Lehigh UniversityLehigh Preserve

Fritz Laboratory Reports Civil and Environmental Engineering

1960

Web buckling tests on welded plate girders. Part 4:tests on plate girders subjected to combinedbending and shear. WRC Bulletin, 64, (September1960), Reprint No. 165 (60-5)K. Basler

J. A. Mueller

B. Thurlimann

B. T. Yen

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Recommended CitationBasler, K.; Mueller, J. A.; Thurlimann, B.; and Yen, B. T., "Web buckling tests on welded plate girders. Part 4: tests on plate girderssubjected to combined bending and shear. WRC Bulletin, 64, (September 1960), Reprint No. 165 (60-5)" (1960). Fritz LaboratoryReports. Paper 67.http://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports/67

~ j '.

Welded Plate Girders, Repert No. 251-14

Submitted te theWelded Plate Girder Project Comm1ttee

for approval as a pub11cat10B

WEB BUCKLING T,~TS ON WELDEDPLAT-E 'GIRDERS

Part 4: Tests OE. Plate Gi'rders Sub,jected toCombined Bending and Shear

by

"Basler, K., Yen. Bo -. T., Mueller, Jo A., amd Thurl1maJiIl, Bo

Frit~ Em.gineering Lab0-rater,yLehigh University

Bethlehem, PennsylvaniaMay 1960

This is the ~ourth part of a report on plate girder

test,s conducted at Lehigh Universityo Reference must

be made to the first part, Report Noo 251~11, for the

scheme of publication, the properties of the girders,

the nomenclature, and the list o~ referenceso

-1-

4.1 Introduction

While the girders discussed in part 2 and part 3 were

sUbjected to pure bending and high shear respectively,

those in this test series were studied under the combined

action of bending and shear. It is the purpose or this

report to explain how the investigation was carried out

and what observational facts were obtained.

Each bending girder discussed in part 2 consisted of

a middle section, which was the test section proper, and

two end pieces which had stronger webs than the test

section. Since failure always ,occurred as intended in the

preselected teat section, it was possible to splice to­

gether the undamaged end pieces and form new girders to

be tested to destruction. This was done with the end

pieces of girders GI, G2, G4, and G5 and the resulting

girders are termed 'El, E2, E4, and E5, respe?tively. 1£

these spliced specimens were tested in the setup sketched

in Fig. 1.3, bending failures would almost invariably result

because flange yielding would always precede exhaustion of

the shear strength of the relatively strong web. ThUS, in

order to achieve a more severe interaction between bending

and shear, these girders had to be modified.

-2-

The adaptation decided upon was to weld cover plates

to both flanges of the spliced portions. Using different

sizes and numbers of cover plates for the group of girders

having the same web thickness, girdersEl,E4, and E5,

the shear to normal stress ratio S = ~/a (Sec. 1,1) was

sUfficiently adjusted to render a variety of combinations

of bending and shear stresses. For E4, cover plates 15ft x

7/8" were added such that the girder would fail simul­

taneously in bending and shear. Girder ~ was assigned

one more cover pla.te thanE4 to ensure shear .failures,

this additional plate being 18 n x 3/4". On the other hand,

girder E5 had no cover plates.

Having provided a sufficient range of the ratio of

shear stress to normal stress to investigate its influ­

ence, the effect of the web slenderness ratio was the next

thing to be studied. Girders ~2, G8, and G9 were designed

for this purpose. Using the end pieces of girder G2 with

added cover plates of 16" x 1", girder E2 was formed with

a one haIr inch web. a8 and G9, two new girders, had the

same .span, de.pth, and fabrication deta.ils as theE-girders,

but had quite slender webs of t~ee~aixteenths and one­

eighth of an i.noh, resulting in web slenderness ra tics of

about 254 and 382 respectively.

-3-

Thus, this third phase of the investigation consisted

of a total of six girders referred to as El,E2, E4, E5,

G8, and G9. For the cross sectional dimensions and con­

stants, material properties, and the girders' reference

loads and deflections, the summary tables of Part 1 must

be consulted.

4.2 Test Setup

The girders of this series we~e tested in the 5,000,000

pound Baldwin Universal Testing Machine at Fritz Engineering

Laboratory. With the movable crosshead of the machines

guided by massive columns, the movement is strictly vertical

without horizontal' or torsional displacements. For this

reason, all girders were mounted on rollers at both supports 0

Although they had one degree of freedom whIle resting in the

test bed, the girders became stable as Boon as the load was

applied. This systeM is illustrated in Fig. 103.

In the design of the girders subjec·ted to bending or

shear, ~ predetermined test section could be designedo In

this series of girders subjected to combined bending and

shear, the test setup precludes any such section and

failure can occur anywhere. The entire girder is the test

section proper. If failure should occur under the point

of load application, it would be difficult to trace its

primary cause. While this is a disadvantage from the

-4-

rese,arch point of view, these tests simulate true field

conditions. The setup used, when inverted, reproduces the

conditions at an intermediate support of a continuous

girder where the ends 0f the test girder are at the points

of inflection.

Appearing in Fig. 4.1 is the test setup, where a

girder is seen positioned in the testing machine. Besides

the elevation, a plan view of the girder is provided which

shows the lateral brac~ng system. Incorporated in this

system were the supports, the loading point, and two

lateral bracing pipes. While the friction forces at the

loa.ding surface fixed the girder against any lateral

buckling at i ts 1Uids'pan,- the support po ints under load

eliminated lateral movements in their vicinity. The two

lateral braces were located at quarter poi~ts with their

far ends attached to a rigid bracing beam. The conmecting

pins at both ends of each bracing pipe were fitted snug in

the holes so that, unlike the setup ror the bending girders,

no later~l movement of girder was allowed before the braces

actedo

Of importance in the subsequent presentation of results

is the ori:entation of a girder. To this end, the 'Cartesian

coordinate system shown in Fig. 1.3 is needed. All draw­

ings containing a girder1s or panel1s outline will be pre­

sented such that the x-axis points to the right, that ~s,

the lateral braces are hidden behind the girder.

-5-

4.3 Test Results

In this section the tests conducted on the six

girders are explained and the results of all basic obser­

va.tions .presented. Among the "bas 10" measurements made

throughout the investigation are the centerline de£lection,

the state of strain at a panel1s center, the extension of

a panel's diagonals, the strains in a transverse stiffener,

and the web deflection at the centers of certain panels.

Since the method of presentation is Bubstantially the

same for all specimens, the data will be thoroughly ex­

plained for girder El only.

F0r a survey of properties of girder -El, Table I. 1

in part 1 of this report should be conBultedo 'There it is

shewn that the web depth to web thickness ratie was ~ = 131,

and that a total of four tests were run which pr~duced

failure in panels of aspect ratios a = 3.0, 1.5, 1.5, and

loa.

The load-deflection curve, Fig. 4.2, together with

the sketches shown in Fig. 4.3, completely describe the

testing.histery 0f girder El. From these figures it is

seen that the specimen was loaded up to load No. 7 at 540

kips in its first loading cycle. After reducing to zero,

this load was alternately reapplied and reduced to near

zero ten times without causing any additional deflections~

-6-

It is seen that when the applied load was increased above

load No.7, the highest load which could be statically

maintained, the ultimate load, was 555 kipso Upon un~

loading to load N0. 15, the first test was c'omplete. In

this test a clear shear failure occurred in the long panel

where a = 3.0, as is indicated by the right hand sketch in

the first row of Fig. 4.3. A photograph of the failed

panel is included as Fig. 4.4 where it can be seen that

permanent web distortion was located along the general

direction of the yield lines. However, this distortion

was small enough that the panel could be reinforced by

two pairs of transverse stiffeners fitted to the distorted

shape and welded to the web at its third points, as seen

in the third sketch of Fig. 4030 This reinforcing operation

1s always indicated by a welding symbol in the load-deflec­

tion diagrams.

The second test, ~2, extended from load Noo 16 to

load No. 24- According to the definition adopted in Sec.

2·4, the ultimate load for this test was attained at load

Noo 22, where % = 580.kips. Occurring i~ the panel to

the right of the loading point, this failure was identified

as a shear failure, as the photograph of Fig. 4.5 reveals.

Fig. 406 is a photograph taken of the far side of this

~ailed panel. Evidentally, the width o~ the yielded strip

as appearing in these pictures must not be identified

-7-

with the effective width of a tension field, since they

only reveal surface conditions. As pointed out berore,

Fig. 3012, the stresses at the surface are due to both

plate membrane and bending stresses, whereas the tension

field is entirely a membrane actlono

After completion of the second test, the ~ailed

panel was reinforced by welding two single, half inch

thick stiffeners to the far side o~ the web, Fig. 4~3,

third sketch on the left. Upon loading again in test T3,

the recorded centerline deflections rollowed the pre~

dieted ones fairly well up until load No. 29. It is

interesting to observe that the load-deflection curve

exhibited a type of hysteresis loop. This was due to the

fact that before being reinforced, the panels acting in

a tension field manner underwent greater shear deformations

than those predicted by simple beam action. However, after

adding rigid and closely spaced transverse stiffeners, the

shear force in this panel was essentially carried by beam

action and the predicted deflections were followed more

closelyo

Following the load-deflection curve again, the load

was increased to 568 kips and then dropped back to lead

Noo 31, 542 kips, which was less than the Pu obtained from

T20 Since calculations indicated a load well in excess of

the ultimate load of T2, thi,s action was unexpectedo Upon

investigation, it was found to be due to failure or a

reinforcing stiffener at X = -10ge This stiffener, welded

with the one on the opposite side of the web as a rein­

forcement after test Tl to form a. 8n x 1/4" plats,9 did not

act similar to the original stiffeners of exactly the same

sizeo The web distortion'remaining from the previous test

affected the stiffener, which acted as a post, and caused

the failure 0 The repair of this local failure was accom­

plished by welding a strong compression diagonal in the

end panel, as seen from the fourth sketch on the left of

Figo 403. Then, the buckled stlffener~ relieved of its

post action, endured any ~urther- increases in the web

deflections throughout the following tests.

This diagonal reinforcement 9 added between load Noo

32 and load No. 33, is. again indicated in Figo 402 by a

welding symbol$ Continuing with T3, an ultimate load of

Pu = 634 kips was reached at load No. 39 and an unloading

curve furnished by loads Noo 40 and 410 Again~ failure

was in a shear pattern which occurred in the end panel

extending from X = +84 to X = +1590 The corresponding

sketch in Figo 403 shows the additional yield lines created

by this third test, while F1go 407 gives a photographic

verification of this failure 0

-9-

Having produced a shear failure in each panel of

the original girder, the testing could be regarded as

finished. However, to satisfy curiosity as to how strong

the newly formed square panels on the left side were, the

right end panel was reinforced and a fourth test perrormedo

Although subjected to great initial distortions, these

square panels were strong enough to allow an increase in

the ultimate load of 50 kips, with Pu = 684 kips, and held

through quite an amount of straining. Although no unload­

ing had taken place due to this straining, the testing of

girder El was ended with load No. 530

In order to distinguish the tests conducted on panels

which failed in a previous ultimate load test from original

tests, the letter r, referring to retesting, is added to

their ultimate loads l~ted in Table 4.1. Since the rein­

forcing stiffeners were cut to the shape or the distorted

web, the panel borders were not in a planeo Therefore,

the test results should not be used other than to show

that under unfavorable circumstances certain loads could

still be carriede

Attention 1s now focused to Flge 488, a diagram which

compares the actual state of stress in the web to that

predicted by beam theory. The comparison appears at the

very location on the girder where the strain rosette

-10-

measurements were taken~ The loads Nose 17, 18, 19, and

20 were selected as representative ones for this study.

The choice was influenced by the desire to have these

measurements made within the range of a previous loading

cycle (Seco 3.4), and preferably in the particular test

where failure occurred in the instrumented panel.

All principal stresses were determined in the same

manner described in Sec. 3.4, where the solid stress

vectors are the experimental results and the dotted ones

computed according to the beam theoryo Again, the com­

parison between experimental and theoretical stresses shows

that, even in girders with relatively sturdy webs, a tension

field action occurs.

The above conclusion is also confirmed by strain

measurements recorded on the pair of intermediate stiffeners

bordering the failed panel. In Fig. 4.9 is a curve of

applied load versus sti~fener strain as observed throughout

the second test on this girder. The resulting strain,

plotted as abscissa, is the average of four SR-4 gages.

Since the sti£feners used thrOUghout the entire investiga­

tion were the same, the same layout of gages was used as

for girders G6 and G7. For a proper interpretation of

this group of measurements, reference should be made to

Sec o 304.

-ll~

Another basic observation consistently made was the

measurement of the change in distance'between two points

at the ends o~ the panells diagonals 0 With gage marks

drilled in girder panels' corners, the changes in the

diagonals were obtained ,with gages which were similar to

Whittemore gage and specially adapted for different panel

lengths 0 All readings were made in the same way as de­

scribed in Seco 3.50 As an example, Figo 4$10 is included

showing the movements obtained in Tl and T2, both observed

in the same panel shown in Fig. 4~3 where the gage points

for these measurements are also showno The distance be-

tween the points in the upper left and lower right was

shortened (negative in sign) since this is a "compression

diagonaltf~ The other diagonal was stretchedG Using a

common load ordinate, P, the shortening and extension orthe diagonals can be plotted on the same graph and Figo 4.10

resultso

Finally, in Figo 4.11 some web deflection readings as

evaluated and discussed in Sec. 203 are presented. As

before, the upper half of the figure gives the distorted

shapes of the cross sections for a limited number of lo:ads,- ,~

while the graphs at the bottom give complete load-deflection

curves for selected points in the web~ A cross section o~

particular interest is that where the strain rosettes were

mounted, at X = +46 1/20 From the cross sectional shape

-12-

and the graph for this cross section, it is clearly seen

that the first test had a pronounced effect on this panel

such that the "initial deflections" .for the second test,

which started with load No. 16, were more than one-half

an incho For the cross section at X = +121 ~/2, it can\

be seen that the web was still quite plane at load No. 33,

just prior to the test which caused failure in this pane,l.

With this rather complete explanation of the testing

history, the failure modes, and the content of the basic

grapps of girder El, it is possible to study the perform­

ance of all the other girders without much further coMmen-

tary& Therefore, all pertinent graphs and photographs are

grouped together at the back of the report for the re-

maining girders.

In order to study anyone girder, the following pro-

cedure is suggested:

10 Referring to Table 1.1, obtain the ·properties of

the girder, the number of tests conducted, and the locations

of the failures.

20 Use the load-deflection curve to become familiar

with the girder's testing historYa The curves for girders

E2 through G9 are given in Figso 4~12, 4e 22, 4032, 4.40,

and 4050 respectively. Since the observations were re-

corded with an Engineer's level, all support movements

-13-

were readily eliminated using the principles explained in

Sec. 2.3.

3. Cons'ult the appropriate figure from ~ig. 4.13,

4023, 4.33, 4.41, to 4.51 to become in~ormed as to the

appearance of the girder before and after testing. In

addition, these figures mark the locations of the photo~

graphs presented in this report. If a frame appears in

dashed lines, the picture was 'taken from th~ far side of

the girder; if in solid lines, from the near sideo Further­

more, the location of the strain rosettes, the strain gages

on the transverse stiffeners, the measured diagonals,.and

the cross sections at which web deflections were recorded

are all shown in self-explanatory symbols. All these posi­

tions indicated are not the only places where recordings

were obtained; they are the ones at which the measurements

were taken from which graphs presented in this report were

.made. Likewise, the presence of a symbol indioating

measurements before a later test does not exclude observa­

tions with this instrument at an earlier test, but rather

indicates to which test the particular graph pert~inso

40 For the basic test measurements, select the suitable

graphs from the followings for girders E2,_ 'E4, E5, G8, and

G9 respectively:

- Fig. 4.14, 4.24, 4.34, 4.42, and 4052 for the

state of stress in the web as measured by pairs

o~ strain rosettes.

-14-

axial strain in a transverse stiffener.

- Fig. 4.16, 4.26, 4.36, 4044, and 4.54 for the

extensions of the panel diagonals.

- Fig. 4.17, 4.27, 4.37, 4.45, and 4.55 for the

web deflections at two different cross sections

or .the girder.

50 Finally, refer to the photographs or t~e girder

for the failure modes of particular interest. These photo-

graphs are:

Girder F2: Figs. 4.18, 4019, 4020, 4.• 21

'F4'o 'Figs. 4028, 4·29, 4.30, 4031, .E5: Figs. 4.38 , 4039

G8: Figs. 4.46, 4.47, 4.48, 4.49G9: Figs. 4.56, 4~57 , 4·58, 4.59

To conclude this section, a summary of all the ultimate

loads is given in Table 4.1. Here also are listed the

yield, plastic, and critical· loads of each test. The

difference between the ultimate load Pu and the maximum

load Pmax lies in their def'ini tion. Wh,ereas Pu is a

static load, the maximum load is recorded during load

~~ppllca-t-iftiI;- tha; ~~e~__.de:fml"trj;o.ns '<'P-aing gi'v,&n- in· Sec-o ' 2 ~ L~,.

404 Discussion

With the test results given, certain features which

are likely to be otherwise overlooked are presented in

this sectiono

In the description of the test setup, concern was

expressed over the lack of a well defined test section

for each girder. It was feared that failure might take

place locally at the loading point where the combination

or moment and shear was most severe and where the stress

conditions were made obscure by the load applicatlono As

the test results show, this concern was unnecessary. At

the loading point, the girder elements under compression

were braced so that they could strain harden since ,the

compression flange plate was guided by the loading device

and the web was braced by the loading stiffene~so The

tension flange, being self stabilizing, did not require

any special attention.

Although no local failure was developed at the loading

point, the details at the ends of the test girders. proved

to be of more concern. Considering, for instance, the

test of girder E4, one would assume that failure occurred

somewhere near midspan, but the actual case was an almost

Budden failure of an end panel, Figo 4028.

-16-

The reason ror such a railure is that the tension field

action cannot build up to its full extent without a

neighboring panel, unless the end post has enough bending

rigidity to serve as an anchor for the tension fieldo The

end posts made from a 12WF50 section seemed to be sufficient

for a very long panel, a = 3, where the tension rield action

is less pronounced. However, for a shorter panel, a = 1.5,

the end post collapsed in the manner shown in Fig. 407. orcourse the web slenderness also influences the end failure.

For girder G9 having an extremely thin web, the shear re­

sistance depended almost entirely on tension field action

and end failure occurred also for a stiffener spacing a = 3,

Fig. 4~57. When this happened again at the other g~rder

end, two steel plates were tightly clamped to the outstand­

ing web as shown in Fig. 4.58. Thus, the shear strength

of G9-T2 could be increased 30% as born out by the corres~

.ponding .points in the load-deflection curve, whe.re., load

Noso 17 and 20A are the ultimate loads before and after the

reinforcement respectively. In order to distinguish between

true tests and premature failures due to insufficient end

detail, the latter are marked in Table 4$1 with SUbscript

"e" 0 A detailed study of this end .post failure will be

given in the theoretical report.

-17-

Disregarding the premature failure in the end panels,

it can be seen that for girders subjected to both shear

and bending, the shear strength was hardly affected by the

bending moment. Conversely, the bending strength was not

affected by the shear force in the case of Girder G5 which

failed in a panel with closer stiffener spacing,,~ ~ 0075,

rather than in one with a = 1.5. The solution.,ot the prob­

lem of interaction between bending and shear is presented

in Ref. 7 and will be treated again in the forthcoming

theoretical report.

Briefly, the highlights revealed by the tests on this

series or girders can be summarized as follows:

Failure' of a properly proportioned girder is ~nlikely

to occur directly at the point of load application, although

the bending mom~nt is highest there o

The design:of girder ends requires speci~l attention

if the same shear strength is desired in an end panel as

within the girder.

The presence of bending moment little arfects shear

strength, that is, the interaction between bending and

shear is not a pronounced one o

**

*

-18-

In concluding, it should be recalled that the objec~

tive of the entire 'investigation was to study the problem

of web ,buckling. These tests, therefore, are or both

academic and practical value.

The academic value of this investigation is that it

demonstrates convincingly that the web buckling theory

is unable to predict the strength of plate girders with

slender webs. Also the postbuckling strength of girders

cannot be simply expressed on the basis of the critical

str~ss as is often expected, that 1s, the strengtb of

plate girders is not a function of the web slenderness

ratio aloneo Furthermore, these tests led to a new basis

for an ultim~te strength prediction.

The practical value is that, besides obtaining

solutions to some detailing problems, a new design- speci­

fication can be drafted with which more econo~ical girders

can be builta For example, in view of the ex~st~U& speci~

fication in this country, the bending girder test3~-clearly

indicate that the domain of web slenderness ratiosa~ove

170, covered so far only by girders with longitudinal

stiffeners, can be opened to plate girders with only trans­

verse stiffeners. The increase in shear strength, as

e~plained by the tension field action, permits either a

saving in web area or an increase of transverse stifrener

spacings $ The third se~~e8 of the teats, containing girders

-19-

with web slenderness ratios as low as one hundred, directly

suggests a liberation of the web slenderness limitations of

unstiffened plate girders.

Finally, concerning this report, it is hoped that it

will serve an additional purpose'in providing informationI'

on the behavior of b~11t up member~, such as plate girders,

which is not discussed in standard text books or speclfica~

tion manuals.

-20-

Table 4'.1

Summary of Reference and -Experimental Loads

Girder Test Theoretical "Experimental

Per Py Pp ·pu PI maXa

(kips) (kips) (kips) (kips) (kips)

Tl 332 826 920 555 576'El T2 402 826 920 580 598

T3 415 905 920 (634)e 656T4 506 826 920 (684) r 710

Tl 570 716 855 755 774T2 584 716 855 757 810

Tl 445 880 905 (595)e 616F4 T2 513 658 691 634 670

T3 .517 639 666 "645. 700

E5 Tl 314 248 367 3·50 359T2 322 358 386 360 364

Tl 41.5 280 368 170 180

G8 T2 56·4 410 434 (200)e 207T3 48.3 280 368 233. 241T4 57.3 280 368 (259)r 273

Tl 1209 264 35~ (96) e 101G9 T2 16.8 324 33 (150)e 155

T3 1505 264 354 158 162

5,000,000 lb. Testing Machine

)"31-1~

I"3

1-I Y2

JII

("4- 11411x~3~~-y-

)"1'4

31-1~~

II Il'4xq.

1'13'-11'2

271-6"

9"1911

Sym. AboutCl. ExceptFor Transverse Stiffeners

61-311

G4 3/~ WEB

117,1115x Va

1211x34

12"X34

15I1xv'~

6 1-3

CUT FROM

~

Typical also for Girders EI, -E2,E5,G8 a G9

I~

I

I

Fig. 4.1 Plate Girder E4 with Test Setup

P[k]

700

600

500

400

300

200

100

20

Vth

T3

Vth

., T4 ------

".........--",'-'\I !/----, ,'----,.." 0 0 ~ ...

,.., 0 50 51 ~ 53~I 0 49 52

48J

~cr

GIRDER EI

I I 054 I ~2 3 vet-Lin]

Fig. 4.2 Loa1d'-Defllecl'ion Curve. Girder EI

~III

-, I

AFTER TEST

rE I-TI

+159

I

BEFORE-'r -51

9 -PiI

rr i l '0... 1 ,P 1"I I . II )·.. x! ~t I I :II I. 10" 1 '0

I

X= -159

I

L F.4.5 a F.4.6..J

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if II '0.. i, P II I i II I 1 ........

II I JO" ! Il.L "0

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EI-T2

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u~'lu ~

1//~i

II ! III

E I-T4

1I EI-T3I

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iI

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: :I IJ 1

Fig. 4.3 Girdler EI Before and After Tests

Fige 4.4 Shear Failure. E1-TI

Fige 4.5 Shear Failure. EI ~T2 1 Near Si'de

Fig. 4.6 Shear Failure. EI-T2. Far Si'de

Fig. 4.7 Typical End Panel Failure of Plate Girder (EI)

i ~ c.,o 20

~ II

III -k2()'\, ~

20II 11

/If 19

II II /1-II I I ' ()~ 19/'"II II (X=+16Y2) '.<.. (X =+79),I /""11 yt 11 y= +21 19, 20 Y=+2111 II , ~ 18/ 1811

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11 II11 II

~~~7/ 17II IIII

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II II SR4 GagesII r--Ut.-II --- --- --- --t rJ---II

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I

IIX=+46Y2II II

II II y=oII IIII 11 Z=oII I IIII

III

-l'f=+16Y2) (X=+79)~l-II II

\II II

!LJL UL I Y= +21 Y= ... 21 I

!

I I r I I I I J I I 1 Po ne I ScaIeo 10 20 [in]

t----... Computed

I------l.... MeasuredI I I I r I , r I I I Stress Scaleo 5 10 [ksi]

Fig. 4.8 Principal Stresses at Panel Center, Girder EI

.~·tos.........V)

oo

ooN

oor<>

ooq-

ooL{)

rodI

oo<.0

\2 Lo~~

o~~

o ~~

-l!!!!!II~------lI---+---+--+----f----+--+-----+------f.--+----+------I--~ 0

o

T2

22210----0...............023

Lo

_-+__ 9~24_-+-1_--+-__0_16_-+--_+- _--+-__

P_______2~______ 21 [k]

230\ 0'\020

Girder E I \400

(X =t 16 ) d (X=+79 )

Neg.tiL batw. Y=+2 I an Y=- 21

Pos.l:l L batw. (X=tI6) and (X=t79)Y=-21 Y=+21

P[k]

-11------1'1--150-000-0

1-5---+---__9,8,1,8,9

~L[inJ -0.05 0 +0.05 L1L [in] -0.2 0 +0.2

Fig- 4.10 Displacements in the Direction of Panel Diagionals. Girder EI

w

w~o-II

~>-+IIX

w-~<;~>-+IIX

Ioo<.0N

Im ~

I I

dzo~o...J

om+

LO-;

tN

I I II ~, I I

~: r;; :~:....--::::..I=------__e-~-e_~

-(\J

w-~q­+II

><

-Nw-::::::(\J

+II

X

v~ [in]

Girder E 2

32

--.E.Pcr

Vth

TIVth

400

700

500

P[k]800

600

300

I _ _ _ T2 -_----------.....---" , ..--, " .... -- ......,,, " .... ------

" I ,I " ' '~ \ / -,

I" ~' ~ ~ a 36 b' \190 ~o----a3233 34 35 P 37 380/..t-Py 2, ~ Y

018 031

I !0)17 030

~/ I~OO16k Pcr /29

1/15

/28

//14 (277/13 /26

200 +1112 /25100 +20 all 024

alii 12213 i I I I I 039

I ~,of '-v-

Fig. 4.12 Loa,d-Deflection Curv1e, Gir·der E2

BEFORE TEST AFTER TEST

tD_X

~--- j-

~ ~" 4.18

" ~,~ iE2-TI"

i !- 4.19

Ttt

II

TIIII

E2-T2

I 4.20

Fig. 4.13 Girder E2 Before an1d After Tests

E2X= +46Y2

y=oZ= 0

~/ '3229 r ,7 '29

27/'27

32 29

2ef

x

Il!

IYti

-!-.II

II

I

t-----..... ComputedI I I I I I I I t I I Panel Scaleo 10 20 [in]

I I I I I I I I I I I Stress Scale )r Measuredo 5 IO[ksi]

Fig. 4.14 Principal Stresses at Panel Center, Girder E2

N

C\JC\J¢ 0 li">o ww.-a> II L-

+ >- \U (])-cII L-X ill

~ LI (])

C(])

~co bi

~7~C\I

... d (])V)I ...(])

>tOo ~ V)

~o/ ~CtoL-a l-

I to

0 0 0 m .=0 0 0 rt)

"it <D q (\J 0 c

~ f()'OO_6_0-0 6 0 b 6 0I .;000 L-

a.. ~ tf)(\J - 0 en co "" to U') "it ", +-l...-\ tOrt) tf') tf) (\J (\J (\J (\J (\J (\J C\I V)

to.;<«

aLO+~

tilu::

P[k]

Girder E2T2

-0.1 0 +0.1

Displacements in the Direction of Panel Diagonals, Gird'er E2

I I

35 34 33 320-------------0--0--0

31b

3~29 0 600

(X=-+77V8) (X=+15~8)

Pos. ~L betw. y = +20 and Y=-203/S

(X=t771t4) (X=tI53/4)

Neg.l1L betw. Y=-211t2 and Y=+20'tS

tiL [in] - 0.2

Fig. 4.16

NW

~

NI

NNOw-Ui II

v>­+IIX

C\i.

~f ~ t::!£ !!2 ~ ~ £::! :: Q~--~-._1__~--l__l __ 1__ !__• 0

a...~ 0 0 0 0- 0 0 0 0,..... to f{)

'itrf) _ 0 m a:> f"-- CD LO V f'()

~I-~-r:>.:....~--~--";--~--~--~~~-__-_-__- __-_-__-----r------J.O

o to:; doo(/) 0

en lO C\JI I I

o ~z

ore~N LO m

+ + +

Fig. 4.18 Gir,der E2 at Ultimate Loa'd

l-.....

VI(])

l-

NUJ

....(])

~

lDr£

" -. " 0'. +

0Q)

t/)

."~

toLL

'"'I-0

to+

(])£::)

0"0

~

C'ii:

Fig. 4.20 Appearance of Girder E2 After Testing (T2)

...-.-.NI--

I

N~

Q)

C'\f::10

u::Co

·VicQ)

~

0+­10

.;00+­Q)

C

Vt. [in]

Girder E4

Vth

T2 -f T3 -------

033

032

P[kJ

300

Rk P / n _---..... .".-- .....rp ..... __ - \ ". "~Pv ~--, " ,,""" b/'~,..... , .."--,,,....~R '\ /' 6' 40'

,.,,", '\, 0 0 ~Y if \10 ({ ~50 36 37 38 39 \

,_ ,f 27 28 2901 \160 V;026 34 ,

/ . ,l I

iff 24

411'Z

23

#/200+ il'/21

100 +20010 020

o1~8J ! 3Odj31 i I I I I 0'42 I ~~\ \ I 2 3

IOx540k'~ ~

400

700

500

600

Fig'. 4.22 Loa-d--Deflection Curve. Gird'er E4

BEFORE TEST AFTER TEST

1\~~~ ,~~~ rrIj

'·~iliI

I 'l"u.J I

t--\4.28 --\\

E4.:r I \\

+46 ~2+84 +1I6/'2-84 X[in]

1 YI a....

~J,P It

~I i.I ~X

1\

/!- II

~ "0 1

I I I II II-159

[UIUIT] I[IT]-134-109 -59 -34

r --,

E4-T2

L 4.30 a 4.31 ---l

E4-T3

I+Z7

TIIII

4.29

,. ,~\

Fig. 4.23 Girder E4 Before an1d Aft,er Tests

r-,. ~.

15"'- ~flJfS CJO~ tt-l

~15

)- 15 II ! II~

~, 13 ~~ If II

'13 /~II 11

~ 13 II I II13 ~ ~ II II

~~II I 11/ II yt I,I' II,I

II~"I' 11I' II,I

L1

IIII

--- --~ II .~II XII I

II'

IE4II

II X=-46!t211Ii

!Y=o

II Z=o11II 11; I,

?

h II

t--lL LJL

I----~sa~ Measured

1---.... ComputedI I r I I I , I I I I Panel Scaleo 10 20 [in]

I I I I I I I I I I I S'tress Scaleo 5 10[k50

Fig. 4.25 Axial Strain in a Transvers,e Stiffener. Girder E4

vw

.:(J).....c:Q.)

()

v-va roowr-~~ \iJII

t: x0

(\J

dI

'-

~~ ~ dI

~1r~

~C\J 009

~ I I 0?='- ---.:;-~

~8 0

...... 0

Cl.6 0 '0 'l\t

0 0 0<.D V C\J

d+

P[k]

(X=-15) (X= -77)Neg.liLbetw. Y=+21 and Y=-211;4

(X= -15 3/4) and (X =-77 )y= - 20 Y=+20

Pos. aL batw.

L\L [in] -0.1 -0.05

I,

+0.05

Girder E4

TI

+0.1 +0.15

Fige 4.26 Displacements in the Direction of Panel Diagonals. Girder E4

vw9

C\JI

10I

c

(5 ll)

'; d"0u

(J) 0

enI

dzo<tg

o

Fig. 4.28 Premature Failure in End Panel. Girder E4 .

Fig. 4.29 Gird'er E4. After Test'ing

to' ... _

~ ~.. t .. .... . ...

Fig. 4.30 Failure of Girder E4 in Test T2. Near Side

Fig. 4.31 Failure of Girder E4 in Test 21 Far Si'd,e

II)

w

LOW

Q)

>...::s

()

BEFORE TEST AFTER TEST

~I

-159

y

Xun]

E5-TI

E5-T2

L

,d Aft,er TestsE5 Before anGirderFig. 4.33

(\

E5X=-46 ~2

y= 0Z=o

I I f I I I I I I I I Panel Scolea 10 20 [in]

t--- - ~ Computed

1----.....;:),... MeasuredI I I I I I I I I I I Stress Scalea 5 10 [ksi]

Fig. 4.34 Principal Stresses at Panel Center. Gir·der E5

LC')w

a+

o

a.....

~o

\IIaI

U1(\JV<ii'wt-,?>-

II

x

N 0 0o 0f"t1 C\J

Lt)W

10(\1w~

(\I

Q ~ij~~====!=!-~=WI~I'P i-i-i-~I

~w

~...0.... toQ) d

0"0(,,)

z (f)

't:) 002

.~

'".....s:([)

EQ)U10c..'"o

LONOW..:::::.. II

C\J)­+II

X

LONOW":::::-'II

w)-~III

X

C\II

LO

I

mI

om+

l{')C\.1W~

ill~

III

><

oa(\j

o

P[k]

+1.0 liLUn]

Girder E5

T2

+0.5~0.5-1.0

28o

29~27

2\\.:

\\23°100

~-+-----t----+-----+-30,21.30a

(X= -15) (X = - 77)Neg.l\L betw. Y 20 1 and I=+ /2 Y=-20 /2

(X= -15) (X=-77)Pos.dL betw. V=-201/2 and Y=+20

Fig. 4.37 Web Deflections. Gir,d,er E5

Fig. 4.38 Appearance of Girder E5 after Testing

Fig. 4.39 Detail of Failure, Gir,der E5, Test T2

BEFORE TESTy

G8-T2

G8-T3

G8-T4

Fig. 4.41 Id After Tests.Ga Before anGirder

E·IO

G8T3

X=+84Y=Q

~Pcr

P[k]

100

200

G8T2

X=+84y=o

O .2013'6-0~":'="':='-----+-1----+1----+---~~iiiiiJIl-3 I

o -0.1 -0.2 -0.3 E·IO -0.1 -0.2

Fig. 4.42 Principal Stresses at Panel Center. Girder G8

P[k]

100

200

o~·

25 ~e

24

It.I

iIi I !!

~~ ~ 25IIII

I IIIIIi II ::Q2S,(" Q~ 2 .;11II IIII Yt II.

24', ~ ~23II IIII II

"" I 27,/II

iII

II II 23 , ' /h II , 22 /II I I:

~¥22II

LIt 22 ~24 /."

II II/I IIII ---rr- .. -....,. --- ---II

I

II XtlII II G8II 11[I II

X=+46Y2IiII II

IIIII

I

II Y=QIIIIII Z=oII II

II IIII II

III I II

III

~LJL

I I I I I I I I I I I Panel Scalea 10 20[in]

r---- .... Computed

t-------i..... MeasuredJ I I I I J I I I I J Stress Scalea 5 10 [ksiJ

Fig. 4.43 Axial Strain in a Transv·erse Stiffener. Girder G8

Girder G8

T3

230\

10\220022

26o

~025\ 20

024

(X=+16) (X=+78)Pos.liL betw. andY=-21 Y=+21

(X=+16) (x =+-78)Neg.~L betw. Qnd

Y=+21 Y=-21

____+-- 021 I IO.;;;;.28~_---,,_

~L[in] -0.1 0 +0.1 +0.2 +0.3

Fig. 4.44 Displacements in the Direction of Panel Diagonals, Girder 68

co<J)

o

x

eDNO(!)-, II

(\j>-

'+II

X

eDNOC)-' IIc.D>-'d'+II

Ioo(\J

t;j{;;e

III

~\ . m~'"::,--.N oq------.

N rt>____.....N ~ ._

I NINo

ooC\J

ItoT

.....2 toQ) 0ou

(f) 0

CJ')I

dz

o«o..J

I I II

l~~

·-~--·r~=LO--O I0- - __ 0

.-t:

/~(T)

/-•

m+

LO'+

:::::::::..~:

I

Fig. 4.46 App.earance of Gir,der G8 at Load No. II. Far Side

Fig. 4.47 Appearance of Gir,der G8 at Load No. I I. Near Side

Fig. 4.48 Failure of Girder G8 in Test T3

Fig. 4.49 Girder Ga After T1esfing

r<io

.c

'>

.c;>

,.c

->

JooC\J

<l>>.....:::J

()

oLO~

X[in]

BEFORE TESTy ~.4.5r7E~=====:::::y:;:r=f=:rr:r=====n======tAFTER TEST

F.4.56 -,

G9-TI

Fig. 4.51 Girder G9 Before and After T,ests

G9-T3

G9-T2

G9X=+46V2

Y=Qz=o

1------3...... Mea5ured

1------- ComputedI I I I I I I I I I I Panel Scaleo 10 20Dn]

I I I tit I I I I I Stress Scaleo 5 10 [ksi]

Fig. 4.52 Principal Stresses at Panel Center, Girder G9

0"-

N\cD

mt\lqO rt)oL..

<.!)t-~~ \Ii Q)II -c>< "-

ill.q &:

2

0\ d (1)I c:

Q.)

tI=!-.+-

(1)0 en-\ rt") Q)d II)

I L-Q)

>-t:o----o 'It

~c:toL..

(\J I-0 toI

.5c:

~O\ ~ltD

C\JL-

a .....I

V')

to'x«

~o,0

"'0m

1""1 0 0 10a.~ 0L-J 0 .¢(\J q-

~u:

28l-­{27026

P29 28 [k]

50~__-0:'-_--0\

\ 150

22:6\

\lOa

(X=+16) (X=t-78) \Pas. LiL betw. Y =-21 and Y=+21

(X=+16) (X=+:78) 250\Neg.t1Lbetw. Y=+21 and Y=-21

025 Girder G9T3

+0.6

-----I'1__01--_+--_-+-_-+--0.;;;.,2,;;;;.,3---I-I-----t--+---+-'I---+----t~-o~

~L [in] -0.4 -0.2 0 +0.2 +0.4

Fig. 4.54 Displacements in the Direction of Panel Diagonals. Girder G9

(nNO(!)_....... II

c.D>­~'

+II

X

NI

L()

I

L.

.E U")

Q) dCu

(f) 0

enI

om+

~I..:.=.J

>- (\J to+ +

Fig. 4.56 Failure of Gird'er G9 in Test TI

"'I­oQ)

oc:ros-IDCl>c­o..«

·C'u:

Fig. 4.59 Failure of Girder G9 in Test T3