Submitted to the Highway Research Board for

Publication in, the lfHighway Research Record!!

THE CONTRIBUTION OF

LONGITUDINAL STIFFENERS

TO THE STATIC STRENGTH

OF PLATE GIRDERS

by

Peter B. Cooper

Lehigh University,

Fritz Engineering Laboratory Report No. 304.10

July, 1966

304.10

TABLE OF CONTENTS

SYNOPSIS

FOREWARD

INTRODUCTION

BENDING STRENGTH

SHEAR.STRENGTH

LONGITUDINAL STIFFENER REQUIREMENTS

SUMMARY

FIGURES

REFERENCES

ACKNOWLEDGMENTS

ii

1

2

3

7

11

12

13

20

21

304.10

SYNOPSIS

The paper summarizes the results of a research project on the

behavior of longitudinally stiffened plate girders subjected to

pure bending and high shear. Analytical and experimental studies

were conducted to determine the increase in the static strength of

plate girders due to the presence of longitudinal stiffeners.

Requirements for positioning and proportioning longitudinal stiff~

eners are also discussed.

- iii -

304.10

FOREWARD

From 1963 to 1966 a research project was conducted at Lehigh

University with the objective of determining the contribution of

longitudinal stiffeners to the static load-carrying capacity of

plate girders. The research consisted of analytical studies and

tests on a number of fUll-size, welded steel girders. Some of

the results of this work are summarized in this paper. The

subject is treated from a qualitative rather than a quantitative

viewpoint.

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304.10

INTRODUCTION

The provisions in the AASHO Specifications Cl) for determining

the proportions of a plate girder web and the location and size of

web stiffeners are primarily based on stability considerations,

that is, the theoretical web buckling stress is the criterion for

failure or limit of usefulness. However, because of a redistri­

bution of stress in the web and the supporting action of the

flanges, and stiffeners which frame the web, the maximum load which

a girder can sustain is considerably higher than the theoretical

web buckling load C~). In many cases where plate girder design is

based on web buckling theory, the existence of post-buckling

strength is tacit~y recognized by the use of a low factor of

safety against web buckling Cl).

In this paper the type of stress redistribution which occurs

in a plate girder web is discussed for the separate loading cases

of pure bending and high shear. In particular, the effect of a

longitudinal stiffener on the stress redistribution is described

for these two loading cases.

_In investigating the influence of longitudinal stiffeners on

the behavior of plate girders, it is helpful to first study the

behavior of transversely stiffened plate girders C~'~'2)' Based

on this ,information and observations of the behavior of longitudi­

nally stiffened test girders, the effect of longitudinal stiffeners

can then be explored.

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304.10

BENDING STRENGTH

The behavior of transversely stiffened plate girders

subjected to pure bending can be described using the test data

on lateral web deflections and bending stresses shown in Fig. l.

Plotted in Fig. la are the web deflection patterns measured at

four different test loads. At a load of zero· kips the web

deflection pattern corresponds to the deflections due to initial

imperfections. The web deflections increased continuously in the

upper half of the girder, which was subjected to compressive

bending stresses; while the deflections in the lower half of the

girder were somewhat reduced due to the tensile stresses present

in that region as the load was increased. There is no indication

of a sudden change in the magnitude of the deflections such as

would be expected according to web buckling theory.

A further illustration of the behavior of transversely stiff­

ened plate girders subjected to pure bending is provided by the

curves of bending stress distribution in Fig. lb. The dark· lines

represent the measured stresses while the light lines in the

figure are the linear stress distributions computed from conven~

tional beam theory, that is, a = My/I. In the lower portion of

the web the measured tensile stresses correspond very closely to

those predicted by beam theory; however, due to the increasing

lateral web deflections in the compression zone, a redistribution

of compressive stresses from the web to the compression flange

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304.10 -4

occurs. The stresses in a significant portion of the web between

the neutral axis and the compression flange are essentially zero

while the compression flange and a portion of the web adjacent to

it carry stresses which exceed those predicted by beam theory.

A flange stress reduction formula has been adopted for trans­

versely stiffened girders to compensate for the increase in

compression flange stress above the beam· theory stress due to the

stress redistribution (i). The magnitude of the reduction is a

function of the web slenderness ratio since the extent of the

stress redistribution increases with higher slenderness ratios.

A longitudinal stiffener placed in the zone between the

neutral axis and the compression flange reduces or completely

eliminates lateral web deflections and thus has a significant

effect on the stress redistribution described above. This effect

is illustrated by the web deflection and bending stress distribution

data plotted in Fig. 2. The test girder in Fig. 2 was essentially

identical to that in Fig. 1 except for the presence of a longitudi­

nal stiffener located one-fifth of the web depth from the

compression flange. Because of the presence of the longitudinal

stiffener, the extent of the increase in lateral web defLections

from the initial configuration in Fig. 2a is substantially smaller

than that shown for a transversely stiffened girder (Fig. la).

304.10 -5

Further information on the influence of longitudinal stiff-

eners on bending strength can be obtained from a comparison of the

stress distributions in Figs. lb and 2b. Although the large _

initial web deflections of the longitudinally stiffened specimen

caused the bending stresses in the web to deviate somewhat from

the linear beam theory distribution (Fig. 2b), a redistribution of

stress from the web to the compression flange of the type shown in

Fig. lb is not evident. Beam theory could be used to predict very

accurately the compression flange stresses for the longitudinally

stiffened girder.

From the above discussion it may be concluded that if a

suitably positioned and proportioned longitudinal stiffener is used,

beam theory can be used to predict the compression flange stresses.

In this case a flange stress reduction is not necessary. Thus, by

p~eserving the beam-type action the longitudinal stiffener will

have a significant and beneficial effect on the bending strength.

The percentage increase in the bending strength due to the longi-

tudinal stiffener is plotted in Fig. 3 as a function of the web

slenderness ratio and the ratio of the area of the web to the area

For the practical range of-A /A f between 0.5w .

and 2 and with a web slenderness ratio of 400, the increase in bending

strength varies from about 6% to 30%.

It is suggested that a longitudinal stiffener should be

located one-fifth of the web depth from the compression flange to

be effective in controlling the stress redistribution Qnder pure

304.10 -6

bending C~). This is the position specified in the current AASHO

Specifications Cl). Requirements for proportioning longitudinal

stiffeners are discussed in a separate section of this paper.

The bending strength theory described in this paper has been

checked with the results of tests included in this program and

tests conducted by others C~). The web slenderness ratios of the

test girders ranged from 299 to 407. The ratios of the experi-

mentally obtained ultimate .loadsto the ultimate loads predicted

by the theory varied from 0.94 to 1.02 with a mean value of 0.98.

Due to the presence of the longitudinal stiffeners, the ultimate

loads of these test girders were increased from 14% to 26%. The

correlation of the bending strength theory with the test results

is indicated in Fig. 4, where bar graphs are shown for the ratio

of the predicted ultimate load P th to the yieldloadP and theu y

ratio of the experimentally obtained ultimate load P ex to theu

yield load. The test results indicate that a substantial increase

in bending strength can be achieved by using longitudinal stiff-

eners and that the theory provides a reliable estimate of the

actual bending strength of longitudinally stiffened plate girders.

304.10

SHEAR STRENGTH

The type of shear panel which will be considered in this

section is shown in Fig. 5. The panel consists of a rectangu-

lar portion of the web bounded by the flanges and transverse

stiffeners. It is assumed.that the moment present on any section

in the panel is small so that the shear strength of the panel can

be studied independently.

An element subjected to pure shear stresses T is shown in the

left sketch of Fig. 6a. These stresses correspond to the principal

stresses shown in the right sketch, where the tensile principal

stress crl is numerically equal to both the compressive principal

stress 02 and the shear stress T. The state of stress shown in

Fig. 6a is the type usually assumed in simple beam theory; in the

following discussion it will be referred t(k;as flbeam action shearfl .

As the shear force on a plate girder panel is increased, a stage

is reached where the compressive stress cr 2 can no longer increase

as rapidly as the tensile stress 01 because the web deflects

laterally. For an ideal panel which is initially perfectly plane,

this stage starts when the shear force reaches the critical value

predicted by plate buckling theory. The stress in the direction of

the tension diagonal continues to increase as the applied shear

force increases beyond the critical shear force. A field of

tensile stresses of the type shoWn in Fig. 6b develops, and it is

the source of the post-buckling shear strength of the panel. This

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304.10

state of stress is termed Iltension field action-shearll.

-8

Evidence of the redistribution of stresses from the beam

action type to the tension field action type in a plate girder

web is presented in Fig. 7, a photograph ofa longitudinally

stiffened test girder after it has been subjected to the ultimate

shear force (2). The diagonal yield line patterns indicate the

development of separate tension fields in the subpanels formed by

the longitudinal stiffener.

Based on observations of test girders and the shear strength

theory developed by Basler((2.), the tension field model shown in

·Fig. 8 has been used to estimate the shear strength of longitudi­

nally stiffened plate girders (£). The following assumptions were

used:

(1) The ultimate shear strength of a longitudinally

stiffened panel is the sum of the shear strengths

of the twosubpanels;

(2) The shear strength of a subpanel is' the sum of the

beam action contribution and the tension field action

contribution;

(3) The beam action contribution is the shear force

carried by the web at the theoretical web buckling

stress;

(4) The tension field contribution is the vertical

component of the tension field force (see Fig. 8);

304.10 -9

(5) The ultimate subpanel shear forces will be reached

when the combination of beam action and tension field

action stresses cause yielding in the web.

The ultimate shear force of a longitudinally stiffened panel

Vu ' non-dimensionalized by the plastic shear force (the product

of the web area and the yield stress in shear), is plotted against

the web slenderness ratio D/t in Fig. 9 for constant values of

yield strain e and aspect ratio diD. Curves are shown in the. y

figure for three different longitudinal stiffener positions,

illustrating that the stiffener position which provides the

highest shear strength varies with the web slenderness ratio.

The optimum longitudina~ stiffener position moves from mid~depth

toward the compression flange as the web slenderness ratio

increases.

Using the optimum longitudinal stiffener position, the increase

in the shear strength of a plate girder panel due to the use of a

longitudinal stiffener is indicated in Fig. 10 as a function of the

web slenderness ratio. The yield strain and aspect ratio are

constants in this figure and have the same values as those used in

Fig. 9. According to.the theory,the maximum increase in shear

strength is about 26% for a slenderness ratio of about 160 with

an increase of almost 10% for the entire range 120 ~ D/t ~400

(see Fig. 10). The increase in shear strength due to the longi-

tudinal stiffener will be slightly different from that shown in

. Fig. 10 for other values of yield strain and aspect ratio.

304.10

The results of seven longitudinally stiffened plate girder

tests were used to check the shear strength theory described

above (~). In these tests three panel aspect ratios (d/D = 0.75,

1.0 and 1.5) and.three longitudinal stiffener positions (Dl/D =

1/2, 1/3 and 1/5) were used. The web slenderness ratio varied

from 256 to 276. For the seven tests the ratio of the experi­

mentally obtained ultimate loads P ex to the ultimate loads pre­u

dieted by the theory pth ranged from 1.00 to 1.18 with a meanu

value of 1.10. The use of longitu¢inal stiffeners in the test

specimens resulted in an increase in shear strength ranging from

6% to 38%. The ratios of P ex and P th to.the plastic shear loadu u

Pp are shown in Fig. 11 to provide a visual indication of the

correlation of the shear strength theory with the seven test

results. In summary, the tests results indicate that the theory

provides a reliable but somewhat conservative estimate of the

actual shear strength of longitudinally stiffened plate girders

and that the use of longitudinal stiffeners can lead toa sub-

stantial increase in shear strength.

304.10

LONGITUDINAL STIFFENER REQUIREMENTS

Three requirements are proposed for proportioning longi­

tudinal stiffeners:

(1) a minimum width-thickness ratio to prevent premature

local buckling;

(2) a minimum stiffener rigidity to force a nodal line

in the deflected web and

(3) a minimum stiffener column strength to avoid pre-

mature lateral buckling.

The first requirement is the same for both bending and shear.

Although the second requirement is intended to help ensure that

web deflections are controlled for both loading cases, for pure

bending the purpose is to prevent a redistribution of stress

from the web to the compression flange while for high shear the

rigidity requirement is to ensure that separate tension fields

will form in the subpanels. Correspondingly, the numerical

values of the minimum stiffener rigidity are different for the

two loading cases (~). For the bending case,the compressive

.force used in checking the third requirement is that assigned to

the stiffener section according to beam theory. In the case of

high shear the minimum stiffener column strength is required to

transfer the horizontal components of the tension fields from one

side of a panel to the other (see Fig. 8).

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304.10

SUMMARY

The results of an investigation of the influence of longi­

tudinal stiffeners on the behavior and strength of plate girders

have been summarized. For the case of pure bending it has been

found that longitudinal stiffeners, by controlling lateral web

deflections, help to maintain a linear bending stress distri­

bution and thus eliminate the need for a reduction in the flange

stress. For g girder panel subjected to high shear, longitudinal

stiffeners force the formation of separate tension fields in the

subpanels. In both loading cases, a substantial increase in

strength can be achieved through the use of longitudinal stiffeners.

Requirements for proportioning longitudinal stiffeners have

been described. These requirements are applicable for both of the

loading cases considered. The problem of positioning longitudinal

stiffeners has also been treated for the two loading cases.

The study has been limited to the static strength of

symmetrical, longitudinally stiffened steel plate girders. Since

longitudinal stiffeners are effective in controlling lateral web

deflections, they should also have a beneficial effect on the

fatigue strength of plate girders. The effect of longitudinal

stiffeners on the behavior and strength of unsymmetrical girders

has not yet been determined. Research programs are in progress at

Lehigh University to investigate these related problems.

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304.10

FIGURES

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304.10 -14

0=55"

Specimen LB I

dID =1.0 Dlt =444

120k

Deflection:I I

o 0.1" 0.2"

Scale For Stress:, , ,o 5 10ksi

-- Measured

-- Beam Theory

. (a) Lateral Web Deflections (b) Stress Distributions

Fig. 1 Test Measurements on a Transversely Stiffened Girder

0=55"

Specimen LB3

dID = 1.0 Dlt =447

Scale For Deflection:, I

o 0.1" 0.2"

t=0.123"

.For Stress I, , I

o 5 10ksi

-_.- Measured

-- Beam Theory

(a) Latera I Web Deflections (b) Stress Distributions

Fig. 2 Test Measurements on a Longitudinally Stiffened Girder

304.10

~~

J: 40l-t!)

ZLLIa::I-00

30(!)zC5zLi.JCD 20zLLI00<tLLI

10a::u~

o

+1 0 1/0 = ~5

Ey =0.0012

0.5

0

100 200 300 400

WEB SLENDER NESS RATIO,Dlt

-15

Fig. 3 Increase in Bending Strength.Due to a LongitudinalStiffener

1.0

0.9

0.8PI,

Py. 0.7

0.6

0.5

TESTdiDDlt

LB61.0

407

o0.6299

E0.4401

30.6300

40.45400

Fig. 4 Correlation of Bending Strength Theory With Test Results

304.1..0 -16

-

~V

ShearI Panel

0

-V

f

l~ d -IFig. 5 Typical Shear Panel

(a) Beam Theory Shear Stress

(b) Tension Field Stress

Fig. 6 Stress States in a Plate Girder Web

304.10 -17

Fig. 7 Longitudinally Stiffened Test Girder After Shear Test

d . I

Fig. 8 Tension Field Model for a Longitudinally Stiffened Panel

304.10

0.8

0.6

0.4

0.2

Ey =0.0012 tJl.~ . t 0

diD =1.0

1 d .1

-18

o 100 200

WEB SLENDERNESS RATIO. Olt

300 400

Fig. 9 Shear Strength Curves for diD = 1.0

-:.l!~

J:I- 30C)ZllJa::I-(J)

a:: 20«llJJ:(J)-

~10

llJ(J)

«llJa::u~

0 100 200

WEB SLENDERNESS RATIO. Olt

Ey=0.0012 ]0

diD =1.0

I. d ./

300 400

Fig. 10 Increase in Shear Strength Due to Longitudinal Stiffener

304.10 -19

1.0

0.9

LS4-T21.0260

1/2

LS3·T2 LS3-T3 LS4-TI1.5 0.75 1.0276 276 2601/3 1/3 115

LS3·TI1.52761/3

LS I-T2 LS2-TI1.0 1.0

256 275~3 ~3

EJ=:tI t I

0.5

TESTdiDOltOliO

0.6

p 0.8Ip'

p 0.7

Fig. 11 Correlation of Shear Strength Theory With Test Results

304.10

1.

2.

3.

4.

5.

6.

7.

REFERENCES

AASHO. Standard Specifications for Highway Bridges;8th Ed., 1961.

BASLER, K., YEN, B. T., MUELLER, J. A. ANDTHURLIMANN, B. Web Buckling Tests on Welded' P.late

Girders. Bulletin No. 64,Welding Research, Coun,cil, Sept. 1960.

COOPER, P. B. Pla~e Girders. Chapter 8 of StructuralSteel Design, Ronald Press, 1964 .

..BASLER, K. AND THURLIMANN, B. Strength of Plate

Girders in Bending. Trans. ASCE, Vol. 128,Part II, 1963.

BASLER, K. Strength of Plate Girders in Shear. Trans.ASCE, Vol~ 128, Part II, 1963.

COOPER, P. B. Static Strength of. Longitudinallystiffened Plate Girders. Fritz EngineeringLaboratory Report No. 304.9, Lehigh Univers.ity,June 1966.

D'APICE, M. A., FIELDING, D. J. AND COOPER, P. B.,Static Tests on Longitudinally Stiffened.PlateGirders. Fritz Engineering Laboratory ReportNo. 304.8, Lehigh' University, May 1966

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304.10

ACKNOWLEDGMENTS

This paper is based on research conducted in the Department

of Civil Engineering, Fritz Engineering Laboratory, Lehigh

University, Bethlehem, Pennsylvania. Lynn S. Beedle is Acting

Chairman of the Department and Director of the Laboratory.

The financial support provided by the following sponsors is

gratefully acknowledged: the Pennsylvania Department of Highways,

the U. S. Department of Commerce - Bureau of Public Roads, the

American Iron and Steel Institute and the Welding Research Council.

The guidance of Alexis Ostapenko, Director of the project, in

preparing the manuscript is sincerely appreciated.

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