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I

IT

by

Chingmiin Chern

and Alexis Ostapen ko

October 1970--

Unsymmetrical Plate Girders

U I

Fritz Engineering Laboratory Report No. 328.9

L HIG

UNSYMMETRICAL

PLATE GIRDERS UNDER SHEAR AND MOMENT

Unsymmetrical Plate Girders

UNSYMMETRICAL PLATE GIRDERS UNDER SHEAR AND MOMENT

by

Chingmiin Chern

and

Alexis Ostapenko

This work was conducted as part of the project Unsymmetrical Plate Girders, sponsored by the American Iron and Steel Institute, the Pennsylvania Department of Transportation, the Federal Highway Administration of the U.S. Department of Transportation, and the Welding Research Council. The findings and conclusions expressed in this report are those of the authors, and not necessarily those of the sponsors.

Department of Civil Engineering Fritz Engineering L'aboratory:.

Le~igh University . Bethlehem, Pennsylvania

October 1970

Fritz ~ngineer1ng Laboratory Report No. 328.9

TABLE OF CONTENTS

ABSTRACT . • • • . . . . . . . . . . . . . . . . . . . . . . Page No.

1

1 c INTRODUCTION......... ~ • • • • • • • • • • • • • • •• 2

ANALYTICAL MODEL ANO INTERNAL FORCES . . . . . . . . . . . . . . 6 3. ULTIMATE STRENGTH.

• (I • • • • • • • • • • • • • • • • • • • • 14

40 COMPARISON WITH TEST RESULTS . . • • • • . • • • • • . . . • • . 23

CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 26 6 '" ACKNOWLEDGEMENTS. • • • • • • • • • • • • • • • • • • • • • • • 2 7

7. APPENDIX I. - REFERENCES · · . • • . • • . . • • • • . . . • •• 28

8", APPENDIX II. - NOTATION . . . . . . . . . . . . . . . . . . . . 31

9 Q T.i\BLES AND FIGURES • • • • • " • • • • • • • • • • • • • • • •• 35

UNSYMMETRICAL PLATE GIRDERS UNDER SHEAR AND MOMENT

by

Chingmiin Chern l

and

Alexis Ostapenko 2

ABSTRACT

A method of determining the ultimate static strength of

transversely stiffened plate girders subjected to a combination of

shear and bending is presented. The method is applicable to homo-

geneous and hybrid girders with symmetrical or unsymmetrical cross

section. The ultimate strength is assumed to be given by the sum

of,three contributions: beam action, tension field action and frame

The behavior of a girder panel is described by a continuous inter-

action curve which is divided into three parts: web failure portion,

compression flange buckling portion and tension flange yield portion,

The theoretical ultimate loads compare well with the results of th,e

available fifty-three tests on symmetrical and unsymmetrical plate

girders. The average deviation is 5% with the extreme deviation

of 15%1l

lAssistant Professor of Civil Engineering, North Dakota State University, Fargo, N.D., formerly Research Assistant at Lehigh University, Bethlehem, Pennsylvania

2 Professor of Civil Engineering, Fritz Engineering Laboratory Department of Civil Engineering, Lehigh University, Bethlehem, Pennsylv~nia

(1)

328.9 ~2

1. INTRODUCTION

A plate girder in a building or in a bridge has a majority of its

panels subjected to Bome combination of shear and moment; only a few panels

would ordinarily be under pure moment or shear. Yet, most of the theoretical

and experimental research conducted so far on the ultimate strength of plate

gi"rdera has dealt with the simpler cases of pure moment or shear, and the

'*case of combined loads has been treated due to its complexity as some plausible transition between these 'two strengths.

In 1961, Basler sugges~~d that the moment capacity of a piate

girder section be given by the yield strength of the flanges plus the yield

capacity of the web reduced by a shear stress assumed to be uniform. The

effect of web buckling was neglected and the approach is thus valid only

for webs with very low depth-thickness ratios. To overcome this difficulty

it was proposed that the shear capacity V (including the post-buckling u

strength) be not reduced by bending up to M = 0.75 of the pure bending moment

M , causing yielding of the tension flange, and the moment capacity M be y y

not reduced by shear up to V = 0.60 of the pure shear strength V. The u

transition between the two result~ng points was assumed to be a straight

line. If applicable, the moment from this interaction diagram should be

reduced to M which is primarily controlled by the strength of the compression u

flange. (4) This interaction relationship was then adopted by the AISC

*Hereafter, whenever there is no possibility of confusion, "combination of moment and shear" will be called "combined loads."

l

328.9

Specification. (2) Reference 24 introduced a modification of the method by

replacing the tension flange yield moment M with the ultimate moment for .Y

pure bending M u

.

In 1968, Akita and Fujii arrived at another interaction relation-

h " " f h' "h I" (1) h d " dS 1p cons1sting 0 tree stra1g t 1nes. Teen pOlnts were assume to

be given by the ultimate strengths for pure shear V u

and pure moment M v

'

One of the intermediate two points was defined by the shear causing pure

shear buckling of the web and by the moment produced by the yield~d flanges.

The other point was given by the ultimate shear of the web computed assuming

the flanges to be of zero rigidit~ and the moment produced by the flanges

yielded under the axial forces due to bending and the tension field action.

The method neglects the possibility that the compression flange may buckle

laterally.

In all the above described studies, only girder panels with

symmetrical cross sections were considered. However, in many practical

plate girders the cross section is unsymmetrical, that is, the centroidal

axis is not at the mid-depth of the web; most typically, this is the case

for composite and orthotropic deck girders. So far, the only consideration

given to unsymmetrical girders is an adaptation of Basler's interaction

relationship(4) in Reference 24.

The purpose of the present study is to describe a new method which

gives the ultimate strength of a plate girder panel directly for any com-

bination of moment and shear and is applicable to unsymmetrical, symmetrical,

homogeneous, and hybrid girders. The analytical model of the method and the

assumed pattern of the girder behavior are given next.

Due to the complexity of the force interletlan in I plate girder

panel, an exact analysis of its behavior under load has been impossible,

and recourse had to be taken to represent the panel in the form of a model

as closely to the true state as possible and formulating the desired strength

equations on it. Defficiencies of the analytical models employed by previous

researchers have been pointed out. The model proposed here, although not

perfect, provides a means for explaining cases which could not be handled before.

The model for combined loads represents an interaction between the

models which have been developed in the course of this research for the (7) . (8)

case$of pure shear and pure bending. The web plate is assumed to be

flat until it buckles under the combined effect of increasing stresses due

to shear and moment. The Post-buckling strength of the web is aSSumed to

be in the form of the tension field action analogous to, but not the same

as, in References 1 and 3. The Contribution of it is limited by the yielding

of the web plate and both, shear and moment, are taken into accOunt.

The flanges together with an effective area of the web contribute

to the shear strength by forming a plastic mechanism with hinges at the

stiffeners (Frame Action). The etfect of the axial forces in the flanges

is included. The axial strength of the flanges in yielding or buckling

(Ia teral or torsional) controls the magni tude of the moment on:i:he panel.

The horizontal component of the tension field force reduces the flange

capacity available to carry the moment. When the flange bUckling capacity

is reached before the full capacity of the web or frame action is developed,

the reduction of the moment due to their presence is proportionately smaller.

328.9 -s

The modes of behavior described above are equally valid whether

the larger portion of the web is in tension or compression, except that

a full plastification of the web may be possible as the web portion under

compression becomes smaller. Depending on whether or not the flanges fail

before the shear capacity of the panel is developed, two types of interaction

between shear and moment are possible; shear capacity r"educed(,by moment, and

moment capacity reduced by shear. One or the other will control the design.

A complete interaction relationship is thus established .

. Since for a given pattern of loading, both shear and mo