

in same manner-

total moment of inertia of elastic area

IF.7 = 1AX/ 4- IAS/ /w /w

STEP 2: Determine the Fixcd End Moments

The moment diagram from the applied load on the real beam is divided by the moment of inertia ( I ) of the real beam, and becomes the load ( M / I ) on the elastic area which is treated as a column.

The axial load ( P ) applied to the elastic area is equal to the total M/I. This axial load applied at some distance from the elastic center of the elastic area causes a moment ( M ) on tht! elastic area.

'Both of these loads cause "stresses" on the elastic area.

Tlrc following applies if the designer can assume a-unifonn load ( w ) :

axial loud (P) applied to elustic area

and,

P = P, + P.

women (A{) applied to elastic area about its elastic crnlcr

where:

and the total moment-

STEP 3: Determine Stiffness and Carry-Over Factors

1 c Z M A = - - + - A I,,


stifness factor at @ Ka = MA

stiffness factor at @ Kc = M,

carry-ooer factor, @ to @ Mac Cao = - - MA

carry-ouer factor, @ to @ MAC Cca = - -- Mc

Elastic oiea

FIGURE 29

For the uniformly-loaded lmrm shown at top in Figure 30, having fixed crids, find the fixod end moments, stiffness factor, and carry-over f:ictors.

At center in Figtire 30, the solid cmve is the actual moment of inertia ( I ) as it varics along the length of the henm. The dashed Iine is the assumed straight-line variation in moment of inertia along the two halves of the tapered beam.

The following properties arc established:

Then procecd first to find formula elements made up of these properties:

log, n = 2.3026 loglo n

I, (2540) - log, - = log, - - - - log, 3.9276 IA (fi467)

Ic (5930) log, - = log, - -- = log,, 2.3346 11, (2530 )


STEP 7: Determine Properties of tlrf Elastic .4rea

area of elastic urea

b A, _ ~~~~ ~ log, -~ 11.

( L - 11%) 11,

Li- 1 = 200" -4 Topered beam

Moment of inertia

1

1 1 c, = 134.30" -

Elastic orea

0 FIGURE 30


I../ -- ( " )< ( ( I . - ( 1 - 3 1 1 3 ) 11, ,> ( I < - I n ) 2

6.1-26 / Miscelloneous Structure Design

(IH - IA) ( 2 12

- 7 In IA + 11 I*") - la" loge- 1, "I

+ [a (2 L - 3 a ) - c A ( L -- 2 a ) ]

STEP 2: Determine tlic Fixed End Moments

at @

P M,, = - 4- Mr., %

A 17.F

STEP 3: Determine Stilfness and Carry-Over Factors

stifncss factor at @

KA = MA = 25.67 -

Design o# Rigid Frames /

FIGURE 31

stiffness factor at @

Kc = Mo = 74.59 --

carry-ouer factor, @ to @ MAC Cat = - MA

- - - -. (- ~~~ 21.18) (25.67)

= ,825 -- -

carry-over jactor, @ to @ MAC Cca = - hi,.

- - - (-21.18) .. ~. (74.59)

= ,284 -

Problem 3 a For the hannchod hcam at top in Figure 31, having 6xcd ends, find thv fixed end inorncnts (rmiformly loaded). stifrntxs factors. and carry-over factors. Dn:ak h r n into sections :md me ~irinrri?al intcgralion.

Thc elastic ; i r a could bc div idd into rectangular aroas, as ;it ccnicr in Figr~re 31, iinil the resirlting propcrtirs of ~ l l c rlastic area found in this mmncr. Of courst~ s o m ~ tmor will lx, introdirccd 1xr:c;mse these rectang~~lnr arras do not qriitf cqr~iil the actual curve of the clastic a]-ea. I-Iowt:vr~r, as thc ~lnrnhrr of divisions is incrcastd, this error will dccreasc.

\Vithoi~t any ;rdditional \wrk, the following mcthod ~vill morc r~rarly fit the outline of ihc elastic area and will r ( ~ u l t in lcss error. See iowor dingr:~m, Figure ,31. The ( r i rvd portion n.ithin thc clastic a rw is dividcd into irimgrrlar areas. It is noticed that a pair of tri-


angular areas share the same altitude and since the division in lmgth ( s ) is the same, they will have t l ~ e samo area. Therefon:, the cmtcr of gravity of the two triangles lies along their common altitude. (This graphical method is applicable to any beam with a non-uniform change in moment of ineltia along its length).

STEP 1: Determine the Properties of the Elastic Area

elastic center

moinmt of inertia

urc,a ( A ) of section @of MJ1, diagram

w a' A = - ( a + 3 b )

12

ccnfcr of gravity of section @

= 4644 Momenf[Mjhgram of uniform load

- x = 73h'"

1 = 775.46 8 I

I ' ! I

Y I = 1824.71 I 1 = 142062

Elastic center 1 = 1071.54 1 = 882.33 Moment of inertia

FIGURE 32


KA = MA = 17.12 other propertics of M , / I , rliagrun~ .~~~~ ~. ..

These ;we shorn in the table above. stiffness fucior nt @ STEP 2: Determine the Fixed End Moments KO = MO =~ 26.35 ~.

7. READY-TO-USE DESIGN CONSTANTS

'he follo\ving 36 charts-appearing on the following pages-giw the fi.~ctf cnd rnomcnls, sliifiirw facirirs, and ca r ry~vc r factors for h a m s wit11 almipt &tnges in nromt.nt of inrrtia ;it111 may hc med for bmnrs with covrr plates. T h ~ y wwc drut4opi.d hy R. A. Canghy, Profrssor of Civil Enginei.ring, Iowa State Collcgc, mcl Ricl1:rrd S. (:cl~l;r. flc:rcI, Engi~~ccring I>t*p:irtmimt, St. M;lrtiii's (X,llrgc~, 7Iicst. charts appmrtil in Dull. 176 of tlse Iowa Enginwring Kxprrirnent Station.


11.000

io.000

9.000

or KBA terms

EI, L 7.000

6.000

5.000

4.000 ID 1.4 1.8 2.2

Chad 1 . Stiffnerr factors ot either end of ryrnmetr~col beom

Ken in terms

Chorf 3. Stif inell foitot3 large end of vnrymmclricol bcom.

KAE in terms

Chart 2. Stiffnerr foctorr ot small end o f unrymmehicol beom.

Chart 4. Coiry-over failors for rymmetiicol beam from either end to the other.


Chart 5. Carry-over faclorr for unrymmctiical beam from m a l l end to large end.

Mm in terms of PL

Chort 6 . Carry-over foctarr for u n y m r t r i c o l b r o m from i h g e end to rmall end.

Chort 7. Fired-end moments of lef t end of rymmebical beam far concentrated Chart 8. Fixed-end rnomenfr lef t endof rymmetricoi beom for concentrated lood ot . l point. load of .2 point.


M n s in terms

of PL

Choit 9. Fired-end moment$atleftendof rymmetiicol beom forconcentrated Chart 10. Fixed-end moment, at left end of rymmetiicol beom for conceo- load ot .3 point. troted b o d at 4 point.

MAB in terms of PL

Choit 11. Fixed-end moments ot lefl end of ,yrnmetrical beom for concen- Chart 12. Fixed end moments a1 left end of symmetricol beam for roncen- t rded b o d at .5 point. trmted loed ot .6 point.

MA, in terms

of PL

Chort 13 . Fixed-end moment* at left end of rymmetricol beam for ioncen trated lond a t .7 point.


Churl 14. Fixed-end moment? 0 1 lei1 end of rymmrtri<ol beam for conien- troted lood a t 8 poinf.

Me, in terms

of PL

Chort 15 . Fixed-end moments at left end of synmctriiol b c v m for c o n m - Chart 16. Fired-end moments at lorge end of unsymmetrical beom for con- l io lcd lood of .9 poini. centrated iood a t .I point.

Me, in terms

O f PL

Chorf 17. F i x e d ~ i n d momc8its at 1orgc end of unrymmi~ir8iui for mn- Chart 18 . Fixed-<end moments of iolge end of uniymm,,lricul baom for con- ienciufrd load 01 .2 point. centiol?d load "! .3 point.


M., in terms

of PL

Chart 19. F;red.end moments a t large end of un~ymmefrical beom for con- Chorf 20. Fixed-end moments ot large end of unlymmetricol beam for con-

centrated load of .4 point. centrated load ot 5 point.

Me, in terms

of PL

Chart 21. Fixed-end momentr ot lorge end of vnrymmetriial beom for concentrated load at .6 paint.

Chart 22. Fixed-end.momenfs a t lorge end of vnrymmetii i i l i beom for ion. centrated iood of .7 point.

Me, in terms

of PL

Chart 23. Fixed-end moments at la rge end of unrymmetri~ol beom for ion- Chart 24. Fixed.end moments at large end of unrymmetricoi bcom for con.

centrated load a t .8 paint. centrated load at 9 point.


MA, in terms

of PL

Mm in terms

of PL

Chart 25. Fixed.end momentr a, ~ m ~ i l end of vniymmetriioi beom for con- Chart 26. Fired-eod moments at rmall end of uo5ymrnclricoi beam for ion-

centrated load 0 1 . I point. centrated l oad a1 .2 point.

Chart 27. Fixed.end momenfr ol r m d end of ~ ~ ~ ~ ~ ~ e t r i c o i beom for con- rentroted load at .3 pamf.

Chort 29. Fixed-end moment3 at m o l l end of vnrymmetiicol beam for con- ~en t ro ted load of .5 point.

M,. in terms

of PL

C h d 28. Fixed-end momenfr af small end of ~ n r ~ m m e t r i c a l beam for con- reotmted load at .4 point.

Chart 30. Fixed-end moments o t rmail end of unrymmetriial beam for concentrated lood o f .6 point.

iscelloneour Structure Design

Chort 31. Fixed-end moments of small end of vnrytnmetrical beom for can- centraled load af 7 point.

Chort 33 . Fixed-end moments of m o l l end of unrymmetiical beam for concentroted good o t .9 point.

Choi l 35. Fired-end moments at either end of ry!nmetricol.bcam for uniform

Chorl 32. Fixed-end moments ot small end of un~yrnmetiical beom for con- centrofed load of .B point.

Me* in terms

of wLP

Choit 34. Fired.end moment3 ol large end of unrymmetriiai beam for "niform load.

M,. in terms

of wLP

Chort 36, Ftncd.end moments a l imol l end of ~ ~ ~ y r n ~ e t r i c o i beam for

load. uniform load.

S E C T I O N 6 . 2

1. B A R JOISTS

Several available types of bar joists of patented design are fabricated by welding. Where design permits, it is usually more economical to use these standard bar joists than to fabricate special joists. However, to meet special design requirements lmr joists can be quickly and easily fabricated. In some cases, this may be done on the construction site.

Figure 1 shouzs the framework of a factory building. Joists are spaced between beams and support the mctal roof deck. The deck is plug welded to the joists by welding at intervals through the 20-ga metal.

Arc welding also provides an efficient means for securing bar joists to their supporting members. A short tack weld on each side of the hearing plate at the ends of the bar joist permanently joins the joist to the framc- work. Figure 2 shows bar joists arc welded in place. Thus, use of arc welding stiffens the entire struchm by actually tying in the framework.

2. S T A N D A R D S P E C I F I C A T I O N S

The Steel Joist Institute, and the American Institute of Steel Construction have set up standard specifications for the design of Open Web Steel Joists (High Strength Longspan or LH-Series). The following requirements are adapted from these (1962) specifications:

Al lowable Stresses for We lds

E70XX manual clectrodcs or equivalent weld metal shall bt. used; EGOXX electrodes or equivalent weld

FIG. 1 Metal roof deck is plug welded to the open-web bar ioists below.

FIG. 2 Open-web bar joists are welded to beams and girders which support them. This stiffens the entire structure.

metal may be used on steels having a specified yield point of 36,000 psi.

f llet welds

groove welds

-. E6OXX

E7OXX

Tension or compression, same as connecting material.

S h e w ot Throd of Weld Mstd

r = 13,600 psi

r r 15,800 psi

Unit Force

f = 9.600 O

f = 11,200 w

6.2-2 / Miscel laneous Structure Design

Allowable Stresses far M e m b e r s

The allowable stresses shall be based on yield strengths from 36,000 to 50,000 psi.

tension

= 0.60 u,

compression

If L/r S C,

where:

L - length of membcr or component, center to center of panel point

r = least radius of gyration of member or component

L/r of web members may be taken as % (L/ r r ) or I./r,, whichever is larger; r, is in the plane of the joist, and r, is 11orma1 to it.

bending

for chords and web members = 0.60 a,

for bearing plates = 0.75 u7

Maximum Slem!erncss (L/r) Ratios

Top chord intcrior panels Top chord end panels Other cotnpression members Tension members

Other Requirements for M e m b e r s

The bottom chord is dcsigned for tension. The top chord is designed as a continuous mrmber

subject to axial compression stresses (aa) and bending stresses (u,,). The sum of the two (aa + UII) S 0.60 a, at the panel point.

The quality

0-a C m c h ( - o;, 1-- ") ul, 2 1.0 at mid-panel

ufc -

where:

C,, - I - 0.3 u,/u', for end panels C, -- 1 - 0.4 aa/af, for interior panels u, = calculated axial unit compressive stress u,, = calculated bending unit compressive stress at

joint under consideration

FIG. 3 In the fabrication of these bar joists, semi-automatic welding with self-shielding cored electrode substantially increased the arc speed over previous practice.

Open-Web Bar Joists / 6.2-3

FIG. 4 Bar joist studs are quickly welded in place by means of efficient portable stud welders. The studs shown are used to anchor cross- bracing rods running from top chard of one joint to bottom chord of onother, to increase torsional resistance and prevent buckling.

o;, = allo~vable axial unit compressive stress based npO" (I&) for the panel length, ccnter to ccnter of panel points

oa = allou~able bending unit stress, 0.60 u, - ur+: == - ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ - p 13'"000 where ( L ) is the full panel length,

(L/r,I2 center to center of panel points

r, = radins of gyration about the axis of bending The radius of gyration of the top chord about

its vertical axis 5 L/170, where 1, is the spacing in inches hetwcen lines of bridging.

Chard Size

No. 02 to No. 08 inci. I I ' No. 09 to No. 14 i d .

No. 15 to No. I9 incl. 1 1:: The top chord shall be considered to have lateral

support if it is propcrly attached to the floor or roof deck at distances not to excced 36".

The vertical shear values to l ~ c osrd in thc dcsigr~ of web memhcrs shall he detemlincd from full uniform loading, but shall not ba less than 25% of the rated end reaction.

Chord and web mcmhrrs in compression, composed of two componrnts stqmated one from another, shall have fillers spaccd so that the L/r ratio for cach componmt shall not cxcecd the I,/r ratio of the wholc member; if in terision, the L/r ratio of cach component shall not exceed 240. Fillei-s may be omitted in chords having intr.rior pancl lengths not over 24" and in webs of joists not over 28" in depth. In all of these cases, tlrr: least radius of gyration ( r ) is used.

Connection Requirements

Connections shall 11c designed to carry the design load, hnt not less than half of the dlow-able strength of the rnernhvr. Butt welded joints shall he designed to carry the fnll allo\vable strtmgth of the member.

Membcrs connt:cti~rg into a joint shall have their c e ~ ~ t r r s of gravity mect at a point, othem-ise the bending strtwcs duc to cccnntricity shall be taken into ac- conrlt. Eccentricity on either side of the ncutral axis of the chord mcxnbers may be neglected if it docs not t w w d the distance h ~ t w r ~ e n thc n~vt ra l axis and liack of the cliorcl. Whrn a single arrglc compn3ssion member is attached to the outsidc of the stem of a Tee or double angle chord, the wcentricity shall be taken into account.


High-strength steel reinforcing bars for concrete column verticals in the Washington N a t i o n a l Insurance Bldg., Evanston, Ill., permitted reduction of column size and savings in floor space.

Reinforcing bars in concrete columns are field spliced. Simple positioning jig maintains proper alignment during welding. These large size AlSl 4140 allay steel bars were welded with low-hydrogen electrodes.

The American Welding Society has issued Bulletin D 12.1-61 giving the Recommertded Practices for the Welding of Reinforcing Steel, and these should be followed. Table 1 of allowable stresses is adapted from the AWS bulletin.

Reinforcing steel may be spliced by butt welding two ends directly together, using either a single Vee or double Vee groove joint with an included groove angle of 45" to 60°, or a single bevel or double bevel groove joint with an included groove angle of 45". These joints should have a root opening of Vat' and a root face or land of Ys".

This butt welded joint may bc made with the aid of an additional splice member, for example a plate or aoglc connected with 1ongitudin:il flnre-bevcl welds, see Figure I, or a sleeve conncctcd by transvcrse fillet welds around the sleeve and bar, see Figure 2. The

FIGURE 1

splicc m(3mber shodd have a cross-sectional area equal to tlla strength of the connected bar.

Reinforcing steel may also be spliced by a lap joint, either lapped directly together or with an insert plate between the two bars. When the two bars have

LE 1-Allowable Stresses for Joints in Reinforcing Rods

Bevel 8. Vee groove weidi in tension, compression, or shear

4 i ' l o h O ' v' -5

m-mtL[r=/yf Doubie~vrs groove

Some os o l l o w o b l e far base metal

Flare-Vce groove 8. floie- bevel groove welds for anv direction of farce

Sheoi on throat of weld 7 = 6800 psi

Fillet welds for ony diiec- tion of force

Sheoi on throof of weld (minimum throat)

= 13,600 psi or force on weld

f = 9600 o Ibs/lined in.

.3-2 / Miscellaneous Structure

FIGURE 2

the same diameter, the nominal size of a flare-Vee groove weld is the radius of the bar. When the bars are of unequal diameter, the nominal size of the weld is the radius of the smaller bar. The nominal size of the flare-bevel groove weld is the radius of the bar.

In all of these cases, the nominal size is the throat on which the allowable shear stress of 681800 psi is applied. The actual required throat of the finished weld in a flare-Vee groove and flare-bevel goove weld should be at least 3/i the nominal size of the weld, which is the radius of the bar. The maximum gap between the bar and the splice plate should not exceed Y4 the diameter of the bar nor XB".

In general, it is easier to butt weld larger reinforcing bars together than to use a splice joint with longitudinal ccnnecting welds. On smaller bars, it might be easier to use the longih~dinally welded lap joint, althongh the doubling up of the bars within the connection region might take ttm much of the cross- section of the concrete member.

Figwe 3 illustrates a good method to butt weld a reinforcing bar lying in the horizontal position. A thin backing strap, about %" thick, is tack welded to the bottom of the joint as shown in ( a ) . After a portion of the groove weld is made, this backing strap is red hot and can easily be wrapped partially around the bar with the weldor's slag hammer as welding progresses, see ( b ) and (c ) . This provides just enough dam action to support the weld and yet does not interfere with the welding. Finally, the ends of this strap are tapped tight against the bar and the weld is eom- pleted, see ( d ) .

FIGURE 3

2. ROD MATERIAL AND WELDING PROCEDURE

Reinforcing bars are rolled from new steel produced in the open-hearth fnmace, acid bessemer converter, electric furnace, or the basic oxygen process; or, they are re-rolled from discarded railroad rails or car axles.

It is necessary to obtain a Mill Report on the reinforcing bars to be welded; otherwise, they must be analyzed before setting up the welding procedure. See Table 2.

For manna1 welding, E6OXX and E7OXX electrodes shonld be lu;cd, and prcferably be of the low- hydrogen type. Coverings of the low-hydrogcn electrodes must be thoroughly dry when used.

Any E6Oxx or E70xn electrode

TABLE 2-Recommended Welding Procedures for Reinforcing Rods 06 Various Analyses

Preheot not required. If below IO°F,

t o IOO'F

C to .30 Mn to .60

Noo low-hydrogen E60 or E70xx electroder-

Preheat to 100°F

law-hydrogen E60xx or E70xx eiedioder

C 31 to 35 Mn to .90

Thermit or pressure gor welding -- -.

low hydrogen E6Oxx to E70xx eiedroder-

Pmheat to 200°F Other procedure$ w b j e ~ t to procedure iiuolificotian

Low-hydrogen E6Oxx or E7Oxx eiedrodei-

Pieheot to 400°F

1 reqvired. if below 10-F. I oreheat to IOO'F 1

C .51 to .80 Mn t o 1.30

C .36 to .40 Mn to 1.30

+- ! Could also use

submerged-orc. / theirnit. or

C .41 to .SO Mn to 1.30

preSIUie g o i welding

or approval oi the Engineer

1. INCREASING PANEL RIGIDITY

The efficient use of materials is the &st essential to lower cost designs. One way to achieve such efficiency is to use lighter-gage plate that is easily fabricated and to add stiffeners as necessary for the required rigidity.

Regardless of how flexible or rigid the stiffeners are, they will increase the stiffness of the whole panel by increasing the moment of inertia ( I ) of the member pancl sections.

The usual method is to consider a section of the panel having a width equal to the distance between centers of the stiffeners.* In this manner, just one stiffener will be included in the panel section. The resulting moment of inertia ( I ) of the stiffener and the section of the pancl may be found from the following formula:

FIGURE 2

where:

* r / = distance between stiffeners, in.

d = distance between center of gravity of panel and that of stiffener, in.

A, = cross-sectional area of plate within distance b, in.'

**A, = cross-sectional area of stiffener, in.'

t = thickness of panel, in.

** I. = moment of inertia of stiffener, in.+

*If therc i s any question about ihcdistnnce belwcon stiffeners becoming toogreat, Section 2 .1% will provide some guidance. **Data obtained from any stocl handbook

FIGURE 1

In figuring the maximum bending stress in this built-up section, the following distances to the outer fibers must be known.

l

- -h -%- -h ...... (3 )

where: c, = distance from ncutral axis of whole section to

outer fibcr of plate, in.

c. = distancc from neutral axis of whole section to outer fiber of stiffener, in.

Tlic pand section may then be treated as a simply supported beam and designed with sufficient moment of inertia ( I ) to withstand whatever load is applied. Use a 1" wide strip of this panel, and use uniform load of ( w) lbs per linear inch; if entire width of panel ( b ) , use uniform pressure of ( p ) psi.

Fignrc 3 illustrates the technique of treating a panel section as a beam under three different can& tions. Formulas for finding maximum deflection, bending momrnt, and vertical shear are given, with p being the pressure in psi against the panel.

6.4-2 / MiscelIaneous Structure Design

FIGURE 3-Properties of Ponel Section Treated as a Beam

(With reference to Figure 3 ) If due to weight of liquid or granular material:

F

F - app/lcd force N(50%

Condition A Condition B Condition C

where:

h = height of liquid or material, in.

13 = height of liquid or material, ft

s = specific gravity of liquid or material, lbs/cu in.

d = density of liquid or material, lbs/cu. in

D = density of liquid or material, lbs/cu ft.

F I," K . - - - . 384 E r ,,,, \ /3

( 1 - K 2 ) .

The maxi~num stress in the outer fibers of either the panel or the stiffener may be found by using the corresponding value of e and the maximum moment (M,.,) in the following formulas:

(10)

for the panel

. . . . . . . . . ( 5 )

I M,,, = 0.0642 p b ~ ~ 1 . . (8) Mma, = F L K (1 - K ) I (11) Mm,, =

. . . . . . . . . . . . . . . . . . . (12) -1 . . . . ( 6 )

for the stiffener

2. RESISTING TORSION

, ,

/ /

\ i /

- Ihere is no twisting \ \ actioncn 45'diagonel \ \ member since shear components cnncel out \

\ Only diagonal taos/bn a n d \ / ,' rompressioo a r e formed, W which place member in bending; member is very r igid.

FIGURE 4

ow to Stiffen a Panel /

Conventional cross stiffeners on a panel do not offer any resistance to twisting. Howerm, if these stiffeners are placed at 45", they will greatly increase the torsional resistance of a panel. There is no twisting action on tlie 45" stiffeners because the two components from the longitudinal and transverse shear stTesses are equal and oppositc and, therefore, cancel out.

The leg size of the continuous fillet weld required to join a stiffener to the panel may be found from the following formula:

= " a (E70 welds) 11.200 I n

where:

o = li3g jize of contiriuous fillet weld, in

V = total shear on section at a given position along the beam, lbs

a = area held by weld, in.%

y = distance between center of gravity of the area and neutral axis of whole section, in. - .- c , - % t

I = moment of inertia of whole section,

n = ~iuinber of continuous welds joining the stiffener to the panel

If intennittent fillet welds arc to be used, calculate the continuous fillet weld leg size expressed as a deci- mal, and divide this by the actual leg size of intennittent fillet weld used. W ~ c n expressed as a percentage this will give the amount of intermittent weld to be used per unit length. For convenience, Table 1 has various intennittent weld leogths and distance between centers for a given percentage of mntinuous weld.

TABLE 1-Intermittent Welds

Percent of Length d Intermittent Continuovr Weld. and Dirtanoe

Between C e n t e n

75%

3 - 5

57 4 - 7

50 2 - 4 , 44 I 4 - 9

43

40 I 4 - 10


Weld fabrication of large panels, using proper stiffeners, provides required strength and rigidity, while keeping weight to o minimum.

This is a broad classification, covering many types of containers. However, principles and formulas relating to their design are best discussed as a single group. Some of these containers have flat surfaces; some have curved surfaces; some have both. Some carry steam, gasses, or pressurized 5uids that exert uniform pressure in a11 directions; others carry bulk materials such as grain, the weight of which exerts a varying horizontal pressure against the side walls.

The first requisite of a container is that it be tight. It must have sufficient strength to withstand the internal pressure to which it is subjected. In arc-welded constrnction, the joints are made as tight and strong as the plates joined. In large tanks built up from a number of plates or sheets, butt welds arc: customarily specified.

Many containers must he designed and fabricated according to the minimum requirements of certain codes, for example ASME. Most containers have thin

shells in comparison to their diameters and come under the classification of thin-wall shells.

Types of Containers

Flat and/or Curved Surfaces ~ p~

tanks drums chutes vats bins stacks hoppers silos pipe and piping systems

and many others

F T H E CONTAIN

The surfaces of any container must withstand pressure of some type, so it would be well to consider the strength and stiffness of various shapes and forms of plates under uniform pressure.

111 analysis of a given container, the designer ex- plodes it into its various elements and applies the corresponding formulas.

Some containers are of box construction, made up entirely of fiat surfaces. Other containers, many tanks for example, consist of a cylinder closed at each m ~ d by a fiat plate.

Table 1 presents design formnlas applicable to various flat plates subjected to internal pressure.

Determine the required plate thickness of the following tank to hold water, Figure 1.

Since the varying pressure against side walls is due to the weight of a liquid:

p = ,4336 H s

= .4336(6)(1)

= 2.6 psi

FIGURE 1

where:

1% - the maximum height of the liquid, in feet

s = the specific gravity of the liquid

It is nwessnry to consider only the longest side plate, having the greatest span between supports:


120". The top edge is free, the other three are supported. This is recognized as condition 4D in Table 1.

Since the ratio of plate height to width is-

values are estimated from Table 1 to be-

p = .14 and y = ,030

Then the reqnired plate thickness is derived from the maximum stress formula:

or, assuming an allowable stress of 20,ON psi-

P p b2 t2 = --- a

- - ( J 4 ) (2.6)(120)2 20,000

= ,262

:. t = fziE = .512", or use W' &.

Checking the detlection of this plate-

Since this deflection would be excessive, a stiffening bar must be added along the top edge of the tank to form a rectangular frame, Figure 2.

Tank with Top Edge Stiffener

FIGURE 2

The modified tank now satisfies the condition 5A on Table 1, because the critical plate is supported on all fonr edges.

The ratio of plate height to width still being .6, +slues are estimated from Table 1 to be-

p =: ,102 and y = ,0064

Since the same maximum stress formula applies-

= ,191

.'. t = l/-iT = .437", or use &

Checking the deflection of this plate-

It might be advisable to go back to the Yz" plate thickness, still using the top edge stiffener, in which case the bending stress and deflection would be reduced to-

a,,, = 15,300 psi and A,,,, = .92"

There is another method of determining the bending stress and deflection. A description of this follows immediately.

Considering Plate Section as a Beam

A narrow section of the tank's slde panel (width m = 1") can be considcrcd as a beam, Figure 3, using formulas taken from Reference Section 8.1 on Beam Diagrams.

FIGURE 3

Tanks, Bins and Hoppers / 6.5-3

TABLE 1-Stress and Deflection, Flat Plates* Subjected to lnternal Pressure fpl, psi

CIRCULAR PLATE

I I A ) Edge. wpporled; uniform lood

A t center: 1.24 p P

(rnax) O, = c, = - -- t=

,695 p r" Am,= = - -

E t3

(1s) Edger fixed; uniform lood

,1705 p r' A,.. , - E t'

At edge;

3 P P (moxl c, = -

4 ti

,225 p P 0, = -

P

SQUARE PLATE

(3A) Edpsesupparted land held down); uniform lood

At center; 2870 p o2

(rnax) r. = - L--- P

,0443 p 0 4 A,.. =

E 13

ELLIPTICAL PLATE

(2A) Edger supported; uniform load

At center: ,3125 12 - a) p b'

(max) O;, = - t'

1.146 - .1 a) p b4 (appiox) Amrr -- E P

(28) Edges fixed; uniform I h d

At center:

v. = - ,075 p bP (10 a' j-3) P 13 + 2 a' + 3 ad)

At edge: 1.5 p b' a'

(Spon 0 ) cr = tZ 13 + 2 ila + 3 ad)

lmox) (Span b l oa = 1.5 p b"

t' (3 + 2 a" 3 39

At center: 1 6 6 p a*

a. = - -- P ,0138 p A,., = -

E t=

At midpoint of each edge; 308 p a'

(max) o. = + P

*After Roark, "Formulas for Stress and Strnio". Table I continued on following page


Table 1 continued

k - b 4 RECTANGULAR PLATES

(48) Edger fixed; uniform load --

At center; At midpoint of iong edges; p bZ 1.225 + ,382 a' - ,320 a? c.=-- (moxl oa = - .5 p ba- P p b'

P f (1 + ,623 a*) Or = ? 75 p bP

(,"OX) Sb = - B p b' or = -- f At midpoint of short edger:

P ( i + 1.61 a3) .25 p bs

,1422 p bd Y p b4 u, = ------- Lax = - E t' E P U + zTT2ior =--

P

See the following rub-table3 for voluer of P ond Y:

q q ~ p q - - ~ ~ : i ; " . ~ 1.8 I

(4C) Ail edger supported; varying laad Load incieoring uniformly from zero ot one edge to a moximum of lp) psi ot opposite edge (tiiongulor load)

P p bP am.. = - P

Y p b4 Am.= = - E t3

P

1.9

FOR EDGES FIXED p r p >TiiF1 43% 1 ,4252 1

The foilowing values to Condition 4C.

I 2.0 j gc

Toble I continued on facing page

I - -.

FOR EDGES SUPPORTED

,0251 --

,0138 ,0164 ,0188 ,0226 - ,0240


Since the maximum bending moment here is-

Tobie I continued

(40) Top edge free, other three edges wpported; i(1ryiig load -

Lood increasing uoiformly from zero at top edge to o moximum of (p) psi at bottom edge (riiongular loodl

B P bY v,,,*= = P

Y P b4 Am.= = E r

The following volver apply to Condition 4D;

M,,, = ,0642 p hZ m (with h expressed in inches)

. I i .16 2 0 . . .

,026 ,033 ,040 --

= 20,800 psi

instead of the 15,300 psi obtained by considering the entire plate width; and-

.0625 p h4 m A,,, = - E I

1.5

2 8

instead of the .92" obtained by considering the entire plate width.

This method of isolating a I" strip of the panel and considering it as a beam will indicate greater bending stress and deflection than actually exists. The reason is that the stiffening effect of the surrounding panel has been neglected for simplicity.

The previous method of considering the entire panel is recommended for its accuracy and for a more efficient design wherever it can be applied.

2.0

.32

2.5

.35

,064

Adding Another Stiffener

~ r . 0 5 8

When a panel is divided into two parts by a large stiffener, it becomes a continuous panel, triangularly loaded with a rather high negative moment at the stiffener which a d s as a support. There is no simple formula for this; therefore the method of mnsidering a I" strip will be used, and of course will result in a slightly greater stress value than actually exists.

The plate thickness in the tank being considered can be reduced by adding such a stiffener around the middle of the tank, Figure 4.

3.0

.36

,067

FIGURE 4

The first step is to locate the stiffener at the height which will produce the minimum bending moment in the panel, both above and below the stiffener.

3.5

.37

' ,069

4.0

.37

,070


(Again use formulas from Reference Section 8.1 on Trying %," @ Beam Diagrams. ) This dimension ( a ) , the distance between the two stiffeners, is- h.1 M 6 urn** = -- - - -

S t2

a = 5 7 h = .57(72) = 41"

Then, at tbc middle stiffener-

M,,, = ,0147 p h% = 12,200 psi OK

ontainer Sur A Figure of

4. STRESSES IN SHELL

The various container shapes illustrated in Table 2 are formed by a figure of revolution.

In any of these containers, the internal pressure ( p ) along with the weight of the gas, liquid or other media within the container produces three types of tensile stresses in the container's shell. These are:

1. u,, =. tensile stress in the direction of a

TABLE ?-Container Surfaces Formed By A Figure of Revolution

THIN WALL COA :ONT+?INER SMPE IUNIT NALL SEM(EN7

CYLINDER 1

SPHERE 1 Urn.

meridian. ( A meridian is the curve formed by the intersection of the shell and a plane through the longitudinal axis of the container.) This stress is referred to as longitudinal stress.

2. cr,,,, = tensile stress in the direction of a tangent to a circumference. (A circumference is the curve formed by thc intersection of the shell and a plane perpendicular to the longitudinal axis of the container.) This stress is referred to as tangential or circumferential stress but is commonly called the hoop stress.

3. urn = tensile stress in the radial direction. For containers having relatively thin shells (gen-

erally considered as less than 10% of the mean radius) and no abrupt change in thickness or curvature, the radial tensile stress (u,.,) and any bending stress may be neglected.

TABLE 3-Stresses in Thick-Wall Cylinders

Uniform internal

radial pressure only -

smg = 0

ccp = (%.+.i!: re2 - iss

(mox ot inner iuifoce)

a,. = P (man at inner ruifoce)

Uniform internal

prersvre in all

r i z = P (m)

r.p + i t P

(rnox ot inner rvdocei

a lp = P (mox ot inner rudoce)


The biaxial tensile stresses u p ) and u p ) in thin-u,all containt~rs can be calcillated with the basic formulas ~hown in Tahlri 2. where:

t, = thickness of shell, in.

r, = mean radi~ls of a circumference of the shell, in.

r, = mean radius of the meridian of the shell, in.

p = internal pressure, psi

In thin-walled containers, the hoop stress is assumed

to be uniformly distributed across the shell thickncss without serious error occurring in strcss calculations. However, in a thick-walled container grnerated by n figme of revolution thc decreasing variance of hoop stress from the inner surface to ihc ontcr surface of the sbell wall must be considered.

Table 3 presents formulas for calculating the stresses in two eommon thick-\vaIIcd cylinders. In the first condition, the internal prcssurc parallel to the sbuctural (Iongitudinnl) axis is balanced by the external forcc against the moving piston and hy the resistance of the cylinder's support, and the resultant longitudinal stress (c,,,,) is zero. In tha second condition, there is a longitudinal stress (u,,).

and spherical shells, where:

Any prrssure container of any importance undoubtedly p = internal pressure, psi

must conform to the minimum requkements of the us = allowable stress (Scc ASME Sec. 8, par USC- ASME, so it would be well to use ASME Section 8 23 ) "Unfired Pressure Vessels" as a guide. In general this E = joint efficiency (See ASME See. 8, par UW- covers containers for pressures exceeding 15 psi up to a maximum of 3,000 psi, and having a diameter ex-

12)

ceeding 6". Table 5 presents the formulas for calculating the ~ ~ b l ~ 4 presents the formulas for calculating the minimum required thickness of various types of heads.

minimum required wall thickness of cylindrical shells Turn to next page for Table 5.

TABLE 4--Wall Thickness of Shells Subjected to Internal Pressure (p), psi

IASME-8: Unfired Pressure Vessels)

I CYLINDRICAL SHELLS IUG-27c and UA-I) SPHERICAL SHELLS IUG-27d and UA-31

Thin shell - when t. <- 'h rz ond p < ,385 a. E Thin shell - when t, < ,356 i t end p < ,665 a, E ! -- I

Thick shell - when t, > '12 rl and p > ,385 E 1 tn = P i 1 .

21a. E - .I p) Th~ck shell - when t- > ,356 r i and p > ,665 o, E --

t# = r , i f i - I )

iscellaneous Structure

TABLE 5-Thickness of Formed Heads Subjected to Internal Pressure (pi on Concove Side

(ASME-8: Unfired Pressure Vessels)

ELLIPSOIDAL HEAD fUG-32d and UA-41)

Standard head - where h = d i /4 Head of other propartianr ~~ ..~

(h = minor oxir: inside depth of p d l K tn = head minus skiiti 21** E .i d

where: P d,

tn = 21s. E - .I p

TORISPHERICAL HEAD iUG-32e and UA-4dj

Standard head - where r* = .06 r , . . Head of other proportions -- ~~

!ir = knuckle rodiur) = -P~LLM -885 p r i

2 ( 0 , E - .I p) ta = where:

o, E -- .I p

HEMISPHERICAL HEAD Thin head - when ti, < ,356 Thick head -when tt, > ,356 i t

IUG-32f ond UA-3) - and p < ,665 o. E -. and p > .665 m. E

s - ti, = r, ( V Y - I )

= -2-- wheie: 2(0, E - . i p)

2ia, E + p) y = ---- 2 o . E - p

FLAT HEAD (UG-34)

integrol heod

'yi groove weld

t, = twice required ihicknerr of rpheiicol shell or 1.25 t. and not greater than tn

t,, = d, g-

c r 25

bolted

1. BASIC FORCES AND STRESSES

Designing hangers or brackets for snppotting a shell such as a pipe, tank or pressure vessel requires consideration of two important factors:

1. The additional stress of the support forces when combined with the working stress of the shell must not increase the stress in the shell above the allowable limit.

2. The support should not restrain the stressed shell so it becomes too rigid to flex under normal changes in working pressures or loads.

Many types of stresses are involved in any supporting structure. The more common types are the following:

1. The internal pressure of the gas or liquid in the shell, along with its weight, cause tangential (uc,) and longitudinal (e,,,) tensile stresses in the shell.

2. Any radial force (F1) aeting on a section of the she11 causes bending stresses in the ring of the shell (from the bending moment M,) as well as axial tensile stresses (from the tensite force T), both of which act tangentially to the circumference of the shell.

3. The radial force (F1) causes radial shear stresses in the shell, and the longitudinal force ( F a ) causes longitudinal shear stresses, both adjacent to the hanger. These stresses usually will be low.

After proper analysis of the forces involved, the various stresses must be combined to determine the maximum normal stress (G-,.x-teusile or compressive) and maximum shear stress (T ,~ , ) . If the resulting stresses arc excessive, a simple study of the individual stresses will indicate what portion of the hanger is under-designed and should be strengthened.

For example, the bending stresses may he exees- sive, indicating that some type of stiffener ring should he attached to the shell between supports to suh- stantially increase the moment of inertia of the shell section thereby decreasing the bending stress.

The following discussions identify and analyze the &ect of various basic stresses and relate them to material thickness and curvature.

2. STRESSES IN S ELL FROM INTERNAL PRESSURE

As explained more fully in Section 6.5, internal pressure in a shell produces two tensile stresses of importance.

1. e,,, = tcnsile stress in the direction of the meridian. This is called the longitudinal stress.

2. uc, = tensile stress in the direction of the tangent to the circumference. This stress is commonly called the hoop stress, but is also referred to as the tangential or circumferential stress.

The tensile stresses G-,, and ee, can be calculated with the formulas presented in Table 2 of the preceding Section 6.5 and repeated here.


3. EFFECT OF U SUPPORT WELDED TO SHELL

The force ( P ) applied to the hanger (see Figure 1) may be resolved into a radial component (F,) and a longitudinal component (F1) having the following values:

where 0 is the angle between guy cable or support attached to the shell and the horizontal.

FIGURE 1

If these components are applied at some eccentricity ( a and b ) , they will produce mommts applied to the shell section by the hanger and having values:

Combining these values, observing proper signs, will give the total moment acting on the shell from the hanger:

A study of stress distribution in the shell can be resolved into separate analyses of the radial and moment force distributions. Before analyzing these forces, however, the engineer should determine how much shell beyond the hanger is cffective in resisting these forces.

The shell with stiffeners can be compared lo a curved beam with an extremely wide flange, Figure 1. Von Kam~an" suggests that an effective width (e ) of

* "Analysis of Some Tliin-Walled Structures", Von Kalman, ASME paper AER-55.1% Aer Eng, Vol. 5, No. 4, 1933.

RAD/AL FORCE (f-) DISTR/BUT/ON

F ; : f , ~ d t Z x J x f , x e

f, = --- d r e

FIGURE 2

the flange on each side of the stiffening web is approximately-

where:

r, = radius of shell curvature, inches

t. = thickness of shell, inches

The value of "e" should be limited to a maximum of

The radial component ( F , ) of the force (P) is applied directly to the shell. It is reasonable to assume that the radial forces applied to the additional shell width ( e ) would decrease linearly to almost zero at its outer limits. This assumed distribution of radial forces (fa) due to the radial component (F1) is sketched in Figure 2.

The value of f, is equivalent to the force (Ibs) on a 1" wide ring of the shell.

The longitudinal component ( F 2 ) of the force ( P ) because of its eccentricity ( a ) , and the radial component (F,) because of its eccentricity (b ) , combine into moment M, and apply radial forces to the shell having a distribution similar to that of bending forces, i.e. maximum at the outer fibers and zero along the neutral axis. The assumed distribution of the radial forces (fb) due to the action of the applied moment is indicated in Figure 3.

RADIAL FORCE (fA) DI5TRIBU7IOFr

FIGURE 3

Design of Hangers and Supports / 6.6-3

The value of fl, is equivalent to the force (Ibs) on a 1" wide ring of the shell.

The resulting radial forces applied on the shell must hc added, being careful to watch the signs:

4. EFFECT OF ADDING STIFFENING RING

For additional stiffcning of the shell at the sup1>ort, rings may be welded to the shell. 4 s before, the additional width of the shcll on each side of the ring assumed to be effective in resisting the,se forces is-

with e not to exceed 12 t, on each side of the ring. The total radial force ( F ) applied to this built-up

section is the radial force resulting from the longitudinal force ( F ? ) , p h ~ s any radial force ( ) applied at this point of support:

FIGURE 5

where:

A = area of shell ring cross-section or built-up section

S = section modulus of the same section

Part A: Four hmgers are used for guying a smoke slack with its a& in the vertical position, Figure 6.

After determining the bending moment in this p i m p ~ . z s o i b a . 2 ~

built-up ring resdtiny from thc radial forces at the TI. ,OW. 8 .60 . *, z * u. d .,om n . 4 wmm, point of support, the nioment of inertia ( I ) of the -

C d i t m r m i T ~ M ~ ~ ~ ~ # c ~ J /r S w a i ~

section is cdculated. The bending stresses are then F#aw ,#rzewe~ P # , $ ~ w e

r 2 : w * + ti 'II . 6,ooo,, fourrd and later combined with any other stresses. - , . % ;weL;,...... d k

5. EFFECT OF THESE FORCES UPON A SECTIONAL RING OF THE SHELL

Forces (f , ) normal to the shell sct up iangential tensile forces ( T ) and bending moments (M, ) in the ring of the shell, Figure 5.

Stresses u,., and u,., are added to r,, to give u, = total tangential (or circumferential) stress in a section of the critical shell ring.

The maximum shear stress is equal to '*L the difference of the two principal stresses (u) having the greatest algebraic differcnce. See Section 2.11, Topic 2.

The following are typical examples that demonstrate the use of these formulas for calct~lating the stresses in a shell.

6 : P m Q ; Z 5 0 r . d 6 6 ' f i 7 / b - h'f, a i ; ~ b ~ : E ~ 2 i 7 + 0 ~ / l i . 4 % ~ - i a -

k i r i r t Jml f imu ' e ' f h J,DE $6 Hmsn

e ; fi : x/94';xz,v. - 7 2 -- Cnicmnn~s Rnam k c J m m TO Sxiii

f- = $ = 10.4 '%m me a , m m ! - f a :A ia,c,(d,,rC) :s .... ~.*Nc I J, ' - I ZTAL R A O I ~ L FDRCE

4 'f&+r,' ,0.4t iS).-2.9%':* 'B‘ - - FIGURE 6 \ , ,,./

6.64 / Miscellaneous Struceure Design

Determine the total radial force acting on the shell as a result of the force ( P ) applied to the hangers.

Part B: With tangential tensile force ( T ) and bending moment ( M , ) per 1" wide ring of this shell resulting from radial forces ( f , ) applied to the four hangers, cnlcnlate the tciisile (u,,,) and bcnding ( u , b )

stresses ;it the hangers.

FIGURE 7

-- FROM TABLE I I FROM PARi A

K 0 3 0 0 i, f . 259 '%in x w s

Concludon: Combining thesr stresses in the outer fiber of the shell adjacent to the hanger shows our analysis of the shear stress (T,,,) to be-

a,, 3,OOOps,

FIGURE 8 0, a % + % : 6,000+r,5~4~d;.5~Q~w THEN

8 5 4 4 0 ?,hr = A-- = 4,Z7Zps, 2

4 STRESSU WIIMN REASON

I Problem 2 1

Part A: Four hangers are used t o support a vertical 12" stimd pipe. Figure 9. Iletermirre the total radial force acting on the shell as a rcsrdt of the force ( P ) applied to the hangers.

Part B: With tensile forco ( T ) and bending moment (M,-) per I" wide ring of this shell resulting from radial forces (f , ) applied at the four hangers, calcli- Iatc the tc~rsilc (cr?,) and bending ( u ) stresses at the hangers.

Since this bending stress in the ring of the shell is excessive, it is necessary to stiffen the shell in this region. To accomplish this, two '/4" x 2" ring stiffeners are added as illustrated, Figure 10.

&> FIGURE 10

The effect of the bottom ring will be considerecl since it will apply radial tensile forces to the built-up ring and shel! section. Using tho method of finding moment of inertia by adding arcas (Sect. 2.2) , the properties of this section are as follows:

TABLE 2?

THEN MOHENT OF INERT/A ABOUT NEUTRAL ,4115 W f L 5f M1 / 7052; Q.532.iii, 4

IN, z I x - ~ 3.282-- ~- 1 0 5 7 -- AND NtUTRAL AX15 WILL Bf

M 1705 = C, : A : , = + :6 /3 ;n . - , 0 5 7 --

Design of Hangers and Supports /

The radial force ( F ) acting on thc ring section and resiilting from the vertical force ( P ) is-

Porf @: Rwalculation of the tensile ( c r ) and bending (cr,,,) stresses at the haligcrs yields the foliowing results:

FROM J8BL E I T H ~ r / ? - ~ f f$ = 0500 i- : 4 .?OO

T = k; F : osoa r /coo = j q ~ & ~-~ * j""' ?*OM r P a E 2 ) = ic*: i-Q. j,, - - . . . ..

The hoop stress of u,,, = 1,888 psi in the slieil will he assumcil to bc reduced when considered to be acting over the entire cross-section of the built-up ring st!ction:

Combining thcs(s s1rcsst.s in the outer fiht,r of the lower ring, adjacent to the h:inger, we find the maximum shrar s t r t x ( T , ~ , , ~ ) to br-

'6 SIRE35 WIIHIIV REASON DISIGN Oh:

FIGURE 12 -

FIG. 13-Typical Hangers and Supports


F l Part A: What transverse or radial force (F,) can

be applied to the web of this I section through the gusset plate showm? See Figure 14. The resulting bending strcsses are to be kept down to a reasonable value, such as u = 15,000 psi, since the I section is already under applied load. The grlsset plate intersects the web of the I section along a predetermined distance of d = 10".

FIGURE 14

The analysis of this problem again stems from Figures 1, 2 and 3 and related text. Here, the gusset plate acts as a hanger.

Considering the web of the I section as a panel, the section flanges act as stiffeners and give the entire section a high moment of inertia about its x-x axis. However, to be conservative assume the width of web beyond the gusset that is effective in resisting the bending moment on the web to have a maximum value of 12 times the web thickness.

effectioe width of tceb

e = 12 1,

= 12 (294")

= 3.53"

moment on tceb clue to force on gusset

M = F, X 3"

tangential forces applied to web (see Fig. 2 )

total tangential forces applied to web

f = f, + f, = ,074 Fl + ,078 F,

= ,152 F1 Ibs/in.

Consider a 1"-wide strip of the web:

F;L

section modulus of strip

tangcntinl force on strip

- 4( 15,000) (.0141) -

(10.91)--~-

= 79.2 lbs/l'-wide strip

Hut:

. allowable tangential force on web

= 521 lbs

Design of Hangers and Supports /

Part B: What transverse force (F i ) can be applied if it is concentric n,ith the center of gravity of the connection? See Figure 15. There would be no moment ( M ) .

FIGURE 15

Here:

M = 0

hence:

- - FI - -- - (10) + (3 .53)

= ,074 F,

Consider a 1"-wide strip of tllc web. As before:

S = ,0144 in."

f = 79.2 lbs/l"-wide strip

Rut:

General Formula

A gencral formula, if the transverse force ( F , ) is concentric with the center of gravity of the connection, is-

Assume: F, =

6 L e = 12 t-

Part 6': What transverse force (F , ) can be applied if a stiffenrr is added to the web section to increase its be~idiirg strength? See Figure 16.

FIGURE 16

The stiffened web will now have a much greater moment of inertia in the direction of tangential force. Although the gusset plate intersects the web of the I for a distancc of 10", to be conservative only a portion of this ( h 5 t, + 2,) can be considered as resisting the moment on the web.

Following the analysis of a stiffened plate as given in Section 6.6:

Here:

e = 3.53"

A, = 2.2216 in2 (arca of effective stiffened portion of web)

I,, = .01601 in.4

A, 1.5 in."area of stiffener section)

I, = 1.125 in.4

d = 1.647" (distance, C.G. of stiifener to C.G. of web)

.6-8 / Miscellaneous Structure Design

and since

FIGURE 17

moment of inertia of entire section

distance of N.A. to outer fiber

c , = h - c ,

and since

A. d c, = t As + AD + 2

t A8 d c - h - - - . . a - 2 A, + A,

(1.5) (1.647) = (3.294) - (.147) - (1.5) + (2.216)

= 2.483"

section modulus of entire section resistant to force ( F I ) which is maximum at extreme fiber

I S = - cs (3.570) -

- (2.483)

= 7920 Ibs allowable tangential force on web

Alternate Location of Stiffener

The web stiffener could be placed on the back side of the web (Fig. 18). However, additional brackets might have to be used to safely transfer the transverse force (F,) back into the stiffener. Otherwise, both the gusset plate and the stiffener might be overstressed in a localized area where the two intersect (Fig. 19).

"...,u FIGURE 18

S E C T I O N 7 . 1

With today's cooti~iui~lg progress in welding technology and the rapid rxp;~rrsion of \vrldcd coustn~ction~ along with thc ~lcvolopnlcnt of II(:W a i d better steels, the mginrcr or nrchitwt his ;r multiplicity of choices for a givcu p r o j ~ t . The followiiig information is dcsignrd to aid him in sclcvting the proper stri~ctunil steel for his needs. . . on the hasis of streugth and cost.

In Novcmbt.r of 1961, tlie Amcrican Institute of Steel Coi~struction ;~cloptcd a nrw "Spwification for the Design, E ~ b r i i i ~ ~ and 17rcctio1i of Structnral Steel for n i l l i ~ ~ g s " . This Sprcification, which was revisml in April 1063, inclvrdcs dcsign specifications for six lirnerican Society for Tcsting Materials grades

of stcd wit11 specified rniriimum yizld points ranging from 32,000 to 50.000 psi.

In addition to thc stcels sprcifically includcd in the ilIS(: Spccificatiml, a nurnhiv of proprietary structural stccls arc I hring offrred by v;irioiis t ce l prochwrs. Tl~rsc steels have specified minimnnr yield poiuts rangir~g from 45,000 lo 100,000 psi.

As a rrsult, the rngincer or architect tod:~y is f:icid with a problem hr r;ircly encountered 10 )!cars hnforr.: the selection of t l ~ c proper structiird steel that is hwt s ~ ~ i t c d to his rrcrils. Fiirthrrmorc. since weldrd (.oostrirction is iilcrt~asiirgly h h g iiscd for d l tqws of strr~ctures, tho rlrsigncr must b(, assured thnt thc v d d - ing of thcse stwls is performed in a m;mncr which will pro\,idc sound welcls ccono~nically.

ING THE STRUCTURAL STEELS

2. STEEL CLASSIFICATIONS

In the design of hoildings, bridges, and similar strue- tures, the engincer or architcct is concerned primarily with three groups of structural steels:

21. Carbon Steels R. High-Strengtlr Lo~v Allow Steels C. Ireat-Trcatrd Co~~strrictionnl Alloy Steels The first h5.o of thest: categories inclnde the six

basic ASTM grades o i strncturid sted inclodcd in the AlSC Specificntior~. The nrwlranical proprrties arid chr~nistry limitations for tllese six ASTM grades are shown in Tnhles I A arid 1H.

3. CARBON STEELS ASTM Grades A7, A373, and A36

The carbon stiiels for tlie struct~iral field include ASTM Cr:rrlt:s A7, A373, and A%. The prirrcipd strengthening agents in these strels are carbon and manganese. Speci- fied ruininirim yield points range fro111 32,000 psi lor A373 to 36,000 for A36.

ASTM A7

The first ASTM sprcification for stcrl wscd in building co~~stroction was proposcd in 1900, and was adopted one year later as the "St;tndard Specification for Steel

Field welding of vertical member to bottom chord of Vierendeel truss for 17-story Foundation House in Toronto, Conado. Truss is built of high-strength, low- alloy steel with 55,000 psi minimum yield strength.

7.1-1

7.1-2 / Joint Design and Production

for Buildings." When the ASTM adopted a numbering system for its specification in 1914, "Standard Specifi- cations for Steel for Rnildings" was designated as ASTM A9. The designation "ASTM AT was given to "Stan- dard Specifications for Steel for Bridges." In 1936 the ASTM combined A7 and .49 into one specification, ASTM A7, "Standard Specifications for Steel for Bridgrs and Buildings."

This specification was written to provide an economical as-rolled steel which would assure specific minimum strength requiren~ents. The cnrrent version requires minimum tensile strength of 60,000 psi and minimum yield point of 33,000 psi. There are no limitations on chemistry except the sulphur and phosphorus

aximum maxima. The specification also inclndes a m .'

tensile strength and minimum elongation reqnirements. The most economical way to produce a steel of

this nature is through the use of carbon and man-

ganesc in varying amounts. Carbon may be found in thcse steels in percentages ranging from a low of approximately 0.10 per cent to a maximum of 033 per cent or in some cases, even higher. Manganese is generally added to provide increased strength with less carbon to avoid the liardcnahility effect of high mrhon in the stcel. The manganese also improves hot rolling charactvristics of the stecl during production.

ASTM A373

LVith the increased nse of \velding after World War 11, it became necessary to limit the carbon and manganese in A7 steel to screen out "high side" heats that sometimes prescnted welding problems.

In 1954, ASTM .4373, "Strnctur:il Steel for Wcld- ing" was written. This specification limits the carbon and manganese, in addition to the maxima for phosphorus and sulphur, to insure good welds using stand-

TABLE 1A-A Comparison of Steels for Construction ASTM Carbon Steels -

ASTM Grade -

A 7

Mi". Yield Point

Thickness

Chemical Req8

Tensile Sirength

psi Other -

-

ementr (Ladle) Pr

S

~~

Group A 13) -.-+ ------1------------------- - To I/>'' incl.

32.000

. . .

-. - Over I"

Shope. 1 I---

Over lo Ii/2" id.

Over 4" to 8 ioc!.

To 3/4" id.

I over %,, to 11/2" incl.

.2..

[I) Bored upon boric rteeimaking pioceis.

(2) When copper steel i i specified. the min copper ir 0.20%.

!31 G r o w A conn i i re i the fo!lowincl wide flanqe beams

Selection of Structural Steel / 7.1-3

ard high speed welding proccd~ires. However, the limits on carbon a i d mang:nirst :it that tiint: necessitated a slight rediiction in t l r ~ stn~ngth of the stcel, and thc minimirm yield point was placed at 32,000 psi. The specification fnrthcr reqnircs that plates over one inch tliick be producrd folly killed to insure ;i homogeneous steel in these heavier thieknesscs.

With the est:~blishment of A373 by the .4STM :IS

a stcel for \veldd construction, thr Bureau of Public Roads designated this grndc to IF riscil for \wlded bridges.

ASTM A36

By 1980 the mapor prodrm~rs of .47 stccl had begun to realize the fruits of tlic rirotlernization and expansion of their facilities aftcr the war. Through improvements in quality control arrd through hctter heating and rolling techniques, thcy could produce an .47 type steel to a higher strcngth lcvol \vhile maintaining carbon and mangarlPsc \vithin the limitations dvsirable for economical welding.

As a result of these improv(.mtmts, S T M A36 "Structural Stecl" was pi-opnscd, and was xdoptcd in 1960. This specification imposrd controls on carbon and mangancsr to i~lsnre tw~nomical wtkling and specified a mini~n~tm yield point of 36.MW psi, n 10 per cent incrr~asr~ ol.el- A7. In 1962, A36 w s revised to place further limitations on carbon and manganese and was s~ihscqnerrtly xccptad by the Bureau of Public Roads for \vt4dcd bridges.

In essence., the ncw A36 specifiration combines all of the advantages of A373 in a stecl which has a higher rnini~n~im yield point than A7, yet costs no mort, thau A7 i l l shapes and costs only slightly morr than A7 in platos.

4. HlGH-STRENGTH LOW ALLOY STEELS ASTM Grades A242, A440, and A441

??te high-str-mgth gri~i1c.s of stcrl, ASThl A%_", A440. a id r1411, Iin\.r minilnliin spi'cificd yidd points vitryirrg fnmi 12,000 psi to 50,000 psi rltyrndirig on the thickness of the matcrial.

ASTM A242

1)uring the 11)!30's, n rrlini1lr3r of stwl p r o d ~ ~ v ~ x s began offerirtg pr.oprit+ary grades of higlr-strength low dloy steels containing, in addition to carbon mu1 man- g;incse, such clernmts ;is \.an:idium. cbronrinm. copp<,r. silicon, and nickel. These stecls were offcred with spwifitd minimtini yidd poirtts from 12,000 psi to 50,000 psi. I r r additioir. I I X I ~ ? ilf thwe s t d s puovidid grimtly improvrd corrosion rt.sist;tnce ovcr ASTM A7.

By 1941 it became. apparcrrt tliat a spccificntion

was ilrsirahle for thmc stwls, :ind in that year the American Soviety lor T t ~ t i n g hlatcrials wrote .4242, "High-Strmgth 1 . o ~ Alloy Strlrctiird Stccl", ASThl A242 is primarily a strength specification with sprcifiid miniinrrm yiitld points of:

50,000 psi for rnatcrial op to ;tnd including irwh thick

36,000 psi for material over ".k inch thick to 1% in<,lics tliick, i~~cliisive

12,000 psi for material ovcr I?& iriches thick to 4 inches thick, irrclusive.

The chrmical rtquirtmmts are p i t c liberal. An attempt is made to insnre vconoiiiicnl wcliling of these stecls hy limiting c;irhon :md iirnngaltcsc cinitent. I-lmv- fwer: the prest.rlc? of other clernttrlts such ;rs sihxm, copper, ~~Ilrmni~tin. phosplr~mls, ;ind r~ickel, which are often added to provide iinlin>wd strc~iglh and corrosion rcsista~lcc, rrxiy rr\iliiire a special ~vnlili~rg pro- ci.durc for somc nf th tw stwls.

In addition. tlic slxdication rcqri i r~.~ that "these stecls h a w enh:in<rd cvrinsion resistmce q u a 1 to or grmtrr than c;rrlir~n sti~,is with cqiper." C:irhon stwls with vr~ppcr-or "coppw hi::tririg" strrls, as they are freqtrmtly i l l - 1 twicc thr: atmospheric cor- rosio~i r s i s t of A7 steel. There are, howevcr. wrtitin prqxictnry grndcs of A2-$2 hwing ovcr four times the atltri~spli~:ric r~~rrosion rcsistii~icc of A7 stecl.

(:oiiscqumtly, in ordering A142 stsvl, the pro- i l i i ~ w must be consullt~l to insrire th:it the steel can he crorromicolly u ~ l d c d ;md h;rs iinpn~vrd corrosion rtzsistance if t l r~se prnpcrtics arc desired.

ASTM A440

ASTM A441


A441 spccifics ihc same strength requirements as ,4242. The chcmical rt:ipiramc:nts limit carhon and manganese to tile sane levels as A242, hut add 0.02 per cent minimum vant~dium to obtain thc desired strength levels withont the ueerl for more crpensive alloy :ddiiions. As in the case of A4-10, the Sprcification limits the sulphnr a i d pl~osphorns, and requires that the steel l x "copper bearing'' to improvc its corrosion rt,sistance over that of A7.

5. HIGH-STRENGTH LOW ALLOY STEELS Proprietary Grades

P r o p r i r t ; ~ ~ grades of higli-strcngth low alloy stccls are available which arc similar to the ASTM high-strcngth grades hut differ in certain respects. These strels hirw spt:cificd rninimwn yicid points r;uigii~g fi-om 45,000 1x9 to 65_000 psi. Altlroiigl~ tlicsc steels are widely rtsed in manufacturing, they have only recently b e y n

TABLE 15-A Comparison of Steels for Construction ASTM Nigh-Strength Steels

(I) Groups I, il. i l l are defined ci follows:

120 to 190 i d

rNominoi depth ond naioinol width of fionge

(2) Bosrd on boiic ~ t ~ ~ i r n o k i ~ g p iorea.

'3) i h e rhoice o rd use of alloying cismenti to produce the reqllred riicneth or to improve corraiiori rcrirtance, or both, will vary with the manu{aaurer.


to be uscd in the design of buildings and bridges. The first of this grorlp of high-strcngth stcels was

commercially produced in 1958. At that tirnc it was found that minor additions of coluinhium to plairl carbon steel prodilced as-rollcd yield points up to 60,000 psi in the thinner ganges in a weldd>le grade of steel. These "columbium steels'', as they were d e d , were produced to specific-d minimiim yield points of 45,000 psi, 50,000 psi; 55,000 psi, and 60,000 psi in limited thicknesses.

In 1962 another group of high-strcrlgth low nlloy steels was introdrlcrd commcrcinlly which catended thrsc. high strtwgths to n bro;id range of thicknesscs in plates and shapcs. Thcsc stet:ls r t~ul tcd from the discovery that thc addition of small amounts of nitrogen combined with vanadinm in a rarbon-manganese steel prodnced an increase in strength nmch greater than M-odd bc expected froln the eAscts of theso two rlernents individ~xally, while eliminating the cleletcrious effects of adding nitrogon alone.

Similar high-strength stcels are now available from several producers, in a wide range of shapes and platcs with s p u d i d n~inimum yield points of 45,000, 50,000, 55,000, 60,000 and 65,000 psi. (Src Tahle 1C) And the Burcan of Puhlic Roads, in cooperation with the steel producers concerned, is cnmently ( Januav,

1'366) prcpring a specification lor thcse s t ids to :illour their ust* in welded iiigh\v;ty bridges.

The proprict;iry grades ol high-strt31igtli stc2els :ire prcsently (January 1966) limited in their 11sc in h idding and bridge constnictinrl bcc;~usc of code and specification n~qnircm~~nts. Thew sti~cls do not as yct have an AS'TM desipntion. Rmxcxw, tb<:sc steels offcr the arlvantage of prwiding higli strct~gill at ccononiic;il prices in a variety of yidd points arid they enable designers to obtain thc strcngtli thry rleml without the ni:ccssity of pa~rillg for considrrably morc strength than rcqoircd. Fnrtllcrmon~. the c l ~ t m i s t ~ - ~ of these stt& is i~oritrollcd I'm wononric;il w~.Idiilg. (:o~rs<.q~~(.iitl>-, eogi- wers arc taking ~ n t of the ico~iornies to bc gairird in thr use of thvsc steels ; i d 11;ivi. u s d tlicln on ;I great variety of strr ictun~ including inany truildings and several liridgcs.

6. HEAT-TREATED CONSTRUCTIONAL ALLOY STEELS Proprietary Grades

In 1953, thc first of the higtl-strength, hc;~t treated, constri~ctional alloy slccls was m;~rketrd. Thcsc ~ 1 : low-carhon; qnrwchetl and tcrnpcrrd nlloy stc?cls with specified minim~nn yield points ranging from W,WO

TABLE IC-A Comparison ot Steels tor Construction Proprietary High-Strength Low Alloy Steels (1)

Mfr'r Min. . ... . - ..- C h e m i d Reqvirementr (Ladie) Per Cent

Grade Yield Tenriie Clorri- Point Strength N C Mn P ficotian Thickness psi psi Max. Max. Max. Max. Max. I Min. Min.

C"

Shapes 45 45,000 65,000 min.

Plates To i I/>" i d - . . ~

To 3 , I . 131 - . - - . -

Over %- to 1%" incQ ,015

To y8" incl. 13) Shoper

55.000 70.000 min. To %'' inci.

plates

Shoper 60 - - ... 60,000 75,000 min.

Pioter To 3/8" incl. Shoper To 3h1' i d (3)

65 65,000 Plater To l/B" incl. i

( I ! Chemistry of high-strength low oiloy rtcelr varier wi lh producen. This Toble ir bored on Bethlehem V Sloeis as of January, 1964.

(21 When copper rteei is specified, the minimum copper is 0.20~1,.

(31 For rhoper, ]he thickness shown indicater web thickoas.


to 100,000 psi. :mil iillim:itc strmgtlrs rnnging from lO,5,000 to 19.5.000 psi, diqxmding ~ipon tliickncss. Originally tlicsc steels u w c available ol~ly in p1att.s bwausc of ditfici~ltics cnrmmtered tlr~ring hmt trwting in n i ~ t h i g tlie str:~iglrtricss of shapcs. 13). I961 m:my of these dilfieiiitics h;1d hcrr ovcrcornc, ;ind tlicsr stnrls art, nmr. oifercd in certain strl~ctiiral shaprs.

I3ecause of the highor pricc of tilest: stcels, tlrcir use in bnilding constricti~m has so far hccrr rnthcr lirnited. Iiowcwr, thry have heen ~iscd to considcrahlc advantage in scvi~;rl hrge i x ~ d g c h i l l in I-eccnt pears, atid in other types of structures. The major npp l i~ .a t' rons

7. BASIS FOR SELECTION

B. SELECTING THE RIGHT STRUCTURAL STEEL

With the ndoption by tlic AISC of design specifications covering the use of six ASTM s t d s (A7, A373, A36, A440, A311; and .4%2), de:sigiiers are now able to choose tlir particular stecl wliictr is best suited to tlic job at hmd. Ilowever, hcforr dcsignc~s ran take advantage or tlrestx stecis, some irisight inisst be acqoirecl as to wherc each um be iiscd to thc greatest advmtagr.

To i d the &!signer iir this selcction, we shdl compzire thc fivc AS'I'M stct~ls rctmnmerrdcd {or wclded constructior~ on tire ljasis of pricr, and iilso on what we call "yield strciigtl-i pc,r dollar".

We s11;dl also prfw~it gui&s to ;lid in rt,cognizing those situations wlrcwin the use of liigli-strength steels has proven to bc advantageoiis.

. COMPARISON BASED

Pricc is; of course, a factor in tha selection of a steel. Table 2 4 (for shapcs) and Tabli! 213 (for plates) show the comparative prices of the fi\.e AS?'M stnictural steels and proprietary high strength, low alloy stecls.

Carbon Steels

In mu-bon steel shapes, A36 steci is the same pricc as A7, has ;i 10 per ccnt higlier specified minimum yield point, and can he \vcldcd \vitli higli spwd, low cost procedures. Thc rn:isiini~m carbon content is only 0.26 per ccnt, h3i3 has a lriglier ~naxirniim carbon content (0.28 pcr cent), :I Iiigli~i- pice, and a lower yield strength than A36. In sl~apes, tlierefore. A3fi is by far the best bargain of tho c:irbon steei.

In plates, the adrantage of A36 is not quite as pronounced as in sh:~pes. I~fowcver, becaiis~ of its higher specified mi~~ilnrirri yield point, relative ease of rieldi~rg, m d the requirement that the steel be produced fully killed in thicknesses over ll/z inches thick,

A36 is the best biry for constrncti~m purposes.

High-Strength Steels

In tlic high stl-cngih steels, for material tlrichesses 1111 to 3;" in~l~isivc, 1\;111 is the samc price as A410. For thickness ovcr '?a" to "4'' iiichsiw, A441 is only slightly more cxp~risiw t l i i i ~ i A.l-10. Si~icc? A440 steel is not gent~r:iII~- rtwoimi~mded for i:cononiical welding, M 4 1 is I n r vf:rs;itilr ;in11 usdul stwl for constnirtio~r pw,x>scs.

Tlic :il?Qgr:ides are sribstantially higher in cost t1i:rn .4411. Co~iscq~icntly, it worrld be uneconomical to list: rl%-lhunless improvcd corrosion rcsistance is dcsircd If this pmpcrty is desired, it should be so spccifitd; rnert, rcfrronce to tlw .424Z specification does not assure improvcd corrosion rcsistance.

9. COMPARISON BASED O N YIELD STRENGTH PER DOLLAR

I'ricc :ilolie does not always give :III accurate pictiirc oi thi: possiblc cost advant;ige of one steel over anothcr, partia~larly wliere :I differcncc in yicld point is in- vol\:cd. Table 3.1 (for shapes) and Table 3R (for pl:it~,s) cotnpnrc the fivc ASTM structural steels on the basis of comparntivc yield point per dollar of cost, with I A36 stccl rrscd as the basis for comparison.

j Altlro~iglr siich ;I cornparison gives a more accurate

picture than n cornp;irisoii of pricc ;llone, R coinliarison of stcels on the basis of the strc~igtb-to-price ratio I

rni~st be made wit21 the foilovi~ing qualifications: a. Strc.~igth-price valws :ire based on minimum

yield point. IVl~ert: f:a,tors other than yield point (such as 1imit;ltions due to dellcction, buckling or latcrd st;~hiIit!.) dcttwninc the :illtwahlc stress, strength-price vahcs bascd on nrinimiirn yicld point arc not a valid comparison.


ASTM Carbon Steels

ASTM High- Strength Steel6

ProprietoP, High- Strength Low Ailoy Steels

18)

TABLE 2A-A Comporison of Prices of Steels (or Construction Base Price Plus Grade Extra Only, October, 1963 ( 1 )

Strucfurol Shapes

(1) There figures are lor campornfive purposas only. 15) See Tobie iA . Note 3. fo r dcfin;tian a i Group A. and ore ~ i o t to be used lor p w i n g purposes. Fig- urer are based on BEihiehem Steel Company prices, (4) See Tablc IB. Note I. iar defimtion of G m p $ I, October. 1963. li. and i l l .

Grade

(2) indi iotes web thickness.

17: Based upon Bc th l ched i Moyrir i R A242 rtcel, (3) The rotia of the price of t iw steel to the priri. which her on d m ~ r p h e r i c corrosion relistonce o f el

of k36. leoi t 4 to 6 timer tho+ of p la in carbon rtcel.

Group and Thickness (21

(4) The yield rtrength of the slce! per unit price a1 the s ? d ldo l la r i pel- ton) cornpored to the yield r t iongth per unit price far A36. (8) Boicd an Bethlehem V Steels

Min. Yield Point

psi

$ Per Tom

Differ- ent io l

Over A36

I ti". : c r o - Yield

Strength Price per Dollar (3) (4 )


TABLE 26-A Comparison of Prices of Steels for Construction Base Price Plus Grade Extra Only, October, 1963 ( 1 1

Structural Plates

Grade 1 Thickness

ASTM Carbon Stcels

ASTM High- Strength Steels

Piopi ie iory High- Strength Low Alloy Steels

15)

To 3/4" 1x1. -- . Over %,' to I!/>'' incl.

.

~ . - To %" i n d

Ovei %." to i%" inr i . .. - . . . .. ..

over 11/2" to 4 incl. -~ . ..-.- ~ -~ ~-

Over %" to %." incl. ~ ~

A373 Over %" to 1'. i d . ~ ~~~ ~~~~- ~

over I" to i I/?'' incl. . . over I/," to 4" inc!.

over il',,' 10 P incl. ~~-~p-~-~ ~~- ~ -

Over 4" to 8" incl.

ove r 3,;," to IIIf ' i n d ~ --

. -. ~ ~

Ovei 3,$- to 52- 45 L - - ilK

Yield

( 1 ) There figurer ore far compomtive puipasea only, the $!eel ldo l lo r i per ton) cornpored to the yield and ore not to be used for pricing puiporel . Fig. ~ t ~ ~ ~ q t h per unit price for A36 itccl i n the some ures are bored on Bethlehem Steel Company prices, thickness. October. 1963. (4) Bored upon Bethiehem's Moyari R A242 steel,

(2) The ratio of the price of the steel to the price which h o i on atmospheric corrosion resistonce o f of A36. st least 4 to 6 timer that of plain carbon steel.

(3) The yield ~ t i e o g t h of the rteel per unit price of (51 Baicd on Bethlehem V Steels.


h. Strcngth-price valncs are hascd on equivalent thicknesses of material. Use of a iiigh-strcngth stcel \ d l i~sridly rcsult in n thinncr section than that re- ql~ired wit11 A36. Since tlre thinner nraterial may be sold at a lowt:r unit price, actnal savings may therefore he greater than indicated by coinparativc strength- price ratios. It is also truc that using highcr strength, thinner sections d l ptmnit a rtduction in weld size which offsets incrcasrd cost of prt4ieat or other spccial welding procedures.

c. Strength-priix vahres art, based on material costs arid do not inch& fn:ight. fahric;ition, or erection.

Carbon Steels

Based on price alone, ,436 was found to be the! Irest

l>u): in shapes R J I ~ a goor1 h y iir plates. I! we rri:ike oiir comparison 011 the hasis o! strcngth-to-price ratio, as in Tnhlts 3, A36 is foiind to bc ;I hcttcr vnlnr than cithcr A7 or A373 in both slrapcs arrd plates.

Nigh-Strength Steels

\Vhere full advantnge can be t;ikt:ri of higher yield point le~.cls, .4411 is ;! lrt'tter lm!: illan A36, exccpt for Gronp 11% shapcs over 'i inch thick (\re11 thickncss) :ind for Cronp HI* slraprx

I l le A242 steels arc not rt~comrnorded for economical design onlcss high corrosior~ resistance is a rnajor rcquircmmt. .-

' Hrfw to note 1 (in Tahie I B .

*Tho yield strength of the rted per u n i t price of the $:eel (dollarr per tan) cornpored to t h e strength per u n t p,ict !or A36

( I ) Indicates web thickness. 3 See Table IB. Nole I . for deftnliion of Groups I , 1 1 , ond i l l

(2) See Tobie IA , Note 3, for definition of Group A. (4) h i e d a n aethishim V Steels.

TABLE 3A-Comporotive Strength-to-Price Ratios Comparative Yield Strength Per Dollar*

Structural Shapes

r Grade Gram ond Thicknest (1) .80 .PO 1.00 1.10 1.20 1.30

7.7-4 / Join* Design a n d Production

= 81.000 Joules/linear in. of weld

Another condition can be observed by using conditions ( a ) and ( b ) of Figure 7. Two butt joints were made, one in the vertical position and the other in the horizontel position, using a multiple-pass groove weld. The same welding current ( i i 0 amps) was used in both joints. The vertical joint used a vertical-up weaving procedure, 3 passes at a speed of 3"/min., procedure ( a ) . The horizontal joint used a series of 6 stringer passes at a speed of 6"/min., procedure ( b ) . The faster welding of ( b ) , G"/min., produces a narrower isotherm. However, it required 6 passes rather than 3 of procedure (a ) , and the net result is an over-all cumulative shrinkage effect greater than that for (a) .

This helps to explain why a given weld made with more passes will have slightly greater transverse shrinkage than one made with fewer passes. The transverse shrinkage can be reduced by using fewer passes. A further reduction can also be achieved by using larger electrodes.

In the weld on sheet metal, Figure 7 ( d ) , it is noticed that a greater portion of the adjacent base metal is affected as compared to the weld itself. This, combined with the fact that the thin sheet metal is less rigid than the thick plate (its rigidity varies as its thickness cubed), helps to explain why sheet metal always presents more of a distortion problem.

FIG. 8 Transverse shrinkage vories directly with omount of weld deposit.

5. TRANSVERSE SHRINKAGE

Transverse shrinkage becomes an important factor where the net effect of individual weld shrinkage can be cumulative.

The charts in Figure 8 throw some light on transverse shrinkage. In the lower chart transverse shrinkage, for a given plate thickness, is seen to vary directly with the cross-sectional area of the weld. The large included angles only help to illustrate this relationship and do not represent common practice. The relative effects of single and double V-joints are seen in the upper chart. Both charts assume no unusual restraint of the plates against transverse movement. Calculations show that transverse shrinkage is about 10% of the average width of the cross-section of the weld area.

= .lo x aver. width of weld

Where the submerged-arc process is involved, the cross-section of the fused part of the joint is considered rather than simply the area of the weld metal deposited.

Estimate the transverse shrinkage to be expected after welding hvo 1" plates together if plates are free to pull in.'Use a double-V groove weld, Figure 9.

FIG. 9 Transverse shrinkoge of this weld con be closely estimated from computed crors- sectional area of the weld.

area of weld

(%")(I") = ,125

2(%)(%")(.58") = .29

2(2/3)(1")($46'') = ,083 - A, = ,498 in.2

Selection of Structural Steel / 7.1-1 1

stress and often preclrldc advantageous nse of high- strength steels.

For instance, if we considcr an nnbraced colmnn length of 11 feet and rompare the required column size of A36 and A441 for loads of 100k, 4005 and 1600Vve find savings as given in Table A.

through the use of higli-strmgth steols, savings in fabricating costs can be realized. A common oxample is in the lower tier col~lmns of multi-story buildings.

Proprietary Grades

Whenever higll-strength steels can be used advantage- ously, seriorls consideration should be given to one or more of the proprietary steels, if these steels are acceptable under thc local codes. Propietary sterls often provide in<:rcasod economies over -4441. For instance, if we compare the same cohm~n loads and column lmgth (11 feet) as in Table A, we find savings for proprietary steels as given in Table B.

TABLE A

A comparat ive

Factors 1 -G - -

STN

T Size

wt. Sov ingd i t .

Cast Sovinyr/ft. -

Size

wt. Savingslft.

Cart Savingr l f t . * -~ -

Sire

w. Savingr/ft.

Cart Sovings/ft. *

C.mp.,otive (Kips) Factors

Size

Cost Sovingr/ft.*"

ASTM A36

Size

400' wt. Sovingdft .

Cost Snvingr/ft.**

-. 1

Sire

I_* I t . Sov ing jb .

' Cast Souingr/it.*-

' Soving of A411 ovei A36; ( + I indicates o saving (bared on prices in effect Oct., 1963). There voiuer include base p i i r e ood y i ade extra (shown in Table 28) p!ur section and length extros.

Although there is a saving in weight using A431, the cost saving is v:xiable and often nil. Because of the heavy section required for the 1(30OVoad, A441 has a minimum specified yield point of only 42,000 psi.

Weight Savings " Bored an Bethiehem Steei Cornpu,ny'i V50 and V55 Steels

**Saving of grade 50 or 55 ovei A36; If i indicates a saving h i e d on prices in cffei f Oct., 1963. These volues include bore price ond g iode ext ie (shown in Table 281 pius section and length extras.

The judicious nse of high-strength strels will almost always resnlt in an overall reduction in weight of the structure. Wlienc\,or this weight rednction can be translated into savings in the cost of fnundations, supporting stnictures, or in handling, transportation, or erection costs, thcn the high-strength steels can and should bc usod to advantage.

Although ihc minimum specified yield point of 4441 decreases as thickness increases. yield points for the above proprietary stcels arc 50,000 and 55,000 psi respectivcly for all available thickncses. As can be seen in Tables .h and B, the effect on cost of maintaining yicld point throughor~t a broad range of thicknesses is quite evident.

Savings I n Fabrication Costs

Whcnever the nrSd for built-up sections can be avoided

E MILL TEST REPORT: A GUIDE TO WELDABlLlTY

the steel, the paramorrnt question is: "What is the chemical composition and what are the mechanical propertics of the stcel that I must work with?"

Many fabricators and engincers tend to rely on the spt:cification of the strcl for the answer to this ijnestion. Rut such practice has in many cases led to a welding procrdure based on the worst combination of chemistry (as f a as welding is concerned) that the specifjcation

11. SPECIFICATION VS ACTUAL CHEMISTRY

Tht: preceding rnntc~-ial on the dcvelopment of the cnn- stsuction stecls and the sp~cifications and merits of thcse stwls should be hclpful to the cngineer or architect who is scxrching for the most ccoiiomical design.

IIowrvcr, to the fabricator, who must determine the procedure to use for fonning, bnrning or welding


will allow. This practice can result in a more costly welding operation than is necessary.

A more realistic answer to the establishment of welding procedure lies in the steel's "pei1igree"-the mill test report. The mill test report is a certification of the chemical composition and physical properties of the steel in a specific shipment.

To cite an example, an investigation of the mill test reports from a certain mill disclosed that the steel supplied by that mill had a carbon and manganese content considerably less than the maximum allowed tinder the specification. In addition, 85 per cent of the steel purchased from this mill was less than % inch thick. The average chemistry for plates up to 3i4 inch thick rolled on this mill compares with the allowable specification chemistry as follows:

I I I A36 / Soecification 1 0 25% mox 1 -

Mill Average .20 50% - . . ! . .:. . _- .224', mox. 1.25%

Mill Average . I8

Although the above average figores are for a particnlar mill, they indicate that the carlion and manganese content is nsnally considerably less than the maximnm of the specification and will be in a range that will permit significant variations in welding procedures.

12. M I L L PROCEDURE

When a mill receives an order for a particulru grade of steel, prodiiction of that item is scheduled to be rolled from a heat of stcel meeting the chemical re-

quirements of the gradr: ordered and which it is expacted will provide the mech:mical properties reqnired in the finished product.

Each ingot pollred from imp heat of steel is identified with the heat number, and this identity is maintained throughout all subsequent rolling mill operations.

Tha rolling of steel has a definite effect on the rnt:chanical properties of the finished product. Con- firming mechanical tcsts (tensile strength, yield point. and per cent elongation) are, therefore, made after the steel has been rolled to final section and cooled.

The mechanical properties of thc section and the chemical composition of the heat are recorded on the niill test report.

The mill test report is filed by the mill for its own record and certified copies arc forwarded to the customer, when requested, for his use. The report's dis- closure of the particular mill order's chemistry is a valnahlc guide to devclopmcnt of the most economical and satisfactory welding procedure.

The chemistry of the steel in a structural steel fabricator's shop can th11s he readily detcnnined from the mill test report. Fnrtherrnorr, where necessary the chemistry of thc steel can be anticipated to a reasonable degree far in advance of shipment by referring to previons mill test reports on similar products from the same mill.

For greater economy of welding, the structural stcel fabricator or erector can and should base his welding procedure on the actual chemistry of the steel he is welding, rather than ttpon the worst nossible combination of chemistrv allowed under the specification.

CHECKLIST FOR USE OF HIGH-STRENGTH STEEL

In structural steel design, A36 is generally the most b. When deflection limitations are uot a major versatile and econnmical of the construction steels. factor in detcrminir~g scction. However, there are occasions whcre the judicious use c. When deflections can be reduced through de- of high-strength steels can result in overaIl cost and sign features srich as continuity or composite design. weight savings, such as: d. When weight is important.

e. When fabricating costs can be reduced. f . When architectural considerations limit the beam

Tension hlembcrs dimensions.

The high-strength steels can usually be used to advantage in tension members except when the mem- Co1umns And Compression Members

hers are relatively small in section or when holes (i.e. a. When steel dead load is a major portion of for bolts or rivets) sitbstantially reduce the net section desim load. of the member. b. Whcn the slenderness ratio (L/r) of the mem-

ber is small. c. When weight is important.

Beams d. When fabricating costs can be rednced. a. When steel dead load is a major portion of e. When architectural considerations limit the

design load. column dim6 ~ F I O ~ S . . '

S E C T I O N 7 . 2

1. INTRODUCTION

Ordinarily, a correctly desigrred joint :ind properly made weld do not rt-quire special procedures to prc- vent cracks during wdding or ill sci-vier. The need for spcciai procdnrcs i11crcases, however, with hcavy plate structural members ; ~ n d is growing with the cx- panding use of steds having grrater atnotmts of alloying elements in their clrtwistry.

This section first provides some insight into the factors that promote weld cracking and maka s ~ g - gestions for welding proceclurt~s to vorrect or prevcnt a cracking prohlcrn. This section thcn . i d present a comprchensivr discussion of wlim to rise prehrxting to eliniinate or prt3vcnt crac1;ing. It will nlso prrsent a new approach to establishing the prclieat and iilter- pass temperatuw, based on the heat inpnt of the welding proccdrue, thr critial cooling rat<. (dotermint:d by the cheinistw of the steel), and the joint geometry,

Tandem-arc and other modern automatic welding equipment have revolu- tionized the shop fabrication of large bridge girders, built-up columns, and other special structurol members. The welding of thick plotes, or of higher- strength alloys, may require preheating or other measurer not needed with the more common mild steels.

&lost stet~ls c;ni he co~nmercially arc wcldcd, with good rcsr~lts-sonnd, strong \veltIcd joints. The "weldahility" uf a metal rt4t.r~ to the rtllativc mse of producing a sati~factnry~ crack-frm, sound joint. A steel is said to be ideally .iv~Wable if the rctpirtd \veld joint ~m Iw niarle nithont difficnlty or ~xcessive cost.

Soroc stools are rnorc. suitcd to high-speed wclding tli:lii othtxs. Analysis of the t:loctrodo corc \virr, is acctrrntc~ly coi~trolled to prodwe good wrlits, but since the plate mctal heconles part of the weld, control of the plate analysis is nlso irnportant. Whcn higher cnr- rents ;ire nsed to get I~igher welding spocds, mort: of thr plate metal mixes with the wcld. If possihlr, wlect an msily wdded steel that doesn't n>quirc expensive t~li~ctmcl's or coinplicated welding procednres. 'Table 1 gives a rangr of carbon stt:rl analyscs for maximum wrlcling speed.

The comrno~ily used mild steels M i within the

9.2-2 / Joint

In order to evaluate the weldability of steels, a limited kno\vledge of the basic arc welding process is advisable.

Welding consists of joining two pieces of metal by establishing a metnllurgical bond between them. Many different welding processes may be used to produce bonding through the application of pressure and/or through fnsion. Arc welding is a fusion process. The bond between the mptals is produced by reducing to a molten state the surfaces to be joined and then allowing the metal to solidify. When the molten metal solidifies, union is completed.

In the arc welding process, the intense heat required to reduce thr inetal to a liquid state is produced by an electric arc. The arc is formed between the work to be wt~lded and a metal wire or rod called the elcctrode. The arc, which produces a

Welding Machme AC or DC Power Source and Controls

Electrode Holder 7

\Ground Cable I

temperature of about 6500°F at the tip of the electrode, is formed by bringing the electrode close to the metal to he joined. The tremendous heat at the tip of the electrode melts filler metal and base metal, thus liquifying them in a common pool called ;I crater.* As the arens solidify, the metals are joined into one solid homogeneous piece. By moving the electrode along the scam or joint to be welded, the surfaces to be joined are welded together along their entire length.

The electric arc is the most widely used source of energy for the intense heat required for fusion

*For soinc applications, filler metal is deposited by a con- sumnblc we ld ing electrode; for others, a "nonmnsumable" elcctrode supplies the heat a n d s separate welding rod the filler metal.

wclding. The arc is an electrical discharge or spark sustziined in a gap in the electrical circuit. The resistance of the air or gas in the gap to the passage of thc current, transforms the electrical energy into heat at extremely high temprmtures. Electrical power consists of amperes and voltage. The amount of energy available is the product of the amperes and the voltage flowing through the circuit and is meastired in watts and kilowatts. The energy used is affected h y such variables as the constituents in &ctrode coatings, the typc of current (-46 or DC), the direction of cul-rent flow, and many others.

In all modern arc welding processes, the arc is shielded to control the complex arc phenomenon mid to improve the physical properties of the weld deposit. This shielding is accomplished through varions techniques: a chemical coating on the electrode wire, inert gases, granular flux compoi~nds, and metallic salts placed in thc core of the electrode. Arc shielding varies with the type of arc welding process used. In all cases, however, the shielding is intended: 1) to protect the molten metal from the air, oither with gas, vapor or slag; 2) to add alloying and fluxing ingredients; ,and 3) to control the melting of the rod for more effective use of the arc energy.

Gaseous Shield

The arc welding process requires ;I continuous supply of electric cnrrent suflicient in amperage :md voltage to maintain an wrc. 'l'his currcnt may be either altcmating (AC) or dircct (DC) , but it must be provirlecl through a source which can be controlled to satisfy the variables of the welding 11roces" :mmnerage and voltage.

eldability and Welding Procedure / 7.2-3

prefei~ed analysis listed. S111phur contrnt of thcse stcck is usnally h1.low 0.035%, altbongh thr specification limits pcrmit as inuch ;IS O.O.WjOa/,.

Continued progrcss is being made in rnrtallnrgical control of steel, as \vi,ll as in the dwcloprnent of welding proccssm, electrodes and Anxes. This tends to broaden the range of "\veldability" with respect to steel :tnalysis.

The six basic ASTM-specificntion constniction steels usually do not reqnirc spccial precautions or special procedures.

However, u-hcn welding tht tfiicktbr plates i r i oven theso stcels the incr<iascd rigidity and restraint and the drastic quench rlFect makes the m e of thr propcr proccdurc vitally import;rnt. In :rddition, thick plates usually have higher carhon contmt.

We also have :In increasc iir the usc of higher strength low alloy stocls and the heat trcatetl very high yield strength steels. Tlresc steols have somr elernonis in their chemistry that exceed the idcal analysis, Tnblc 1, for high spced n.cIdiiig.

Frequently pre-planned and proven wddiug PXO- cedures are reqiiir~d to assure the production of crack- free welds when joining thickcr platos or the alloy stccls. These proccdnres i~snally call for onr or :ill of the following:

1. Proper bead shape and joint configuration. 2. Minimized penetration to pievent dilntion of tlie

weld metal with the alloy clemcnts in the plate. 3. Preheating, controlled intorpass trmparature and

sometimes cvrn controlled heat inpirt from thv welding procrdurc to retard the cooling rate and reduce shrinkage stresses.

3. BASE PROCEDURE ON ACTUAL ANALYSIS

Pnhlishcd standard production welding procedures generally apply to normal wdding conditions and tlic, more common, "prcfcrrcd analysis" mild steels.

Whim a steel's specification analysis falls outside the preferred analysis, tlie user often adopts a special welding procedure based on the cxtrerncs of the material's chemical content "allowi~d" by the steel's spcci- fication. IIowever, since the chemistry of a specific heat of steel may run far bolom the top limit of thc "allon-

TABLE I-Preferred Analysis Of Carbon Sfeel for Good

/ Normal 1 Steel Exceeding Any One of Element the Following Percenlogel

j % / w i l l ~ ~ ~ b ~ b l ~ Require Extra Core

nl~lrs". a spcrial p~-owdnrc rnay not he rquired, or may rcqniro only ;I slight changc from standard pro- cdurcs and thcrchy luini~nize any incrt:asc in welding cost.

For optimum vxnomy and qnality, under either f;rvorablr: or ndv<mt: corrditions, the welding proccdurc for joining any type of steel should he based on the stcel's ncftrirl chemistry rather than thc marimurn alloy co~~tt.lrt allomcd by the sprrification. This is hccause a mill's avinlge production norinally rnns considi!rnhly undi:r the m:~xinrum limits set by the spceificstion.

Usn;dly a Mill Test Kcport is availnhle which giws the spci:ifi(. ;inalysis of any given heat of steel. Once this information is o h i n c d , a \vciding proccdnrc can be s1.t that will assure the production of crack-free \scids at thc lo\vcst possible cost.

Manganese

Silicon

Sulphur

Phoiphorui

4. WELD QUALITY

The main ohjectivc of any w ~ i l h g proccdore is to join the, pieccs as reqnirod with tlrc most cfficicnt weld possihlc ;ind at thc lcast possiblc cost. "As wqnired means thrk wt.ld's size and q~lnlity niust he consistent with the scr\kc rtquirr~nents. Excessivr precautions to obtain unncccsswy quality, heyond that ni:eded to meet svrviw rquircmcnts, st:rvc no practical pnrposc and can bc rxpensivc.

Hccanst it grcatly ii,crrs:ises cost withont any hcne- fit, i~isprction should not rcqnt:st the correction of slight nndi.rcot or minor rxliographic dcfech snch as limited scattered porosity 2nd slag inclusions, unless thorough s i ~ ~ d y shows sncli ddcets cannot be tolerated because oi specific scruice reqoircments.

Mn

Si

S

P

elds Crack an

3 5 - 80 1 1.40

.30 ,035 niox 050 030 man 040

5. WELD CRACKS 1. weld cracks occ~~rring during wclding,

A crack in 3 weld, howcver, is nwer minor and cannot 2. cracking in thc heat aficcted zone of the base be condoned. Good design and proper welchng pro- metal. ct?dure will prevent thcsc cracking problems: 3. welded joints failing in service.


Plote 1s liiter preheated, and submerged arc weld wfll remelt tack weld ond hardened zone in

ib/

FIGURE 1

Factors that Affece Weld Cracking During Welding

1. Joint Resfruint that causes high stresses in the weld.

2. Bead Shopc of the deposited weld. As the hot weld cools, it tends to shrink. A convex bead has s~fficient material in the throat to satisfy the dcmancls of the biaxial pull. However, a concave bead may rcsult in high tensile stresses across the weld surface from toc to toe. Thcse h r s ses frequently are high cnough to rupture the surface of the weld causing a longitndinal crack.

An excessively penetrated weld with its depth greater than its width under conditions of high restraint may carlsc internal cracks.

Both of thesc types of cracking arc greatly aggra- vated by high sulphur or phosphorus content in the base plate.

3. Carbon and Alloy Content of the base metal. The higher the carbon and alloy content of the base metal, the grrater the possible scdoction in ductility of the weld metal through admixture. This contributes appreciably to weld cracking.

4. Hydrogcn Picliup in the wcld deposit from the electrode coating, moisture in the joint, and contamin- ants on the surface of thc base metal.

5 , Rapid Cooling Ratc which incrrases the effect of items 3 and 4.

Factors fhot Affect Cracking in the Heot-Affected Zone

1. Nigh curbon or alloy content which increases hardenability and loss of ductility in the hmt-affected zone. (Underbead cracking does not occur in non- hardenable steel.)

2. Hydrogen embrittlcnient of the fusion zone through migration of hydrogen liberated from the weld metal.

3. Rote of cooling which controls items 1 and 2.

Factors that Affect Welded Joints Failing in Service

Welds do not usually "crack in service but may "break" because the weld was of insufficient size to fulfill scrvice rtquircments. Two other factors would be:

1. Notch toughness," which would affect the breaking of welds or plate when subjected to high impact loading at i9xtrcmely low temperatures.

2. Fatigue cracking* due to a notch effect from poor joint gcomctry. This occurs under servicc conditions of nnusually severe stress reversals.

items to Control

I. Bead Slzupe. Dcposit beads having proper bead surface (i.e. slightly convex) and also having the proper width-to-depth ratio. This is most critical in the case of single pass weids or the root pass of a lnultiple pass weld.

2. Joint Restraint. Design weldments and structure to keep restraint problcms to a minimum.

3. Carbon and Alloy Content. Selcct the correct grade and quality of steel for a given application, througll familiarity with thc mill analysis and the cost of welding. This will ensure balancing wcld cost and steel price using that steel which will develop the lowest possible overall cost. Further, this approach \\.ill usually avoid use of inferior welding quality steels that have excessively high percentages of those elements tht~t always adversely affect weld quality-sulphur and phosphorus.

Avoid excessive admixture. This can be accomplished through procedure changes which reduce penetration (different clcctrodes, lower currents, changing

" N&w notch toiighncss nor fatigue cracking are discussed herr. See Srction 2.1, "P~.opcrtics of Materials," Section 2.8, "Desi~ming for Impact Loads, and Section 2.9, "Designing for Fatigue Loads."

eldability and elding Procedure / 7.2-5

polarity, or improving joint design si~ch as replacing a sqllare edge butt weld with a bevel joint.)

4. Hydrogen Pickup. Select low-hydrogen welding materials.

5. Ifeat Inpot. Control total heat input. This may include preheat, weliiing heat, heating between weld passes to conh.01 interpnss temperature and post heating to control cooling rate. Control of heat input lowers the shrinkage stresses and retards the cooling rate helping to prevent excessive hardening in the heat- i~ffected zone, two primary causes of cracking.

6. TACK WELDS

The American Welding Society's Building Code and Bridge Specifications both require any tack welds that will be incorporated into the final joint, to be made under the same qr~aliw requirements, including preheat, as the final welds.

However, this docs not recognize the deep penetration characteristics of some welding processes, for esampfc, submerged-arc. i f the initial tack welds are relatively small compared to the first submerged-arc weld pass, they will be entirely remdted along with the adjacent heat-affected area in the plate.

In this case, no preheat should be required for small single pass tack welds i~nless the plates arc so thick and restrained that the tack welds are breaking. See Figure 1. If the tack welds are breaking, the corrective measures previously listed relating to bead shape and weld throat should he applied with prc- heating called for as a last resort. I t is always a good idea to usc low-hydrogen welding materials for tack welding plates over 1 in. thick.

7. THINNER PLATE

Welds that join thinncr plates rarely show a tendency to crack. The licirt input during wclding and lack of mass of the thinner plate create a relatively slow cooling ratc. This, pli~s thc rcduccd intcmal stresses resnlting from a good weld throat to plate thickness ratio and the fact that the thinner plate is less rigid and can flex as the weld cools and shrinks, controls the factors that induce cr:icking. Cracking is almost never a factor on thinner platc rrnless un~~sually high in carbon or alloy content.

. THICK PLATES

In the steol mill, all sted p1att.s and rolled sections 1111dergo n ratller slow rate of cooling after being rolled while red hot. The red hot thick sections, bccausc of their greater mass, cool morc slowly than thin sections. For a given carbon and alloy content, slower

cooling from the critical temperature r ( d t s in n slightly lower strength.

For the nornld thickncsscs, the mill has no difficulty in meeting the minimum yield strength required. However, in extremely thick mill sections, because of their slower cooling, the carbon or alloy content might have to be increased slightly in order to mcct the rcquired yield strength.

Since a weld cools faster on a thick plate than on

, (b) Preset before welding

(c) Weld free to shrink; stress-free

FIGURE 2


a thinner plate, and silrce the thicker plate will probably have a slightly higher carbon or alloy content, welds on thick plate (beca~rse of admixhuc and fast cooling) will have higher strcngtlis but lower ductility than those made on thinner plate. Special welding procedures may be required for joining thick plate (especially for the first or root pass), and preheating may be necessary. The object is to decrease the weld's rate of cooling so as to increase its ductility.

In addition to improving ductility, preheating thick plates tends to lower the shrinkage stresses that develop because of excessive restraint.

Because of its expense, preheating should he selectively specified, however. For csample, fillet welds joining a thin web to a thick flange plate may not require as much preheat as does a butt weld joining two highly restrained thick plates.

On thick plates with large welds, if there is metal- to-metal contact prior to welding, thcre is no possibility of plate movement. As the u&Is cool and contract, all the shrinkage stress must be taken up in tlie \veld, Figure 2(a) . In cases of severe rcstraint, this may cause the weld to crack, especially in the first pass on either side of the plate.

By allowing a small gap between the plates, the plates cnn "movr in" slightly as the weld sluinks. This reduces the tmrtsversc stresses in the weld. See Figures 2.(b) axid 2 (c ) . I-leavy plates shoul~l always have a minimum of %," gap between them, if possible % G " .

This small gap can bc obtained by means of: 1. Insertion of spacers, made of soft steel wire

between the plates. The soft wire will flatten out as the weld shrink. If coppcr uire is used, care should be taken that it does not mix with the weld metal.

2.. A deliberately rough flame-cut edge. The small peaks of tlie cut edge keep thc plates apart, yet can squash out as the weld shrinks.

Molten weld

FIGURE 3

3. Upsetting thc edge of the plnte with a heavy center punch. This acts similar to the rough flame-cut idge.

TIw platrs will nsually be tight together after the w ~ l d h;rs cooled.

The abovc discussion of metal-to-metal contact and shrinkage stresses espt~ially ;ipplies to fillet welds. .4 slight gap betwrcn platcs u i l l hclp assme crack-free fillet welds.

B r d shape is anothw important factor that :affects fillet wclti cracking. Frcczing of the molten weld, Figure O ( H ) : due to the qumdling cffect of the plates commences along thr sides of the joint ( b ) where the cold mass of the heavy plate instantly drams the heat olrt of the molten wcld metal mid progrcsses uniformly inward ( e ) until the u d d is complrtely solid ( d ) . Kotice that the last matcrial to freeze lies in a plane along the ccnterline of thc wcld.

To d l ester~ial appearances, the concave weld ( a ) in Figure 4 ivorlld seem to be larger than the convex weld ( h ) . Ho\vever, a check of the cross-

(a) Concove illet weld (b] Convex weid

FIGURE 4

eldability and elding Procedure / 7.2-7

section may show the concave \veld to have less pme- tmtion and a smaller throat ( t ) than first thought; therefore, the convex weld may actually he stronger w e n though it may h a w lcss deposited metal (darker cross-section);

Designers originally favored the concave fillet weld because it seemed to offer a smootlrer path for the flow of stress. However, experience has shown that single- pass fillet welds of this shape have a greater tendency to crack upon cooling, which unfortunately usually outweighs the effect of improved stress distribution. This is especially true with steels that require special \\&ling procedures.

When a concave fillet \veld cools and sl~rinks, its outer face is stressed in tension, Figure S(a) . If a surface shrinkage <:rack should occur, it can usually he avoided by changing to a convex fillet ( b ) . Here the

ce not in lension

(a) Concave weld (b) Convex fillet weld

FIGURE 5

weld can shrink, while cooling, without stressing the outer face in tension and should not crack. For multiple- pass fillet \velds, the convex head shape usually iipplies only to tlre first pass.

For this reason, \vlren concave welds are desired for special design considerations, such as stress flow, they should he made in two or more passes-the first slightly amvex, and the other passes built up to form a concave fillet weld.

On heztvy plate, it is usr~ally thc first (or root) pass of a groove weld that r rq~~ i re s spccinl preca~~tions. This is rspccially true of the root weld on the hack side of a doubic Vet: joint hecansc of the atlded restraint from the weld on the front side. The weld tends to shrink in all dircctiol~s as it cools, hnt is restraincd by the plate. Not only arc tensile shrinkage stresses set up within the weld, but tlre wcld frequently mrdergocs plastic yielding to accommoclatc this shritrkngc.

Some idea of tlrc possible locked-in stress and plastic flow of the wcld may be sccn in Figure 6. lmaginc the plate to bc cut near the joint, allowing the

weld to frccly slrrink (dotted lines). Tl1e11 pull thc phtes hack to the origit~al rigid position thztt they \t.onld norm:ill>- he in i l~~rinfi ; i d after w~,lding (solid lincs). This ncct.ssitatt~s a stretching of the wdd.

FIGURE 6

In :~ctual practice all of this stretch or yielding call occur only in the weld, since the plate cannot move and tho weld has the loast thickness of the joint. Most of this yielding takes place while the weld is hot and has lower strength and ductility. If, at this time, the intcrnal stress exceeds the physical properties of the weld, a crack occurs which is rrsually down the centerline of the weld.

The problem is enllanced by the fact that the first (or root) head usually picks up additional carbon or alloy by admixture with the base metal. The root bead thus is less ductile than subsequent beads.

'4 concavc head surface in a groove weld creates the sume tendency for surface cracking as described for fillet welds, Figure 7. This tendency is further incre;ised with lower ductility.

Wrong Right Too concove Flat or slightly convex

FIGURE 7

Incrcasing thc throat dimtsnsion of the mot p:iss will llrlp to prewnt cracking; nse clcctr.odc.s or pro- c i~ l~ i r c s t h t d~:vclop a c~mvcs )wad slrapo. L.ow hydro- gtw wclding m:~terinls are somctimcs nseful and finall" prehmt can he slwcificd. Oln~ionsly prclrcating should h(: zuhptcd as I hst rcsort sincc it will causc the grcatest iocrc:asc in wcld cost.

The prohhm of crnterlinr cr;irking can wen occnr in the succeeding p; issr~ of ;I m~~l t ip l r pass mcld if tht, psscs ;Ire exccssivclv widc or concavc. Corrcc- tivc measnrcs call for a i~rocedure that spccifies a narr~rwcr slightly convex bead shape. making thc corn- p l e t ~ d \veld two or moro heads widc, side by side; Figure 8.

7.2-8 Joint Design and Production

Wrong Wrong Right Too wde and concave Washed up too high Flat or slightly convex

FIGURE 8

[Also poor dog rernovol) and concove not qutte full width (Also good slog removal]

10. ~NTERNAL CRACKS AND WELD W I D T H TO DEPTH OF FUSlON RATIO

Where a cracking problem exists due to joint restraint, material chemistry or both, the crack usually appears at the weld's face. In some situations, however, an internal crack can occur which won't reach the weld's face. This type of crack usually stems from the mis- use of a welding process that can achieve deep penetration, or poor joint design.

The freezing action for butt and groove welds is the same as that illustrated for fillet welds. Freezing starts along the weld surface adjacent to the cold base metal, and finishes at the centerline of the weld. If, however, thc weld depth of fusion is much greater than width of the face, the weld's surface may freeze in advance of its center. Now the skrinkage forces will act on the still hot center or core of the head which could cause a centerline crack along its length without this crack extending to the weld's face, Figure 9(a) .

Internal cracks can also result with improper joint design or preparation. Figure S (b ) illustrates the results of combining thick plate, a deep penetrating wclding procrss, and a 45" included angle.

A small b m d on the second pass side of the double-V-groove weld, Figure S(c) , and arc gouging a groovc too deep for its width, led to the iviterlial crack illustrat~d.

Internal cracks can also occur on fillet welds if the depth of fusion is srrfficie~itly greater than the face width of the bead, Figure 9 (d ) .

Although internal cracks are most serious since they cannot be detected with visual inspection methods, a few preventive measures can assure their elimination. Limiting the penetration and tho volume of weld metal deposited per pass tliror~gh speed and amperage control and using a joint design which sets reasonable depth of fusion requircrnents are both steps in thc right direction.

In all cases, irowever, the critical factor that helps control internal cracks is the ratio of weld width to depth. Experience shows that the weld width to depth of fusion ratio can range from a minimum of 1 to 1

Width of M7cld = to Depth of Fusion

co i ie i t I n ~ o l i e c ,

Wrld depth Weid wd t i Weld depth VJeld width

/ A K gnuge too narrow I"'"""' ""'k

FIGURE 9

eldobiiity and elding Procedure / 7.2-9

11. UNDERBEAD CRACKING

Underbead cracking is not a problem with the controlled analysis low carbon steels. This problem if it occurs is in the heat-affectcd zone of the base metal. It can become a factor with thick plate as the carbon or alloy contcnt of the steel increases. As an example, this can occur with the heat treatable very high strength, high carbon low alloy steels like 4140 or 6150. The construction alloy steels which have over 100,000 psi tensile strength and are heat treated before welding, also can experience underbead cracking in thick plates. When armour plate was used, underbead cracking (toe cracks) was a problem. The point is that the problem is only important on hardenable steels.

Low-hydrogen processes should be used to join these materials since one cause of underbead cracking is hydrogen embrittlement in the heat-affected zone. Hydrogen in the welding arc, either from the electrode coating or from wet or dirty plate siufaces, will tend to be partially absorbed into the droplets of weld metal being deposited and absorbed into the molten metal beneath the arc.

As the welding arc progresses along the plate, the deposited hot weld metal (which has now solidi- fied) and the adjacent base metal heated by the weld above thc transformation temperature are both aus- tenitic at this elevated temperature, and have a high solubility for hydrogen. Fortunately, a considerable amount of hydrogen escapes through the weld's surface into the air; however, a small amount may diffuse back through the weld into the adjacent base metal. (The rate of diffusion decreases with decreasing temperature.)

by weld, hydrogen is

roluble in this iegmn - men to < This rewon rernolns or

diffuse ony further ferrite; no solubility for hydrogen

FIGURE 10

Beyond the boundary of the heat-affected zonc, the hasr metal is in the form of ferrite, which has practically no solubility for hydrogen. This ferrite boundary becomes an imaginary fence, and the hy-

drogen tends to pile up here; going no farther. See Figure 10.

tipon further cooling, the lieat-aifcctetl area tmns- forms back to fcri-itc with almost no solubility for hydrogen. Any hydrogen present tends to separate out bctuwn the crystal lattice and builds up prcssnre. This pressure, when cornhined with shrinkage stresses and any hardening cfft:ct of the steel's chemistry, may cause tiny cracks. Since weld metal is usually of a lower carbon than the hasc plate, this trouble occurs ma i~~ ly just beyond thc \veld along the austcnite- fcrritc boundary and is c;~llecl "underbead cracking" See Figure 11. I i some of these cracks appear on the

FIGURE 1 1

plate surface adjacent to the weld, they are called "toe cracks". Slower cooling by welding slower and preheating allows hydrogen to escape and helps control this problem.

The use of low-l~ydrogen welding materials eliminates the major source of hydrogen and usually eliminates underbead cracking.

12. SUMMARY O N CRACKING

The first requirement of any welded joint is to be crack-free. Cracking may occur in either the weld metal or the heat-nffectcrl zone of thc base plates.

Most stock can be welded in the average plate, tllickness without worrying abont weld cracking.

As plate thickness incl-cases, and as the carbon and alloying content incrcasc, weld cracks and nnderhead cracks may become prohlems and require special precautions for their control.

This ncccssitates in order of importance: a ) good welding procedure, especially in respect to bead shape, control of admixtmc, h ) reducing rigidity by intcn- tional spacing of plates, c ) use of loiv-hydrogen welding materials, and d ) controlled cooling rate, including welding cur-rent and travel speed, and if needed corn trol of preheat and interpass temperature.


reheat and Ho eat Temperature

HEN A N D WHY TO PREHEAT

Preheating, while not always ncccssary, is w r d for one of the following reasorrs:

1. To rcdttce shrirrkagc stresses in the wcld and d jacent base metal; especially important in highly restrained joints.

2. To provide n slower rate of cooling through the critical tempcmturtz range ( a h w t 1800' F to 1330" F) preventing excessi\.e i~;irtlcning and lowermi ductility in hot11 wcld arrd heat-:~ffectd area of thc hasr plate.

3. To provide a slower rate of cooling through the 100°F r;rnge, allowing more t in~c for any hydrogrn that is prtxscnt to diHl~sc away from the weld and adjacent plate to avoid r~ndcrhead crz~cki~lg.

1. To increase thc ;~lk)w;ible critical ratc of cooling below \ahich there will he no underbead cracking. Thus, with the mekling procedure held constant, a highcr initial plate temperature increases the maximum safe ratc of cooling while slo'iving down the actual ratc of cooling. This tends to mnka tho hcnt input from the welding proct:ss less critical.

Cottrcll and Hratlslrcet* show thc following critical cooling rates (R,,) for ;I given steel at 572'F (3(W°C) using low-hydrogrm electrode in order to prevent under- bcad cracking for various preheats to be:

5. To increase the notch toughness in the weld Zorlc'.

6. To lower the transition temperature of the weld a n d adjaccnt base metal.

Kormally, uot much p r t h x t is required to prevent ur~dcrheacl cracking. This is held to a ~r~inimum when low-hydrogen vddirtg materials arc uscd. Higher preheat tcmpcratr~re might be required for some other roiison. e.g. a highly restrained joint between very thick platos, or a high alloy content.

Preheating makes other factors less critical, b r ~ t since it invariably increase the cost of welding, it cannot he indi~lgrd in ~tsrtrecess:~riIy.

14. AWS M I N I M U M REQUIREMENTS

Thc AWS has set t ~ p minimum preheat arid interpass rrquircmcnts given in Table 2.

These minimum prrhrxat requircmcnts may need to be adjusted, according to welding heat input, spc- cific steel chemistry, the joint geometry, and other factors.

TABLE 1-AWS Minimum Initial and Interpass Temperatures1,V(1966)

I Welding Pioceas

To %, lncl. none" ..

-. Over I]/> to 2%. inc!. 225-F 150°F

Thickness of Thkkert Port at

P d n t of Welding (inches)

' Weiding shall not be done when the ambien t temperowre i s iower than OFF. 'When the bare metal is betow tho temperature listed for the welding proceri being used and

t h e thickness of moteiiol being weided, it shall be preheated f a r both toik welding and welding in such m a n n e r that the iurfocer of the parts o n which weid mctol is being deposited are at or above the m i n i m u m tcrnperotuie for o distnnce cquoi to the thickneii of the port being weided, but not less thon 3 inches, both iotcioily a n d in advance of the welding. Preheat tcrnperoiure shall not exceed 400DF. (lntcipnii temperature is not subject to a m a x i m u m

Shielded Metol-Arc Welding with Shielded Metol-Arc Welding with Low-Hydrogen Electrodes

Other t h a n Low-Hydrogen Electrodes and Submerged Arc Welding A36". A7', A373' A36'. A7" A373', A441'

, A242' Weldable Grade

limit.) "sing U O X X a r E70XX electiadei other thoii tho low-hydrogen types. 'Using E6OXX or E7OXX iow-hydrogon electrodes I E X X 1 5 , -16. -18. -281 or Grade SAW-I or SAW-2. 'Using only E70XX lawhydrogen rleitioder lE7015. €7016. E7018, E7028) or Grode SAW-2. W h e n the boie metol temperatwe Is below 32°F , preheat the bore metal to at leort 72°F.

eldobility and elding Procedure / 7.2-1 1

15. HEAT INPUT DURING I One factor that \vould reducc preheat recluiremcnts 1 is tlic use of greater welding heat input; for example, the welding heat input for vertical welding with weave [i x passes at an arc speed of 3 in./min. is greater than that 5 - oo ing rote 'F/rec

of horizontal welding with stringer hcads at 6 in./min. + - Prah--. , -

I - - -..curecl

The heat input ( J ) ~ for :I spedfic weldiug procedure - - - - I-= - - _ 3 0 0 " ~

can be detcrn~ined ~ ~ s i n g the formula:

E 1 0 Time ---+ J = -- " (1) FIGURE 12

\vilere:

J :=: Heat input in Jodss/in. or watt-sec/in. E = Arc voltage in volts I = Welding current in amps

V = Arc speed in in./min

Since all of the welding heat input at thc arc does not enter the plate, the following heat efficiencies arc snggested for rise with this fonnula and subsequent formulas, charts or nomogrnphs: -- (3-809; manual welding

'30-10(1'2 submerged ;uc welding

Most preheat arid interp:iss te~llpcrature recommendations are set np for manual welding where there is ;I rr:lativcly low hi%~t input. For example, a current of 200 amps and a speed of 6 in.jmin. would produce a welding heat input of so bout 48,000 joules/in. or watt- sec.,'in., asslirning an efficicrrc). of 80 percent. Yct, it might hc nccessauy to weld a 12-gmrge 3heet to this plate in thc vertical drr\\-n positim with 180 arnps anrl ;I specd of 22 irr. jmin. This would rsduce the wclding heat input to 9800 joul(~siin. If this werc a thick plate, it \vould indicate thc need, wit11 this second pro- ccdure, for n ~ o r ~ : prelhaat, althongh existing prcheat tab la do not r t m p i z c the cffect of diEcrctit welding hcat inputs.

On the other I ~ ~ i n t i , somc do\i;ii\vard i~djustn~ent in preheat from the \ d i w list011 in the prclieat tables should he ~nade for standard welding procetlures which providc a mlich grcatrr welding h a t i~~pi r t . We are considering here a stable heat-flow- condition after some welding has progresstd.

This does r~ot consider the more severe cooling conditions at thc moment wdrling commerrces. Un- dorrht~dly, some initial hcat could bt: supplied to a localized arra at thv start of tllc weld on thick plate. Tho qncstion hecomcs Iiow much, if any, preheat is nerded for thc rernaini~ig length of joint.

For esainplt:, i t is st;uidard practice today to use submerged-an antom:~tic welding to build up columns and girdcm from heavy plate. Onc method of fabri-

cation uses a single-arc, submerged-are automatic weld at 850 amps and a speed of 20 in./min. (for a %'' fillet weld), wit11 the ginicr positioned for flat welding. This would provide a heat input of 86,000 joules/in. An alternate metbod positions the girder with its web vertical so t l~a t both welds are made si~nultaneously in the hrxizontal position, and uses two sets of tandcm arcs (each set with two wclding heads); the heat input from e:icb arc would he 73,600 joules/in.-a total of 147,000 joules/in. of weld for ezreh fillet. Because of the resdtirig lower cooling rato, less preheat should be required once the weld has been started. This may be a considerable advantage for the comfort of welding - operators, especially when welding inside 1,lrge box girders.

16. COOLING RATE

When a \veld is made, thc weld and adjacent plate cool very rapidly. Thc rate of cooling depends first on the combination of initial plate temperature (To) (int,luding cffccts of preheat or interpass temperature) and the welding licat input ( J ) , and secondly, on the plate's capacity to absorb this heat in terms of plate thickness and joint geometry.

Fignro 12 ilh~strntcs the temperatrires in the heat- :dFectcd zone of the plate as the welding arc passes by. Under a givm set of coriditions, the cooling rate will vary as ropres<.~ltcd by the changing slopes of both curves.

For a particnlar cheinistry: at a given tempcratrire level ( T , j thir-e is a critical cooling rate (R,,) whicli shoold not bc cscreded i n order to avoid u~~dcrbead cracking. This temperature level is in the range of J00"l' to 750°F. American investigators tend to use a higher value sucli as 750", while English and Canadian invcstigators favor a lower value such as 300°C, or 572°F. In this discussion, wc have placcd this temperature levt4 (Ti) at 572°F. . , Ihe iiivestig:ition of cooling rates has been based largely on two rxtreme conditions, which have been d t d o p c d rnatheniaticaily.* These are:

I. The thin platc, in which the combination of


heat inpnt, preheat and intorpass temperature. For a given heat input, the cooling rntr indicated by the "thick platc" formula is tlw maxiinurn (R,,,) that can occur rcgardiess of the plate thicl\-ness.

At any given plate thickness the lower cooling ratc value is the more nearly correct. Using the two curves of Figure 15 as a limit and a guide, a new curve (solid line) lhns hcen dr;iwn in Figure 16.

Piote thickness (tj --+ FIGURE 16

Notice, Figure 16, that the upper half of the variable part of this cnrvc is almost a perfect reversal of the lowcr half, and the lower half belongs to the curve for the "thin plate". Thereforc, the curved portions will be expressed mathematically as-

lower portion

upper portion

If a welding proccdwe for a given plate thickness lies in the lower portion of the cnwc, it is easy to solvc directly for the r eqn in~ l preheat (To) using formula ( 4 ) ; howcver, this w u l d be very difficult for thc upper portion using formula ( 5 ) .

Thc chart is further limited in use since it only covers n single valuo of prchcat and heat input. There- fore, to expix l the application of this approacl~, wc will put both formnlas ( 4 ) and ( 5 ) into morc usable non-dimension formnlas (6) and ( 7 ) . This calls for inclnsion of the maximum cffcctive plate thickness (t,,:,), and the corresponding maximum effective prcheat (T,)/,,,) for this thickness.

l o w r portion

t = actual thickness of the plate, in.

tm = maximiim effective plate for given values of (1) and ( R )

TI = clcvatcd tcmpeiaturc at which cooling rate is c.on\idercd (572°F)

T, -- prehcat tcmperatnrc for given values of ( J ) , ( R ) , and ( t ) , "F

To/,,, = maxunum effrctivc preheat temperature for a given value of ( J ) and (R), "F

Formulas (6) and ( 7 ) produccd the curve shown in Fignrc 17. This can he nsed to determine To the rcquired prt:hcat ternprrature.

17. BI-THERMAL VS. TRI-THERMAL HEAT FLO

This work is based upon bi-thermal hcat flow wherc thc heat bas two avenues for escnpc; for example, a (:onvcntional butt joil~t consisti~~g of two plates, Figure 18(a) .

Tri-thermal heat iiow lias three avcmm for escape, ;iri oxamplc is ;i tee joint made of three plates, Figure 18(h) .

Mjhcrt, tri-thermal heat WOW condition exists, the abovr work should hc modified either hy:

1. Using ?!3 of the actnal hcat input ( J ) , or 2. Adjusting the plato thickness ( I ) to allow for

the extra plate by using '/i of the sum of three thicknesses.

73-14 / Joint Design and Production

1.0

.9

.8

.7

T' -- - T d i , ,b Tb - To

Upper portion of curve

.5

i 4

.3

.2

1

I .2 3 4 5 6 7 .8 .9 1.0 i i 1.2

FIGURE 17

FIGURE 18

. CARBON EQUIVALENT

As a resrilt of rccent experiments and studies, it is possihlc to simplify the relationship of all chemical rlrments in a stocl to the occurrenct: of nnderhead cmcking. l'hc simplification is cxprtwed in a single formnla krro\~n as thc cart)on tyliivaleilt. This forn~ula expresses the inifuenrc of each elemant rrlativc to that of carbon.

Invrstigators* have shown ;I definite relationship in the percent of nndcrhcad cmcking to the carbon equivalent. Figure 19 sllows a 1" thick test plate on which a single bead was deposited nsing Ya" E6010 electrode at 100 amps, 25 v, reversed polarity, at 10 in./min. The chart, Figure 20, shows the percentage of uirderbcad cracking for diffcrent equivalents that occurred with this test. A deposit made with low- hydrogen E6015 electrodes on ;+ specilnen of this thickness did not have undcrhaad cracks. The AWS

E6015 rlrctrodt~ is comp;irable to today's E7018. The results were plotted, Figure 20, to give curves for three different preheat temperatures (T<>).

K. Wintertorl* has listrd I4 diftcrcrt carbon eqoivaltmt formulas and recommended the following:

" Stout and Doty, "\Veldability of Sttds", Welding Rcsearcl, Council, 1953, p 150; WilIi;ims, Roach, hfartin and Voldiich, "Wcldnbility of Carllon-hlarignnese Stcels", WELDING JOUR- NAL, July 1919, p. 311-s.

This forinula is applicable to the low-carbon low- alloy stcels for constniction and machinery manufacturing.

19. COOLlNG RATE AND CARBON EQUIVALENT

Altho~rgh not too well defined, for :I given analysis of s t rd there is a lnaxirn~rrn rate at which the vidd and adjacent plate may B e coo l~d without undcrbead cracking occurring.

"; .K. \Viiitrrton, "Wcliiahility I'rctlictiorr fmni Steel Cornpo- sitior ti, 4 i Hw-AKcclrd Zcnr Cracking", TVI'XDINC

FIGURE 19

Weidability and lding Procedure / 7.2-15

The higher the carbon equivalent, the lower will c;~rbon r~!~inivalt.nt-criticnl cooling mtc cnn.i, sliowrr be this critical (allowable) cooling rate. Thus, the in Fignrc 21 has l x ~ n PI-odnccd to usv :IS ;i gnide in highcr tlic steel's carbon equivalent, t h more in>- casc thl, CTS test on the particolar steel is not inad(,. portant becomes the nse of lowhydrogen \velding and This cwvc may he c~npresscd by the fol iowi~r~ forrnnla: preheating.

Cottrcll zmd Bradstreet" kavc used a type of R , - - -16.26 . . . . . . . . . . . . ( I ] ) Roeve Restraint test, calltd tho CTS (Controlled C,,, u . 3 0 7 4

nesscs are tested - '/a, ?b, and 1". Each test requires

m Thermal Severity) test. For any given steel, three thick- is critical ctw,iing rate T, - 572eF,

The critical cooling rate (I:,,) (,an be tlntcrmincd by a ) actual test of thc p;xrticnlar stacl to see what cooling ratc nil1 not cause cracking, or h ) using

100 forrnula (11) ilased upon Canadian inwstigations.

8 @ 80 - 2 " 0 60

0 a

% Suggested relation between critic01 cooling rote (Rl ond 2 40 carbon equivalent [C,,) for lowhydrogen rlectrodei

u ol ? : 20 c*, R 4 0 Values from A 40 57.6

B .45 36.0 0

0 C 5 0 19.8

Carbon equivolent, Cm, = C + -M_"_ + Si D 5 5 10.8 4 4 E .60 7.7

F 65 3.6 FIGURE 20

two fillet welds--one a bi-thermal weld (two avenues ,40

for heat to escape), the other a tri-thermal weld (tbrce avenues for heat to escape). This gives a to td of 6 different values for TSN (Thermal Severity Num- ber) , and for the given wdding heat input (about 32,000 joules/in.) produces 6 different cooling rates. .30 I t is then observed a t what cooling rate cracking 0 10 20 30 40 does or does not occur, and the subsequent welding Critical cooling rote [R ) . 'Fjiec procedure is adjusted so this critical cooling rate will FIGURE 21 not be exceeded.

Both of these men have produced tables in which relative \veldability has been expressed along with the critical cooling rate. More rcccntly, Bradstrrct** has tied in this relative weldability with carbon equivalent. By working hack through this information, the

" C. L. bl. Cottmll, "Controlled Thelma1 Severity Cracking Test Simulates Practical Welded Joints", WELDING JOURNAL. Junr 1953, p. 257-s; Catticll and Bradstreet, "A Method for Calculatin~ the Effect of Prcheat on Wcldahilitv". BRITISH WELDINE JOURNAL, July 1955, p 305; ~ot t rc l f and Bmd- street, "Calculating Preheat Temperatures to Prevent Hard Zone Cracking in Low Alloy Steels", BRITISH WELDING JOURNAL, July 1955, p. 310.

20. FlNDlNG REQUlRED PREHEAT

, , ( T I - Tdme).

b ) Determim: from lon i~u l ;~ (8) the value of

, . , , ... . , '" B. J. Hradstreet, "hlethods to Establisli Procedures for Weld- d ) FI-o~n the chart, Figtire 17, using ( c ) read the ing Low Alloy Steels", EXGINEERlNG JOURNAL (Engineering Institute oC Cmada) , November 1963. value for


(y$) I:) Knowing this value ( d ) and tlic value of

( T - T o from item (:I): determine the reqnircd preheat temeprahire (To).

An easier and faster nlcthod for deteimining the required preheat nses the nomograph, Figurc 22. This non~ogmph is actr~ally two nornographs superimposed uDnn each othcr. The first n o n ~ o r r a ~ h (snbs~xipt a ) - . will provide a vslur for

~

The second nomograph (snbscript b ) will provide the . . . - . rcqr~ircd prchcar and interpass temperature (To).

A set of cight graphs, Figure 23, \rill also providr this same infomintion.

I Example I Using Chart (Fig. 17)

Given:

watt-sec J = 2Q,000 Y me11

find required preheat temperature (T,):

a ) Determine Ti - To/,>, =

b ) Determine tmr = 42457

t I" c ) Determine rclativ~: thickness: = -, -- tm 2.26

= ,4429

d ) From chart, Figure 17, read relative preheat

temperature: T?. ...- T&E = ,73 T, - To

T - T o 289.6 e ) Therefore: T, - T o - - --- = .73 .73

= 396.7

572 - T, = 396.7

or T,, = 175.3 "F

1 Example I Using Nomograph (Fig. 22)

watt-see (:;iveri: J = 20 000 ---- ~

mch

find preheat tcmpernture (T,,):

watt-sec (2a) J = 20,000 ---

lllell

(321) Read t,, = 2.26"

Use this number as a pivot point

(4a) t = 1 . 0

2nd nomograph

(1) R = 25 "F/sec

watt-sec (2b) J = 20,000 ---- inch

(3b ) Red To/,,,, = 282 "17

Use this nnmbt~r as a pivot point

(4b) % T1 - To/rm = 73% (from 1st nomograph) T I - To

(5b) Read T , = 175 "F

21. OTHER POINTS OF CONSIDERATION

Test data has indicatod h a t thin plates result in slightly higher coding rates than calculated. It is believed this is because thin plates have a relatively greater surface arm for heat loss per volume than thick plates.

Normally, in the in\restigation of a groove weld, the pass completing the joint is considered rather than the root pass. This is hecausrz the face pass usually has a slightly highcr cooling rate due to the larger cross- section of the joint (assuming the same interpass temperature).

There is some indication that fillet welds have slightly higher cooling rates than the bead-on-plate welds used in the investigative work. This is because the 90" intersection of the two plates presents a larger area of contact with the weld, therefore absorbing hoat at a slightly greater rate. A groove weld similarly \vould offer a larger area of plate contact with the weld than a bead-on-plate weld.



SECTION 7 .3

1. FACTORS AFFECTING PROCEDURES

For every welding job there is one procedure which will complete the joint at the lowest possible cost. The accomplishment of this task requires a knowledge of the factors affecting the type of weld to be performed.

The main factixs to be considered are:

1. Type of joint to be made, included angle, root opening, and land (root face).

2. Type and size of electrode. 3. Type of cur rent , po lar i ty a n d amount

( amperes ) . 4. Arc length (arc voltage). 5 . Arc speed. 6. Position of weIds (flat, horizontal, vertical,

and overhead).

A large number of the above-mentioned factors can he detcrnlinctl by actually welding a sample joint. Such items as the type and size of electrode, polarity, current, arc characteristics, and shop techniques are best determined by the fabricator. The engineer must realize that these problems are present and should il~clude them in his consideration of the joint designs.

Figure 1 indicates that the root opening ( R ) is

the separation hrtwcen the mcmbers to be joined. A root opening is used for electrode accessibility

to the base or root of tllc joint. The sn~allcr the angle of the bevel, the larger the root opening mtist be to get good fusion at the root.

If the root opening is too small, root fusion is more difficult to ohtain and smaller electrodes must he med, thus slowing down the welding process.

If the root opening is too large, wcld quality does not suffer hut more weld metal is roqi~ired; this increases weld cost and will tend to increase distortion.

Figwe 2 indicates how tbc root opcning must be increasril as the bevel's included angle is decnrased. Backrip strips are used on larger root openings. .4ll three preparations arc ticceptahle; all are conchcive to good welding procedure and good weld quality. Selcction, therefore, is rlsually base11 on cost.

Root opening and joint preparation will directly affect weld cost (pounds of metal nquired) . and choice should bc made with this in mind. Joint preparation includrss the work required on plate edges prior to welding and inclndes beveling, providing a land, etc.

In Figure 3a if bevel and/or gap is too small, the weld will bridge the gap leaving slag at the root. Excessive hack gouging is then reqoircri.

Figure 3b shows how proper joint preparation and


\ ' ~ p o c e r " To Prevent Burn Through, This Will Re Gouged Out Before Welding Second Side.

FIGURE 4

procedure will produce good root fusion and will minimize back gauging.

In Figure 3c a large root openirig will result in b u r d ~ r o n g h . Spacer strip may be used, in w~hich case the joint must be back gonged.

Backup strips are commonly used when all welding must be rio~ie from one side, or when thc root opening is excrssive. Backup strips, shown in Figure 4a, b and c, are generally left in place and become an integral part of the joint.

FIGURE 5

Spacer strips may be used <:specially in the case of double-vee joints to prevent bum-through. The spacer, Figure ?d, to prevent burn-through, will be gonged out before welding the second side.

Backup Strips

Backup strip material should conforn~ to the base metal. Feather edges of tlic plate arc recommended when using a txickup strip.

Short intermittent tack u&ls should be used to hold the hackr~p strip in place, and thesc should preferably be staggered to rcduce any initial restraint of the joint. They should no? be directly opposite one another, Figure 5.

Thc backup strip should be in intimate contact with both plate edges to avoid trapped slag at the root, Figure 6.

Weld Reinforcement

On a bnt? joint, a nominal \veld rrinforcement (approui- mately $',c," above fiush) is all that is rleccssary, Figure 7, left. Additional buildup, Figure 7, right, serves no useful pnrpose, and will increase the weld cost.

Care shodd be takcn to h e p both the width and the height of the reinforcement to a minimum.

Joint Design / 7.3-3

2. EDGE PREPARATION

Thc main p~~rposc of a land, Figure 8, is to provide an additional thickness of nirtal, as opposed to a feather edge, in order to minimize any bum-through tendency. A feather edge preparation is more prone to bum-through than a joint with a land, especially if the gap gets a little too largc. Figrxe 9.

A land is not as easily obtained as a feather edge. h ft:atlier edge is generally a matter of one cut with a torch, while a land will usually require two cuts or possibly a torch cut p111s machining.

A land usually requires back gouging if a 100%

weld is required. A land is not recommended when weldirrg into a backup strip, Figure 10, since a gas pocket would he formed.

Plate edges are beveled to permit accessibility to all parts of the joint and i n s ~ ~ r c good fusion throughout the entire weld cross-section, Accessibility can he gained by compromising between maximum bevel and ~ni~iirn~rni root opening, Figure 11.

Degree of bevel may be dictated by the importance of maintaining proper electrode angle in confined quarters, Figr~rc 19. For tlic joint illustrated, the minimum recommended bevel is 45".

FIGURE 6 ?lqt,t

L w Reinforcement . - rRe~nforcement -

FIGURE 7

FIGURE 8

. . F GURE 9

FIGURE 10 Not Recommended


\ /

, FIGURE 11

U and I versus Vee Preparations

J arid U preparations are excellent to work with but economically they have little to offer because preparation requires machining as opposed to simple torch cutting. Also a J or U groove requires a land, Figure 13, and thus back gouging.

Back Gouging

To consistently obtain complete fusion when welding a plate, back gouging is required on virtually all joints except "vees" with feather edge. This may be done by any convenient means: grinding, chipping, or arc-air gouging. The latter method is generally the most economical and leaves an ideal contour for subsequent beads.

Without back gouging, penetration is incomplete, Figure 14. Proper back chipping should be deep

enough to expose sound weld metal, and the contour should permit the electrode complete accessibility, Figure 15.

FIGURE 12

FIGURE 14

Right-, Wrong -, Right?

FIGURE 15


FIGURE 16A-Prequaiified A S Building Joints (Manual Welding) Complete Penetration G~oove Welds-Par. 209

SINGLE (Welded From Bo th S ~ d e s Withouf Bockina Striol

SINGLE (Welded From One Side

Usinq Backing Strip)

DOUBLE (Welded From Both Sides Without Spacer Bar)

DOUBLE (WeMed From Both Sides Using Spacer Bar1 --

~mitotlons Far Jalnfs o ! P / P8rnitf*d Weldin%-

45./',./ A , , PO,i,i."l M.i% / F4.l mnd Orerh.06 onll 20./',d TI" on6 0.erhs.d oni,

NOTE: The size of the fil let weld reinfoicing aioove ~ d d r in Tec nod corner iointi rho11 t / 4 but rha i i be ?b' mox.

i. Gouge root before welding second side 'Par 505il

2. Use o i this weid l imi ted to bare metal thickness of 5%'' or larger.

when laser plcie is bevelled, firs: weld mat p a s fhi i ride.


FIGURE 165-Prequalified AWS Building Joints (Manual Welding) Parfiol Penetration Groove elds-Por. 2 10 t e ZG

8-P6 C-P 6

NOTE: I . Gouge root before welding second side lPar 505i)

2. Use of this weld preferably l imited to base metal thicknosr of 5/r" or larger

'When lower plate is bevo l l d . first weld root pais this ride.

3. TYPES OF JOINTS bevel, J, or U. Certain of these joints lave been prequalified by the Americm Welding Society (Am's)

The type of joint to he made depcnds on the design and are illustrated in two charts, Figure I6 for manual condition and may be one of the following: groove, welding and in Figure 17 for submerged-arc automatic fillet, plug or T joint. These joints may be made using welding. various edge preparations, such as: square butt, Vee, The choice between two or more types of joint

Joint Design

FIGURE 17A-Prequalified AWS Building Joints (Submerged-Arc Automatic Welding)

Complete Penetration Groove Welds-Par

SINGLE SlNGLE

(Welded From Both Sides (Welded From One Side

DOUBLE

(Welded From Both Sides)

Welds Mvrt 8e Centered on loin?

TC-US-S

NOTE: The size of the fi l let weid reiniorcing groove welds in Tee and coiner joints i h o i l equal t!4 but 1ha1i be niax

1 G o q c roof before welding second side lPo i 505i l

2. Use of th is weld preferably limited to bore nieioi thickness of SIR'' or la iger.

' When lower ,dote is bevelled. i i r r t wcld root poir this ride.

is not always dictated solely by the design function. The choice often directly affects the cost of welding. For example, Figure 18 illust~ates this influence. The choice is to he made between 45" fillet welds or some type of T groove joints.

( a ) For frill-strength wolds, the: leg of the fillet u d d must be about 75% of the plate thickness.

(1)) Full strength map also he ohtaincd by double beveling the edge of the plate 15" and spacing the plate so the root opening is '/s" to allow for colnplete

penetration. The amount of weld metal compared to the conventional fillet weld varies from 75% for a 1" plate to 56% for a 4" plate. For plates up to about I'iz" thickness, the extra cost of beveling the plate and the probable need to use lower welding current in the 15" groove tend to offset the lower cost of weld metal for this typo of joint. But for heavier plate the reduction in wcld metal is great entmgh to overcome any extra preparation cost.

( c ) Full strength may also be obtained by bevel-


FIGURE 175-Prequalified AWS Building Joints

8-P2-S Single B-P3-S Double

Single -Vee Corner

C-PZ-S

(Submerged-Arc Automatic Welding)

Portia1 Penetration Groove Welds-Por. 212

Single Or DouMeBeve I Comer

C-P4-S Single C-P5-S Double

Tee

T-P4-s Single T-PS-S Double

Single Oi- Double - U Butt

6 -P6 -S Single 6-Py-s Double

Single - U Comer

Single Or Double - J Corner

C-PB-S Single c-P9-s Double u inside joint angle

is 45 '

Single Or D o u b l e d Tee

NOTES: * Welded in the f lot position. e It mot face i r less than 1/4", there should be at leoit one moouoi beod to picvent burnthrougtt - . Minimum effective throot = \ l t i 6 . where I is thickness of rhinnei part.

* Plote thickness: single groove joint t 2 3/,,'; double groove joint t Zli/:". . Effective throat = t.,.

in2 the e d ~ e of the plate 60" so as to place some of is about I'h" date. The GO" .. the weld within tbc plate; a 60" fillet is thcn placed on the outside. The mini~nnm depth of bevel and the additiond leg of fillet are both equal to 29% of the plate thickness. For all plate thicknesses, the amount of weld metd is approsimately half that of the conventional fillet. This joint has the additional advantage that almost high udding current may be used as in the making of the fillet weld.

All of this is shown in thc graph, Figure 18. The cross-over point in this chart between the conventiolial fillet welds and the 35" full penetrated T groove joint

hevcl, partly prc t ra ted joint, wit11 60" fillets appcarstto he the lowcst in cost above 1" in thicknesses. Tlic relative position of these curves will vary according to thr wt,lding :~nd cntiing costs uscd.

It uwuld hc a good idea for each cornpanp to make ;I similar cost stndy of tho welding in their shop for gniilancr of their cngint,ers in qirickly selecting the most cconomical weld. Natr~r:~lly thc variotis costs (labor, \velding, cutting, handliug. asscmblp, etc.) will vary with each company.


4. WELDlNG SYMBOLS

Tobie of Relative Cost of Full Plate Strength Welds

I

I

v2 1 li% 2 21'2 3 Plate thickness. In.

FIGURE 18

The symbols in the chart, Figure 19, denoting the type of weld to be applied to a particular weldment have been standardized and adoptcd by the American Welding Society. Like any systematic plan of symbols, thcse welding notations quickly indicate to the designer, draftsman, production supervisor, and weldor alike, the esact welding details established for each joint or connection to satisfy all conditions of material strength and service required, Adapting this system of symbols to your engineering department will assure that the correct welding instructions are transmitted to all concerned and prevent misinterpretation of instructions, and resulting production cost increases.

Although at first it may appear that many different symbols are involved, the system a£ symbols is broken down into basic elements or fundamcntals. Any combination of these elements can then be b d t up to conform to any set of conditions governing a welded joint.

Therefore, it is wise in the initial stages to limit the use of symbols to just fillet welds and simple groove welds and to detail any special welds on the drawings. After the shop and draftsmen get uscd to these simple symbols, then they can branch into the ones that are more rarely used. Figure 20 shows the practical application of these symbols to various typical joints.

4 &- t i c

,OD .".,. ".. ./De*s I)O"h,. 1.. n-b>* x ,.--". S'"*l< @G l % l / e c

FIG. 20-Typical Applications of AWS Draft ing Symbols far Welds.


T Y P E S o f

But!

Tee

Corner

La

Edge

5 . TERMINOLOGY

Single

People who specify or are otherwise associated with welding often use the terms "joint" and "weld" rather loosely. For clarity in communication of instructions, it is dcsirahle to keep in mind the basic difference in meaning between these two terms. This is illustrated by Figure 21.

The left-hand chart shows the five basic types of joints: butt, tec, corner, lap, and edge. Each is clcfinrd in a way that i s dcscriptivs of the relationship thc plates being joined lrave to each other. Ncither the

FIGURE 21

gwnletry of the wcld itst4f nor iljc method of edge nrerxcatior-I has anv in81ic11cc on the hisic deiinition . A

of tllc joint. For instance, the tce joint could 1,s either fillet weldcd or gnmve w<,ldcd.

The 1.ig1lt-liii11d clliirt shows the h s i c typcs of \velds: fillet, stltiii~-c, brvcl-groow, V-groove, J-groove, and U-groove,. Tlre tylx: of joi~it does riot afFcct ~vlult we cdl tho I i l t l ro~tg l~ thc silrglt: bevt+groove weld is ill~rstr;itrtI ns a lxitt joilit. it may be iisrd in a I)~itt, tee or conler joint.

Tlrt completr: dt~fiiiition oL a welded joint must include (lescriptio~i of Imtlr the joint :ind tbe \vcId.

7.3-12 / Joint Design & Production

Efficient fobricotion of large curved roof girders for the University of Vermont gymnasium was assured by submerged- arc welding, using semi-automatic guns mounted on s e l f - p r o p e l l e d trackless tractors.

Here production of large box-section bridge girders is speeded by submerged- arc weiding and self-propelled trackless trolley which follows the ioint with minimum guidance.

S E C T I O N 7 .4

1. W H E N TO CALCULATE

Overwelding is one of the major factors of welding cost. Specifying the corrt:ct size of weld is the first step in obtaining low-cost welding. This demands a simple method to figure the proper amount of weld to provide adeqi~ate strength for all typcs of connections.

In s t r eng th connections, c!)ml>letr-p(>netrntjon groove u d d s must be made all the way through the plate. Since a groove weld, properly made, has equal or better strength than the plate, there is no need for calculating the stress in the wcld or attempting to determine its size. However, the size of a partial-pme- tration groove weld may sometimes be needed. When welding alloy steels, it is necessary to match the weld- metal strength to plate strength. This is primarily a matter of proper electrode selection and of weldilig procedures.

With fillet welds; it is possible to havt. too small a weld or too large a weld; therefore, it is necessary to determine the proper weld size.

Strength of Welds

Many engineers are not aware of the p a t reserve strength that vidds have. Table I shows the recognized strength of various weld metals (by electrode designation) and of various structural stecls.

Notice that the minimum yield strengths of the ordinary EGOXX electrodes are over 50% higher than the corresponding minimum yield strengths of the A7, A373 and A36 structural steels for whicli they sllould be used.

Since many EGOXX electrodes meet the speci6- cations for E70XX classification, they have about 75% higher yield strength than the steel.

Submerged-Arc Welds

AWS and AISC require that the bare electrode and flux combination used for submerged-arc wclding shall be selected to produce weld metal having the tensile properties listed in Table 2, when deposited in a multiple-pass weld.

2. FILLET WELD SIZE

The AWS has defined thc cffective throat area of a fillet weld to be equal to the effective length of the

weld tintrs the effecti1.e throat. The effective throat is defU1ed as tlre shortest 11ist:rnce from the root of thc diagrammatic weld to the face.

According to AIf5 tlre leg s i x of a fillct weld is rnrasnrtd by the 1;irgcst riglit trianglr which c;rn be iriscrihrd within the wcld, Figure 1.

This drfinitioti would nllow nneqnal-legged fillct welds, Figure 1 ( a ) . Aiiothcr AWS definition stipltlatss the largest isoscde.; iiiscribrd right triangle and wor~ld h i i t this to en eq11a1-legged fillet weld, Figure I ( b ) .

Unequnl-legged filkt wel& are sometimes uscd to get additioiinl throat arm; licnce strength, when the

TABLE I-Minimum Strengths Required of Weld Metals and Structural Steels

(AWS A5.1 & ASTM A 2 3 3 (or-welded condition)

/ Mciteriol I Min. Yie:siS+rength / Min. Tend; Strength

1 £6010 1 50.000 psi 1 62,000 psi

TABLE 2-Minimum Pvoperties Required of Automatic Submerged-Arc Welds

rAWS & AISC) (as-welded; multiple-pass)

Gmde SAW-1

tenrile strength 62,000 to 80,000 psi yield point, min. 45,000 psi elongotion in 2 inches, min. 25% reduction in nrco. mi". 40%

I Grade SAW-2 I tensile strength 70.000 to 90.000 psi yieid point, min. 50.000 psi elongotion in 2 inches. mi". 22 % reduction in aieo, mi". 40%


FIGURE 4

For an <:qua]-legged fillct weld, the throat is cqual to ,707 times t l ~ e leg size ( w ) :

The allowable force on the fillet weld. I" long 15-

where:

f - allowable force on fillet u~eld, lbs per linear inch

w = leg size of fillet weld, inches

r - allowable shear stress on throat of weld, psi

The AWS has set up several shear stress allow- ablos for thc throat of the Mlet weld. These are shown in Tables 6 and 7 for the Building and Bridge fields.

Minimum Weld Size

(AWS Bldg Art 212(a)l , AWS Bridge Par 217(h), AISC 1.1'7.4)

In joints connected only by fillet welds, the minimum leg size shall correspond to Table 3. This is dctcrmined by the thickness of the thicker part joined, but does not have to exceed the thickness of the thinner part joined.

The American Welding Society recognizes that

LE 3-Minimum eld Sizes for Thick Plates (AWS)

THICKNESS OF THICKER I MINIMUM LEG SIZE PLATE JOINED OF FILLET WELD

t W

to %" ind. over fi" thru %" over %" thrv 1%" over 1%" thru 2'14' over 2%'' thrv 61.

Minimum leg sire need not exceed thickness of the thinner plate

over 6"

thick plates offer greater restraint. and produce a faster cooling rate for the welds.

TaHe 3 is pretlicatd on the theory that the reqnired minimnm weld size will provide sufficient welding heat input into the plate to give the desired slow rate of cooling.

This is not a complete answer to this problem; for example, a plate thicker than 6" would require a minimum weld size of W', yet in actual practice this would he made in several passes. Each pass would bc equi\dent to about a 4: fillet, and have the heat input of approximately a 5:o'' weld which may not be snfficient unh~ss the plates are preheated.

A partial solution to this problem worlld be the following: Since the first pass of the joint is the most critical, it should be made M-ith low-hydrogen clectrodes and a ratht-r slow travel speed. Resulting superior weld physicals, weld contour, and maximum heat input provide :i good strong root bead.

1

Moximurn Effective Weld Size (AWS Bldg Art 212(a)2, AWS Bridge Par 217(c), AISC 1.17.5)

Along thc <:dgc of material lcss than %" thick, the maximum effective leg size of fillct weld shall be equal to the plate thickness ( t ) :

FIGURE 5

Along the edges of material '/ar' or more in thick- nt:ss, the maximum eff:fiective k g size of fillet weld shall be ('qua1 to the plate thickness i t ) less ' / / l G w . unless noted on the drawing that the weld is to be built out to full throat:

7 . 4 4 / Joint Design and Production

Minimum Effective Length (AN'S Bldg .4rt 212(a)4, AWS Bridge Par 217(d), .41SC 1.17.6)

The minimum effective length (I,,) of a fillet weld designed to transfcr a force shall he not lcss than 4 times its leg size or l'A2". Otherwise, the effective leg size (a,.) of the fillet weld shall he considered not to exceed % of the actual length (short of the crater unless filled).

Effective lenqtt, [La)

FIGURE 7

If longittidinal fillrt welds are nsrd alone in end connections of flat bar tension members:

FIGURE 8

(AWS Hldg Art 212(a)3, USC 1.17.6)

nnless additiorral melding prevents transverse bending within the conncction. - *In addition, the affective length (L,) of an intennittent Iillct weld shall not be less tlian 1W (AISC 1.17.7).

3. OTHER WELD RE

Minimum Overlap of Lap Joinfs (AWS Bldg Art 212(h)l, MSC 1.17.8)

FIGURE 9

where t = thickness of thinner plate

Thickness of Plug or Slot Welds

(AWS Bldg Art 213, AWS Bridge Par 218, AISC 1.17.11)

FIGURE 10

1. If t @ 5 W"

then t, = t &

2. If t @ > %"

then t , 2 '/z t e z '%"

Spacing and Size of Plug Welds (AWS Bldg Art 213, :iWS 13ridge Par 218, AISC 1.17.11)

FIGURE 11


s 2 4 d

d 2 t* + < 2% tw

Spacing and Sire of SIof

L s 10 t,

w 2 t * + X8" 5 2% t, s , 2 4 w ST, 2 2 L

r 2 t*

4. PARTIAL-PENETRATION GROOVE

Partial-penetmtion groove welds are allowed in the building field. They have many applications; for example, field splices of cohimns, br~ilt-up box sections for trnss chords, etc.

For the V, J or U grooves made by manual welding, and all joints made by snhmcrged-arc welding, it is assirn~ctl the hottom of the joint can he rcached rasily. So. thc effective throat of the weld ( t , ) is equal to the ;ictlinI throat of the prepared groove ( t ) . See Figure 13.

If a hevcl groove is tvclded manually, it is assumed that the wcldor may not (p i t r reach the bottom of the groove. Thcrefore, AWS and AISC deduct 36" from the p rcp rcd groove. IIere the effective throat ( t , ) will q ~ a l the throat of the groove ( t ) minus %". See Figure 13(a) .

(a) Single bevel joint (b) Single J joint

FIGURE 13

Tension applied parallcl to the weld's nsis, or compression in any direction, has the same allowable stress as the plate.

Tension applied transverse to the weld's axis, or shear in any direct~on, has a reduced allowable stress, e q d to that for the throat of a corresponding fillet weld.

Jnst as fillet wolds have a minimnm size for thick plates because of fast cooling and greater restraint, so partial-penetration groove welds have a mininium cffective throat ( t , ) which should be used -

> t, =

where:

t, = thickness of thinner plate

a. Primary welds transmit the entire load at the particular point where they are located. If the weld fails, the member fails. The weld must have the same property as the member at this point. In brief, the weld becomes the member at this point.

b. Secondary welds simply hold the parts together, thus forming the member. In most cases, the forces on these welds are low.

c. Parallel welds have forces applied parallel to their axis. In the ,case of fillet welds, the throat is stressed only in shear. For an cqnal-legged fillet, the maximum shear stress occurs on the 45" throat.

d. Transverse welds have forces applied transversely or at right angles to their axis. In the casc of fillet welds, the throat is strcssed both in shear and in tcl~sion or comprrwion. For an wpal-lcggcd fillet weld, the m;iximum shear stress occurs on the 67'h" throat, and the masin~um normal stress ocmrs on the 22%" throat.

7.4-6 / Jcint Design and Producticn

TABLE &Determining Force on Weld

I tens ion or

c o m p r e s s i o n

I vertical V shear 1 :

standard design

formula Type of .Loading

, I 1 ' - I I SECONDARY WELDS I

treating the weld as a line

stress force IbaIinZ Iba/in

6. SIMPLE TENSILE, COMPRESSIVE OR SHEAR LOADS ON WELDS

f PRIMARY WELDS

For a simple tensile, compressive or shear load, the given load is divided by the length of the weld to arrive at the applied unit force, lbs per linear inch of weld. From this force, the proper leg size of fillet weld or throat of groove weld may be found.

7. BENDING OR T ISTlNG LOADS ON

The problem here is to determine the properties of the welded connection in order to check the stress in the weld without first knowing its leg size. Some design texts suggest assuming a certain weld-leg size and then calculating the stress in the weld to see if it is overstressed or undcrstresscd. If the result is too far off, then tlie weld-leg size is readjusted.

This has the following disadvantages: 1. Some decision must be made as to what thoat

section is going to he used to detcrmine the property of tlie weld. Usually some objection can be raised to any throat section chosen.

2. The resulting stresses must be combined and, for several types of loading, this can be rather corn- plicated.

In contrast, the following is a simple niethod to determine the correct amount of welding required for adequate strength. This is a method in wliich the weld is treated as a line, having no area, but a

definite length and outline. This method has the following advantages:

1. I t is not necessary to consider throat areas because only a line is considered.

2. Properties of the welded connection are easily found from a table without knowing weld-leg size.

3. Forces are considered on a unit length of weld instead of strcsses, thus eliminating the knotty problem of combining stresses.

4. I t is true that the strrss distribution within a fillet weld is complex, due to eccentricity of the applied forcc, shape of the fillet, notch eifect of the root; etc.; however, these same co~iditions exist in the actual Ellet welds tested and have been recorded as a unit force per nnit length of wcld.

8. DETERMINING FORCE ON

Visualize the welded connection as a single line, having the same outline as the connection, but no cross- sectional area. Notice, Figure 14, that the area (A,) of the welded connection now becomes just the length of the wcld.

Instead of trying to determine the strcss on the weld (this cannot be done unless the weld size is known), tlic problem becomcs a much simpler one of determining the force on the weld.

FIG. 14 Treating weld as a line.

By inserting t l ~ c property of the welded connection tmltecl as a line into the standard design form~ila used for that particular type of load (see Table 4 ) , the force on the weld may he found in terms of ibs per linear inch of wcld.

Example: Rending .~ . . - - ~ ~ ~ ~ ~ ~~ ~~~~~~ ~~

Standard dcsigi formula Same formula used for weld (bending stress) I (treating weld as a line)

h4 Ibs ~~~~ -- ~~ - .-" strcss M Ibs

f - force in.- S , in. --

Normally the use of time standarcl dcsigu forrnulas resnlts in a unit stress, psi; however, when the weld is treated as a line, these formu1;is resdt in a force on the weld, ibs pcr linear inch.

For secondary welds, the weld is not treated as a line, hut standard design formulas are used to find the forcc on tlie weld, lbs per linear inch.

In prol~lams involving bending or twisting loads Table 5 is used to determine properties of the weld treated as a line. I t contains the scction modillus (S,), for bending, and polar momcrit of inertia (J,), for twisting, of some 13 typical welded connections with the weld treated as a line.

For any given connection, two dimensions are necded, width ( h ) and depth (d) .

Section modulris (S,) is used for wrlds subject to bending loads, arid polar moment of inertia (J,) for twisting loads.

Section modnli (S,) from these formulas are for maximum force at the top as well as the bottom portions of the meliled connections. For the nnsyrnmetrical connections sho\~n in this tabk:, maximum bending force is at the bottom.

If there is more than one force applied to the weld, thcse are found and eomhinod. .411 forces which al-e combined (vectol-ially added) mmt occur at the same position in thc welded joint.

Determining Weld Size by Using Allowables

If there are three forces, c,ach : ~ t right angles to each other, the resultant is tqual to the square root of the sum of the squares of the three forces.

Weld size is obtained by dividing thc resulting force on the weld fonnd above, by the ;~llowable strength of the particrilar type of weld u x d (fillet or groove), obtained from Tables 6 and 7 (steady loads) or Tables 8 and 9 (fatigue loads).

If therc are two forces at right angles to each othcr, the resultant is equal to the square root of the sum of the squares of thew two forces.

One important advantage to this method, in addition to its simplicity, is that no new formulas mnst be wed, nothing new must be learned. Assume an engineer has just designed a beam. For strength he has used the standard forinnla rr = M/S. Substitnting the load ow the beam ( M ) and tlre property of the beam ( S ) into illis forn~iila, lie has found the bending stress (u). Now, he substitutes the property of the

f, = \/ f? -t fz2


TABLE 5-Properties of Weld Treated as Line

. . . . . . . . . . . . . . . . . . . ( 3 )

weld, treating it as a linr (S,v), obtained from Table 5, into the same formula. Using t l ~ e same load ( h 4 ) , f = hl/S,%: he thns finds the force on the weld ( f ) per linear inch. The \veld size is then found by dividing tlie force on tlie \veld by the allowable force.

Applying System to Any Welded Connection

1. F i d the position on the \vcldcd connection trhere thc combination of forces \ d l bc maximum. There may h13 snore than one which should be considered.

2. Find the value of each of the forces on the \velded connection at this point. ( a ) Use Table 4 for the standard desigri formula to find the force on the n-eld. ( b ) IJsr Table 5 to find the property of the u d d treated as a line.

3. Combine (vcctorially) all of the forces on the weld at this point.

4. Determine the required weld sizc by dividing this resdtar~t ivdt~e 1)y the alloivahlc force in Tables 6, 7, 8, or 9.

7.4-8 / Joint Design ond Production

LE L A l l o w a b l e s for elds-Buildings (AWS Bldg & AISC)

compietr- Penetration Groove Welds

Por(ia1- P~-netration Groove Welds

Type of Weld

Filict Wold

Steel Slrerr

Plug

tension transverse to axis of weld

or rheor on effective throat

Electrode

- tension parailel to oxis of weld

o r cornpreliion on effective thioot ~~~~~ . -.

Allowable

I ~. . ~. ~ .. shear on effective

1 A7, A36. A373 / !:E60 or SAW-I 1

I A441. A242* €60 Iow-hydrosen I c ., . _ 13.600

or SAW-I i

/ A7, A36, A373 IE60 or SAW-I I

~ I some or fP.

A7, A34. A373 E60 or SAW-I . .... . . - . - ~ 4 ~ -- - -

E6O iaw-hydrogen r = 13.600 psi

f 7.: 9600 w i b l i n

E70 or SAW-2 7 -=: 15,800 psi

I Same os far fillet weid

* wddnble A242 :I E70 or SAW-2 could be used. but would not increase allowable

and

TABLE 7--Allowables for Welds-Bridges

Slot

Type of Weld

oms I

Complete- Penctioiion Groove Welds

Fillet Weld?

E70 low-hydrogen r = 14,700 psi

or SAW-2

rhoor on A36 5 I" thick t i 6 0 or SAW-I effective -~ . ~- 12,400 psi

oren A36 > 1 - thick $E60 lowhydrogcn A441, 4242- or SAW-I

* weldoble A242 $ E70 or SAW-2 could be used, but would not incrcore allowable


Datermine the sizc of rrquircd fillrt weld for the !)racket shown in Figure 15, to carry a load of 18,000 lbs.

u FIGURE 15

Step I : FIND PROI'EI3TIES OF Wl<LD. 'I'REAT- I I 4 A I (use Tuble 5 ) .

2 1 - ) b' ( b -+ d) ' J - . . .. - . ~ . . , - 12 ( 2 h + r l )

TABLE 8-Allowable Fatigue Stress for A7, A373 and A36 Steels and Their Welds

2,000,000 600,000 cycler cycles

ease Metal @ < = 7500 d = 0

10,500 In Teniton

psi i 2 1 3 K i - 2 ;3K

C"""..A"A

By Fillet Welds 1 But not to exceed +w+ PI

I I . . . ~ -- -- ~ ... .

Bore Mcto l compreii ,on

1 0 Connected 7500 r = ~~ ~ . * 10,500

~

I 213 K P54 psi

By Fillet : -- 213 K W e l d i

.-

eu t t Weld In Tension

Butt Weld Cornpieiiion

~

Filie: Welds u =: Leg size

@ ,800'" f = K l b l n ' - 2

But Not to Exceed

Adopted from AWS Bridge Specifications. K - nin /mux P. = Allowoble unit camproii ive s t i e s for member. Pr = Allowoble unit tensile r t r c i i for member.


Step 2: FIND THE VARIOUS FORCES ON WELD, INSERTING PROPERTIES O F WELD FOUND ABOVE (see Table 4 ) .

Point a is where combined forces are maxirnurn. Twisting f&e is broken into horizontal and vertical components by proper value of c - (see sketch).

tcisting (horizontal component)

Bare Metol In Ten~ion Connected By Fillet Welds

. . -. . - . .. .

Bare Metol Compression Connected By Fillet Welds

-. ..

Buff Weid In Tension

Butt Weid Comprerrion

..

Butt Weid in Shear

- ~- ~ ~ ~ ~ ~ ~ . .

W e t Welds w = leg sir

fwirting (tiorticul component)

- ( 18,000) - ( 2 0 ) = 900 lbs/in.

(Continued on page 11)

TABLE 9-Allowable Fatigue Stress for A441 Steel and i t s

2,000.000 cycler

600,000 cycler

0 19,000 * = .. ~~~ psi I -- 7 R

~

0 24.000 * = pri i - R

100,000 cycler

0

@ 13.000 = psi

I - I/, R

But Nol to Exceed

PC psi

-

P, psi

.~

13,000 psi

Adapted from AWS Bridge Specificofion! * i f SAW-1. use 8800 R = m i n i m a x load Pt -- Allowable unit compreiiive i treir for mcnihei P, = Aliowabie unit tensile sties$ far m e m b e r .

Determining Weld Size / 7.4-1 1

Step 3: DETERMINE rlCTUA1. RESULTANT FORCE ON WELD.

f r = J f,,,. + ( f , , -+- f n Y j 2 - - J (2'40)' -+ (2650)?

= 3540 lbs/in.

Step 4: NOW FTNL) REQUIRED LEC SIZE OF FILLET WELD CONNECTING THE B R C K E T .

actual force 0 -- . .~. . .~ . allowable forcc

- ,316 or use %ot' h 9. HORIZONTAL SHEAR FORCES

Any wold joining the flange of a heam to its web is stressed in horizontal shear (Fig. 16) . Normally a designer is acorstorncd to spt:cifying I certain size fillot weld for a given plate thickness (leg size about % of the plate thickness) in ordcr for the \wid to have full plate strength. IIowever, this particular joint be-

FIG. 16 These flonge-to-web welds ore stressed in horizontol sheor and the forces on them can be determined.

twtrrr the flangr and \ r ~ h is one eucrption to this rule. In order to prc\.cnt web buckling, a lower allowable shrnr stress is iisunlly ostxl; this rcsnlts in a thicker wt.l~. The wel& ;ire in air :trca ncut to the flange \vlicrc thew is no buckling 11n>blcrr1 nod, thcreforc, no reduction in allowable lo;~d is ilscd. From a design standpoint, these welds may 1,c very small, their actual size somctirnr.~ dcterinin(:rl by the ~niliirn~rm allowed hecause of the thic~krrrss of tlic flange plate, in ordar to assnrc thc pnlpcr slow cooling rate of thc weld on the heavier plate.

General Rules

Outsirle of simply lrolding thra flanges and web of 21

tmm togetiier. or to tr;mslnit any rrnusunlly high forct. twtwrcn tho fange arid web at right angles to

Siwply supported roncenrra:ed loud5

FIG. 17 Shear diogrom pictures the omoun t ond l o c o t i o n of

[ . i - _ L 7

welding required to transmit horizontal shear forcer between n

flonge ond web. ---

. the mcmber (for cx.iinl , l~euring supports, lifting

7.4-12 / Joint Design a n d Production

lugs, etc. ), the real purpose of the weld between the flange and web is to transmit the horizontal shear forces, and the size of the weld is determined by the value of these shear forces.

It will help in the analysis of a beam if it is recognized that the shear diagram is also a pictnre of the amount and location of the welding required between the flange and web.

A study of Figure 17 will show that 1) loads applied transversely to members cause bending moments; 2 ) bending moments varying along the length of the beam cause horizontal shear forces; and 3) horizontal shear forces require welds to transmit these forces between the flange and web of the beam.

Notice: 1) Shear forces occnr only when the bending moment varies along the length. 2 ) It is quite possible for portions of a beam to have little or no shear-notice the middle portions of beams 1 and 2- this is bemuse the bending moment is constant within this area. 3) If there should be a difference in shear along the length of the beam, the shear forces are i~sually greatest at the ends of the beam (see beam 3). This is why stiffeners are sometimes welded continuously at their ends for a distance even though they are welded intermittently the rest of their length. 4) Fixed ends will shift the moment diagram so that the maximum moment is less. What is taken off at the middle of the beam is added to the ends. Even though this does happen, the shear diagram remains un- changed, so that the amount of welding between flange

FIG. 18 Shear diagram of frome indicates where the amount of weldins is criticai.

and web will be the same regardless of end conditions of the beam.

To apply these rules, consider the welded frame in Figure 18. The moment diagram for this loaded frame is shown on the left-hand side. The bending moment is gradually changing throughout the vertical portion of the frame. The shear diagram shows that this results in a small amount of shear in the frame. Using the horizontal shear formula (f = Vay/ln), this would require a small amount of welding between the flange and web. Intermittent welding would probably he sufficient. However, at the point where the crane bending moment is applied, the moment diagram shows a very fast rate of change. Since the shear valne is equal to the rate of change in the bending moment, it is very high and more welding is required at this region.

Use continuous welding where loads or moments are applied to a member, even though intermittent welding may be wed throughout the rest of the fabricated frame.

Finding Weld Size

The horizontal shear forces acting on the weld joining a flange to web, Figures 19 and 20, may he found from the following formula:

where:

f = force on weld, lbs/lin in.

V = total shear on section at a given position along beam, lbs

a = area of flange held by weld, sq in.

y = distance between the center of gravity of flange area and the neutral axis of whole section, in.

I = moment of inertia of whole section, in.4

n = number of welds joining flange to web

load

FIG. 19 Locate weld at point of minimum stress. Horirontoi shear force is maximum along neutral axis. Welds in top example must carry maximum shear force; there is no shear on welds in bottom example.


FIG. 20 Examples of welds in horizontal shear.

The leg size of the required fillet weld (continuous) is found by dividing this actual unit force ( f ) by the allowable for the type of weld metal used.

If intermittent fillet welds are to be used divide this weld size (continuous) by the actual size used (intermittent). When t,xpressed as a percentage, this will give the length of weld to he used per unit lcngth. For convenience, Table 10 has various intermittent weld lengths and distances between centers for given percentages of continr~ous welds.

calculated leg size (continuous) % - - . ..~ . . - . .. actual leg size used (intermittent)

For the fabricated plate girder in Figure 21, determine the proper moun t of fillet welds to join flanges to the web. Use E70 welds.

FIGURE 21

horizontal sl~car force on weld

where:

V = 189,000 lbs

I = 36,768 in.'

a = 27.5 in."

y = 24.375'

n = 2 welds

;rt:trial force w _ ~ ~~ ~ ~ ~

:illow~xhle force

This worild he the minim~tni leg size of :i continw ocw. fillet w ~ l d ; ho\vcvcr, ?"i' fillet welds are rccom- mended hccmse of the thick 2%" flange plate (see table). In this particnlar case, the leg size of the fillet weld need not excctd the web thickness (t11innt:r plate). Because of the greater strcngtl~ of the M" fillet, intcrmitteut welds may be used but must not stress the web above 14,500 psi. Therefore, the length of weld must be increased to spread the load over a greater lcngth of web.

Weld vs Plate

2 (11,200 w) I, 2 14.500 psi t x L

TABLE TO-Intermittent Length and Spacing

Continuous Length of intermiftent welds ond weld, % di3tmce between icnterr, in.

75 . . 3-4 . . 66 . . . . 4-6

= 1720 lbsjin

7.614 / Joint Design ond Production

For this reason the sizc of intermittt:nt fillet weld w e d in design calculritions or for determination of Icngth must not excetd % of the web thickness, or here:

2h of MI' (web) =: ,333"

The percentage of eontinuonr weld length needed for this intcrrnittent weld will be-

continuous leg size % = ---_- ~nterm~ttent lag size

M" 1\ 4" - 8" (see Table 10) 'Q

I Problem 3 1 A fillet weld is required, using

that is, intcrmiltent welds having leg size of %" and Icngth of 4", set on 12" renters. A ?W fillet wcld ~is~rally rtquires 2 passcs, nnlrss the work is positioned. A 2-pass weld rcqnirt:~ more inspection to maintain size and weld quality. The shop would like to change this to a %,," weld. This single-pass weld is casier to m:tke and thcre is little chance of it being undersize.

This change could he made as follows: The prewnt :k" is welded in lengths of 4" on

13" ccnters, or 33% of the length of the joint, reducing the leg size down to 3/,6" h or of the previous wcld. Tliis would require the percentage of length of joint to be increased by the ratio 6 / 5 or 33% ( x ) = 40%.

Hence, use---

P - lop * In other words, %" intermittent fillet welds, 4"

long on 13" centers, may be ~.cplaced with % welds, 4" long on 10" centers, same strength. This change would pennit welding in one pass instead of two passes, with a saving of approx. If%% in welding time and cost.

Determinc the leg size of fillet weld for the base of a 30 lhs/sq f t or pressure of p = ,208 psi. Use A36 Steel signal tower, Figure 22, assuming wind pressure of & E70 welds.

FIGURE 22

Step 1 : FIND PROPERTIES OF WELD, TREATING IT AS A LINE.

-. (20.5)" (6%))" - ~~

6 = 1386 in."

- - ri (6%)9 .- - 8

- 114 in? Total I, = 1500 in?

= 146 in.'

Step 2: FIND THE FORCE INVOLVED.

Moment acting on tower due to wind pressure:

bending stress in pipe (column)

M e 0- = --

I

=r 23,600 psi --

Step 3: FIND FORCE ON FILLET WELD AT COL- UMN BASE.

eld Size / 7.4-15

= 1370 lbs/linear in.

Step 4: NOW FIND REQUIRED LEG SIZE OF FILLET WELD AT BASE.

actual force 0 = allowable force

= ,123'' but use Xo" ~~ all -~ around, the mini-

mum fillet weld size for 1" base plate

To determine amount of fillet weld to attach masoniy plate to beam, using E70 welds. The following conditions exist:

FIGURE 23

properties of section

= -2.145" bclow axis x-x

Built-up member

IW WF 45#

1 8 x '/z"

T o m - 11

0 -

1-253.8 ~-

Ir

248.6

-

A

13.24 -- 9.00

.p--.-...p..- 22.24 - 502.4

d

. 0

-- 5.31

M

0 ~

---47.79

-47.79

7.416 / Joint Design and Production

horizontal shear force on weld

V a y fh = ---- I n

- (5000) (9.0) (3.415 ) - --- - .- -. (399,T) ( 2 welds)

= 192.0 lbs/in., max. at ends

properties of zoeld, trrating it os a line

S , = b d - *-- = (120)(8) d = 8 '

P - i i = 960 in." k-- b = 120' A , = 2 b

= 2(120)

bending force on weld

vertical slrear force on weld

~csultant force on t w l d

leg size of weld

= ,0207" if continuous

If using 3/,," internlittent weld, then

calcrilatrd continuous leg size := ~ ---- ~~p

actrial intermittent leg size iised

Hcnce, use

:4 ,;" V 2 - 8% on each side (25%)

DRIVE ROLL FOR CONVEYOR BELT

FIGURE 24

Determine sizc of required fillet weld for hub shown in Figure 2.4. The l~earing load is 6300 1bs. Torque transmitted is 150 HP at 100 RPM, or:

T = 63,030 x I-IP RPM

Step I: FIND PROPERTIES OF iVI<I,D, TREATING IT AS A LINE (use Table 5).


= 67.6 in.'

Step 2: FIND THE VARIOUS FORCES ON WELD, INSERTING PROPERTIES OF WELD FOUND ABOVE (use Table 4).

bending

twisting

Seep 3: DETERMINE ACTUAL RESULTANT FORCE A N D ALLOWABLE FORCE O N T H E WELD.

1 inch of fillat weld f at hub

f? = \/ fb2 + ftB + fr2 - - 4 (746)? + (1880)2 -+ (250)'

= 2040 lbs/in. (actual rcsultant force)

oi N = 2,000,000 cycles and use Table 8 formula. In this case, assume a complete reversal of load; hence K := min/max = -1 and:

5100 f = - K 1 - - 2

- 5100 - I - + % = 3400 lbs/in. (allowable force)

Step 4: NOW REQiTIRED LTX SIZE OF F1I.LET WELD AROUND IIUR C4N BE FOUND.

= ,600" or use %" h

I Problem 7 /

Since this is fatigue loading, assume service life FIGURE 25


A 3" X 4" angle for support of a pipe extends out from the transverse intermediate stifFe,ners on a plate girder, Figure 25. This must be field welded. It will be difficult to weld in the overhead position along the bottom edge of the angle as well as to make the vertical weld along the end of the angle next to the girder web because of poor accessibility. Check whether just two fillet welds would be sufficient, assuming the pipe's weight on the hanger is 300 lbs and a possible horizontal force of approximately 200 ibs is applied to the hanger during erection of the pipe.

properties of ae ld trcatcd u s a line

1. For twist about connection's center of gravity, due to P,

( b + - 6 b2 @ Jv = 12 ( b + d )

- ( 3 -t 4)4 - 6(3)2(4)2 - --

12 ( 3 + 4)

= 18.3 in."

2. For bending about (y-y) axis, due to P,

twisting force on weld

1. Horizontal

3. Vertical

t crtical shear

hending force on t ~ c l d (about y-yj, due to PI,

resz~ltont force on weld at hottom of connection

FIGURE 26


leg size of fillet weld r-7

= .048" or x," h would he sufficient

10. MOW TO MEASURE SIZE OF FILLET

The size of a fillet weld is difficult to measure without proper gages. Fillet shapes are concave, convex, or flat. They may have equal or unequal legs. However, the true fillet size is measured by finding the leg- length of the largest isosceles right triangle ( a triangle with a 90" corner and legs of equal length) which can he inscribed within the weld cross-section, with the legs in line with the original surface of the metal.

The gages shown in Figure 27 give quick, easy

FIG. 27 Convex fillets may be measured with gage of type shown on right; in this case it measures the leg size. Concave fillets are measured with gage like the one on left; in this case it meosures the weld throot.

measurement of fillet size. Two gage types are available: one for a convex fillet, another for a concave fillet. See Section 7.10 for series of illustrations which dra- matically show how poor gaging can seriously offset the accuracy of engineered welds.

TABLE 11-Maximum Allowable Shear Stress and Shear Force For Given Applied Normal Stress on Fillet

or Partial-Penetration Groove Weld

Max. oliowoble shear rtres ( 7 ) which may be opplied to throot o i fillet weld or portid penetration groove veld

Max. dlowable sheor forcs (f) which may be opplied to fillet weld

- E60 welds E70 welds -. L - 9,600 11,170


11. WELDS SUBJECT TO COMBINED STRESS

Although the (1963) AISC Specifications are silent concerning combined stresses on welds, the prcviolls specifications (See 12 b ) rcqnired that welds snbject to shearing and externally applied tensile or compressive forces slrall be so proportioned that the combined unit stress shall not exceed the unit stress allowcd for shear.

Very rarely does this have to be elreeked into. For simply supported girders, the maximnm shear occr~rs near the ends and in a region of relatively low bending stress. For built-up tension or compression members, the axial tensilc or compressive stresses nay be relatively high, but thcoretic;illy there is no shear to he transferred.

In the case of continuous girders, it might be well to check into the effect of combined stress on the connecting welds in the region of negative moment, because this region of high shear transfer also has high bending stresses.

Even in this case, there is some question as to how much a snperimposed axial stress actually reduces the shear-carrying capacity of the weld. Unfortrmately there has been no testing of this. In general, it is felt that the us(: of the following combincd stress analysis is conservative and any reduction in the shear-carrying capacity of the weld would not be as great as wor~ld be indicated by the following formulas. See Figure 28.

In Figure 28:

7 = shear stress to be transferred along throat of weld, psi

u = rrormal stress applied parallel to axis of weld, psi

From the Mollr's circle of stress in Figure 28:

From these formulas for the resulting maximum shcar stress and maximrim rrormal stress, the following is tme:

For a given applied normal stress ( u ) , the great- cst applicd shear stress on the throat of a partial- pm~&ation groove weld or flllet weld (and holding the rnaxirnu~m shmr strcss resulting from these combined stresses within the allowable of T = 13,600 psi for EGO welds, or 7 = 15,800 psi for E70 welds) is-

for 1:60 toelds or SAW-1

for E70 welds or SAW-2

This same forn~r~ta may be cxprcssed in terms of allowable unit force (Ibs/lincar inch) for a fillet weld:

for EGO welds or SAW-1

. . . . . . . . . . . . . . . (8a)

for E70 welds or SAW-2

For the same given applied normal stress (u), the greatest applied shear stress ( 7 ) on the throat of a groovt: weld or fillet weld (and holding the maxirnr~m normal stress resulting from these combined stresses within the allowable of u = .60 u,) is-

Formulas #7 and #8 are expressed in table form, as in Table 11. The general relationship of these formulas is illustrated by the graph, F i y r e 29.

Determining Weld Size / 7.4.21

Ruilt-up tension

Teniioti flange to chord in t r u s s

web of or box glider

FIG. 28 Analysis of weld, using Mohrjs of Stress,

7.4-22 / Joint Desiqn a n d Production

Applied noimol stress ( 0 1 porai!el to weld, k i i

FIG. 29 Relationship of Formulas #8 and #9; see Table 11, page 19.

SECTION 7.5

1. COST FACTORS

There are several methods which may be used to study welding cost, and these depend on the need for such a study. For example, is it needed to estimate a new job for bidding? Or, it is needed to compare one procedure against another? Or, is the chief need one of determining the amount of electrode to order?

A good methocl of cost estimating should give the final cost quickly; yet indicate what portion of the operation is more expensive, i.e. where the welding dollar is really being spent.

The h a 1 cost includes a t least these items: a ) labor and overhead for plate preparation, assembling, welding, cleaning, and sometimes stress-relieving; b ) elcctrode, flux, and gas; and c ) electric power.

Table I includes a number of useful formulas for determining various cost components.

Unfortunately there is no one all-inclusive formula By which all types of welding jobs may be studied. The simplest type of cost estimation is a job that requires a long, single-pass fillet or groove weld. Next comes the long, multi-pass weld, where a different procedure may be used for each pass. In both examples, it is sufficient to assume a reasonable operating factor due to the downtime between electrodes consumed and to apply this to the actual arc time. This downtime is affected by the weldor, as well as the job. A more complicated weld may require a handling time factor. This handling time is affected more by the job, than by the welding.

Three items which are difficult to tie down, yet greatly affect the cost of a weld, are these:

1. The amount of filler weld metal required; this varies with size of weld, size of root opening or fit up, amount of reinforcement, included angle of groove, etc.

2. The operating factor used, i.e. the ratio of actual arc time to the over-all welding time.

3. The amount of handling and cleaning time. This section includes various tables and nomo-

graphs which are helpful in making true cost estimates. No estimating system, however, is satisfactory without the estimator applying his good judgment and per- ception.

2. COST OF WELD METAL

The cost of welding is directly affected by the amount

of weld metal required. Very few people realize the great increase in weld metal and cost that results from a slight increase in weld size.

The cross-sectional area of a weld generally varies as the square of the weld size. For example, making a %," leg size fillet weld when a W' weld is desired, increases the leg by 25% but the area is increased by 56%. The amount of reinforcement is diEcult to specify and control; yet the range of its variance can substantially affect the amount of weld metal required. A slight increase in root opening increases the amount of weld metal for the entire thickness and length of the weld. The resulting percentage increase in weld metal is usually surprising.

Computing Weld Weight

Designers or associated personnel frequently have to compute the weight of weld metal required on a particular job, as a matter of either cost estimating or determining the amount of material to be ordered for a particular job. Sometimes these computations must be based on the size and configuration of the joint. The normal procedure to follow in such a case is to compute the cross-sectional area of the joint in square inches and then convert this into pounds per linear foot by multiplying by the factor 3.4. To simplify these computations, Tahle 2 (weight in lhs/linear f t ) has been developed; its use is illustrated in Problem 1.

Tables 3, 4, and 5 provide precalculated weights for specific joints and read directly in lbs per foot of joint. Tahle 6 is a similar table for AWS prequalified joints. Tables for the direct reading of weld metal for partial-penetration grwve or Met welds are included in Section 3.6, "Fabrication of Built-up Columns."

For estimating the weight of manual electrode required, ronghly add another 50% to this amount of weld metal.

In order to arrive at the labor cost per foot of joint, it is necessary to know the speed at which the joint can he welded. This may be found in prepared data on standard welding procedures, both for manual welding as well as the submerged-arc process. For special joints for which no information is available, the deposition rate (Ibs/hr) may be determined from tables and charts for given welding currents. The joint speed is then funnd by dividing this deposition rate by the amount of weld metal required (lbs/linear ft.).


TABLE 1-Useful elding Cos! Formulas

SPEED I TIME I JOINT SPEED

in i t . 5 - - - min 60 1 2 1 h r min ft i t /hr = m/mm 2 + l t l

S, S2 S3 ~~ ~ ~~- ~

-. - 7----

JOINT SPEED 1 ROD ME1 TED PER FOOT 1 ROD MELTED P E R HOUR

i t 6OD . - % - I lh rod mel& z~ ib rod melted 6000 M (OF) hr J it wcid N L,*. S hr N L,. 1 -

ROD MILEAGE I ROD CONSIJMED P E R F0O.I' 1 ROD CONSUMED I'EK HOUR

APPROXLhlnTE R1EI.T O F F I U T E E(wc volt$ Ilwcldinp current) lb rod m c E

- 1000 h r

APPROXIMATE COST O F SUBMERGED ARC _ - & ,00663 I (FtW) - 10 L AUTObL4 TIC WELD i t S

WELD COST

I p e r foot of tach pass I p e r l b of deposit

LABOR OVERHEAD 5 L " L I ft - s (OF)

MANUAL EI.ECTRODE 12lNIMW

ft N L S

AUTOMATIC $- 1 2 m W+RF) - J ( U ' ) WIRE & FLUX S Ez

GAS

L = lnbvr + overhead ($/hr) W = wire o r rod cost (Clh) N = number rods/100 lbs

F = flux cost (C/lb) I = welding cur ren t (amperes)

G = gas cost ($/hr) S : (in weld/min) = L-/T

R = ratio of flux to wire T = t ime to melt one rod (min)

D = (lb weld deposited/rnin) L- = (in rod meltcd/rod)

M = (in rod melted/min) = I,..;/T 1.. = (in weld/rod)

C = (lb rod consumed/min) with s tub J - (lb weid/it of jaint)

m = (Ib rod mclted/min) no s tub O F = operating factor

Wr = weight one rod with s tub (Ibs) = 10O/N W, = weight of one s tub (lbs) Ei = deposition efficiency lb weld d e p o s w _D

Ib rod melted m E2 = overall deposition efficiency a i d deposited D

= El Er lb rod consumed

El - melting efficiency lb rod melted m . W, - W, lb rod c o n s u m ~ i =

= ---- W,

elding Cost. / 7.5-3


eight of Weld Metal (Ibs/ft of Joint)

TABLE &Weight of Weld Metal ( Ibdf t of Joint)

Estimating Welding Cost / 7.5-5

Reinforcement: 10%


FIG. 1-Weight of Weld Metal (Ibs/ft of Joint)

Based on Procedures, Using Submerged-Arc Process

Weight of Weld M e t a l (lbs. p e r foot of joint)

DC - Dct

T r a v e l Speed ( inches p e r m i n u t e )

elding Cost / 7.5-7

I Problem 1 ( Computing the Weight of Weld Metal Rascd on Joint Dosign

With Table 2, computiltions based on joint design are easy. Essentially, it is a matter of dividing the cross-section of the area to be filled with weld metal, into standard geometric areas. The contributions of the individual areas can be found in the chart. Totaling these, gives the pounds of weld metal per foot required by the joint. For example, consider the following joint design (Fig. 2 ) :

1 . , ...$ iK,'

A -. --

j/q rad:

FIGURE 2

This joint can be broken into component areas A, B, C and D. Referring to Table 2, the contribution of each 06 these component areas to the total weight of weld metal required by the joint is simply picked off the chart as follows (Fig. 3 ) :

Since t = Ys" and d = 1%'' read from Table 2:

,318 Ibs/ft

Since included angle is 14" and d = 1" read from Table 2:

,417 Ibsjft

Since t = %" and d = 1"

11 read from Table 2:

1.7 lbsjft

Since r = Y4" read from Table 2:

,334 lbsjft

FIGURE 3

Adding these, the total weight becomes 2.77 lbs of weld metal per foot of joint.

When the welding procedures for a particular job are known, it is a simple matter to detennine the weight of weld metal that will be deposited per foot of joint through the use of the nomograph foq submerged arc welding Figore 1. Simply line up a straightedge through the point on the left scale that represents thc welding current being nsrd and the point on the middle scale that represents the travel speed being used. Where the straightedge intersects tbe right scale, read the amount of weld metal per foot of joint.

There is one note of caution. Be sure to use the proper side of the Welding Currcnt scale, depending on the size of electrode used, and the correct side of the Weight of Weld Metal scale, depending on the polarity used.

As an example, the line drawn on the nomograph represents the procedure which uses 590 amps on Ys" electrode at a travel speed of 30 in./min. The resultant weight of weld metal is .10 lbs per foot of joint if DC positive polarity is used, or .13 lbs if DC negative polarity is used.

I Problem 3 / Adjusting Procedures to Provide the Required Amount of Weld Metal

For some types of joints, there are no established welding procedures. When such is the case, the normal method is to find an established procedure for a similar joint and alter it slightly to accommodate the desired joint. The nomograph for submerged-arc welding, Figure 1, can eliminate a lot of hit-and-miss approaches to the selection of the proper procednre.

For example, consider the following suhmerged- arc automatic joint (Fig. 4 ) :

FIGURE 4

/ Problem 2 1 Computiag the Weight of Wold h4etal Based on Weid- ing Procedures

There are no established procedures for this joint. Probably the closest is that for the following joint (Fig. 5):


FIGURE 5

Power: DC+ Amperes: 670 Volts: 29 Electrode Size: $h2" Travel Speed: 16"/min.

3. OPERATING FACTOR

The selection of a proper operating factor (OF) is difficult, and yet affects the final cost more than any other single item. Even though some difficulty is en-

111 adjusting this procedure to the new joint, it is reasonable to assume that the 670 amps would be about right and, therefore, the simplest thing to do would be to slow down the welding speed enough to provide the amount of 611 required. To do this, first determine the amount of weld metal required to fill the new joint in the manner outlined in Problem I. In this case, it is determined to be ,404 Ibs/ft of joint.

Then, nse the uomograph to determine the proper speed setting as follows.

Locate 670 amps on the left-hand side of the welding scale (for vG2" electrode) and ,404 lbs/ft on the DC+ polarity side of the weld metal scale. Draw a straight line between them. This intersects the travel spced line at Y"/min, which is an estimate of the s p e d which should be used to provide adequate fill in the joint. With this much of the procedure Sxed, it is a simple matter to adjust the voltage to provide the desired bead shape.

countered in obtaining this value, it is necessary to establish an approximately true value rather than to simply ignore it or assume it to he 100%. Consider the following:

.- ~. METHOD A

1 - METHODB

In other words, the operating factor does affect the welding cost sufficiently to be considered. .4 \vclrling snginecr is interested in replacing his

Since one might question the practice of assmn- present E-6012 electrode on a ccrtnin job with the iron ing the same operating factor for various electrodes powder E-6024 elrctrodc. Thc following is his cost and procedures, consider the followir:,: example. study:

~ , ' ,o lcc t rode A @ 20$/lb

uses i 4 it rodift of weld

speed is 18 in. /min

labor & overhead, $6.0U/hr

Total cost of weiding using 100$ operating factor:

11.7 C/ft

'/rMe1ectrode B (d 14$/lb

uses i: Ci rodift of weld

spced i s 16 in. /=in

labor & averhesd,$E.Oo/hr

Total cost of welding using 100% operating factor:

10. 9 $/it

This indicates that, with10070operatingfactor, electrode B would have the least cost, and would save 6 . 6%.

... ~ ~,~~~~~ ~ - - - - - ~ ~ ~ ~ - ~ - ~~~--~--~~~ppp

Total cost of welding using Total cost of welding using 30% operating factor - 1 307, operating factor

27.2 $/it 28.4 $iff

This indicates that, with 30?:operating factor, electrode A would have the least cost and would save 4.1%;.

elding Cost / 7.5-9

E-6012 ELECTRODE - %" leg iillet . 30# rorl/R % a " leg fillet . 30'1 rorl/it

$116"E-6012 rod @

melt-off rate M

speed S = 9 in. /min speed S = 1 3 in. /min

length rod melted

time T = 2.06 min/rod time T = 1 . 5 7 min/rod

Assume a 50% operating factor (OF) and $6.00/hr labor and ovorhead (L)

labor cost / labor cost

o r a saving in labor of 30.7% by using the iron powder electrode E-6024.

But this analysis reveals the following: The arc time for the E-6012 electrode per rod is 2.06 minutes; using a 50% operating factor, this represents a downtime of 2.06 minutes per rod. This downtime between electrodes includcs time to lift up the helmet, clean the slag off the weld, insert a new- electrode into the holder, etc. On the same basis the arc time for the E-602.1 electrode would he 1.57 minutes per rod; and using the same operating factor of SO%, this means a downtime of only 1.57 minutes per rod.

It might appear at first that simply snbstituting the E-602.1 electrode into the holdcr would dccrease the downtime; i.e. the operator can lift np his helmet faster, knock off the slag faster, pick up and insert the next clrctrndr faster, etc. Of course this is not true.

A more accurate method wonld be to use a fixed downtime, adjusting the operating factor accordingly. Re-examine this cost study, using an average downtime between electrodes of 2.06 minutes:

- ~~

E-6012 ELECTRODE E-6024 ELECTRODE .. ~~~ . .~~ ... ~ . .~ ~~~~-~~ t .....

operating faclor = 50% operating factor = 1. 57

(1.57) ! (2.06)

labor cost ' labor cost

or a saving in labor cost of 21% by using the E-6024 electrode. -~ . ~~~~. . ,~ ~ .-

lbs rod melted Assume E = Ibs consumed = 90%)

Total 26. 7 c 4.9 = 31.6 $/R j Total 21. 2 + 5 . 1 = 26.3 C/R

or a total saving In labor and rod cost of 16. 89 by using the E-6024 electrode.

7.5-10 / Joint Design and Productton

Notice that the decreased arc time with the E-6024 study of the job, which we are trying to avoid. results in a slightly lower operating factor, 43.5% in- The nomograph, Figure 6, map be ured to quickly stead of 50% although the joint does cost less. read the labor and overhead cost per foot of weld.

One might further suggest using a downtime per 4. PER HOUR electrode and a handling time per foot of weld. These figures, if available, would give a more true picture .4s a matter of interest, consider the cost per hour for of the welding cost, but it would mean making a time these two procedures:

E-6012 ELECTRODE E-6024 ELCC I'RODE - -. - -- -- - .

rod consumed p e r hi- consumcd per h r

= 7.37 lhs/hr 1 = 8. 49 lbs /hr --

rod c o s t rod cost

7 .37 x 14.9 $/lh = $1. lO/hr 8. 49 x 16. 9 $/lb = $1. 44/hr

labor cos t = 6.00, labor cos t = 6.00 7

Total = $7 lO/hr 1 Total = $7. 44/hr -.

It can be expected then that the cost per hour for making the same size weld will increase slightly with faster procedur's. Obviously the increase equals the difference in cost of electrode consumed. Of course the number of units turned out per hour is greater, so the unit cost is less.

5. ESTIMATING ACTUAL WELDING TIME

After the length and size of the various welds have been determined, there are three ways to estimate the a c t ~ ~ a l welding time:

1. Convert these values into weight of weld metal per linear foot, and total for the entire job. Determine the deposition rate from the given welding current, and from this find the arc time. This method is especially useful when there is no standard welding data for the particular joint.

2. If standard welding data is available in tables, giving the arc travel speeds for various types and sizes of welds, in terms of inches per minute, apply this to

the total lengths of each type and size of weld on the job.

3. Time the actual weld or job. Most welding procedures are based on good weld-

ing conditions. These assume a weldable steel, clean smooth edge preparation, proper fit-up, proper position of plates for welding, sufficient accessibility so the welding operator can easily observe the weld and placc the electrode in the proper position, and welds s&- ciently long so the length of crater is not a factor in determining weld strength. Under these standard conditions, the weld should have acceptable appearance. Failurc to provide these conditions requires a substantial reduction in welding current and immediately increases cost.

It is impossible to put a qualitative value on these factors, therefore the designer or 'ngineer must learn to anticipate such problems and, by observation or consulting with shop personnel or other engineers who have actual welding experience, modify his estimate accordingly.

FIG. 6-Welding Cost Estimator (Does Not Include Cost of Filler Metal)

i a bor and overhead

q h r . J,P;o

0

0 /o O p ~ r a t r ' n ~

factor

&+ P r o b l e m : Find cost of ki" f i l le t weld -. ~ - a Labor a,nd overhead - d5°--oper h o u r @ Owrat ing factor - 50% @ Sp,peed of jo int - 1 0 /riches per minute

@ Reod cost = 20d per foot dote; This cost f~gure docs not/i7c/ude elactrodz c o s ~ , Toduterniina this i/se 'Ibs o f electrode r&redper foo to

jmnt''from above refcrerms and mnultjpb by e/cct,+ode sal/;ng prtce. Add t h i s t o that obta ined in sfep @


SECTION 7.6

1. LOAD CARRYING CAPACITY OF CONNECTION

In the modification or repair of buildings, it may be rrecessaly to weld to the existing steel framework.

When welding and riveting are combined on the same strength joint, the riveted portion of the joint may slip or yield slightly, thus throwing the entire load eventually on the weld. Normally, on new construction where welding and riveting are combined, the joint would he figured on the basis of the weld takiug the entire load. Since 1930, most of the old riveted railroad trestles havc been reinforced by melding becanse of the newer and heavier locomotives.

Riveted connections can ba reinforced with plates. with holrs to fit over the rivets. The plate is welded to the existing connection with fillet welds all around its edge, and is plug welded to the plate at each rivet hole. This technique, however, rcquires a considerable amount of out-of-position welding with small electrodes.

2. EFFECT OF ELDING HEAT ON MEMBER'S STRENGTH

Frequently, a question arises as to the effect of welding on the strength of an existing structure already under a stress. Actually the strength of steel does uot drop off upon heating, until a temperat~~re of about 650°F is reached. This is brought out in the table of allowable strengths of matorials in the ASME Unfired Pressure

Vessels, Section 8. Here the same allowable is used from minus 20°F all the way up to 650°F. The ASME code body recognizes the fact that the strength of sterl riscs slightly upon heating and docs not start to drop off until a trmpcrnture of 600°F or 700°F is reached.

In wclding to an existing structure, the amount of material actually l~rated monrentarily above 700" umild he a very s~nall spot right at the wslding arc. Figure 1 shows the temperature rise in a plate while making n ,7{i;" fillet weld in the vertical-up position. This indicates that in wing a E6010 electrode, the temperature on the hack side of the %'' thick plate opposite the weld was held below 600°F. Figure 2 shows the same wcld using a $$?" E6010 electrode. Here the temperature on the back side of the 'h" thick plate was held below 650°F. Also see Figure 3.

The very tiny area of the member heated above this temperaturr does not represent a sizable percentage of the entire cross-section of the stress carrying member. This has been the opinion of rnany fabricators and erectors u:ho have been welding 011 existing structmes for several years.

All welds will, however, shrink. This creates a shrinkage force wlrich, if welds are not placed symmetrically about the mcmber, will result in some dis- tortio~, of that member. This could occur in melding to an misting member if most of the welding is donc on one side. For rxample, if all of the welding is done on the tmttom flangr of a beam, the unsymmetrical welding will tend to distort the beam upward in the

Temperalure back sade of 3A" plote opposite weld below 600" F

I

FIGURE 1

5 / 3 2 E6010 Vertical up

140 amps - 25 volts 3'/2"/min. i = 45,100 j ou led in .

Temperature bock side ot Y2" pplte opposite weld below 650" F

FIGURE 2


Approximate distance of 65D'F isotherm from v d I I 1 I I I

FIG. 3 A guide to establishing proper welding procedures for minimum heat input.

opposite direction as the applicd load to the beam. If the welding were done along the top flange only, this would tend to distort the beam downward in the same direction as the applied load. Therefore, it might be wcll, in some cases, to temporarily shore up a beam in order to reduce some or all of the beam load while \velding.

3. AWS, AlSC AND AASI-10 SPECIFICATIONS

Section 7 of the present AWS Code for Welding in Building Construction, and the SpeciGcations for Welded Highway and Railway Bridges, cover the strengthening and repairing of cxisting structures.

The engineer shall detenninr whether or not a member is pennitted to carry live load stresses while welding or ouygen-cutting is being perfonned on it, taking into consideration the extent to which the member's cross-section is heated as a result of the operation being performed.

If material is added to a member cwrying a dead load stress of GOOO psi, either for repaking corroded

parts or for strengthening, it is desirable to relieve the member of dead load stresses, or to pre-stress the material to be added. If neither is practical, the new material to be added shall be proportioned for a unit stress equal to the allowable unit stress in the original member minus the dead load unit stress in the original member.

( Problem 1 I To reidorce an existing member to withstand an additional live load of 20,OM) Ibs. The existing section has a cross-sectional area of 10.0 in.', with an allowable working stress of u = 18,000 psi. The original design loads- dead ( D L ) , live (L,L), and impact (1)-gave the following:

DL force 100,000 ibr + 10.0 in? = 10,000 psi LL + i ioice 80,000 ibr i 10.0 in.* = 8,000 psi - .. DL + LL + I force 180.000 ibs 18.000 psi

ond 18,000 psi 18,000 psi OK

The member must now be increased in section for an additional 20,000 lbs of live load (LL):

Aliowabie st rep i in oiiginoi member = 18.000 psi Deod load sties in original member = 10.000 p s i

-. To be wed in n e w steel to be added = 8,000 psi I

I 20,000 ibr = 2.5 in2 = orea of new ircei to be added

8,000 ibr 1 Check this as follows:

I DL force i00.000 lbi I iO.O in.' = iO.000 psi LL + i force 100,OW ibs i 12.5 in.' = 8,000 psi

~ I DL + LL + I 200.000 ibi 18.000 psi

and 18,000 psi 5 18,000 psi C K

- 10,000 pri Q 18,000 psi

i 8000 pi,

0 0 i n . @ 10.000 psi = looK 12.5 in.' @ 8,000 psi = 100" -

200'

FIGURE 4

Welding a n Existing Structures / 7.6-3

In making alterations to structt~rcs, existing rivets may be utilized for carving stresses resulting fronr dead loacls and welding shall he provided to carry all additional stress, However, if the framing is shored during repairs and the meniber to be reinforctd is thus relieved of stress, the welding shall carry the entire stress.

AISC Sec 1.15.10: Riv~ts nnd Bolts in Combination \i.ith Welds. In new work, rivets, bolts or high strongth 1)olts used in bearing type connections shall not be considered as sharing the stress in combination with welds. Welds. if nsrd, shall be provided to carry the entire stress in the connection. High strength bolts installed in accordance with the provisions of Sec 1.16.1 as friction-type connections prior to welding may ho considered as sharing thr stress with the wrlds. In making wrlded altc,rations to structures, existing rivets and properly tightened high strength bolts may be tltilked for carrying stresses rrsnlting from existing dead loads, and the, welding natd be :tdeqltate only to carry all additional stress.

AASHO Requirements

.4.4SfIO 1.127: The unit working stresses used in determining the load-can-ying capacity of each member of a structure shdl take into account the type of material from which the nmnber is made. The unit working stress assnmed for the inventory rating shall not cscerd 0.3-15% of the yield point and for the operating rating shall not exceed 0.82 of the yield point.

Where infornration concerning the specification under which the metal was supplied is not available, it will be assumed that the yield point docs not rxcwd 30,000 psi for all bridgcs hnilt after 1005.

Rridgcs built previous to 1905 shall be checked to see that thc matcrial is not of a fibrous nature. If it is fihl-ous or of doiihtfnl character, the yield point will be assumed to bc equal to that of wrought iron which shall be taken ;IS 26,WO psi.

In the ahsencr of definite information, it shall be assninctl that the yicld point of wrooght iron is 26,OOO psi, and the unit working stress shall be taken as 14,000 psi.

4. GENERAL

Pmlmxd repairs and mrthods shonld be considered 2nd approved by a qnalified enginrer. Welding on a job of this type should be of the best quality and adeq~tately inspected. An tl6010 type of electrode would nomrnlly he recommended for this welding, if

it involves vertical and overhead positions or painted or dirty material. Material should be cleaned as thoroughly as possible before wrlcliiig. If the nntcrial is nnnsoally thick, a low-hydrogrn electrode should hc nsed, and it would be wrll to check for any preheat w11ic.h might be recornmcnded. See the following topic, Temperature for Welding.

When making a rt:pair on a structnre it is ntLcessary to know the type of steel it is made of. It may be possible to get a mill rcport from the steel mill which fornislied the stecl. Sornetirnes on wry old structures this information cannot be ohtained. If this is an irnportant structure, it wot~ld he a good idca to get test drillings and have them analyzed.

An erperionced weldor will sometimes weld a small piece of mild sterl to the structnre and then knock it off with a hammer. If the weld cracks out of the base metal, taking some of it with the weld, this indicates that thc stecl is hardenable and the heat- affected zone adjaccnt to the weld has bren hardened. If the w d d itself cracks, this indicates higher carbon or alloy in the steel which has been picked up in thc molten weld and become hard during cooling. In both cases, preheating imd low hydrogen electrodes should be used. If the mild stecl bar bends down without the \veld breaking, this indicates good weldable ductilc steel.

All structural work for a rnaior addition to the Jordan-Marsh Deportment Store in Boston wos completed without interruption of business. The concrete wall was penetrated and new steel welded successfully to vintage steel under load -without removal of the load.


There is little chance that the strnctwe to be re- paired is made of wrought iron, which was used in structmes prior to 1900. Wrought iron contains slag rolled into it as tiny slag inclusions or laminations, and is low in carbon. The slag pockets might bother the welding operator a little; but this should he no real problem. Some cngincers recommend that extra effort he made to fuse or penetrate well into the wrought iron surface, especially if the attached member is going to pull at right angles to the wrought iron member; otherwise, they reason, the snrface might pull out because of the laminations directly below the snrface.

It is also possible for the sulphur content of wrought iron to be excessive, and it should be checlced. Keep in mind t t~a t any chemical analysis for sulphur represents the average value in the drillings of steel taken for analysis. I t is possible in u ~ o n g h t iron to have the sulphur segregated into small areas of high concentrations. The lowhydrogen electrodes (EXX15, EXX16 and EXXl8) should he used where sulphur might be a problem.

The AISC published in 1853 a complete listing of steel and wrought iron beams and columns that were rolled between 1873 and 1952 in the United States.

5. TEMPERATURE FOR WELDING

The AWS Building and Bridge codes require that welding shall not be done when the ambient temperature is lower than 0°F. When the base metal temperature is below 32"F, preheat the base metal to at least 70°F, and maintain this temperature during welding.

Under both codes, no welding is to be done on

metal which is wet, exposed to ice, snow, or min, nor when the weldors are exposed to inclement conditions, including high wind. unless the work and the weldors are properly protected.

In general, the AISC and AWS specifications on minimum temperature for welding are a good guide to follow. See Table 1. The following thoughts might supplement them in producing better welds at thcsr cold temperaturcs.

Welding on plates at cold temperatures results in a very fast rate of cooling for the weld metal and nd- jacent base metals. With thicker sections of mild steel, A7, .4373_ and A36, this exceptionally fast rate of cooling traps hydrogen in the weld metal. This reduces ductility and impact strength of the weld and may cause cracking, especially of the root bead or first pass. This type of weld cracking has been shown to occur almost entirely in the temperatwe range below 400°F.

With a preheat or interpass temperature of 2W0F, this cracking does not occur, even with the organic type of mild steel electrodes. This is because the higher temperature results in a slower cooling rate, and inare time for this entrapped liydrogcn to escape.

Lowhydrogen eiectrodes greatly reduce the source of hydrogen and, therefore, the cracking problem. This weld metal has greater impact strength and a lower transition temprrature. In gcncral, the use of low- hydrogen electrodes will lower any preheat requirement hy approximately 300pF.

The fastest cooling rate occurs with so-called "arc strikes", when at the start of a weld the electrode is scratched along the surface of the plate without any metal being deposited. This can be damaging and

TABLE 1-Minimum Preheat and interpass Temperatures 1. " Welding Process -- -. - --

Thickness of Thickest Port at

Shielded MetoCAr~ Welding with in inches Other than Law-Hydrogen Eiectroder Submerged Arc Welding

. ASTM A36'. A7I.". A373" ASTM A36". A7'.'. A373'. A4418

' Welding ihol l not be done when the ambient tempeioture i s lower than 0°F. ' When the bare mctol ir below the temperature listed for the weiding process being used and the

thicknerr of material being welded, it shall be picheoted for a l i welding (including tack welding) in such monnei tho? the suifocai of the parts on which weld metol is being deposited are at or obove the spec i f id minimum temperature for o dir!ance equai to the thickneir of the port being welded, but not l e u than 3 in., both loteiolly and in advance of the welding. Preheat temperature sholl not exceed 400°F. llnterparr iemperoture ir not rub jed to o maximum limit.! Uring E6OXX or E70XX eiectiader other thon the low-hydrogen types. See limltotionr on use of ASTM A7 rteei in Poi. 105(b).

' Using low-hydrogen e!ectrodcr (€7015. E70i6, E7018, €7028) or Giode SAW-I or SAW-2. ' Uring only low-hydrogen eiectioder (E7015, €7016, E7018, E7028) or Giode SAW-2. ' When the bore metal temperature ii below 32-F. preheat the base metal to ot ieart 70'1.

To %, i n d Over % to i inci. Over i l/ to 24/2. incl. Over 2$

None' 150°F 225°F 300°F

Noner 70°F

lSO°F 225'F

elding on Existing Stpuctrares / 7.6-5

should be avoided. Next to this in seriousness are very short tack welds.

The following will illustrate the effect which weld length has on cooling rate. The length of time to cool from 1600°F to Z W F when a single weld is placed on a %'' plate is:

Length of Weld 9- .

Time (Secondr) 300. 2000.

A weld 9" long made at a temperature of 70oF has about the samc cooling rate as the samc weld 3" long at a preheat of 300°F. Welds of larger cross- section have greater heat input per inch of weld. High welding current and slow travel speeds slow down the rate of cooling and decrease the cracking problen~.

Perhaps the greatest difficulty in cold temperature welding is the discomfost of the welding operator. It becomes more awkward to move amund tlie weld be- cawe of the extra clothing required. The welding lens continually hecomes frosted or fogged from the breath of the operator. The helmet must he removed and the lens wiped.

ELDING OF INSERT PLATES

For thick plates, a donble V or U joint would reduce the amount of weld metal and therefore transverse shrinkage. The halanced weld would preclude any angular distortion.

(a) Single Vee

(b) Double Vee

FIGURE 5

The use of round corners will tend to reduce any notch effect at the mmers of the weliled insert.

Sometinics the plate to be insert& is prr-dished. providing n little excess material in tlie plate to offset the transverse shrinkage. However, longitudinal shrinkage stresses will build up around the periphery of tha plate, hccanse the edge welded lies in a flat plane and therefore is more restrained.

The following sequence is usually used:

Weld side (1 ) complete. So far this should hc rather unrestrained. A fcw tack welds on the opposite side might crack; if so, they should he realigned and rewelded. Weld side ( 2 ) completc. It might he argued that this is free to shrink because the* opposite side (3 ) is un\velded. However there is some restraint o f fmd by the weld along side (1). Now side (3 ) directly opposite side ( 2 ) is welded; this will start to lock-up now. Then weld side ( 4 ) opposite side (1 ) . If either \veld ( 3 ) or ( 4 ) should crack. it should be gonged out to sound metal and rewelded. Finally, the four corners (5 ) are completed.

Another suggestion is to estimated the amount of transverse shrinkage and to open up the joint initially by this amount, by driving in sevaral harrlened steel drift pins. The joint is thcn welded, full throat, lip to these pins. The pins are then removed, and the joint completed.

FIGURE 7

Figure 7 illustrates the geometrical method of obtaining the weld area. This value is needed to dcter- mine transverse shrinkage:

weld area transverse shrinkage ( A ) = 10L%

thickness := 10%, average width of weld

awa of weld

( XG") (.62") = ,1162 'h (.62") (.30") = ,0930 M ( .W)(.30") = ,1350 Z l j (1.0") (.lo") = ,0667

- ,4109 in.2

(.411) A = .I0 ("I' ; " ~~~-

7.6-6 / Joint Design & Production

In production of large plate girders, flange i s commonly tack welded to the web. Then, with the girder web held at a 45O angle, the web-to-flange weld can be efficiently made using a self- propelled submerged-arc welding unit. This (/2" fillet is here being mode in two passes. Flange is 4" thick, web %". Improvements in equipment and technique are currently permitting many (/2" fillets to be made in a single pass.

SECTION 7.7

1. WELDING FACTORS THAT CAUSE OVEMENT

In making a weld, the heating and cooling cycle always causes shrinkage in both base metal and weld metal, and shrinkage forces tend to cause a degree of distortion. Designers and engineers must anticipate and provide control of this shrinkage to achieve the full economies of arc-weld& steel construction. Suggested solutions for correction or elimination are based on both theoretical analysis and the practical experience of fabricating shops.

FIG. 1 Properties of a metal change at elevated temperatures, complicating the analysis of weld shrinkage. Graph is for mild steel.

The enormous temperature differential in the arc area, creates a non-uniform distribution of heat in the part. As the temperature increa~cs, such properties as yield strenbph decrease, the modulus of elasticity decreases, the coefficient of t h m a l expansion increases, the thermal conductivity dccreasrs, and the specific heat increases. See Figure 1. To anticipate the move-

ment of material from a straightforward analysis of heat is difficult.

Restraint from external clamping, internal restraint due to mass, and the stiffness of the stecl plate itsclf also must be considered. All thesc factors have a definite influence on the degree of movement.

Finally it is necessary to consider the factor of time as it affects the rapidly changing conditions. The period of time during which a specific condition is in effect controls the importance of that condition.

These variable conditions arc further influenced by the welding process itself. Different welding procedures, type and size of electrode, welding current, speed of travel, joint design, preheating and cooling rates-all these bear significantly on the problem.

I t is obvious that distortion cannot be analyzed

FIG. 2 An unbalance of forces resulting from shrinkoge of weld deposit tends to couse ongulor distortion or bowing.


by viewing each one of these factors separately. A solution based on correcting the combined effect is the only practicable approach.

2. EVIDENCES AND CAUSE OF DISTORTION

When distortion occurs, it appears as a shortening of the weld area. This generally can be cataloged as longitudinal shrinkage and transverse shrinkage, Figurc 2. Further, if transverse shrinkage is not nniform throughout the thickness of the weld, a n p l a r distortion \ d l result. When longitudinal shrinkage acts in a direction that is not along the neutral axis of the memhcr, the result is bowing or cambering (also shown in Fig. 2) .

Distortion results when a condition of non-uniform expansion and contraction is crcated. Distortion can be anticipated by evaluating the following factors:

I . The weld along with some adjacent metal contracts on cooling, producing a. shrinkage force, F.

2. The shrinkage force acts about the neutral axis of a member. The distance between the center of gravity of the weld area and this neutral axis represents the moment arm, d.

3. The moment of inertia of the section, I, resists this contraction. The I of a section also resists straightening, should it be necessary.

3. THE INFLUENCE OF OVERWELDING

Overwelding increases the shrinkage force, F, and the tendency to distort. Anything that reduces the amount of welding such as decreasing the leg size, reducing the weld length, or using intermittent welding techniques, will minimize this condition. See Figure 3.

Overwelding can be caused inadvertently by a chain of events. The designer may specify the next larger weld sizc because of a lack of confidence in welding. When the part reaches the shop floor, the shop foreman, wishing to play it safe, marks the piece up for the next weld size. The weldor, having just

FIG. 3 Excessive distortion i s frequently caused by overwelding.

heen criticized for making u~idersize welds, makes real surc that these welds are still larger. The resnlt- a 94" fillet has become a K" weld. Thesc men usually do not realize that weld metal increases as the square of the leg size. The apparently harmless %" increase in the leg size has increased thc amount of weld metal. deposited, the weld shrinkage and the weld cost by 1 times.

4. CONTROL OF ELD SHRINKAGE

One te~hnique wed to ~nritrol weld shrinkage involves prehending the member or presrtting the joint before welding. In this way the net &ect of weld shrinkage pulls the member or connection back into proper aligr- ment (Fig. 4) .

Whenever possible, welding should be balanced around the ne~~ t ra l axis of the member. This makes thc moment arm, d, cqunl to zero. Evtw though a shrinkage force, F, does exist, the slrrinl~age moment ( d X F ) becomes zero (Fig. J) .

Freqnently the nentral axis of the member is below

FIG. 4 Parts ore often present so that weld shrinkage will pull them back into correct alignment.

Control o f Shrinkage and Distortion / 7.7-3

FIG. 5 Balancing welds or weld beads about the neutral axis of the member, reduces ongulor distortion to zero.

the center of gravity of the welds as shown in Figure 6. By making the welds with the submerged-arc automatic welding process, the deep pelletration character- istic of this process further lowers the center of gravity of the weld deposit :md reduces the moment arm, thereby reducing the shrinkage moment.

FIG. 6 Deep-penetrotion welding processes and procedures piaces the weld closer to the neutral axis, reducing moment arm and net effect of rhrinkoge forces.

Ad jacen t Base

Shrinkage of weld metal alone is not sufEcient to account for the amount of shrinkage sometimes actually encountered. The heat of welding causes the metal just adjacent to the weld deposit to expand. However, this metal is rest~ained by thc relatively cooler sections of the remainder of the plate. Almost dl the volume exprsion must take place in thickness. On cooling, this heated section undergoes volume contraction, building up shrinkage stresses in the longitudinal and transverse direction, and this adjacent base mrt:il tends to shrink along with the weld metal.

Ef fec t o f H i g h W e l d i n g Speeds

The volume of this adjacent base metal which contributes to the clistortion can he controlled by weldiug procedures. Nigher welding specds through the use of powdered-iron-type manual electrodes, semi-automatic and frilly automatic submerged-arc welding equipment, or vapor-shielded automatic welding equipment reduces the amount of adjacent material affected by the heat of the arc and progressively decreases distortion.

M O W J O r d emmlo Lnim ~ h i r boiid cur- sic., ,sn* s"vm *,<* piat. ihahrdcuwe &- 'iitxr'd)

FIG. 7 Vorionce of welding technique. In eoch case, surface isotherm of 300°F is shown surrounding welding source.

The effect of welding current and arc speed on adjacent base metal is illustrated in Figure 7. Approxi- mately the same weld size was produced with procedures ( a ) and ( c ) . The important difierence lies in the fact that the higher-speed \\;elding technique produced a slightly narrower isotherm, measuring outward from the edge of the molten pool. The width of this isotherm of 300°F can be used to indicate the amouut of adjacent metal shrinhgc along with the weld, and therefore distortion; this helps to explain why in general faster welding speeds result in less distortion. This slight difference i s also evident in a comparison of the quantity of welding heat applied to the plate.

For ( a )

= 85,000 Joules/lhear in. of weld

7.7-4 / Join* Design a n d Production

= 81.000 Joules/linear in. of weld

Another condition can be observed by using conditions ( a ) and ( b ) of Figure 7. Two butt joints were made, one in the vertical position and the other in the horizontel position, using a multiple-pass groove weld. The same welding current ( i i 0 amps) was used in both joints. The vertical joint used a vertical-up weaving procedure, 3 passes at a speed of 3"/min., procedure ( a ) . The horizontal joint used a series of 6 stringer passes at a speed of 6"/min., procedure ( b ) . The faster welding of ( b ) , G"/min., produces a narrower isotherm. However, it required 6 passes rather than 3 of procedure (a ) , and the net result is an over-all cumulative shrinkage effect greater than that for (a) .

This helps to explain why a given weld made with more passes will have slightly greater transverse shrinkage than one made with fewer passes. The transverse shrinkage can be reduced by using fewer passes. A further reduction can also be achieved by using larger electrodes.

In the weld on sheet metal, Figure 7 ( d ) , it is noticed that a greater portion of the adjacent base metal is affected as compared to the weld itself. This, combined with the fact that the thin sheet metal is less rigid than the thick plate (its rigidity varies as its thickness cubed), helps to explain why sheet metal always presents more of a distortion problem.

FIG. 8 Transverse shrinkage vories directly with omount of weld deposit.

5. TRANSVERSE SHRINKAGE

Transverse shrinkage becomes an important factor where the net effect of individual weld shrinkage can be cumulative.

The charts in Figure 8 throw some light on transverse shrinkage. In the lower chart transverse shrinkage, for a given plate thickness, is seen to vary directly with the cross-sectional area of the weld. The large included angles only help to illustrate this relationship and do not represent common practice. The relative effects of single and double V-joints are seen in the upper chart. Both charts assume no unusual restraint of the plates against transverse movement. Calculations show that transverse shrinkage is about 10% of the average width of the cross-section of the weld area.

= .lo x aver. width of weld

Where the submerged-arc process is involved, the cross-section of the fused part of the joint is considered rather than simply the area of the weld metal deposited.

Estimate the transverse shrinkage to be expected after welding hvo 1" plates together if plates are free to pull in.'Use a double-V groove weld, Figure 9.

FIG. 9 Transverse shrinkoge of this weld con be closely estimated from computed crors- sectional area of the weld.

area of weld

(%")(I") = ,125

2(%)(%")(.58") = .29

2(2/3)(1")($46'') = ,083 - A, = ,498 in.2

Control of Shrinkage and Distortion / 7.7-5

shrinkage

A, A,,.,. = .10 - t

Iron powder electrodes should reduce this shrinkage, and submerged-arc automatic welding should further reduce it. Also, a procedure resulting in fewer passes should reduce the shrinkage.

Notice that Figure 8 would indicate a transverse shrinkage of about .08". However, in the above work, if the root opening were increased to %" rather than the %" shown here and if the reinforcement were increased accordingly, the weld area would be increased to .75 in.2. Thus the indicated shrinkage would increase to ,075". This shows good correspondence between Figure 8 and the above method of estimating shrinkage.

Use of Tables 6 and 7 in Section 7.5 (for weight of weld metal for various joints) makes it unnecessary to compute the cross-sectional area of the weld. Sunply divide the weight of the weld (-lhs/ft) by 3.4 to obtain the weld area in square inches.

For example, this 1" double-V joint is equal to two %'' single-V joints. From Table 6 (Sect. 7.5),

urea of weld

= ,494 in." a d from this

FIG. 11 Pull-in can be estimated readily.

transaerse shrinkage

(.494) A,,,", = .lo -

(1.0) = .05" the same as before -

FIG. 10 Radial movement can be expected after welding large multi-segment ring as the cumulative effect of transverse shrinkage of each weld.

A steel tension ring, %" x lo", is to slipport a dome of 136' diameter. Each segment of this ring is to be groove welded to a stcel insert plate directly over each of the 24 cd~mms. See Figure 10. When fabricated, no allowance was made for the transverse shrinkage of thcse field welds. It was later found that the circumference of this ring had shnmk, causing each column to pull inward about 'h".

How should this have been estimated in ordcr to open u p the joints by this amount before welding?


area of weld

'h(l")(%s") = ,125

(%")( lh'r) = ,125

'A(%")(%") = ,125 ---

A, = ,375'' in.'

average width of weld

transverse shrinkage

Atpans = .lo (.545")

= ,055" estimated

Since there are 24 columns or 48 groove welds,

oucrall shrinkage in circumference

A?\,,,, = 48 (.05Y1)

= 2.64" or a

radial pull-in of columns

Of murse any poor fitup (increasing the root opening) or excessive weld reinforcement will grcatly increase this transverse shrinkage.

. ANGULAR DISTORTION

The formula for calculating warpage is-

i automat ic

u t u a l A . .I2 "

ia / iu /ntddA. ,146'

Figure 12 gives both the actual and caIculated warpage for each of eight different flanges, fillet welded as indicated. The close agreement between the two values verifies the formula used. Only three exceed the -4merican Welding Society allowable (%% of the width of the flange). It should be noted that these were overwelded.

7. BENDING OF LONGITUDINAL MEMBE

Distortion or bending of longitudinal members results from developmtmt of a shrinkage force applied at some distance from the ncntral axis of the member. The amount of distortion is directly controlled by the magnitude of thc shrinkage moment and the member's resistance to bending as indicated by its moment of inertia.

Assuming no unusnal initial stresses, thc following foimula indicates the amonnt of distortion or bcriding that will result from any longitudinal welding on a given member:

where:

A, = total cross-sectional area within the fusion line, of all welds, in.'

d = distance between the center of gravity of tlie weld group and the neutral axis of the member, in.

L = length of thc member, assuming welding the

full length, in.

I = moincnt of inertia of the member, in.4

A = resulting vertical movement, in.

Control of Shrinkage and Distortion / 7.7-7

FIG. 13 Actual meosured distortion corresponds well with calculated distortion, using the formula given.

Measurement of actual distortion verifies the formula for theoretical calcnlation of distortion, Figwe 10.

111 some instances when equal welds arc positioned symmetricdly around nentral axis of a member, a certain amount of distortior~ still occnrs even though the magnih~tlcs of the shrinkaga moments are e q d and opposite. It is believed some plastic flow or ilpset occurs in the compressive area next to the weld area after the first weld is made. Heca~ise of this upset, the initial distortion, from the first wdd, is not quite offset by the second weld on the opposite side. Where multiple-pass welding is involved, this condition can be corrected, as illustrated in the groove-weld sequence, Figure 5. Herc Pass 1 is on the top side. Pass 2, deposited on the opposite side, does not quite pull the plates back into flat alignment; therefore Pass 3 is added to the same side. The net resnlt will usually pnll the plate slightly beyond the flat position and Pass 4, on the top side, should bring this plate back into flat alignment. Frequently this probltm is of no major importance since the sections to be w c l d ~ d arc large enough in respect to the size of the weld to prevent the oecur- rence of this upsetting. As a result, on large sections the second w-eld on the opposite side is jnst as effective as the first weld.

In cases where the welds are not symmetrically balanced ahout the neutral axis of the section, advantage may be takcn of this Meren rx in distortion by first completing thc joint nearest the neutral axis (it has the shorter moment arm) and then welding the joint on the side farthest from the nentral axis (taking advantage of its greater moment arm). See Figure 14, which illustrates a masonry plate welded to the bottom flange of a rolled beam. On the icft, thc welds are not symmetrical, so weld ( a ) was made first. Weld (b ) follows since it has a grcater moment a m . On the right, the widcr masonry plate extends slightly on the

left, and allows both welds to he made at the same time (since they are both in the fiat position). The equal rnomcnt arms in this situation should result in no s w c q of the beam. In both cases the welds will produce some cambc;r but this is usually desirable.

Many long slender members are made by welding together taw light-gage fonnecl stctions. Waiting until the first weld has cooled brfore making the second

FIG. 14 Where welds ore not bolonced obout the neutrol axis of the section, distortion con be minimized by welding first the ioint nearest the neutral oxis ond then the joint farthest from the neutral axis. Similarly, weld sizes moy be varied to help bolonce forces.


FIG. 15 To avoid bowing of long, thin box sections welded up from two channels, the first weld is protected against cooling until the second weld is completed. The two welds ore then allowed to cool simultaneously.

weld on the opposite side, usually results in some find bowing since the second weld may not quite pull the memlxr hack, Figure 15. Notice ( a ) the heating of the top side of the member 1)y the first weld initially causes some expmsion and bowing ripward. Turning tlic member over quickly while it is still in this shape and depositing the second weld, increases the shrinking effect of thr second weld deposit and the member is ~isirally straight d ter cooling to room temperature.

The sequence for aiitoinatic wvlding to produce the four fillets or1 a fabricated plate girder can he varied without major effect on distrotion. In most cases this sequene is based on the type of fixture used and tire method of nioving the girder from one welding position to anothcr (Fig. 16). When a single automatic welder is used, the girder is usually positioned at an angle between 30" and 45', permitting the welds to hc deposited in the flat position. This position is desirable since it makes welding easier and slightly faster. It also permits better control of bead shape and the production of larger welds when nec- <:ssary.

Pernrissiblt: AWS tolerances for most welded

FIG. 16 Proper welding position and sequence for fabrication when girder is supported by inclined fixture (top) or trunnion-type fixture (bottom).

1nlcmtd8sie ililfmm m 36th Sidtr oi W e b , I, , : L<,% Tho* &, ~ - &

, : ~ w m m A = - &

FIG. 17 AWS permissible tolerances for corn mon welded members.

Control o f Shrinkage and Distortion / 7.7-9

FIG. 18 Small clip angles and wedges can be used to economically maintain alignment of plates during welding If clips are welded thts fh!cKnsss ,ssomo os on one side only, they can later be knocked root opcnlng of p n t

off with a hammer.

botiom ,doh osr.mb& PM= assambly n t h wdge

members are illustrated in Figure 17: ( a ) deviation between centerliuc of web and centcrlinr of flange; ( b ) camber or sweep of columns; ( c ) at left, tilt of flange, and at right, warpage of flange; ( d ) deviation of camber of girders; ( e ) sweep of girders; ( f ) deviation from flatness of girder web.

8. PROPER ALIGNMENT OF PLATES

Various methods have been used for pulling plate edges into alignment and maintaining this alignment during welding. The most widely used technique (Fig. 18) calls for welding small clips to the edge of one plate. Driving a steel wedge between each clip and the second plate brings both edges into alignment. Weld- ing the clips on one side only, simplifies removal.

In the top part of F i y r e 19, pressure is applied by steel wedges whereas, in the bottom part of this figure, pressure is applied by tightening the strongbacks with bolts previously welded to the plate.

9. PEENING A D FLAME SHRlNKlNG

Peening is used occasionally to control distortion. Since the weld area a~ntracts, peening, if properly applied, tends to expand it. However, this expansion occurs only near the surface.

Upsetting or expansion of the weld metal by peening is most effective at higher temperatures where the yield strength of the metal is rathcr low. Unfortu- nately, most of the distortion occurs later at the lower temperatures after the yicld strength has been restored to its higher value. For this reason, peening docs not accomplish the desired results. An additional disadvantage of peening is that it work-hardens the sudace of the metal and uses up some of the available ductility.

Flame shrinking or flame straightening is another method of correcting distortion, through localized heating with a torch. The heat causes the metal in this area to expand, and this expansion is restrained in all directions by the surronnding cooler metal. As a result, this

FIG. 19 Large plates can be aligned against Platcs forcadinto olignmmt and haid t h a n by mlrons of

strongbacks, the plates being pulled up by b~i,,. The pmssvrrk;ng opp/kd b~ O + a means of and wedge combination; or, " d s c dr.van ," botw<en a j a r s and thc strong bark.

bolts are welded to the plates and run through the strongbacks to facilitate alignment.


area of the metal expands abnormally through its thickness and upon cooling tends to become shorter in all directions. The section so treated will become shorter and stresscd in tension with each successive application of heat.

The bending of a member by welding and its straightening by flame shrinking is analogous to the case of a stool which will tilt to one side when the legs on one side are shortened but will again become erect when the opposite legs are also shortened the same amount.

10. SUMMARY AND CHECK LIST

Transuerse distortion

1. Depcnds on restraint. 2. Is eqwal to about 10% of the average width of

the weld arca. 3. Increases with the weld area for the same plate

thickness. 4. Increases with the root opening and the in-

cluded angle. 5. Is directly proportional to the welding heat

input per inch, that is, Joules per inch.

Angular distortion can be reduced by.

I. Use of a double bevel, V, J, or U for butt joints. 2. Alternating welds from side to side. 3. Beveling the web of a T-joint; this will reduce

the moment a m of the weld and reduce the angular movement.

4. Use of the smallest leg size for fillet welds, since the distortion varies approximately with the 1.3 power of the leg size of such a weld.

5. Use of thicker Aanges; distortion varies approximately inversely with the square of the flange thickness.

Bending of long membcrs by lorlgitudinal welds can be partially controlled by:

1. Balancing welds about the neutral axis of the member.

a. Making welds of the same size at the same distance on the opposite side of the nentral axis of the member.

b. For welds of different sizes-if at different distances from the neutral axis of the member-making

the wdds that are farther away smaller. 2. If the welding is not symmetrical, this result

is achieved by: a. Prebending the member. h. Supporting the tnember in the middle and

letting the ends sag, and for the opposite effect, by supporting the member at the ends and letting the middle sag.

c. Breaking the manher into sub-assemblies bo that each part is welded about its own neutral axis.

Ddlrction is directly proportional to the shrinkage moment of the welds (weld area times its distance from the neutral nsis of the member) and inversely proportional to the moment of inertia of the memher. Although a high moment of inertia for the member i. desired to resist bending. it also makes the member more difficult to straighten, once it has become distorted. Flame shrinking may be applied to the longer side if welding has bent the member.

Assrmhly pror~durcs that help control distortion

1. Clamp the member in position and hold during welding.

2. Preset the joint to offst:t expected contraction. 3. Prebend the member to oifszt expected dis-

tortion. 4. Before welding, clamp two similar members

back to back with some prebending. 5. If stress-relieving is required, \veld two similar

members back to back and keep fastcned until after stress relief.

6. Use strong-hacks. .. I . Use jigs and fixtures to maintain proper fit-up

and alignment drtring melding. 8. Make allowances for contraction when a joint

is assembled. 9. Arrange the erection, fitting, and welding se-

quence so that parts will have freedom to move in one or more dire&ions as long as possible.

10. Use subasscinblies and complete the welding in each before h a 1 assembly and welding together.

11. If possible break the member into proper sections, so that the welding of each section is balanced about its ouw neutral axis.

12. Weld the more flexible sections together first, so that they can be easily straightened before h a 1 assembly.

1. THE MATURE OF RUSTING

Any steel surface* will gradually and progressively mst if left unprotected. For this reason it is important to keep most steel stnictures painted.

Most of us are so familiar with the rusting of steel that we fail to recopize several important facts about this:

Fe + O' (moisture) 2 Fez 0, (steel) (air) (rust)

1. Most chemical reactions will come to a stop if just one of the reqnired elements or compounds is not supplied, or if one of the prodncts is not removed from the reaction.

2. A moist condition (water) is required for steel to rust in the presence of air (oxygen). Steel will not rust in dry air.

3. Under ordinary conditions, there is a continuous supply of air (oxygen) and moisture, so this reaction never comes to equilibrium. The result is a continuous rusting action, unless prevented by some protective coating.

2. PROTECTION OF TUBULAR AND OTHER CLOSED SECTIONS

It is believed the inside of closed-in hollow box structural sections can be left impainted. This is because any slight oxidation of the steel would soon come to equilibrium, since there is no continual supply of air and moisture.

The question is whether box sections must be made airtight, rntwly protected from rain, or left completely open. If airtight, should any precaution he takcn to dry the air before sealing, and should any untisual test methods be taken to insure complete tightness?

To shed more light on these questions, comments were solicited from several leading authorities in the structural field in the United States, Canada, and - * The rusting of certain proprietary steels produces a thin protective oxide layer that hihibib further corrosion. Such steels (for example, A242) an, often used unpnintcd.

Europe. Foreign reaction is particularly significant since the adoption of welded box-section structurals has progressed further there than in this country, no- tably in German bridges built in the past 15 ypars. What follows is a symposinm of their replies.

@ Frorn an article, "Corrosion l're\mtion Inside Closed Hollow Bodies, by Seils and Kranitzky, in DER STAHLRAU (Germany), February. 1959, pp 16-53. (Translated in abstract form. ) :

Investigations on behalf of the German railroads are reported on six groups of weldcd structures: Four railroad bridges; three highway bridges; hollow supports on a Munich railroad station; a locomotive turntable; traveling platform on a rail car; and one experimental weidment.

These welded steel towers carry two 30" pipe- lines % mile across the river. The 273' towers are hermetically-sealed box-section members internally reinforced to keep skin from buckling. They will stand for many years without concern for internal corrosion.


Detailed inspection substantiated the present assumption that condensation in hollow steel sections is very slight. Inaccessible or difficult-to-reach sections should :~lways he welded airtight. Any manholes shonld bc c losd with rnbber gaskets. With these precautions, corrosion protection of inner p r t s becomes unnecessary.

Wherever possible, large, accessible liollow weldments should be madc n airtight as is practical. Closure docs nnt lead to any observable tenciency for water condensation and resulting corrosion. If sections are to hc ventilated, adetlnate numbers of openings should be provided on the front and side walls to allow for soma eircnlation of air. Openings in the floor are not very sr~itablr for ventilation, particularly when sidewalls have no openings. U ~ ~ d e r this condition humidity coiild he higher.

If water pipes have to pass tl~rough hollow sections; there should be an opening in the hollow member to allow water to escape in case the pipe should later develop a lcak. This opening, however, can be prolkled with a t w e of relief or check valvc which will automatically opcn when rerjnired and later reseal. Areas in the vicinity of any of t h e e opcnings shonld be particularly well protected. The pipe system itself should be insulated to n\roid possible condensation.

Experience has shown that if any condensation does occur in the interior of scaled sections, the upper cover plate is tlie most vulnerable area.

In contrast to the outside coatings, a simpler corrosion protection can he applied to the inside sor- faces. Areas subject to frequent use, such as manhole openings or in some cases the bottom side of a cover plate, should be given additional protective coating.

A recent type of corrosion protection for the interior of hollow sections is zinc powder paints. They have two important propertics: First, they are largely imaffected by the welding heat; and, sec~ndly, they do not influence the quality of the weld metal.

5 Several of the new mnlti-span German bridges across the m i n e make nse of welded orthotropic (orthagonal anisotropic) plate decks, with savings in dead weight of steel as high as 50% over mnventional bridges. In this section, Boor beams and longitudinal rihs are s!iop welded to the top deck plate, the latter thus serving as a common top flange.

Many times torsionally rigid ribs are used, either U-shaped or trapezoidal, forming a closed box section with the top deck plate. Thickness seldom oxceeds 5 , ,,, ,r , and occasionally is as little as :KG". The box-

shaped rihs are either butt welded to the webs of the fioor hcarns at each intersection, or pass through thcrn and are attached with fillet welds.

Orthotn~pic plate decks naturally have many sealed sections. Tlicy are not given any special corrosion pro-

tection insidc. It is felt that after the initial minor corrosion resnlting from entrapptd moist air, Little further advance will he experienced, and even undcr the most adverse conditions could not detract from the strcngth of the section.

* From a structural engineer at Eindhoven, Netherlands, representing an American international construction company:

"All modern fabricators make completely closed sections. There arc a few which have taken some pre- cantions for corrosion protection, probably at the insist- imce of the customer. One has used a normal type of manholn in large girders, for inspection pnrposes. The girders were not painted on the inside.

"Another company is using this mnstruction in colnmr~s. Near the bottom of the d u m n is a hole abont %" dian~ett~r, drilled and than closed with a ping. 7Bi. holc is nsed in two ways. First, bcfore the column is shipped, pressure is applied to thc inside to determine whether welds are airtight. If they ;are, the plug is replnced, the column erected and then inspected after a few years hy removing the plug, to see if any water has collected. Until now, there has never been an!; water for~nd insitlc thc columns.

"E.D.F. iri France has in use a large number of long welded steel colurnns closed at both ends, with n o access holes.

"It is bad practice to completely close columns filled with concrete. Holes should be punched or drilled to avoid the possibility of explosion in case of Ere. Water in the concrete may vaporize nnder heat. causing tremendous pressure on the inside if no escape hole is lxesmt.''

5 From a London striictural engineering director, active with one of the 1argt:st companies in the field there:

"This 'bogey' of internal corrosion in hollow sec- t i o ~ ~ s is constantly cropping up. . . In general, in order to be ahsohttely certain of the absence of internal corrosion, it is always preferable to insure that the structure is scaled completely."

5 The papi,r, L'ESERGIA ELETTRICA (Italy). July, 1953, discusses tlie mechanics by which water can enter an iinperfectly sealed stnictnre--condensation, hrei~thing resnlting from heating and cooling, capillary infiltration, etc.

A passage from this research study is worth quot- ing for its basic informatio~~.

"To produce internal corrosion, one essential condition must be fulfilled, i.c., an aperture of appreciable size in order that water and oxygen can he present in sufficient quantity and a lack of either will delay cor-

Painting and Corrosion / 7.8-3

rosion. In the case of a closed tube, chemical equilibrium between water, oxygen and rust is reached as soon as a practically imperccpiible layer of oxide has been formed.

"Tests we have made indicated that corrosion was unlikely to occur through holes having direct access to the atmosphere. provided they were shielded from actual films of water. The test, of course, refers to structures under ordinary airnospheric couditions whew

>, no artificial agcncy was teuding to draw air into the structure.

"We would prefer that a hollow welricd section be airtight, and if this is do~ie there is no nced to dry the air hefore sealing unless, of course, a slight initial currosiol~ must be avoided."

From the chief structrrml engineer of an eastern structural fabricator and erector:

"On light structures such as schools, we have observed many designs which use tubular sections. Some are Bled with concrctc and many are not. Sonre require sealing and others do not. '4pparently no concern is shown in regard to the rusting of the unsealed sections.

"If tubular sectioiis are used and moisttue is apt to accumulate, provision should hc made to drain thcm. To seal fully tubular sections does not appear a feasible proposition."

e .A consulting engineer in Phoenix, Ariz., now active on higliway work in Alaska has this to say:

"There has always been a question in my mind as to the feasibility of closing the box sections so as not to permit the circulation of air through the member. I believe that if air is allowed to circulate, rusting will take place, but any good paint should take care of that and will last considerably longer if not exposed directly to the air and liglit.

"Some of the states have used a galvanized pipe or square section for a (bridge) railing member; however, galvanizing would be impracticable for a large bridge inemher. I have placed somc hopes on the new epoxy resin which apparently has characteristics making it an almost ptxrma!ient protection coat."

e From the assistant chief engineer of a major steel producing company:

"Our own corrosion experts have assured me that if the box member is completely sealed, any moisture or other corrosion causing substance will soon react and become neutralized, so that after a very slight amount of corrosion there will be no Further action. How-cver, if there is any opening to permit any air circulation, there will be new un-neutralized moisture from condensation, etc., and corrosion will be continued.

"If, however, sealed members are used, then some provision should he n~ade for frequent checking of the seal by testillg the tightness of the box under air pressi~re."

From the geueral secretary of the -4rnerican Welding Society:

"For many ycars clevatcd storage tanks in thh country have been supported by towers consisting of closed tubular mcmbers. Companies in the structural field have had extensive experience in the usc of such closed sections in which normally the i n t e n d surfacc receives no spccial trcatment. Some of these have been sealed sections and somc not scaled. Service generally has been entirely sat is factor:^ in both casos. Whcre the section has been snalcd: no rffort his been made to dry the containcd air before sealing."

Tower masts, roof girders and havnched framer for the Tulsa (Oklahoma) Exposition Center ore box sections, entirely weld fabricated. Mem- bers such as these are copped to prevent entry of water; otherwise receive no special protection agoinst internal corrosion.

7.8-4 / Joinr Design and Production

@ From a partner in a New York city consulting engineering firm:

"Closed box sections should be sealed, but if possible should be covered with a protcctive intcrior paint beforehand. The use of higher alloy steels, such as \vcldable A242, adds a measure of pmtection at low additional cost, and the added strength may offset the extra cost.

"I have seen no general applicatio~rs in this country. However, some of the older bridges using the old Phoenix shapes (arc form with ends bent up at right angles) have been sealed and have stood up well.

"The subject of interior corrosion is very important, not only for columns but also for lnrgc closed box girders which at some f ~ ~ t u r e time may become popular in this country."

@ From tlrc manager of technical research for a Canadian bridge company:

"One of our erection engineers who has worked on bridge erection in England, India and other coun- tries states that bridge hox chords, either welded or riveted, are often sealed to avoid air movements. This sealing is accomplished by gasketing the manway openings into the chords. When this is done, painting on the inside can be a single coat or can be eliminated entirely. Seding of box sections to avoid rusting on the inside is increasing in popularity.

"It is presnmcd that where welding is continuous to seal any box section completely, rusting will be inconsequential, being limited by the amonnt of air present wl~cn sealed."

The chief engineer of the same company's Vancouver, B.C., plant adds:

"The practice of hermetically sealing struchual mcmbers to avoid inside painting and corrosion origi- natcd in Europe when c losd welded sections were introduced. No type of closure short of hermetic sealing is dep'ndable. In such structures, no manholes were providcd and no paint was applied on the inside."

"Completely logical" is how this engineer describes the practice of hermetically sealing closed welded members.

@ The Port Mann arch bridge in British Col~~mbia uses an orthotropic deck. The longitudinal stiffeners are U-shaped and when continuously welded to the deck, form a closed tnbular section. The ends of the stiffeners have openings for field bolting. At a distance of 15" from each end of each stiffener, diaphragms are continuously welded inside to seal off' the remaining length frorn the ontside. This sealed portion of the

stiffener was not painted on the inside

There may be an occasional problem with paint discoloring, flaking, or blistering over welds or in an immediate adjacent area. There are several possiblc reasons for this. Dnst, smoke film, iron-oxide film, grease and similar materials on the surface of the weld and immediate adjacent area prevent the paint from coming in contact with the snriace of the steel and properly bonding to it. These materials form a barrier between the paint and the steel surface. h surface that has been bnrnishrrl very smooth with a power wire brush might also prevent proper bonding.

Elements in the fumes of wclding, when deposited in the slag as a film on the stet:l surface, may combine with moisture in the air to produce an alkaline solution that reacts wit11 paint. This may cause discoloring and blistering. This problcrn incrrascs with increasing humidity.

Submerged-arc welds :ire relatively free of paint problems because thp slag is ncarly always removed and the process leavcs no filn~ of smoke or iron oxide on the adjacent plate.

Clcaning is thc obvious first step. Removing slag, spatter, smoke iilm, iron-oxide film; and other similar materials, helps cliniinatc both causes of problems. First, it provides a cleon smface to which the paint can bond. Secondly, it removes from weld deposits most of the chmnicals ihat might read with a paint. In most cases, cleaning will eliminate paint problenrs, but don't burnish the surface with a power brush.

If discdoration or blistering prcvails after normal cleaning, two additional steps will help. First, a wash in a mild acid solution, such as boric acid, followed by a good rinse with clear water will neutralize the alkaline solution so that it won't &cct the paint. Sec- ondly, a more alkaline-resistant paint m.ay be substi- tilted. Paints with a vinyl, epoxy or chlorinated rubber base are the best.

Just wiping the snrface with a shop rag will removr much of the film 'and improve paint bonding. Painting with a bmsh instead of a sprayer lrelps the paint get under the film and make a hetter bond to the sudace. Painting the affected area as quickly as possible after welding will prevent the chemicals in the deposited film from picking up much moisture. Therefore less alldine solution will be formed to attack the paint. Two coats, including an alkaline-resistant primer put on as soon as practical, is usually better than a single coat.

1. REJECTION VS. PREVENTION

The structtiral w-rlding of br~ilclings and bridges cnjoys :t good rqntation in the scLnsc that weld faih~res of a c v . '1 ,rstrophic nature have not occurred. But, it is not

uncommon to find welds whicli hxve failed in the sense that they did not meet final irispoetion xquirrments.

Then: are mrny ronsons why \velds may be rejected at final inspwtion. Before repairing the weld, howcver, s e m d w r y appropriate qwstions should be resolved. I<'or example, it is always good policy to review the inspection methods; to look for and insist upon some reliable correlation bctween the reztsons for rejection and the service conditions. When such correlation does mist, prompt @ion should be taken to corrcct thc rejr&:d welds and to prevent tlieir rvcuncnce. If, 0x1

thc other har~d, the inspcction mcthods arc rmrealistic or inappropriate, they shorrld 11c replacd.

When wcld rtjcction is j~lstificd, a person can be certain that somebody cithrr did not know what his job was, or jrrst did not do it properly. There is a logical ~:xplanation for any sc+rious weld defect, and there is an ecpally logical remedy and correction. Many \veld defects are rrhtr t l to proeetl~~res arrcl can be visnally detected as the job progresses.

Early detection of weld dcft:cts permits economical vorn:ction. If left for final inspwtion after the. job is complete, a ni:ijor loss of t i~ne 2nd riioncy nsnally rrsults. Pcrfnnnance standards on the production floor and the. enSctirm site :u.c needed to assrtrc thc quality of the weld 1)eing produced.

2. WHAT I S A GOOD WELD?

To a great mmy people, the answer to "What is a ~ o o d weldy would be, "Any wcld that passcs final i~rspectiotr." We can hardly blame production-minded pcopIe for g o i ~ ~ g along with this answer. But is this a good answer when you realize that frequently there is little or no conriection behveen the defects found during inspi>ction and the performance of the weld in service? (See Section 1.1, an Tntrodnction to Welded I h i r m . 1 - ,

An improved definition uwdd be, "A good weld is any weld which will continua indefinitely to do the job for whicli it was intended." The problem with this definition is that we do not h a w any thoroughly satis-

factory nondc~strrictive trsting device that car1 provide a "yes" or *now answer. Instead, we look for; 2nd hope

not to find, \veld drfccts. if thty art: found, ilic weld is jndgd "goacY or "h:~d" as wr. think the dcfccts may or may not influmce its pcrformnnce in scrvicc.

3. WHAT 15 THE SOLUTION?

First, find out what these defects arc and what causes tlicin. S < ~ ~ x i d , set rrp welding procrdurcs that will clirninatc tlrarn. 'This is not as (liffiailt as it inight appea' It dot^, howevc*r, mean that a great inany snrall, bnt irrrportmt, details must be spe1lt:d out m d nccomited for.

It is m m ~ ~ r a g i n g to note that good qualified u-el& ors and wcldirig machine operators undr.rstand tho importanw of those sinall drtails. They arr also generally capable of prctlicting t~xnctly what fiilal inspection will n w d . ..\ conscientinns wrldor or welding operator can provide fnll-timc visual inspection. Since llo s rw evcry head, he is hettcr infomiccl than any inspector \vho only sccs a finished weld or some srnall portion of t h~ . wcld as it is heing madc.

4. WHEN DOES INSPECTION START?

'l'he dccisim to inspect only d t c r welding is completed is extnwely dangcnms and not the best way to assure product quality. This puts thr iirspwtor in the position of a combir~:rticn physician-coroner with the dubious distinction of being tho one to declare the weld dead or alivc, and if dead, to decide "the cause of death."

A batter approach to quality mltrol allows inspection to provide constant checkr~ps as welding progresses- prwentivc inspection. This promotes early detection of symptorns and corrrction of procednrcs :is well as minor Ilaws, both of which might otherwise lexl to scrions dcfrxts. LVII~II this approach is follow~xd, final inspcction hecorncs a nxitinr function to confirm the fact that good welding procednres have bcen employed and that ol)jcctionablo defects haw: not been permitted to occur.

Inspection should start bcfortb the first arc is struck :md shonld not bt* the sole responsibility of an inspector p r ,w. Evcryont: iirvolved in the preparation and pn)dr~ction of a wclded connection or joint should at least visually inspect his own work to make snre that

7.9-2 / Joint Design a n d P ~ o d u c t i a n

(a) No problem for next pass to [b) Not enough room left between

fuse properly into i ide of joint iide of ioint and lait porr; will ond weld not fuse properly; moy trap slag

it has hacn dents properly and in a ilialiner consistent \vith tlw t~stablisltcd stmdarcls of qiiality. This goes for p m p k wlm prepire plate cdges, assembly men, wcld t a c h s , wdding operators, weldors' helpers, :md everyone whose riforts can in any way affcct the qi~nlity of tllc welds.

5. R E C O G N I Z E S M A L L DEFECTS AND CORRECT THE

l'erliaps the most common weld rejections occur as ;t rcsult of r;diographic inspection, This method has the ability to espose lack of fission and/or slag inchsions that wolild not be apparent to visrial final inspection tcclmiqrrcs.

With very few exceptions, a good, conscientious v ~ l d o r can h:ll by visi~d inspection whcthcr or not he is p t t i ng good fusion, Figure 1. This irlcll~drs what he sees 61s he makc,s the bcad as well as what he sees

FIG. 2 Correct opplicotion of the various semi-outo- motic welding processes con tremendously increase deposition rote and lower costs.

FIG. 1 The conscientious weldor visually inspects each bead as it is made. He knows that bad bead contour, poor wash-in ot the edges or uneven edges are symptoms of trouble and tokes steps to correct them before they produce weld reiects.

uhen the bead is concluded. Bad bead contour, poor wash-in at the edgm or uneven edges are all indications of poor fusion at tile moment, or that it will occur on s~~bseqoent beads.

Tlisre are marig symptoms of trouble which the \veldor can spot. This is the time to correct the condition either by gouging trixt the questionable portion :tnd/or cl~ar~ging the procedure. The wrong attitude at a timt: like this is to assume, as some weldors are inclined to, that "the defect can be 'burned out' on the n c ~ t pass." This is a game of Russian Roulette that invariably pays off only in weld rejccts.

6. "PREQUALIFIED JOINTS"

Thc term "preqnalifisd joints" has led to some mis- imdcrst:mding and, in 21 sense, it is a misiiomer. It is certainly a mistake to think that just hcciuse pre- rlualifird joints have been nscd the final results will be completely satisfactory.

The AWS Code for Wclding in Building Constroc- tiori (AWS D1.O-66) and i\WS Specifications for Welded I-1igh:hil.a~ and Railway Bridges (AWS D2.0-66) c1o not suggest that it is that simple. They say that these joints are to be "w-elded in accordance with Sections 3 and 4," :tnd then they may be considered "~~~- '~ l~~al i f ied ." A carefd study of Sections 3 and 4 rt:\,c& 12 pngcs of good sound advice, recommenda- tio~is, restrictions, etc., all aimed in the direction of producing good \velds.

If joints are prepared as "prriql~alified joints" and ;ill of the rcqiiirements of Sections 3 and 4 have been met, it would appcar to be nearly impossible to pro- (lrsce welds wliich worild not pass final inspection. Also, it should he inidt:rstood that prequalified joints have hren put in the code and are recommended only hecause past osperienct: has demonstrated that these joints arc cayablr of prodi~cing good weld qnality zchen they ure rrscd together with good welding procedures.

The establishment of preqnalified joints, however, docs not p r d u d e the fact that other joint designs can Irad to equally satisfactory results. The progressive-

eld Quality and Inspection / 7.9-3

minded fabricator or mnstrnctor who wishes to use other joint preparations and has valid reasons should he n~conraged to do so.

The code allows adoption of alternate joint desigr~s. I t also logically requires special tests be performed to prove the acccptnbility of wckls made with the alter- nntc dc.sign. 111 most cnscs, thcse special tests, although admittedly tinic consuming, ;Ire worth completing to pcnnit the q~plication of a progressive proccdnre that Icads to iinprov(:il pcrform;lnce or cost reduction.

7. GOOD COMMUNICATIONS ARE NEEDED

With the hroai lntitodc that wiMing offrrs to the designer, it is only natural t11:lt hridgrs and buildings takc on ;I "one of x kind" natnrc. Tlicse connection variations present a challenge u-hich welding is quite cqmblr of mwting. Rirt not v~ithout good comm~inicn- lions hct\vr:rn all intmrstrd parties.

Comnru~riceting is most important 1 in the gamt., especially \vl~iltb welding proctd~rrcs are being worked out. This is tlrc time for dcsign vs, p rod idon discnssions to bring up and solvv questionable issim before they become points of major c1is:igrecrncnt.

. FIVE P'S OF GOOD STRUCTURAL WELDING

There are fivr ;mas which reqnire close atttwtion to assore good \vdd qr~ality:

1.. Process selection (\velcling process mnst be right for the job).

2. Preparation (joint preparation rnnst he corn- patible with the pro~css being used).

3. Procedures (dctailcd p roc<~hres are essential to assure uniform results).

CURRENT VOLTAGE POLAR/ r Y

1. Pt~rsonnel (qnalified personnel should bc :IS- signed to the job).

5 . Prove it (pretcst procednres and preparations to prove needed u ~ , l d qriality will result with their use).

Process Selection

Tbi: first and most important step is selecting the best weldiiig proccss for the job. This is a very cl~allenging dccision to make, espt~ially if the job is suited to semi- ;mtoniatic welding wlme there are so many cliflerent choices. Anti yet, in this area lies the greatest oppor- tunity for i~nprovemcnt, Figure 2. Since manual weld- i~ ig is inhcrcntly slow a ~ ~ d espensive and subject to the 111nnan cltvntmt, it is hecoming a matter of rconomic si~rviral to convert whenwcr possible to a semi-auto- nrntic process, Figure 3.

The entire indnstry is involved in this transition, but the progms is n:i;itivdy slow. This is &a in part to the rl:itnral rcluctancc to acccpt new methods. It is also iror that raclr of the newer processes has its own pecnliaritirs. ;dvarrtagcs rind limitations, and all introduce somc prohltrms affecting weldor training, joint prcparatiorr and welding procedures.

Th? semi-ar~tomatic processes (exclusive of sub- in t~gel -arc) do not enjoy the "prequalified status of ~na~iua l and suhmergcd-arc welding. This shonld not, however, picvent their use. since the AWS Code and Specifications statr, "other welding processes and procedures may be: nscd, provir1:d the contractor qualifies thrm in accordance with the requirmnients of Article 502."

Srlection of a st.mi-;~litornatic process may also scqniro joint quailification since appropriate joint prepa-

FIG. 3 This cost comparison of manual and semi-automatic welding methods demonstrates the important role process selection plays in the control of weld costs.

7.9-4 / Joint Design end Production

ration may not be tlw smnc as "PI-eqoalified rnanunl" or "pr~y~~al i f ied s~~bnnergcd-arc joints."

Where coiiditior~s pcrnnit, the rrst: of frill-;tr~tomatic welding providrs rrvm~ greater ecmomv arrd control of weld quality.

Preparation

Acccptahlt: butt joint preparatioiis arc r~othing more than a coinpromise between the inclr~ded angle of bevel and thc root spacing dimer~sion. A large iincluded anglc will permit a smaller root spacing; convsrsely, a small i11c1uclc.d angle requires a larger root spacing. 'The tyix of joint, the vi~elding position, arid the process

being r~scd will all irifhimcc t i )< , lxw4 ; i r ~ i root \paciiig. AII of tllest. fnctol-s h;ivi, h w r takt511 into wrrsiilrr;ition i n tllr p~-tyr~alifi(d joir~ts.

The joints detailed in the ;~pprriilis of th i code I)ook iudicntc ;I nomind tlimension for hevrl and root spacing. Sinw tlri. joint design (hrvrl angli, root spacing) must priwidc ;~cwss of the arc to tine basts of th? jllint, it is importaiit to ~u~ticrstand that the dimcnsi~ms of tlw rtmt opening mtl groow, ar~glc of tht joiqts are minimi~rn v d o w (:ill of this and rnme is c11vcn~1 i l l the fine print of tire sprcificatirm ! Also set. Srct i i )~~ 7.:) mi joint I>csign

Not only rnt~st thc mot spacing and bevel bc

Maximum S i z E l d r o d = a

Vertical f i l l e t Graovo

1 * If Exx 14, 15, 16, or 18 electrode i s used

FIG. 4 The code book places specific limits on electrode size for specific joint designs and weld positions.

e ld Qual i ty a n d lnspection / 7.9-5

FIG. 5 Mock-up welds, such as shown here, provide o first-hand check of welding procedures before they reoch the production floor. They can later be used as workmanship samples

treatcd as nrinimt~m climcnsions, but tlre rtlcctrode size rnust he compatible with the combirratio~r hcing i~sed. Hew again, the AWS Code arrd AWS Specification specifics lnaxirnrirn pcmissible clcctrode s i ~ c s which may be used mrdcr certain conditions Figure 4..

The first insprction action considered vitally important is to chcck thc joint prepfration before weldiug. hldic sirre that the, joitrt prrparatiorr corresl?onds to the joirrt dr~t;~iJs ns specifivtl ~ I I the prnccdore. Re sure that the joint has hrcn propt2rly assrmhled and correct fit-rip and root spacing ol~tained.

Procedures

'l'lie imprtairt \velded connectiorrs of ;my s h c t u r e ~leserve a u.i:ll i , l ; u ~ ~ i t ~ t , thoro~ighly investigated and coniplcttaly drtailcd w.;cldirrg prr~ctdiirc.

Reliahlc \vrl<Ii~ig l?xx"lirrcs are hcst obtained tlrroi~gli first-tranl-1 qwrii:ncr~. In the strnctrlriil field. it is ofte~r helpfnl to prod~~ct: a f d sc;dc mock-up of the aclwl joint prior to its i - f h w to the productio~r floor. I f possihl(~, use t l ~ c identical stcel, same type, chtmistry, sin3s and siiaprs that will be iised on the job. Figure 5 corrtnirrs csamplt~s of "mock-up" welds.

FIG. 6 A completely detoiled welding ~rocedure helps guarantee uniform weld quolity, It ~rovides o rood map for the weldor ond a check list with which inspection con check weldor performonce. In some cases more detoils will be required thon ore shown in this example.

4 proccdiir~~ properly dcvrloped riilder these con- liti ions worild inch&:

1. Irirntification of tlrc joint. 2. Joint dirnrnsim det;iils and tolc~airccs. 3. Identification of the welding process. 4 Type and size of clcctrodr.

WELDING PROCEDURE:

T'h Electrode:

Technique:

Preheat:

Inspection Req'd.:


5. Type of flux, gas, etc. (as req~iinxi). 6. Current and voltage (with changcs as required

for diffcrent passes ). 7. Preheat and interpass temperature. 8. Pass sequence (show sketch if necessary). 9. Type of inspection required. 10. Any comments or information that will help

the weldor, such as special techniques, electrode angles, wdd bead placement, etc., Fjgme 6.

This method of establishing the welding procedure takes time. It, nevertheless, is an almost foolproof approach to guaranteeing weld quality since it provides firsthand experience, workmanship sampIes. sa~nples

for destructive testing and positive evidence that the ailopted procedure can produce the required results. And perhaps most important of all, it gives all weldors one "proved procedure" so that the job is no longer subject to the multiple choice of several weldors.

Personnel

In the case of manual wclding, it is true that the weld quality cannot be any better than the skill of the weldor. This skill should be evaluated before the man is permitted to do any actual welding.

The simple and relatively inexpensive device for doing this is the AWS weldor quaiification test, Figure

5 Weidor Qualification Test Resuirements

..,,.. .... , . > I . s .,,. * ,.,., FILLET WELD TEST GROOVE WELD TEST GROOVE WELD TEST ~ , , , ~ " ~ , ~ r " , ~ . ~ ~ ~ ~ " , , , ~ , , ,,,kk"*~,", ica *oax w,,i raoovir ,/A. <>a ioa wow w,r* aaoovir a i aw

TEST PLATE PREpARATlON

>/r ,.". ,I.,#" . ,.rr.d". i,"r,.,,u.,, a'."air _,ll lul,, ,,, ,.,, <,*d

FLAT POSITION

H O R I Z O N T A l POSITION

l E R T l C A L POSITION

V E R H E A D POSITION

S P E C I M E N PREPARATION

FIG. 7 AWS Weldor QwoI- ificotion Test requirements ore completely detailed in the code books.

eld Qual i ty and Inspection / 7.9-7

Pretest It

FIG. 8 Sample welds, such or those shown, made under typicol conditions should be made and subjected to the vorious types of destructive and non- destructive tests needed to establish the degree of quality required for the iob. With this approach, many tests con be applied that might be impractical or impossible to use during final inspection.

., i . This tcst is ns~ially adequate. But in a great many instances, it is qurstionahlr \vhether this siniplc test (~stahlishes thc ability of tile weldor to do the actiial job and proves that ho can make the welds 011 thc job that will satisfy final inspcction rquirements.

For example, i f the weldor will be rap i red to make vertical butt wrlds on %" thick plate and final inspection calls for radiographic inspection (Section 1-09 of the I1ridge Specifications), will the AWS weldor qualification test prove the wr:ldor can produce these ivelds in a satisfactory manner? Obviously, it will not because radiogl-aphic inspection is not nornlally called for in the AWS \ve,ldor qualification tcst. The test hrcomes Inore mexningfr~l i f radiographic i~~spection is added to the normal testing reipircments.

TIE contractor is in the hcst position to evaluate the actual skill required for the job as opposed to the skill reqnired to p:iss an AWS weldor qualification test. When the actual j (~b demands more of the man than he would otherwise hc able to demonstratr on a standard weldor qualification tcst, the contractor for his own protection is jrlstified in requiring more realistic tests.

Most srmi-autoniatic processes present some problems relative to wt:ldor training. If, however, the process has been properly selected for the job and correct welding proccrf~irt:~ h a w been worked out, weldor training should not pose a difiicult problem. With competent instiuctiorr, this can be handled as a joint weldor-tr:~ining, wt:ldor-yr~i~lification program.

The question of pn)perly qualified personnel also involves people other thm weldors, and attention should be given to their training also.

Once a udd ing pmctdnre has been established, nobody shonld be more cager to prove it than the contractor, and nolwdy is in a better position to do so. Mock-~rp sample viclds m d e under typical conditions can he subjected to all kinds of destructive and nondestmctive tests, Figurc 8. Many of these tests woiild bc cornplrtely impractic;il or even i~npossiblc ;as a final inspection requirement. Testing at this stage is relatively inexpensive, and the latitude is much broader than wonld he pcrn~ittc<l or [lcsired as h a 1 insp("ctior~. h4asi1num testing at this time gives assur- ance that fi13al inspr:ction c m he held to a minimum.

9. PREVENTIVE INSPECTfON

I n summary, it shorild be nnivrrsally recognized that i~~spcction aftcr \v~4dirrg, while often rssential. is somc- what too late. Any excessive wt:ld cracks, undercuts, undcrsize wclds, poor fusion or other defects detected that late will hc cxprnsive to correct. All parties con- ccrned slior~ld insist on good wclding, supervisim" conscientious q~~alilied wtMors, and a thorough system of prcivtmtivo inspection.

Preventive inspection, in which cveryont: con- c e r n d should sharc rcsponsihility, involves a systematic obst.rv;xtion of wcldiug prncticcs and adhertmce to sp~dicat ions hefom. dnring, and after wclding in order to visi~ally detect and stop any occurrences that may result in st~bst;~nitard wi4ds. Thc: check list that follows will aid in dweloping this pattem of operation.

FIG. 9 This "mock-up" beom-to-column connection was mode with scrap ends, ~ r e ~ o r e d and assembled to specifications then welded to work out procedure details.


eck List of items That influence

Points to be Visually Checked for uring and After

0 9 0 Check During Welding 0 0 9 Check After Welding

( 1 ) Proper Included Angle

0 0

The incli~dcd angle most bc snificient to allow electrode to rcaeh root of joint, and to ensure fr~sion to side walls on multipk~ passes. In gcn'rnl, the greater this angle the more weld metal will be required.

(21 Proper Root Opening (Fit-Up)

Spacer bo i

U'ithorrt a backing bar, there is a possibility of burning through on the first pass; so, the root opening is reduced slightly. Lack of fusion of the root pass to the verv bottom of the joint is no roal problem becausc the joint must be back gouged before the pass may be m:de on the hack side.

With a backing h; ir, the mot opening is increased to dlow proper fnsion into the backing bar, since it will riot be hack goiigmi; :tlso thcre is no bnrn-through.

\Vith a spoccr bar, it serves as a hacking bar but milst be back gougcd hefore welding on the back side to cnsure sonnd fusion.

(3) Proper Root Face

A root face is r~soall)- specified in joints welded by the snbrnergcd-arc process to prevent bum-through on the first or root pass; therefore, there is n minimum limit to this (limension. Thcre is also a maximum limit so that the hack pass, wlren madc, will fuse with the first root pass to provide :I somd joint. This fusion of root and hack passes can hc checked niter welding, if the joint rrms out to an esposcui edge of the plate and onto nni-off bars.

(a] Too m a l l ioot face; [b) Too large ioot face; (c] Proper ioot fcce;

burn-through lock of penetration proper penetration

The above items, included angle (1) and of plate, there is ;I range in thc combination of root opening ( 2 ) , go hand in hand to ensure inchided angle and root opening that will result clearance for tlie electrode to enter the joint ill a minitnnm amount of \veld metal consistent sufficiently for proper fusion at the root, and yet with the required \veld qnality. rnot reqnirc excessive weld metal.

In general, as the included angle is decreased to rednee the amount of weld metal, the root must be o p e n d up to maintain proper fusion of weld metal at thc joint root. For any given thickness -i r-3/8" r r%"

Weld Quality ond Inspection / 7.9-9

(41 Proper Alignment

. 0 0 . . . . - - - -

Misalignrner~t of plates bring joined may resnlt in an t~npcnetrated portion between root and back pass~s. This would r r q ~ ~ i r c more back gonging.

(51 Cleanliness of Joint

e e e Joint arsd plate surface must bc clean of dirt, rust, and moisture. This is especi;illy important on thosc snrfaces to be f u s d with the deposited weld metal.

(61 Proper Type and Size of Electrode

Electrodes must suit the metal being joined, the wciding position, the function of the weld, the plate thickness, the sizn of the joint, etc. Where standard procedures specify the electrodes, periodic checks should be made to ensure their nse.

(7) Proper Welding Current and PoloriCy

Welding current and polarity must snit the type electrode used and the joint to be made.

(81 Proper Tock Welds

0 . 0

These should be small a d long, if posible, so they won't interfere with subsequent snhmerged-arc welds. On heavy pl;it~.s, low-l~ydr-ogerr clwtrodes shonld bc ~zsed.

19) Good Fusion

(101 Proper Preheat and lnterposs Temperoture

T l ~ c nced for pre'nwt a i d rerjuil-ed temperatnrt: lcvel 11tye11ds on the plate thickness, the grade of steel, the w~lding prnccss, and ambient temperat~n-es. Wherv thme conditions dictate thc nt.cd, periodical clsccks sl~ould be made to r n s ~ ~ r c adherence to rcquiremmts.

( 1 1 ) Proper Sequencing of Passes

0 . 0

(01 No prohiern for next poi$ to jb) Not enough room left between fuse properly into rde of joint side of joint and last posr; will ond weld not fuse rnoy trop slog

The srqi~rneing of passrs shoilld ha such that no unfused portion results, nor distortion.

(12) Proper Travel Speed

o @a 0 n

Ii travrl speed is too slow, molten wcld mctal and slag will tend to ran ;thead and start to cool; the main body of u&l mctal will I - I I ~ over this without the arc pmetrating far cnongh, 3 r d the trapped slag will rrducc fusion.

Each pass slionlci fuse properly into any backing plate, prccedirig pass, or adjacent plate metal. No unfillcd or unfused pockets should be Icft between weld beads.

If t r a \ ~ l speed is increasetl, good fnsion will rcsait because t l ~ c nroltrn weld inctal and slag will be forccd backu.ard, with the arc digging into the plate.


0 3 ) Absence of Overlap

m-,"ndeicur along upper leg of weld

Reiagniic Chi5

by rolling-over efieit along this edge

penitroti. beyond MOY *how rl'ohf root of joint ""fused portion . .. . dye

if specd of travel is too slow, thc cxcessivo :mount of \veld metal 1 1 h g (Icpositcd will tend to roll ovcr along tlrc edges, prrventing prqwr fnsii"~. This roll- over :rctioi~ is easily noticed dnring wkling. Thc (.or- rection is very si~npli.: increasing the. travd speed will achieve the desired cffect (Itrlow).

(141 i n Vertical Welding, Ti l t of Crater

0.0

T h e c ra t e r pos i t ion should be kept t i l t ed slightly so slag will run out toward the front of weld and will not inter- fcre. This will help ensure good fusion.

Spend enough I 3 time ot middle I& of weld so extra ye, weld metal here /*'will keep shelf

ttlted upward . *-- ' ,

Weaving Crorr-seclion Front wew

technjque of weld of weld

(15) Filled Craters

It might he argued that craters are a problem if- 1) they arc undcrsize. i.e. not full throat, and/or 2 ) they art: concave, since thoy might cr:tcl< upon

cooling; of course, once tlioy cool down to room temperature, t l~is would no longer 11c a problem.

Normally, 011 wntin~rons fillet \velds, there is no crater p n ~ h l e ~ n htxanse arc11 crater is filled by tho nest \vcl(l. Thc weldor starts his arc at the outer end of the last crater and n~ornr~ltarily swings h c k into the crater to fill i t hc~forc going ;ih(,ad for t11ca next wcld.

For a s i ~ ~ g l c connrction, it is important at tho end of thr wcld r~ot to lravo the crtltcr in a highly stressed ;u-t.a. If nrwssary to do so, estr:r wre shor~ld he taken to carrfolly fill the crater to ffdl thniat.

Esonrplc: On a hcam-to-col~~mn connection nsing a top connecting plate, thc crater of the fillet weld joining the plate to the beam flange shoold be matlo full throat.

9 Esamplc: In shop \idding a flexible seat angle to the srrplmrting col~irnn flmgc, t h ~ weltling saqiirncc should pcrrnit the weld to start at thc top portion of the seat :trrglc, :and carry clown ;11ong the edge. u-it11 the crater :tt t l ~ t hottorn; as shown.

harmful

On intcimittrnt fillet \velds, in~fillrd craters should normally hc no prohlrm hecnnse:

1. Thc ;~dditio~r:rl strwigtl-i obtained b y filling the cr:ttcr woi11d not lx' nrcdcd in this lov-strcsscd joint. for \vhicl~ intt~nnittant fillet wclrls are sufficient.

2. An!: notch cffoct of an rirrfilletl crater shnnld hc no worsr ttrm tilt, notch prrscrrted hy the st:~rt end of thc Gllct weld; sho\vrr bclow. No rn:rttcar what is clone to the crater, it will still rtyi-i~si:~it thc lermirration Of

tl11. \veld, in other \vord ;111 ~ t n w ~ ~ l d ~ d po r t io~~ ~ncctirrg a weldcd portion.

Hold rod momen- tary ot rides;

I will build up / -._ ' .-- I weld to full 0--, 3 , size and will /A, -- , prowde piope: ;==Z , weld ihope

Crorr-sedion Front view Weoving techniaue of weld of weld

~ o t i h effecl of (Giding croter up to

crater i r no worse full thiaol doer not

t han that at stoil reduce its notch

of weld effeil at etid of weld

Weld Quality and lnrpection / 7.9-11

(16) Absence 04 Excessive Undercut

0 . 0

Double undercut of Cover ie of rolled hcoin

I Undercut along cover plate would not represent any aoorec~oble loss in area; would not be hoirnful

@ If 1% force must bc transfrrred transverse to the

( a ) <liggiIlg efft>ct of tile arc lnelts a of axisof thc ~indrrcut, \vhich may then act as ti notch the base plate. or stress riser.

( a ) Ncre the tensile force is (b) :lidriu,

applied ti-ansverse to the un- dwcnt ntrd presents a stress riser. This would h 1 , harmfnl.

( b ) If the arc is too lone. tlic inoltrn weld mrtal , , from the end of the electrode may fall short and not

( h ) Hcre thr axial tensile completely fill this tnclted zone, thus lealing an undercut along the upper leg of thc weld.

not present a stress riser. This should not be hannful.

(c)

( c ) Htw t l ~ c h e a r force is applied parnilel to the ~mdcr- cut and wolzld not present a stress riser. This shoold not be harmful.

( c ) If the arc is shortened to the proper arc length, thc molten weld metal from tltc end of the electrode will completely fill this melted zone and will leave no

The AWS :rllows imdercrrt up to 0.01" in depth if it lies transverse to tire applied force, and :42" if it lies parallel to the force.

* Althonglt hotlr nndcrcnts in this tensile joint are Undercut should not he accepted on a recurring trarlsvrrsr to the twtch, ttrc rlpper undcrcnt imdonbt-

basis sincc it can be eliminated with proper \velding cdly has less effect upon proditcing a stress raiser

procedure. If, hou~rver, ondercnt docs occi~r, the ques- heeai~sc the stress ilows smoothly below the surf:ice of tion to be nns\vered at this point is \vhrther it is tho root of the notch. On the other hand, thc lower harmful and ireeds repair. i~rtdercitt does reurescnt a stress raiser because thc flow u, If the undercut results in a sizeable loss of net of stress is greatly disttirbcd as it is forced to pass

sectton that cannot he allowed. sharply :iround the root of tire notch.


Uooer undercut

In addition, any eccentricity would produce bending stresses in the region of the lower undercut.

Bending rtreiier and tearing octon along lower undercut

"

reinforcement

.4 nominal weld reinforcement (about X6" above Hrish) is required. Any more than this is unnecessary and increases the weld cost.

(18) Full Size on Fillet Welds

0 0 .

Goge for concave oge or convex

iil letr measurer fillets measurer leg

Proper gaging of fillet welds is important to ensure adequate size.

einforcement on Groove (19) Absence of Crocks

Q @ @ 0 8 9

There should be no cracks of any kind, either in the weld or in the. heat-drected zone of the welded plate.

e p1 a The following beam diagrams and formulas have been fonnd useful in thc design of welded

steel structures.

Proper signs, positive (+) and negative (-), are not necessarily indicated in the formulas. The following are suggested:

Shear diagram above reference line is ( +)

Shear diagram below reference line is (-)

Reaction to left of (+) shear is upward (-k)

Reaction to left of (-) shear is downward (-)

Reaction to right of (+ ) shear is downward ( - )

Reaction to right of ( - ) shear is upward ( + )

Moment above reference line is ( + ) Compressive bcnding stresses on top fibers also tends to open up a. corncr connectjon

Moment diagram on same side as compressive stress

Moment below reference line is ( - ) Compressive bending strcsscs on bottom fibers also tends to close up a corner connection

open coiner

Angle of slope, 0 clockwise rotation ( - ), counter-clockwise rotation (+)

On the next page is a visual index to the various heam diagrams and formulas. As indicated, these are k e p d by number to the type of beam and by capital letter to the type of load.

For some conditions, influence curves are included to illustrate the effect of an important variable. These are keyed to the basic beam diagram and arc positioned as close as practical to the diagram.


VISUAL INDEX TO FORMULAS O N FOLLOWING PAGES FOR VARIOUS BEAM-LOAD CONDITIONS

Type of

Type of \ (i t 3 free

fixed

(2

I\\ guided f '

fixed

(2 Simpiy rupportec

F-3 supported

E

H fixed /'

-- (5

4 supported

fixed

E

m Single span with averhong

e f7-7

Continuous two rpon

Ioncentruted force

@ P

IAo a /

Uniform lood entire span

0

10

Uniform ioad port101 span

Vorying ioad

@

I Do

1 Db

Fa Couple

70

See odjocent to @

Beam Formulas /

.l-4 / Reference Design Formulor

Beam Formulas /

@ Beam supported a t both ends Two equal concentrated loads. equally spaced from ends

P P R = V = P

M,,,.,, = P a R When x < a M, = I'x

Mi P a At center, An18x = - (3 LZ - 4 ai 24 E I

/ i rhea, ' 1 When x > a - , Pa but < (L - a, AT =-(3Lx - 3xZ - a2

6EI P a

At ends, 8 = -(L - a) 2 E I

Beam supported a t both ends Two unequal concentrated loads, unequally spaced from ends

Max when Hz<;P? Mz = Rz b

M, = Ri x

moment but x ( ( L - b) M, = Ri x - Pi (X - a )

Beam supported a t both ends @ Uniform load partially distributed over span

W M, = Rrx - - ( X - aj2 : but x < ( a + b) 2

i Whenx>(a+b) Mv = Kz (L - x)

moment

When a = c

w b R = V = - 2

b V~ = w ( a +-- -

w b ~t center, MnaX = -(a + $1

2

w b x W h e n x < a M>=-

2

When x > a wbx w My=- - - but x < (a + h )

(x - a)= 2 2

wb At center, An =- (+EL3 - 4bZL + bJ)

384EI

Beam Formulas / 8.1-7

BEAM FORMULAS APPLIED TO SIDE OF TANK. BIN OR HOPPER ( p = pressure, psi; m = width of panel considered)

h4 m An,ax = ,00652 !?-.-- E I

(at x = ,5193 h)

Also see fo rmulas on page 7

( * These values are within 98% of maximum.)

Maximum bending moment is least when

a = . 5 7 h

b = .43 h

M,,., = .01:7 p h%

(negative moment a t middle support, 2)

Ri = + ,030 p h m

Rz = + , 3 2 0 p h m

Rs = i- .150phnl

V,,,., = + ,188 p h m

(at middle support, 2 )


@ Influence Lines

Effect of location of middle support (2) upon reactions (R) and moments (M)

.40 .45 .50 .55 .60 .65 .70 .75

Position (a) of middle support R,

Bea

m s

uppo

rted

at

both

end

s

I @ M

omen

t ap

plie

d a

t on

e en

d

I

Mx =

Mo +

Rlx

= M

,,

Whe

n x

= ,4

22 L

M

,] L2

Am

ax = .0

642 -

E I

I I

I I

6EI

Bea

m f

ixed

at

both

end

s C

once

ntra

ted

load

at

mid

-spa

n P

R R

I-

'-

"-

--

--

L

At

cent

er a

nd

load

-

P L

M

,,i"y

= -

, a

t en

ds,

8

Bea

m s

uppo

rted

at

both

end

s @

Mom

ent

appl

ied

at

any

poin

t

4

Whe

n a >

b M

, M

,, R,

R

,=--

=V

R2=-

L

L

Whe

n x <

a M

e x

M,=

--

Wh

en

x<

a

M,,x

P

X =

+-(

LZ

-3bZ

-xZ

) W

hen

x >

a G

EIL

wt

A,

= M

" (L

- xf

(3aZ

- 2L

x +

x2

GEI

L

At

cent

er,

M"

M4.

= -- 2

At

cent

er,

M,

A&

= +

-(L

Z-4

bZ

) 16

E I

Whe

n a

= b

= L

/2

J?

At x

=

L =

.288

67 L

, 6

Am

ax =

M

n L

Z

124.

71 E

I

M,

L

At

cent

er,

0s =

- 12 E

I

earn Formulas /


Influence Lines

Effect of position of force (F) upon moments Ma, MI, M2 and upon kmax

0 .1 .2 .3 .4 .5 6 .7 .8 .9 1.0

Position jo) of applied force F

eam Formulas /



@ Intluence Lines

Effect of position of moment (Mo) upon Mi, M2, M+ and M-

Porttion (o] of moment Ma

@ Influence Line for Maximum Deflection


Beam Formulas /

Single span, suoply supported beam, w ~ t h overhang 1 @ Uniform load over entire beam w IL + 01

W V3 = -(L2 + aZ)

2 L

M, Betweeusupports, V, = Hi - w x

I v For overhang, Vxi = n (a - xi)

W x Between supports, M. = - (L2 - a2 - x 1.)

2 L w

For overhang, Mki = - (a - xi)* 2

\\ x Between supports, Ax = - (L'-21,'x' + Lx3 - 2 a 2 LZ + 2a2x ' )

24 EIL wx,

For overhang, A.1 = -- (4aZ L - L1 + 6a2xi - 4 a xlZ + xi') 24 E I

w a At free end, A =- ( 3 a 3 + 4 a Z L - L 1 )

24 E I

When a = ,414 L, M I = M2 = OX579 w L2

@ Single span beam, overhanging a t both ends Uniform load over entire bean1

w(2'i + Lj

w xiz For overhang, Mxi = -

2

w a2 At support, M = - 2

W Betweensupports,-- (L x - x2 - aZ)

2

W At center, b l c = - (L' - 4 a2)

8

wa At ends, A = - (L1-6aZL-3a')

24EI

A t center, wLZ

Ac = - (5LZ-24a2) 384EI

When a = ,207 X total length or a = ,354 L

Single span, simple supported beam, with overhang Uniform load over entire span

At center, w LZ M,., = - 8

W X M , = - 2

(L - x)

At center, 5wL ' A"., = -

384 E I wx A, = -

24EI (L"ZLxZ+x3)

W L ~ X L Ax, = - 24EI

@ Single sPW simp!^ supported beam, with overhnng Uniform load on overhang

W"


@ THEORY OF THREE MOMENTS

Consider the following continuous beam:

The above moment diagram may he considered as made up of two parts: the positive moment due to the applied loads, and the negatlve moment due to the restraining end moments over the supports.

For any two adjacent spans, the following relationship is true:

where:

Mi, Mz, and M3 are the end moments a t the k t , 2nd, and 3rd supports.

LI and I,2 are the lengths of the 1st and 2nd span

11 and 12are the moments of inertia of the 1st and 2nd span

A * and A2are the areas under the positive moment diagrams of the 1st and 2nd span.

a1 a n d azare the distance of the centroids of the areas of the positive moment diagrams to the 1st and 3rd outer supports.

By writing this equation for each successive pair of spans, all of the moments may he found.

Beam Formulas / 8.144

The moment diagram for a simply supported, uniformly loaded beam is a parabola; and a concentrated load produces a triangular moment diagram. The following shows the area and distance to the centroid of these areas.

w uniform load concentrated load

Area - - Area

A = 2 / 3 iM L A = L / Z M L

Distance to centroid Distance to centroid

a = L/2 m + L a = - 3

@

Tw

o sp

an, c

onti

nuou

s he

am

Con

cent

rate

d lo

ad a

t ce

nter

of

one

span

onl

y

t m

om

enl -

13

RI=

VI=

--P

32

I1

R

2 =

VZ

+V

I =

-P

16

3

R3

=V

a=

--P

32

19

Vz

= -

P

32

At

load

, M

,,,,,

= 13 P

L

64

At

R2,

3

MZ

=-P

L

32

@

Tw

o sp

an, c

onti

nuou

s be

am

Con

cent

rate

d lo

ad a

t any

poi

nt o

f on

e sp

an o

nly

P

R,

R,

1 I I

At

load

,

4t

R2.

P m

om

en

t -

Pb

R

1 =

VI

=-[

4L2-

a(L

+a)

] 4L

3

Pa

RZ

= V

2+V

3 =

-[2

LZ

+b

(L+

a)]

2~~

Pa

b

Rs

=V

3 =

-(L

+a)

4

L3

Pa

V2

=

- [4

LZ

-b(L

+a

)]

4 L

"

Pa

b

Mm.. =

--

[4L

1-a

(L+

a)]

4

L"

P a

h

Mz

=-(

L+

a)

4 L

Z

Tw

o sp

an, c

onti

nuou

s be

am

3 U

nifo

rm lo

ad o

ver

one

span

onl

)

r m

om

enl

I R

I =

VI =

- wL

16

5 R

z=

Vz

+V

a=

-wL

8

1 R

~=

V~

=-

WL

16

9 v

2=

-

WL

16

49

At

x =

7/1

6 L

, M

max

= - w LZ

512

At

Rz,

w

LZ

M

I=

- 16

WX

W

hen

x <

L,

MX

= -

16 (

7 L

- 8 x)

e R

apes

8 a

nd 9

fo

r b

eam

-lo

ad c

on

dit

ion

7C

- Member

T I T = T

L- At support, @ =- T L Es R

Torsionai d i ag ram

At support, T = t L

t LZ H z - 2 E, R


FIGURE 1 - BEAMS O N A HORIZONTAL CURVE, UNDER VNIFORM LOAD (w)

W

Scde view

5 10 15 20 25 30 35 40 45

Angle (a), degrees

Date post:	27-Nov-2014
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Design of Welded Structures

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