CHART OF COLUMN PROBLEMS

INTERIM REPORT NO. 4

A COMPARISON: AREA (1968) AND CRC GUIDE (1966)

by

Joseph S. Huang

Fritz Engineering Laboratory

Department of Civil Engineering

Lehigh Univers~ty

Bethlehem, Pennsylvania

September, 1968.

(revised)

Fritz Engineering Laboratory Report No. 217,36 A

217.36

ABSTRACT

NOMENCLATURE

-i

TABLE OF CONTENTS

1

2

AREAArticle

1.3.14.1

1.4.1

CRCSection

6.7

6.2

6.3

6.3

6.4

2.4

Topic

Beam-Columns in Biaxial Bending

Beam-Column Design Based on Load atInitial Yield

Beam-Column Strength in Bend~ng With­out Lateral Buckling

Beam-Columns (Wide-Flange Shape)

Strength of Laterally UnsupportedBeam-Columns (I-Shaped)

Centrally Loaded Columns

io

11

11

12

12

12

.1.4.1

1.4.1

1.4.1

2.8

4.2

4.4

Effective Length of Compression Members 12

Laterally Unsupported Beams-Rectang- 12ular or Box Sections

Laterally Unsupported Beams~-Method A: 13The Basic Procedure for Doubly Symmet­ric I-Shaped Beams and Plate Girders

1. 5.1

1.5.4 .

1.6.2

1.6.2

1.6.2

1.6.2

5.4

3.3

3.3

3-.4

5 . .4

Lateral Buckling of Plate GirderFlanges

Slenderness Ratio

Thickness of Material

Local Buckling (Elastic)

Local Buckling (Plastic)

Effective Width

Torsional (Local) Buckling of PlateGirder Flanges

13

13

13

14

14

14

14

217.36

AREAArticle

CRCSection

-ii

TABLE OF CONTENTS (Cont'd)

Topic

1.6.4.11.6.4.3

1.6.4.2

1. 7.3

3.13

3.14

3.12

Columns With Perforated Plates

Columns With Batten Plates

Laced Columns

Thickness of Web Plates of PlateGirders

15

15

16

16

5.4

5.5

5.6

1. 7.8 5.5

1. 7.8 5.7

5.9

7.2

Vertical Buckling of Plate 16Girder Flanges

Shear Strength of Plate Girders 16

Ultimate Strength of Plate Girders 17in Combined Bending and Shear

Transverse Stiffener Spacing of 17Plate Girders

Plate Girder Transverse Stiffeners 17

Plate Girder Longitudinal Stiffeners 18

Buckling of the Compression Chord 18of Pony Trusses

1.11.1

SUBJECT INDEX

Bracing of Top Flanges of ThroughGirders

18

19

217.36.

ABSTRACT

The objective of this, report is to look at the stability

portions of the most recent draft of the AREA Specification(l)

and make a comparison with the provisions in the ~econd edition

'of the CRC 'Guide.(2)

It is hoped that this' report will be helpful to pinpoint those

areas where perhaps further study is needed, since it will show

potential differences in philosophy--some of which are necessary;

and a number of which undoubtedly wili be simply the result of

differences in practice.

It is also hoped that the material presented may be of help in

. the future deliberations of both organizations.

-1

(l)American Railway Engineering AssociationSPECIFICATIONS FOR STEEL RAILWAY BRIDGES, AREA Bulletin61i,January 1968, as revised for approval in September 1968

(2)Column Rese~rch CouncilGUIDE TO DESIGN CRITERIA FOR METAL COMPRESSION MEMBERS, 2ndEdition, John Wiley & Sons, Inc., New York, 1966

217.36 -2

NOMENCLATURE

Symbol

A

A.R.E.A.

Defining Statement

Area of entire flexuralmember section

Area of the compressionflange

C.R.C.

Defining Statement

A coefficient. Areaof cross section

Area of flange

Area of stiffener

cross section

Area of web

Symbol

A

.A·s

Aw

a Length of perforation Length of side of astiffened plate.

Length of perforationin a perforatedplate. Torsionbending constantfor an I-section

A coefficient

Width of rectangularcross section..

Width of pony trussbridge, center tocenter of trusses

Effective plate width

Half-width of flange

A coefficientTransverse pony truss

bridge frame springconstant

Coefficients forlateral-torsionalbuckling

Required transversepony truss bridgeframe springconstant

B

b

be

217.36

NOMENCLATURE (Conttd)

-3

A.R.E.A.I-------r------

C.R.C.

Symbol

c

d

Defining Statement

Spacing of perforations

Overall depth of themember.

Clear distance betweenstiffeners

Axial stress thatwould be permittedif axial forcealone existed

Defining Statement

Distance to extremefiber of beam orcolumn section inbending.

Distance center-to­center of perfor­ations in aperforated plate.

One-half distancebetween battenfasteners,measured longi­tudinally.

Flexural rigidity ofa plate per unitwidth

Depth of a section.Transverse distance

between lines oflongitud ina1fasteners in aperforated plate.

Stress-strain modulusof elasticity

Strain-hardening modu­lus (initial)

Eccentricity of endload in a beam­column

Assumed equivalenteccentricity

(representing defects,-etc.)

Allowable averagecompressive stressin axially loadedmembers

Symbol

c

D

d

E

Est~

e

eo

217.36

NOMENCLATURE (Cont'd)

A.R.E.A. C.R.C.

-4

Symbol

f

h

Defining Statement

Compressive bendingstress about axes 1-1and 2-2, respectively,that would be permittedif bending aloneexisted.

Extreme fiber stress inthe compressionflange

Computed axial stress

Computed compressivebending stress aboutaxes 1-1 and 2-2,respectively, at thepoint underconsideration

Clear distance betweenthe flanges.

Width of plate.

Defining Statement

Elastic shear modulus

Clear depth of plategirder web betweenflange components.

Depth of pony truss attruss vertical,

·meaiured from centerof floorbeam tocenter of top chord.

Moment-of-inertia offloorbeam in apony truss

Moment-of-inertia oftruss vertical ina pony truss

Moment-of-inertia ofthe compressionflange of plategirders

Symbol

G

h

217.36

NOMENCLATURE (Cont1d)

A.R.E.A. C.R.C.

-5

Symbol

k

Defining Statement

Effective length factor

Effective lengthfactor of thecompression memberabout axes 1-1 and2-2, respectively

Length of the compres­sion member.

Distance between pointsof lateral supportfor the compressionflange .

Length of the compres­sion member aboutaxes 1-1 and 2-2,respectively

Length of compressionlacing-bar connec­tions

Defining Statement

Optimum moment-of­inertia of webstiffener in aplate girder

Moment-of-inertia ofcross section abouty axis

Torsion constant

Effectlve or equi­valent lengthfactor

Coefficient of pro­portionality, w/p

Coefficient appliedin plate buckling

Length of member,particularly alaterally unbracedlength

Sublengthof lacedcolumn; distancebetweeD lacing-barconnection ordistance betweencenters of battenplates

Symbol

I o

J

K

k

L

L.'\ 0

217.36

NOMENCLATURE (Cont1d).

-6

Symbol

p

A.R.E.A.

Defining Statement

Allowable compressiveaxial load on member

C.R.C.

Defining Statement

Parie~ length iri apony truss bridge

Bending moment

Moment resisted byeach group offasteners

Applied end moment

Moment in a beam­column withoutregard to momentcaused bydeflection

Ultimate bendi ngmoment in theabsence of axialload in a beam­column

A factor-of-safety.Number of parallel

planes of battensin a battenedcolumn

Column axial load

Chord stress in atruss at maximumload

Euler buckling load

Ultimate load ofaxially loadedcolumn

Column axial load atfUll-yield c9ndition

Symbol

M

Mo

Mo(x-x),Mo(y-y)

M ,M ( )u u x-x ;Mu(y-y)

n

P

Pc

Pe

Pu

PY

217.36

NOMENCLATURE (Cont'd)

-7

Symbol

p

r

S

A.R.E.A.

Defining Statement

Allowable extreme fiberstress

Radius-of-gyrationof the compressionmember

Radius-of-gyrationof the compressionmember about axes1-1 and 2-2,respectively

Radius-of-gyrationof the entiresection about theaxis in the planeof the web

Unit shearing stress,gross section, inweb at pointconsi­dered

C.R.C.

Defining Statement

Transverse sh~ar incentrally loadedcolumn

Radius-of-gyrationof member

Radius-of-gyrationof column flange

Radius-of-gyrationof one chord in abattened column

Radius-of-gyration. about the centroi­

dal axis x-x. (strong axes)

Radius-of-gyrationabout the centroi­dal axis y-y(weak axis)

Section modulus aboutx-x axis

Symbol

Q

r

ro

ry

217.36 -8

NOMENCLATURE (ContTd)

Symbol

t

U

v

v

A. R. E.A.

Defining Statement

Thickness of plateThickness of web

Maximum transverseshearing force inthe plane of theperforated plate

Shearing force normalto the member inthe plane of lacingor plates

Allowable unit shearspecified for plategirder webs

C.R.C.

Defining Statement

A thickness

Thickness of compres­sion flange

Thickness of web platesof box-section beam.

Thickness of web

Transverse shear forcein plate girder

Symbol

t

t w

v

Uniformly distributed wtotal lateral loadin a beam-column

Aspect ratio a/h for astiffened plates

Load ratio pip. e

Buckling parameter for ya stiffened plateEI/Dh

Optimum relative stif- Yofness of stiffenerto web in a plategirder EIti/Da,EIo/Dh

Buckling parameter for 5a stiffened plateA /hts w

217.36

NOMENCLATURE (C6nt'd)

"':9

A. R. E. A. C.R. C.

Symbol· Defining Statement Defining Statement Symbol

, -- Elastic strain at €yyield stress

-- Moment coefficient Kfor lateral torsi-onal buckling

-- Slenderness function A/; .(jy (jc

-- Normal stress (j

-- Critical s'tress erc

-- Average stress at (jeEuler bucklingload

~

-- Yield stress level (jy

-- Shear stress 'I"

-- Shear stress at buck- 'l"cling load forplate girder

-- Ultimate shear· stress 'l"u. for plate girder

-- Shear stress at ten- 'l"ysion yield inplate girder

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217.36

SUBJECT INDEX

Allowable stresses, 12

cent,rally loaded columns, 12

bit Ratio, 14

Battened columns, 15

effective length, 15

Beam-columns 10

biaxial bending, 10

design, incipient-yield procedure, 11

interaction formulas, 11

I-shaped sections,' 12

laterally supported, 11

laterally unsupported, 12

secant formula, 11

wide-flange shape, 12

,Beams, 12

box, 12

doubly symmetric, 13

laterally unsupported, 13

rectangular, 12

Biaxial'bending, beam-columns, 10

Buckling, critical stress, 17

flat plate, 14

k factor, 14

plate girder flange, 13, 14, 16

plate girder web, 16

pony trusses, 18

Columns, "12

battened, 15

centrally loaded, 12

effective length o~, 12

laced, 16

perforated cover plated, 15,

-19

'.

•

.-

217.36

Column strength, basic, 12

Doubly symmetric I shapes, 13

basic procedure for lateral buckling, 13

Effective length, 12

, battened columns,15

compression members, 12

Effective-length factor, k, 12

compression members, 12

laced columns, 16

Effective width of plates, 14

Euler formula, 12

Factor-of-safety, 11

in secant formula, 11

I shapes, see also Doubly

symmetric I shapes

Interaction formulas, 11

basic equation, 11

beam-columns, 11

biaxial bending, 10

equal end eccentricity, 11

Galambos-Ketter, 12

laterally unsupported beam-columns, 12

K values, 12

see Effective length factor, K.-

Laced columns, 16

Lacing, effective length factor, K, 16

Lateral buckling,

box girders, 12

plate girders, 13

rectangular sections, 12

beams, 13

-2C

-.

'"

217.36

'Lateral Buckling Strength, 13

doubly symmetric I shapes, 13

'pony truss chords, 18

Laterally unsupported beams, 13

Local buckling, 14

, eJ,astic, 14

plastic, 14

Maximum limiting bit, 14

Minimum thickness, 13

Perforated cover plates, design

suggestions, 15

Plate girder, 13

compression flange buckling, lateral, 13

torsional, 14

vertical, 16

elastically braced compression flange, 18

stiffeners, area, 17

longitudinal, 18

relative rigidity, 17

transverse, 17

thickness of web plates, 16

ultimate strength, combined bending and shear, 17

shear, 16

web-slenderness ratio, 16

see also Doubly symmetric I shapes

Pony trusses, 18

compression chord buckling, 18

Engesser theory, 18

HoltTs solution, 18

transverse frame spring constant, 18

Post buckling strength of plates, 14

Rectangular sections, lateral buckling of, 12

-21

-.

,

•

217.36

Slenderness ratio, 13

Tangent modulus theory, 12

.Through girders, 18

Torsional buckling, compression flange of plate. .girder, 14

.Torsion constant, box secti?ns, 12

Vertical buckling, compression flange of plate g~rder, 16

Web buckling, plate girders, 16

Web-slenderness rati~, plate girders, 16

Width-thickness ratio, flat plate, 14

-22