Beam-to-Column Connections

FURTHER STUDY ON WEB BUCKLING STRENGTH

OF STEEL BEAM-TO-COLUMN CONNECTIONS'(Preliminary Report)

by

D. E. Newlin

and

·-.'-W., F. Chen

Department of ~ivil Engineering

Fritz Engineering LaboratoryLehigh University

Bethlehem, Pennsylvania

t.'Iarch 1971

Fritz Engineering Labo~atory Report No. 333.14

,/

333.14

FURTHER STUDIES ON WEB BUCKLING STRENGTH

OF STEEL BEAM-TO-COLUMN CONNECTIONS

by

D. E. Newlin 1

W. F. Chen 2

ABSTRACT

In the design of an ~nterior beam-to-column

connection, consideration must be given to column web

stiffening. The present AISC Specifications require

stiffening of the compression region of web column on

the basis of two formulas. The first formula compares

the strength of the compression region" as a function of

web and flange thickness to the' applied load from the

·beam flanges. The second formula precludes instability

on the basis of the web depth-to-thickness ratio. If

stability is the more critical) web stiffening is re-

quired regardless of, the magnitude of the applied load.

~oth for~ulas are conservative.

IGraduate Stttdent, Department of Civil Engineering,Lehigh University, Bethlehem, Pennsylvania.

2Assistant Professor of Civil Engineering, FritzLab., Lehigh University, Bethlehem, Pennsylvania.

i

333.14

This report is a further examination of the

criteria for stiffening the web opposite the beam com-

ii

pression flange (5). This compression region is simula-

ted in a manner allowing rapid and easy testing of

specimens. A simple formula is developed for predicting

the load carrying capacity of the compression region for

sections in the range of instability. Moreover, the

effects of strength and stability ar~ combined into a

single formula. Simulation tests are also made to inves-

tigate the effect of column flange thickness and less

common loading conditions on the strength and stability

of the compression region.

333.14 1

1. INTRODUCTION

In the present AISC Specification [1] there are two

formulas governing the requirements for stiffening the

compression region of an interior beam-to-column moment

connection as il1ustJ;ated in Figure 1. Formula (1.15-1) [1]

or (ASCE Manual No. 41,' Eq. 8 .21 [2]) gives the strength

a column web will develop in resisting the compression

forces delivered by beam flanges when expressed in the

form

pmax (1)

This formula was d~veloped from the concept ~hat the

column fla?ge acts as a beari~g plate as illustrated in

Figure 2. It distributes the ,load caused by the beam

compression fla~ge from an initial width, t b , to some

larger width at the edge of the column web. The distance

from the beam flange to the e~ge of the column web is k

(Fig·. 2). The stress, distribution proportional to k' was

developed by curve fitting of. test results on A36 steel

reported in Ref. 4. 'The formula was shown to be conser-

vative for high strength steels as well by the t'est

reported in Ref. 3.

The application of this formula is limited by the

AISC Specificati9ns to cases where the column web depth-

to-thickness ratio, d It, is small enough to precludec

instability. The limiting ratio is defined by the formula

333.14 2

dc

t=180

I""(Ty

(2)

This formula can be derived using the concept.of

simply supported edge conditions for the column web panel

with a linear elastic solution for the buckli~g of a

simply supported long plate compressed by two equal and

opposite forces [3]_. The test results of Ref. 3 and Ref. 4

show formula (1) to -be conservative for all sections tested

regardless of d It.c

Furthermore, the present AISC' Speci-

fications do not permit consideration of any load capacity

com-

in .the compression region of sections with d It ratiosc

Development of a feasible andgreater than 180/~.y

reliable method of determining ultimate loads for the

pression region of sections with d It ratios greater than, c

180/va- will, therefore, be the first objective of thisy

report.

It will be demonstrated herein that -strength and.

stability are not entirely distinct; rather that strength

and stability are interrelated, espec-ial1y when the d Itc

ratio is near 1801/(1.Y

The second objective will be to

develop a single formula for predicting the ultimate

load carrying capacity of "the compression reg-ion regard-

less of the d It ratio of the column section.c

Within the compression region, the column flange

simulates a shallow continuous beam. The bending

333.14 3

stiffness of the flange as a beam is primarily a function

of its thickness. It is the third objective of this

report to investigate the contribution of the" column

flange as a shallow beam to the load carrying capacity of

the compression region. It will be shown that the con­

tribution of increased fla~ge thicknes's is relatively

insignificant.

Occasionally, the opposing beams of an interior

bearn-to-column moment connection will be of unequal

depths. This may result in a situation where the loads

applied to the compression region are. eccentric (Fig. 4).

Investigation of the effect of this type of eccentricity

on "the strength and stability of the compres-sion region

will be the "fourth objective of this report.

/

333.14 4

2. DESCRIPTION OF TESTS

2.1 Test Pr6g~am

Fifteen tests were performed invest~gating web

crippling, in general, as affected by various types of

loading conditions and column flange variations. Refer

to Fig. 3 for a schematic of the web crippling test set­

up. The tests are summarized in Table 1.

The first series of tests simulated the compression

zone of a column loaded by moments from two opposi~g

beams of unequal depth. This is illustTa~ed schematically

in Fig. 5.

To observe the effect of increased column flange

thickness a set of tests were per£or~ed on sample specimens

with and without cover plates., Cover·plates used were 1

inch thick, 20 inches lo~g, and slightly wider than the

specimen fla~ges to permit fillet welding all around~

The role of the column. flange as a continuous

stiffeni~g beam was analyzed by another set of tests. "The

specimen flanges were slotted from the outside edges to

the web on both sides of the load points. The ends of the

cuts near the web were"pre-drilled to insure rounded

smoothness and prevent notches. On one test the distance

between the slots was equivalent to t b + Sk and equivalent

to d' on another specimen.

Two additional tests were also performed. One was

with the load applied by a T-shaped bar to study the effect

333.14

of load from the beam web,"

5

The other was a standard web

crippling test on a heavy welded section.

2.2 Test Procedures

A test set-up was devised ~hich permits rapid testing

of specimens. Itis basically the same one used by Graham

et al Cl ). " .T~e test set-up is shown in Figs. 2 and 3. In

this simulation test, a column'is placed horizontally be-

tween the loading platens of the testing machine and com-

pressed by two steel bars placed in the same vertical plane

on the top and bottom surfaces of the column, The bar was

tack-welded to the column fla~ge to simulate a beam flange

framing in. All the specimens were tested in the ~hicl~

800 kip mechanical machine at Fritz Laboratory.

The instrumentation consisted of" dial gages to

monitor the deflection in the 'direction of the applied

load and another gage to monitor the lateral·deflection

of column web. This lateral deflection indicated the on-

set of buckling.

Two tensile specimens were cut from each specimen,

in the orientation shown in Fig. 1, in accoidance with ASTM

standards.

3. RESULTS

Table 2 summarizes the measured properties of all

test specimens including the tests reported in Ref. 3.

Table"3 summarizes the test results and the theoretical

333.14

predictions.

6

It also lists d It ratios for all specimens.c

It can be observed from the load-deflection curves in

Fig. 6 and Fig. 7 that the ultimate load is essentially

unaffected by the eccentric ~oad condition.

eccentrically has the effect of adding a small amount of'h.,

.... ::....+

stiffness to the web. Design based on the assumption of

non-eccentric loading will be conservative. Fig. 8 shows

the comparison of the control test with the eccentricity

test.

The load deflection curves of the control tests,

Figs. 9 and 10, exhibit the usua~ properties of beams of

this size made 6£ 36 ksi material. From no load to

approximately half. of ultimate, load the curve is almost

linear and reasonably steep. The upper half of the curve

to ultimate load is at a lesser slope indicating the

oc~urence of some yielding and redistribution of stresses

from the increasing load. The maximum destgn load, as

determined by the AISC formula (tb + Sk)tcr is reachedy.

soon after the initial yield point on the load deflection

. curve with considerable reserve capacity remaining.

With the addition of a heavy cover ~late, reasonably

long, a significantly different situation exists. The

load deflection curve is essentially linear all the way

to ultimate load with no stress redistribution exhibited.

333.14

The (tb

+ Sk)tay

formula leaves only 4.8% of ultimate

load as reserve capacity as compared to 43% in the

7

WIO x 29 section without cover plate. These figures are

4.8% and 33% respectively for the W12 x 27 section.

Correspondi~g specimens at the end o£ test are shown in

F~g. 11.

It can be concluded that for v~ry thick flanges

the t b + 5k formula does not meet present standards of

reliability. Thus, in the design of beam-to-column

connections the presence of a cover plate on a column

flange should not be considered as part of the k dimen-

sian.

The load deflection curve is typical of web crippli~g"

of sections of 36 ksi material. It deviates from linearity

at about half of the ultimate load. There is considerable

reserve capacity after first signs of yielding (Fig. 12).

3.4 Slotted Flange Test

Slotting the flanges as shown in Fig. 13 had very

little effect on the load deflection curve. Stiffness

was essentially uncha~ged and ultimate load decreased

6nly slightly." Specimens at the end of the test are

shown in F~gs. 14 and 15.

3.5 Beam Web Cont.ribution Test

The load deflection curve, Fig. 16, of the beam

loaded by a T-shaped bar is steeper and reaches a higher

333.14

ultimate load. The design assumption that a moment

8

delivered to a column flange by a beam acts entirely

through the fla~ges of th~ beam is, therefore, a con-

servative assumption.

This is upheld by the test. When we, permit the

applied load'to act through a simulated beam flange and".~-:.I,o",

web T-bar, the column is able to carry a larger load.

4. DEVELOPMENT OF BUCKLING STRENGTH 'FORMULA

One 0-£ the major contributions of the f_lang-es is

provision of lateral,supported edge conditions for the

web panel. The fla:nges. provide web edge supports because

of the very high bending stiffness of the flange in the

plane of the fla!1ge. The flanges' provide simple supports'·.

with 36 ksi material because there is early yie,ld~~g near

the juncture of the web and £1 a~ge·. Wi th the us e of

high strength materials this early yielding will not

occur and the flanges will closely simulate the role of

fixed e,nd supports 'for the web panel.

From observations of the test results in the P!e-

sent and previous tests, it appears reasonably

justified to assume that the concentrated load acts only

across an effective width, and this width forms a square

panel, de x de. Thus, the critical buckling stress

becomes

cr cr

pcr

= (it =c

33;400

Cd /t)2c

(3)

333.14

as developed in Ref. 3.

9

In Ref. 5 the buckling load of a fixed end lo~g

plate compressed by two equal and opposite forces is

twice the buckling load of the same plate when it is

simply supported. It was also observed in previous

t est s [ 3 ] t h.~~ t sec t ion 5 ill a d e 0 flO 0 k 5 i mat e ria1 wit h

.d It ratios greater than Eq. 2 did ·realize str·essesc

approaching twice the critical stresses predicted by the

simply supported theory. This is illustrated graphically

in comparison with test results in Fig. 17.

It can, therefore, be stated that a = 33,400/er

Cd /t)2 is a lower bound for 36 ksi material and 2ac cr

is an upper bound for 100 ksi material.

This 'is closely approximated by making (J a functioncr

of a as follows:y

(Jer

.p

= -Ttc

(4)

If the expression for cr in Eq. 4 is adjusted tocr

fit the most critical test, test No. 21, the resulting

equation

p =cr

4100 t 3 ra­yd c

(5)

will be s~fe for all tests.

333.14 10

It should be noted that because t is cubed while d c

remains first order, web thickness is a more significant

parameter in determining the buckli~g load, Pcr Graphical

comparison of formula (5) is made with test results in

Fig. 18 using nominal values of yield s"tress. A good

~greement is observed.

5. DEVELOPMENT OF THE INTERACTION FORMULA

Figure 19 is a non-dimensional comparison of test

results with AISC design formulas for strength and stabi-

lity. There are some inherent drawbacks. The first is

that when a section's d It ratio exceeds the allowablec

values of 180//(J, the specifications declare that they

section has no l~ad carryi~g capaci~y and is to be

stiffened regardless of the magnitude of the applied load.

In the range where d It is within the allowablec

limits and the load capacity of the section is controlled

by the strength formula, P = (tb + Sk)to , other diffi-y .

culties arise. The test data is much too scattered to

make an accurate prediction of the ultimate load capacity.

It is readily' determined that, . although the AISC strength

formula is conservative for normal rolled sect,ions, it

does not describe what really occurs in the column

compression zone of, a beam-te.-column connection.

If we return to the assumption that the compression

·zone of the column is effectively a square web panel with

dimensions d x d and thickness, t, a differentc c

333.14

perspective reveals itself. Compressive stress in the

11

columns is now determined as cr = P/d t. From the resultsc

plotted against d It on a non-dimensional form in Fig. 20c

it is observed that the data is considerably less scat-

tered. However, if the formula P = d tcr was used toc y

predict ultimate load instead of the AISC formula, P =

(tb + Sk)tcry

, premature failure would occur as values of

d It approach l80/vcr-. This is observed because of testc y

failures occurring within the limits of the two formulas.

There is a l~gical conclusion to be drawn from this

behavior. It is supported both intuitively and by obser-

vation of the plotted results. Interaction between

strength and stability criteria does occur near the

beg inn i n g 0 f the s tab iIi t Y c r i t eria r ..an g e .a s des c rib e d by

18 Icrn Fig 20 this interaction is cons

described by a 'straight line from 1.75 on the abscissa to

1.75 on the ordinate. The equation ,of this line can be

written as

(6)

In compari~g values predicted by this formula to

test values it was discovered that the equation provided

excellent results for all tests except on those specimens

mad'e· of 100 ksi material. For these 'specimens the axis

intersection point in Fig~ 20 would have to be at least

2.2 or 2.3.

333.14

Making the constant 1.75 a function of the yield

12

stress presented itself as a possible way of accomplishing

the desirable effect of shifti~g the interaction line

upward for hi~h strength steel. Changing '1.75 to 1.75

(~/v36) produced premature failures in 50 ksi materials.y 4 4

Chan gin g 1. 7 5 t 0 1. 70 (1(1" /1"36) prov ide d the des irab 1 ey

effect. For 0 = 100 ksi, 1.70 is changed to 2.17 andy

1.85 for 50 ksi material. The interaction equation takes

the form:

41,.70. rcr

p = ( y4136

(7)

When the formula is solved for t it takes the form:

d 2rcr 180 Ci Af ,c +

t = Y4

125 d ra-e y

where C1 is the ratio of beam yield stress to column

yield stress and Af

is the area of the beam flange .

delivering the concentrat~d load, P. Thus, CI Af

=

PIa. Then t becomes the required web thickness in th,ey

column compression zone regardless of d It.c

The predicted ultimate loads from this formula for

re cent Lehi gh Un i,ve'r s i ty t est s are tabu 1at ed on Tab 1e 4

(8)

and comparative'ly plotted against actual values in Fig. 21.

Fig. 21 shows the interaction formula (7) to be as

333.14

accurate as the stability formula (5) and for 100 ksi

13

material the interaction formula provides·better accuracy

than the stability formula. In the ra~ge where the

stability formula is not applicable, i.e. d It, < 180/;cr-,c y

the interaction· formula is compared with AISC predictions

in Fig. 21.. Where the stability formula is applicable,

AISC makes no predictions.

In terms of required web thickness, t, a comparison

is made to actual web thickness -in.Table 5. Since the

applied load is Pult ' the required web thickness should

be greater than the actual web thickness which permitted

failure. This occured in all cases except test No.8 of

Ref. 3. However, the a~tual yield stress of that ?pecimen

was less than required for ASTM A36 material, which

negated its usefulness for this study.

6. SUMMARY AND RECOMMENDATIONS

6.1 Par~met~rs

·It has been show~ that the parameters most pertinent

to the strength and stability.of the column compression

zone in a bea~-to-column connection are four fold. They

are web thickness, t, .column depth, d , yield stress, cr ,c y

and the role of the column flanges as.suppO!ts f~r·the

web panel. The column flanges vary in their support

effect from a lower bound of simple edge supports to an

upper bound of -fi~ed edge supports with increasing yield

stress.

333.14 14

6.2 Formulas

The formulas developed or under consideration in

this study are summarized below. They are shown both in

a form readily useful to the designer and in a form for

predicti~g the maximum permi'ssible load that can, be

carried by the column compression zone in a beam-to-

column connection.

. VI timate Load Form

Strengt_h

-.

p = (tb + Sk) to'. Y

Stability

p = 0

Design Form

Strength Stability

C1

Af

d /(Jt. < & t < c y

- t b +5k - 180AISC

t <

Strength &'Stability

- lay de f-,125p - 180 4----

. ra. y-

Strength &Stability

d 2 .e to; + 180 C1 Af

4125 ra- d" y c

Interaction

Jd rcr>tc y-

t .?: 180P = (tb + 5k) toy

Strength

Stabili.ty

p =d

c

Strength

~1 Aft < -----~- tb+Sk

Stability

410-0 t 3d >

c - C1

Atcr;

~,fo di f.i edAISC

The present AISC formulas are conservative. This

has been shown pr'eviously and is reconfirmed in this

report. The AISC formulas are incomplete in that they

333.14 15

/

offer no estimate of the load capacity of the compression

zone when dcf t exceeds 180f~. The (tb + Sk)t0y

formula is not an accur'ate expression of strength and, in

the case of very thick flanges, is unconservative.

The interaction formula is considerably more

accurate. It has the advant~ge of being a conservative

fit to data that is far less scattered than the data

per·taini~g to the AISC formula. This fact' alone makes

it more pertinent than the AISC formula. Another impor-'

tant advant~ge is that it permits the designer to make a

one step analysis of the compression zone of a connection

to determine whether a stiffner is advisable.

The last set of formulas, herein referred to as

Modified AISC, adds to the present AISC approach the

advantage of bei~g able to predict- ultimate loads in

the stability range very accurately. Wh~n the constant

in the formula P = 4l00t 3 ;O-/d is increased to 4400y c

this equation is an excellent ·fit to the test results·

of specimens made of 36 ksi and 50 ksi material and is

conservative for 100 ksi mater~al. When the constant

is left at the conservative 4100 value it is a reliable

design aid.

6.3 Reco~metidations

After thorough evaluatio,n of ,the test results set

forth in this report, it is the considered opinion of

the authors that the proposed "interaction formula"

333.14 16

offers a decided improvement to the present AISC appr~ach

on the basis of simplicity, safety, accuracy, and

thoroughu'es s .

Also-the addition of the stability formula P ~ 4l00t 3

17J"/d to the AISC Commentary would be an asset to thaty c

text and to persons interested, in, greater accuracy for

determini~g buckling loads of rolled sections of 36 or

50 ksi material.

7 • ·REFERENCES

1. AISC Specification for the Design, Fabrication, andErection of Structural Steel for Buildings,American Institute of Steel Construction;February, 1969.

2. ASCE Manuals of Englneering Practice No. 41, Commen­tary on Plastic Design in Steel, the WeldingResearch Council and the Ame~ican Society ofCivil Engineers, 1961, (Revision to Appear in197~) .

3. Chen, W. F. and Oppenheim, I. J., Web BucklingStrength of Beam-to-Column Connections, FritzEngineering Laboratory Report No. 333.10, 1970.

4. Graham, J. D., Sherbourne, A. N., Khabbas, R. N~, andJensen, C. D., WELDED INTERIOR BEAM-TO-COLUMNCONNECTIONS;· AISC Publication, Fritz EngineeringLaboratory Report No. 233.15, 1959. Also,Bulletin No. 63, WELDING RESEARCH COUNCIL, NewYor~, August~ 1960.

5. Timoshenko, S. p~ and Gere, J. M.THEORY OF ELASTIC STABILITY, 2nd edition,McGraw-Hill, New York, 1961 ..

333.14

8. ' 'NO~1ENCLATURE

17

dc

d '

E

k

area of one flange (of the beam frami~g ~n);

ratio' of the' beam yield stress to the column

yield stress;

column web depth between colqrnn k-lines or

between toes of fillets;

depth of beam;

distance between column fla!1ges, F~g. 2;

fillet, F~g. 2;

P concentrated load;

t b thickness of the beam fla~ge;

t column web thickness;

cr normal stress;

cr actual yield stress in ksijya

a nominal yield stress in ksi;yn

V Poisson's ratio;

vertical displacement, Fig. 2',

333.14

Table 1

SUMtvIARY OF TESTS

18

. . . .... tt ..... .. , ... • 4 • ~

De's' COr i'p't' i' 0 n " "Se'c"t'i"on Ma't· e'r ia,l Te"s't" No.

Eccentric Loadi~g alb == 10/20 W12 x 45 A440 W-ll

Eccentric Loadi~,g alb = 10/18 W12 x 36 A514 W-13

Eccentric Loadi!lg alb = 5/50 _W12 x 36 AS14 W-14

Eccentric Loading Control Test W12 x 45 A440 W-12

Eccentric Loadi!1g Control Test W12 x 36 A514 W-15

Increased Fla!1ge Thickness Test WID x 29 A36 W-16

Flange Thickness 'Control Test WID x 29 A36 W-17

Increased Flange Thickness Test W12 x 27 A36 W-19

Flange Thickness Control Test W12 x 27 A36 W-20

Bearing Plate Test (tb + Sk) W12 x 45 A440 W-22

Bearing Plate Test Cd ' ) W12 x 45 A440 W-24

Bearing Plate Control Test" W12 x 45 A440 W-21

T-Shape Load Test WID x 29 A36 W-18

r-Shape Load Test WIO x 29 A36 W-17

Web Crippling of Welded Section HID x 62 A36 W-IO

/

333.14 19

SECTION PROPERTIES

I

N'ominal ActualMeasur e d 'D i men s ion s , in.

C5 aTest y y dNo. Section ksi ksi c t k d'

W-3* WIO x 39 100 121.9 8.15 0.344 0.91 9.05

W-4* W12 x 45 100 118.2 9.87 0.344 1.11 10.93

W-5* W12 x 31 36 39.8 10.59 0.270 0.70 11.22-

lV -.6 ~ WI0 x 29 36 41~9 8.91 0.308 0.73 9.32

W-7* WIO x 54 50 57.8 8.05 0.380 1.02 8.86

W-8* W8 x 67 36 30.9 6.60 0.575 1.22 7.21

W-9* W12 x 120 100 97.7 9'.95 0.700 1.57 10.96

W-IO HID X 62 36 33.7 7.82 0.504 1.33 '9.72

W-12 W12 x 45 50 54.0 10.02 ,0.377 1.00 10.92

W-15 W12 x 36 100 110.6 10.74 0.324 0.82 11.28

W-17 WID x .29 36 42.2 8.91 0.310 0.73 9.32

W-20 WI2 x 27 36 40.7 , 10.62 0.269 0.69 11.22

W-21 W12 x 45 ·50 56.8 10.02 0.385 1.00 10.88

*Tests Reported in Ref. 3

."

/I

333.14

TEST PROGRA~1

20

d .. 180.d .I.t (t

b+5k) Test pc x(to ) P u1t PTest c -- ultrcr- 180/~

ya . ul td tcrNo.•.... _..~ ... ya ..- . ya .kips. kips c ya (tb+ 5k )tG ya

W-3* 23.7 16.4 1.44 212 253 0.74 1.19

W-4* 28.6 16.7 1.71 246 260 0.65 1.06

W-5* 39.2 28.6 1.37 43 61 0.54 1.42

W-6* 28.9 27.9 1.04 53 90 0.79 1.71

W-7* 21.2 23.7 0.89 123 215 1.20 1.75

W-8* 11.5 32.4 0.36 125 250 2.14 2.00

W-9* 14.2 18.2 0.78 612 980 1.45 '1.60

W-IO 15.5 31.0 0.50 112 166 1.78 1.96

W-12 26.6 24.5 1.09 165 235 0.81 1.48

W-15 33.1 17.1 1.94 - 54 95 0.61 1.42

W-17 28.7 27.7 1.04 43 64 o .'81 1.76

W-20 39.5 28.2 1.40 120 168 0.55 1.49

W-21 26.0 23.9 1.09 121 237 0.77 1 .. 40

. *Test Reported in Ref. 3

333.14

PREDICTED CRITICAL LOADSWITH

NOMINAL YIELD ·STRESS VALUES

21

S.t-aq.i-l i ty Inter-...'t:~ AISC & AISC action-:.... p p P Tests

(J cr cr cr pTest y Eqs.l,2 Eqs.5,2 Eq.7 ultNo. Section ,ks.i kips ki,ps ,kips kips

---.,.

W-3* WIO x 39 100 0 205 246 253

W-4* W12 x 45 100 0 169 204 260

W-5* l~12 x 31 36 0 46 40 61

W-6* . lVIO x 29 36 0 81 73 90

W-7* WID x 54 SO 123 123 155 215

W-8* W 8 x 67 -36 125 125 180 250

W-9* W12 x 120 100 612 612 978 980

W-IO HID x 62 36 121 121 157 237

W-12 W12 x 45 50 0 155 151 166

W-15 W12 x 36 100 0 130 123 235:

..

W-I7 WIO x 29 36 0 82 74 95

W-20 W12 x 27 36 0 45 39 64

W-21 W12 x 45" SO 0 165 159 168

*From Previous Tests, Ref. 3

333.14 22

..

PRED1CTED WEB THICKNESS REQUIREDTO CARRY ULTIMATE LOAD

USING INTERACTION FORMULA, EQ. 8

Nominal Actual

Testa a Pult Actual Required*y y

'·.No. ~." ...... ......S.e.c.t.i6.ri. ,'. ". ..... ·,ks.i '," . " .ksi. . .kip.s, , . . .t~

- -~- ..-

3 WID x 39 100 121.9 253 0.344 0.347

4 W12 x 45 100 118.2 260 0.344 0.370

5 W12 x 31 36 39'.8 61 0.270 0.301~.

6 WI0 x 29 36 41.6 90 0.308 0.3'40.-

'7 WID x 54 SO 57.8 215 0.380 0.460

8 W 8 x 67 36 30.9 250 0.575 0.575-

9 W12 x 120 100 97.7 980 0.700 0.904-

10 HID x 62 36 33.7 237 0-.504 0.648

12 W12 x 45 50 54.0 166 0.377 0.386

15 W12 x '36 100 110~6 235 0.3.24 0.371

17 WIO x 29 36 42.2 95 0.310 0.349.'

20 W12 x 27 36 . 40.7 64 0.269 0.307.,

.21 W12 .X 45 .50. . ,56.8. ...168. o.. 385 0.395

* 2 . ,P'ul td, ~. + 180 (--)

t = c y , .cr.y4'

125 d r0­c y

Nominal cr y

Table 6

TEST RESULTS REPORTED BY GRAHAM, SHERBOURNE, KABBAZAND JENSEN (SEE REF. 1)

Actual (tb

+ Sk)Test

1 ....r f'~

(deft)tb

a 180 d (to' ) p u1t . Pu1t Pu1tTest -- x

y ;cr c yd to . d tcr y Cd It)No. Section in. ksi y t kip kip c ya c n c a

El W12 x 40 0.5 40.2 28.4 33.20 81.6 102.5 0.89 0.99 1.17

E14 W 8 x 48 0.5 34.4 30.7 15.70 . 89.8 137.0 1.54 1.47 0.51

'ElS W 8 x 58 0.5 . 36.2 29.9 12.50' 119.1 202.5 1.72 1.73 0.42

E16 WIO x· 66 0.5 . 40.0 28.5 l7.23 143.9 175.7 1.22 1.36 0.60

E17 WID x 72 0.5 35.0 30.4 15.40 129.6 190.0 1.35 1.31 0.51

EI8 W12 x 65 0.5 37.2 29.6 25.00 93.2 143.0 1.01 1.04 0.84

EI9 W12 x as ,0.5 37.8 29.3 19.69 151.2 247.5 1.35 1.42 0.67

E20 W14 x 61 0.5 36.,2 29.9 30.10 110.0 137.5 0.88 0.88 1.01

E21 W14 x 68 0.5 38.3 .29.1 27.20 132.1 164.0 0.90 0.96 0.93

E22 W14 x 84 0.5 39.3 28.7 25.22 133.6 221.0 1.09 1.19 0.88

E23 W14 x 104 0 •. 5 .38.5 _ . 29 •.-0 I .23 •. 0.0 . 16.0.• ,2 .. , 250.0 1.15 1.23 0.79

~

v:ItN

..,....a~

NV1

:;-n-:-1424

T... ,..

J --- ~ ';1

.....

" --- ---

Conp~eSSION£e&loN

~NE/?,.9r/c Or TYPIChJI- .:zNrGe/o,e

Be:.&H - ro - Co.t.-tl.H# NOH€N r dN/V€ cr/oN .

(

tTy t t t t t t t '--i r-- tb +5 k

Uy~+ ~~~ ••

tp

Fig. .1. Simulation of the Compression Region

25

.C,i SOOk Machine

~ '. ,

Fig. 3 .. Test Set-up

t," •

:'" + ...

26··------..--+-..,.--,.3~3-......,.--;I4~-------------------------f-------1

e

. e - ECCEJV7£./C/7Y .

FiGUZE .</.

p

p{o5t)I-I!fl---__b__~_a..---.-. p /.. b ':\. (Q+ b )

dGtJ£E S.lEST S'ertlP k..e CCCdN'TAZ./C/r,Y'

S//vULRT/O'/v

333.14 27

./

Fig. 6

333.14 28

c

Fig. 7 / /-'7 -!~II?-b /

333.14

a) Eccentricity Test

b) Control Test

Fig. 8

,29

333.1430

333.1431

(

/

Fig 10

333.14

a) Increased Flange Thickness Test

b) Control Test

Fig. 11

32

333.1433

C)

c.r-'

.F~_g. -1·2

333.1434

(

Fig. 13

J !Jr-~l .'

[;) -

333.14

W-22

a) Side View Slotted Flange Test

b) .Top View, Width = .tb

+ Sk

Fig. 14

35

/

a) Side View Slotted Flange Test

b) Top View~ Width = d'

Fig. 15

36

333.1437

(\

333.14 38

I!

//

/

Fig. 1 7

Comparison of Theory Developed from Ref. 5Specimens with d It R ..atlo Greater than orAllowabl.e C

withClose

Teststo

of

333.14 39

C·~.·... ~...

Fig. 18

Comparison of Stabilitywith d It Ratio GreaterC .

Formulath.an or

with Tests of SpecimensClose .to Allowable.

(

333.14~

-.p

, (J" =-------( tb+ 5k }w

2.0

'1.5

o

8o

oc

zo5 ao

,S.:_.AISC EO. 1.15-1

I.OJ--------------.

0.5

o

o

SofeRegio~

'.0.5

c 0 []

:t>t-t(f)0

ITtP-.-01

I

rv

1.0

(dc/\v)

(dc/w >0

4G

r.' • - - - - -- __ __ .-.. L_-.,.... - -_ +- , ~ .~ ~._ ..~~ ~ ~~ ~ ~.~ _ ~.-~ _- _ ~_~~~r ~•• , •

1.5 .

". '.

Fig. 19 CompC!rison of Te'st Resul tsI

With AISC Formulas"

J-JJ. ~ ....

41

(.I

C.-")

- - /

Fig. 20

Comparison of Test Results with Interaction Formula.4 Points not Numbered. ~ef.

333.14

--.................-t-·· ..··+-t'......... +- ............ "0-

'~r.;.-i~-=-:

~~ct· --+-+-.--~--+-~

.......~.

r=:---:I -~~-~-

.~=~:

.=-~f-~_~... f .~ • / ._.. ~ r

_:-.-._p-~- ~.. ~:-.._.:_..~. -_._ ..~-_.. . -...-.-.~.- ..~

Lult~~~:?ti;a-

42

Fig. 21

Composite .Comparison of Ultimate Test Load with PredictedUltimate Load as Determine by-the Vari6us Formulas