Welded Continuous Frames.and Their Co~ponents

TESTS ON THE STABILITY OF STEEL FRAMES

by

Yu-Chin YenLe-Wu Lu

George C. Driscoll,. Jr.

This work has been carried out as·apart of an in­vestigation sponsored jointly.. by. the WeldingResearch Council· and the·Department of the~avy

with funds furnished by the following:

American Institute of Steel Construction. American Iron and Steel Instituteaftice of Naval Research· (contract Nonr6l0(03))Bureau of Ships

. Bureau of Yards.and Docks

Reproduction of this· report in whole or in. part ispermitted for an~·purpose of the United StatesGovernment.

Fritz·Engineering LaboratoryCivil Engineering Department

Lehigh UniversityBethlehem, Pennsylvania

.. September 1961

Fritz: Engineering Laboratory· Repori No. 276.9

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ABSTRACT

In order to determine the inelastic buckling strength

of pin-ended rectangular portal frames, three sets of

frames with varying heights were testedo The frames were

fabricated from a specially rolled mild steel fence post

'section having geometric properties similar to those of a

wide flange rolled shape and were subjected to three con­

centrated load50n each beam and one at the top of each

column 0

Load, was applied by a lever system and metal dead

'weightso In each test, observations were made to deter­

mine the critical load which would cause sidesway of the

frame. Thus the maximum load carried by a frame was

determined. The test results were compared' with those

obtained from theoretical predictions.

27609 iv

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TABLE OF CONTENTS

• Page

10 INTRODUCTION 1

20 DESCRIPTION OF FRAMES 6

201 Characteristic Features of Test Frames 6

2 02 Sectional Properties 7

203 Material Properties 8

204 Loading Condition 10

205 Design of Test Frames 11

2 06 Lateria1 Bracing System 11

,30 LOADING SYSTEM AND TEST APPARATUS 13

.. 301 'Requirement and General Arrangement 13

302 Beam Loading System "14

303 Column Loading System 15I

304 Column Base Fixture 16

305 Deflection Measurement 17

306 Strain' Measurement 18

40 TEST PROCEDURE

401 Test Setup 19

402 Alignment of Test Frames 19

403 . Testing 20

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276.9

'5. TEST RESULTS AND THEIR ~CbMPARISON WITHTHEORETICAL PREDICTIONS

5.1 Test Results

5.2 Comparison of Test Results with. Theoretical Predictions

5.3 Comparison with the AISC·Formula

6. C0NCLUSIONS

7. "ACKNOWLEDGEMENTS

8. TABLES AND FIGURES

9 •. REFERENCES

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..10 INTRODUCTION

The method of plastic design in steel structures has

been rapidly accepted in this countryo So far several hun­

dreds of plastically designed buildings have been erectedo (1)

For a general introduction to the concepts involved in such

methods ~ reference can be made to (2) and (3) 0

One of the important assumptions made in the plastic

methods ot designing structures is that no buckling of any

type should occur prior to the formation of the plastic

mechanismo Local buckling and the buckling of individual

members are not the scope of this investigationo However,

the maximum load which the structure as a whole can carry

may be less than the load computed on the basis of the

strength of its individual members if sidesway is not pre­

vented o In this case the possibility exists that the frame,

as a whole~ becomes unstable before the plastic mechanism is

formedo If this occurs the structure is said to have failed

by "frame instability~o

The phenomena of overall instability are illustrated

in Figo 1 for a portal frame which is not prevented from

sideswayo

In case 1 the frame carries no primary bending moment~

therefore the behavior of the frame is analogous to that of

-2

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a centrally loaded column, in which bifurcation of equili­

brium is possible at a certain critical load o In the ~lastic

range the problems are solved both theoretically and experi­

mentallyo However, not much work has yet been done in the

inelastic rangeo

In case 2 of Figo ljl the frame carries primary bending

moments at the instant when the system passes from stable

to unstable equilibriumo This is the more practical s!tua­

tion since rigid frames are primarily designed to support

loads by bending action rather than by compressionoThe

solution to this type of stability problem becomes very

complicated and only a few attempts have been made to solve

themo Among these are the investigations by Chwalla~4,5~,

Puwein(6) and Masurjl et al(7) jl in the elastic range and

experimental work by BOlton(8), Salem(9), Gurney (10) and

Low(ll) in the inelastic range o

Until the completion of Lu I'S (12) dissertation, there

was no analytical method by which inelastic frame instability

of this type could be predicted preciselyo LUiS method is

based on ,the modified moment distribution procedure due to

Winter,et al(13), in which stiffnesses are modified for

the effect of axial force present in the members at a given

loado In this analysisjl all the required stiffness and

carry over constant~ are modified not only for the effect of

27609 . -3

axial force but also for the effect of yieldingo The method

of analysis is outlined as followso

First the frame is assumed to be braced from sidesway

instabilityo By a numerical ~ntegration process the moment

vSo angular rotation curve of the beam due to vertical load­

ing and end moment is obtainedo The end moment VS o rotation

curve of a column was developed by Ojalvo in Reference 14.Applying the boundary condition of equal beam and column

rotation at the knee of the frame~ the moment and rotation

at the knee are determined at the assumed total vertical load.

Knowing the two end moments~ the moment diagram of the

beam may be easily constructed by staticso Since the effec--

tive flexual rigidity (El)effo of the section can be deter-

mined as the instantaneous slope on the M=¢ diagram corres­

ponding to the applied moment~ the width of the analogous

column may be determined. By the method of column analogy,

stiffness and carryover factors of beam may be determined.

The stifrness factor of the column with a hinged end can be

determined as the slope of the moment-rotation curve of a

beam-column. Having the stiffness and carryover factors of

the members, it is then possible to determine the effects of

a small lateral displacement 0 By introducing arbitrary fixed·

end moments due to sidesway displacement of the column tops

and performing.a moment distribution computation for the

frame, the moments at the knees of the columns are determined.

-4

From the moments in COlunnlS~ the horizontal shear force in

the frame can be obtained. As a criterion of sidesway

buckli~g, the critical condition will be reached when the

sum of the resulting shears becomes zero. In other_ words,

no lateral force is required to push the frame sidewise as

it is in actual loading condition. The load corresponding

to this critical condition determines the inelastic buck­

ling strength of the frame. This paper presents the results

of tests made to verify the theoretical solution for the

instability of symmetrical frames loaded vertically only

and having primary bending moment in the frame.

A third type of frame instability is shown in Case 3

of Fig. 1. The frame is sUbjected to a combination of hori­

zontal and vertical forces. It deforms laterally from the

first load application. The change in. geometry introduces

additional beb4~ng moment in the columns. The whole frame

becomes unstable in this deformed ~osition much like an

eccentrically loaqed column. At a certain critical loading,

the structure continues to deform without an increase in

load. This leads the frame to a failure. This· problem is

important in the design of multi-story buildings subjected

to wind loads. Future work both analytical and experimental

is required on this subject.

-5

-.Since 1958 research on the problem of frame stability

has been carried on at Fritz Engineering Laboratory as a part

of the broad investigation titled "Welded Continuous Frames

and Their Components". Several model frames of welded box

sections .were tested. Their results will be found in'

Reference 15.

In order to verify the inelastic buckling solution in

Luts work, three sets of model frames with column slenderness

ratios of 40; 60 and 80 were proposed for test in June 1960.

The frames simulated the first floor of a three story building.

Fig. 2 shows tA8 dimension and loading of the frames. The

frames were loaded by dead weights magnified by a lever system

so that there was proportional ioading and the loading system

could sway freely with the frame. After reaching a certain

load the frames would sway sidewise and the horizontal de­

flection would increase continuously without additional load.

Thus the ultims'-te loads of the frames were obtained -and." co~­

parisons with those of the theoretical predictions were made.

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.' ... '.. ''';.•..201 Characteristic Features of Test Frames

The frames were single ba~ rectangular rigid frames as

summarized in Table 1 and detailed in Figo 30 Three sets19 .

of frames with span lengths of 87 32 inches and heights of11 11 1943 16 P 65 16 and:87 32 inches·respectively were designated

as W-I,ll W-2 and' w-3 in sequence of their heighto

The following features of the frames distinguish the

present investigatiqn from its predecessorso

(1) Frames were subjected to a primary bending moment

and were loaded into the inelastic rangeo

(2) The most practical structural shape of WF section

was a,doptedo

(3) Members of a frame were subjected, to strong axis

bending,ll therefore,ll two frames with a bracing

system between themw~re tested at the same time

'to eliminate premature lateral-torsional buckling.

(4) The lo'ad vs 0 slenderness ratio of the columns were

chosen as variables in this investigationo

27609 -7

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From the theory of eccentrically loaded columns, it is

known that the effect of eccentricity upon buckling strength

is considerable in the plastic range of buckling but tapers

off in the elastic range with increasing slenderness ratio

of the columns 0 This implies that the slenderness ratio of

the columns of a frame plays an important role in the buck­

ling strength of the frame in the inelastic rangeo Therefore,

three sets of frames with different column heights were

testedo The slenderness ratios ,of the columns were chosen

such that inelastic buckling of a frame would occur prior

to the formation of failure mechanism in simple plastic

theoryo The variables governing the buckling strength were

the load P on the column and slenderness ratio ~ of thex

column~ while the span length and cross sectlon of the member

were kept the same for the three frames o

:2 0 2 Sectional Properties

The shape of the cross section of the member is one of

the 'important factors affecting the buckling load o Some

frame stability tests have been conducted using box sections,

tubes or solid bars but so far no test of this kind has been

conducted using WF se.ctiono In practical building frames,. .however, WF sections are commonly usedo Therefore, the

frames were fabricated from 2 t x l~ WF shapes designated

276 0 9 -8

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Noo M-2362 by Bethlehem Steel Companyo The cross sectional

dimensions were measured with the aid of a micrometer and

actual properties of the section were compared with those

given by Bethlehem Steel Companyo A-comparison of the actual

and nominal properties is shown in Table 2 0

203 Material Properties

The material properties of the member were determined

by tension coupontest g stub column test and control beam

testo Two coupons cut from the flanges and one from the web

of the section were tested in a screw type testing machineo

Load and elongation over a 6 ino gage length were measured

and plotted by means of a Tinius~Olsen extensometer and a

low-magnification automatic stress=strain recordero The rate

of application of load was about 0 0 025 inch p~r minute and 0.1

inch per minute after strain hardeningo After the yielding

region had been reached but before strain-hardening had

commenced g the strain rate was reduced to zero for a period

of a few minutes to allow the load to reach an equilibrium

point~ From this reading the lowest possible.yield stress

could be calculatedjl thus insuring that in the actual test

structure the yield stress would be equal to this or greater.

The results of coupon tests are summarized in Table 40

A cross-section (stub-column) test was made to find the

compressive stress-strain curve of a full cross=section of

-9

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the member of the .frameso This was an axial compression test

which gave the integrated effect of different web an~ flange

strengths in one testo The main purpose of the test was to

obtain·a compressive yield value to use in predicting the

theoretical buckling loado It should be pointed out that

there is.a substantial difference of yield stress level be­

tween flange and web, as shown in the results of coupon tests

in Table 3. Therefore, the stub column test is necessary and

the result of the test gives' a more reasonable yield stress

level. The specimen was 6 inches in lengtho Two SR-4 strain

gages were provided for the measurements of strains. Prior

to the stress~strain test, the specimen was aligned to insure

concentric loading. The result of the test is shown in Fig. 4.The average yield stress level of flange coupons is very close

to the result obtained from stub column test. Therefore, the

average value of 42~693 ksi was adopted as the y~eld stress

level.

In order to obtain the actual moment-curvature relation­

ship of the section as shown in Figo 5, a con~ol'beam test

was necessary. The test setup is shown in Figo 5.· The beam

was simply supported at its ends and loaded at its third points

causing pure bending in the portion between the· concentrated

loads. Two optical mirrors were attached to rods welded per­

pendiCUlar to the plane of the beam at:;the .load pointso The

mirrors reflected the image of a "graduates scale 10 feet away

..

from the ·center of the beamo When load was applied, the

beam and the attached mirrors as werl, rotated o Readings

of the reflected image of the scales in each mirror were

obtained through a transito The increments of the scale

readings were used . to calculate the angular rotation be­

tween the points of the two mirrorso The unit angular

rotation gave -the curvature of the beam under the applied

moment 0 The moment-curvature curve of the 'section is

plotted in Fig o 60 SR=4 strain gages at~ached at the

flanges also provided additional results for check. The

plastic moment Mp from the test result was 4706 kips-in.

However~ another Mp of 46.87 kips=ino was obtained by cal­

culation based on the measured area of the section and the

adopted yield stress level~ Therefore it was decided that

Mp value of 47 kips-ino would be adopted for theoretical

predictions 0

2 0 4 Loading Condition of Test Frames

As shown in Figo 2 a uniform beam loading was approxi­

mated by three concentrated loaq.s El0 . A concentrated 10adP

at the top of the column represented the loads .. from the upper

floors. This particular loading condition would simulate a

condition that may be expected in the lower stories of a tall

building. A parameter a which relates the magnitude of th&

concentrated column load P to the beam load PI was kept con­

stant for each case o This implied that the beam and column

loads were assumed to increase simultaneously with a fixed

27609 -11

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ratio a between themo The total number of stories was then

a+l~ In this experiment a was about two, therefore, the

frames could be considered as the first story of a three-

s tory bUildingo

205 Design of Test Frames

The frames were designed according to the method of

plastic design outlined in References (2) and (3}0 Since

the loading pattern and the size of the beam had been

selected in advance, maximum moments and forces throughout

the frame could be determined on the basis of a simple

plastic analysis considering a beam mechanismo Knowing

-. these moments and forces, base fittings and welded connec- i

tionswere designed.

The knees, column base plates and loading points on

the beams were of all-welded construction. The frames were

fabricated in the laboratory by welders and fitters who~e

re'gular jobs involve similar operations at the plant of a

steel fabricatoro'

2.6 Lateral Bracing System

Past experience in testing rigid frames into the plastic

range had shown that adequate lateral support was essential

if the theoretical ultimate load was to be attained. This

would prevent lateral-torsional buckling of the member o In

this investigation two frames' connected by a lateral bracing

276e9 -12

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..system were tested at the same time 0 Thus eliminating possi­

ble frictional forces to be developed between the model frame

and lateral supporting guide if a single frame would be tested.

The system was composed of welded purlins made from

1 ~n x i" c.hannels and cross braces 0 The cross braces were

1" ¢ 1made of 4 threaded steel bar, 2 2" turn buckles and hooks.

The cross sectional properties of the purlins are given in

Table 30 The spacing of purlihs was less than 45 r y of the

main frame member which was well within the critiG~l length

for lateral torsional buckling in the inelastic range as

suggested in· Reference 16, where r y is the radius of gyration

about the weak axis of the sectiono The lateral bracing

system can be seen in the photographs of the test frame in

Figso 7, 8 and 90

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3 e LOADING SYSTEM AND TEST APPARATUS

301 Requirements and General Arrangement

There are several basic principles upon which the load­

ing system and test apparatus were designed o These require­

ments~on the other hand~ characterize the peculiarity of the

test setup" Fig,,' 3 shows a general arrangement of test setup

which was designed to meet the following requirementso

(1) Proportional loading should holdo

(2) Loading systems should not restrain the frame from

sidesway movemento

(3) Loadingsystem~ apparatus as well as the frames,

should be symmetrical in both directionso

(4) Nearly perfect pin-ended column support ,was required"

(5) Deformation of the frames at every stage ".of loading

should be measured precise~yo

According to the above mentioned requirements, the load

was applied on the frames by five sets of· lever systems to­

gether with dead,weight on loading basketso One end of the

.'mUltiplication lever was connected with the base beams (ground)

by wire ropes and turnbuckles~ while the loading basket was

hung on the other "endo ' The turnbuckles were used to adjust

the lengths of wire rope so that the multiplication lever

could be kept in levelo The lever ratios of multiplication

lever were designed to magnify the dead weight on the loading

basket and also to produce a proportional increment of load

,on the frames o By proportional loading it is meant that the

" ratio of column load to the beam load was constant at the

value and throughout the loading process o The frames to-

gether with loading system were fixed in position by four

sets of column base fixtures on the base beams so that the

frames could sway freely only in the plane of the frames o

The two l4WF3l4 oase beams and one l4WF61 bea~ in between

were anchored to the concrete floor of the test beg by two

bolts of four inches in diametero The base beams were heavy

enough to transmit the load to the floor without any appre­

ciable deformationo The weights used for loading were 20

and 50 pound steel blocks and assorted round blocks with

·varying weights of 10 to 55 pounds as shown on the baskets

in FigsolO, 11 and 120 They were provided by Bethlehem

Steel Company0

3 0 2 Beam Loading System

.Section A-A of Figo 3 indicates the type of loading

device which transmits the loading weight on the basket to

the beams of ·the frames 0 There are three identical devices

hung on the middle of the third point of the beamso Since

the systems were connected with the base beam by wire ropes,

initiation of sidesway of the frames would not bepreventedo

At the six loading points on the beams, specially designed

hangers connected the loading syst~m to the frames o At the

point of attachment of the 3I507 multiplication lever to the

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315'.7 spreader beam ,l a screw device was provided to allow

equal distribution of the load to each frame. Any error in

the lever ratio of the multiplication levers could produce

an incorrect load on the beams. This could be corrected by

putting a slightly different weight on 'the l()ading ~asket so

that the six readings from the dynamometers were nearly equal.

The reading from the dynamometers gave direct~y the, magnitude

of the concentrated load ~l on the beamo

303 Column Loading System

, Referring to the elevation of Figo 3 ,l there are two sets

of column loading system ,l one at each end of the frame. Each

column loading system applies a concentrated load to the pair

'of columns at its end of the frame. A multiplication lever

made from a 6 B 12 with welded 1/4 inch cover plates was

rested on a spreader beam of 6 B 12 sectionoA roller support

between the spreader beam and the multiplication lever en­

abled'the frames to sway f~~ely without introducin~ serious

frictional force. As shoWn in Figo 13 a shaft and,two sets

of roller bearings were fitted into a pillow block and a

pillow block was screwed to each spreader beamo A sample

bearing was proof tested under vertical load of 20 kips to

assure adequate rolling capacity of the bearing during the

test. '

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..One end of the multiplication lever was ~ied down to

the base beam by a 1/2 inch di~meter wire rope, a dynamometer

and a turnbuckleo The turnbuckle was used to adjust the length

of the wire rope to keep the multiplication lever in level o

Otherwise a horizontal component of force from the loading

beam would tend to push the frame sidewiseo rhe column load

-P was obtained by ~dding the dynamometer reading in the tie

down wire rope to the weight of the loading beams plus the

weight of the loading basket and added weightso

304 Column Base Fixture

Since a slight restraint at the column end tends to in­

crease the buckling load considerably as shown in Refo 17, a

perfect pin-ended support free from any restraint was

necessaryo ·Figo 14 shows the details of one of the column

base fixtures usedo The column base plate·was connected to a..shaft which was cut flat at the top sOc.:that the base plate

could fully rest on the shafto F~ur3/l6"'¢ screw wer~used

to fix the column to the shafto ·The shaft was fitted into

two roller bear ings of ·40 ton capacity e,acho .The'"Rearings

were held in, a pillow block which was acrewed.to.~_stiffened

base box" The base box was then clamped to the flange of a

.. base beam" In order to assure that no slip would..o,c cur be-

tween the base box and base beam during test,.spot_welding of

about one inch in length was done after alignment of the

frames was completedo -Then the frames could only sway freely;

in the direction of the plane of the frameo

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305 Deflection Measurement

The deflections of the beams and columns of the frame

at the end'of each loading increment were measured by a

graduated scale and transit o :The scale was.·about one foot

in lengtho One end of the scale was pointed so that it

could be inserted into punched holes on the frameo The holes

were punched 6 inches apart throughout the outer surface of

the flanges of the frame members 0 The pattern of the holes

is shown in Figo 150

Three transits~ one for each me~ber~ were set up in

front of the frame for deflection measurement. Reference

points were marked on the floor and wall to fix the positions

of the transits and their directions of observationo The

deflection was. read accurately to 0001 inch and .estimated

to the next digit o

As shown in Figsci 10 ~ 11 and 12~ there was a vertical

rod beside each columno Horizontal lines on the rod were

drawn at the same level as the punched holes on the columnso

By holding the scale in the punched holes ;:and along the line,

horizontal deflection of the column was read through a transit

which could only rotate in a vertical plane parallel to the

column 0 In order to measure the vertical deflection on each

beam, a triangular plate was used to assure the vertical

position of the scaleo The transit was fixed against vertical

rotation but it could rotate in a horizontal plane along the

beams for taking vertical deflection of the beamso

. .27609 -18 .

30~ Strain·Measurement

• strain in the frames was measured by attached strain

gages 0 ,All strain gages were electric resistance SR-4 type

A-I linear gagesoThe location of the gages on the frame is

shown in Figo 160 There were 24 gages throughout the frameso

The gage readings were used to align the point of application

of the loado The alignment would not be perfect until the

strain reading showed symmetrical figures in both directions~

A relatively small number of gages was used on the tests,

because the elastic behavior of the frame was not being

emphasized in theinvestigationo After the yield point has

been reached at a gage location, knowledge of the exact

magnitude of strain is not of prime importance, however, all

of. the strain readings were taken after each increment·of

load throughout the testo The strain gages were connected to

a switch box and then to the strain indicatorso. ,

276,,9

5", TEST PROCEDURE

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5,,1 Test Setup

After the frames were erected on the base beam, s.train

gages were mounted and wires were connected to the switch

boxes and indicators" Then the frames were whitewashed I,

with hydrated lime" Flaking of the whitewash during testing

indicates the progression of yielding" Initial readings of

strains and dynamometers were taken before the heavy loading­

beams and baskets were put on the frame" After the loading

beams were set in position, turnbuckles were~djusted to

keep the loading beams level"

5,,2 Alignm~t of Test Frames

Around 200 pounds of weight was loaded on each loading

basket" By taking increments of the load dynamometer read­

ing, it was easy to figure out which side of the frames was

overloaded" .. The weight was unloaded and the lever ratio of

the multiplication lever was adjustedoThe process was re­

peated until the difference was within 5%"

After alignment of the multiplication lever was fini~hed,

strain readings were taken" Unsymmetrical strain readings

indicated that the point of application of the loading system

was deviated" Again the weight was removed to adjust the

position of the spreader beam on the columnsd' Alignment was

continued until the increments of reading 'from strain indi­

cators and dynamometers gave symmetrical values within 5% error"

27609 -20

It is of interest to point out that for the first and second

sets of load increments~ the readings were not quite satis=

factoryo However~ when the load was increased more~ the

results tended to be more reliableo' An explanation for this

could be that the initial deformation in the wire and multi­

plication lever affected the initial reading very mu~ho

503 Testing

Figures 10~ 11 and 12 show the testing of frames W-l,

W-2 and W-3 respectivelyo In order to keep the relationship

of proportional loading~ 80 pounds of weight was. loaded

initially on each of the thre'e baskets of the .. beams 0 This

was an adjustment to the different weight of multiplication

levers~for the columns o From then on, the same weight on

each basket would produce proportional loading on the frames o

Two men were necessary· for reading and rec,or.d-+ng the

dynamometers and strain indicatorso The applied. loads on

the beams were calcula~ed by mu~tip~ying the measured strain

increments by the constants obtained from dynamome:lier;:; cali­

brationso In case the loading obtained from the dynamometers-.

was not satisfactory~ it could be adjusted by putting on the

baskets a slightly different weight for the next loadingo

Another couple of men took care of the deflection measure-

ment o . One held the scale, while the other took the.readings

through thetransit o The scale was shifted· from one position

to another, and hence the deflections of the beams and c'olumns

were obtainedo

· -21

After each increment of load g the deflections at the

centers of the beams were measured and plotted on the pre­

dicted curveo This load vSo deflection. curve would justify

that both the testing apparatus and the frames were function­

ing satisfactorilyo

For frame W=l, the first five sets of load increments

were about 200 pounds in each basketo:The IhcramaDt~··was

gradually decreased to about 10 pounds at the final loading,

Noo 190 After loading Noo 10 visible yielding on the frames

was observed at the inner surface of the right colUmn at the

cornaro This'was the first indication that the frames might

sway to the righto The frames started to sway-visibly at

loading Noo 110 From then on g it took more than 20 minutes

of waiting for the frame to slow do~ the sidesway motiono

Several jacks and wood blocks were put under 1;he_b~skets to

assure that no sudden failure of the frame would occuro At

the final loading the frames swayed slowly and continuously,

therefore, no deflection was taken and the test was finishedo

Frame.W-2 was 22 inches higher than frame W:"lo The

wire ropes on the loading be'ams were made 22 inches longer 0

The load increment was 200 pounds for the first· five sets,

then seven sets,of 100 pound increments followedo Finally

three sets of 30 pound increments concluded the testo

-22

Frame W-3 was about 9 feet in height above the floor so

it vibrated co~siderably after each loading processo At the

end of test the "frames swayed considerably so that the rotation

at the knee caused the spreader beam at the top of the column

to tilt too mucho Eventually the spreader beam overturned and

multiplication beam above slid down on the frame o

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. _ . ., . ,. . ' . .' '. ;'\ .1 . <' • r .'"t' • ;'. -". • -: ••• -.' • - • ",- ....' •• ~ -.- ....". , ,

TEST RESULTS ANDT.HEIR ,C.OMPARISON WITHTHEORETICAL PREDICTIONS

5.. 1 Test Results

Generally speaking, the test frames and the apparatus

behaved satisfactorily throughout the testo

The deformed shapes of the frames W=l and W=2 are shown

in Figo 17 and 18 respectivelyo The last set of deflections

was not taken due to overturning of one of the spreader b~ams

a t the top of 'the column,\> .therefore,\> the deformed shape of

frame W=3 is not shown 0

The dotted lines in Figo 17 and 18 show the deflected

shape of the frames when the horizontal deflection of the

column top first became noticeable.. The load corresponding=

to this point is defined as critical load Pcro The solid

lines show the shape of the frames just before the ultimate=

load Pult was reachedo ,Any further increase of the.applied

load would have caused continued sway of the frameso ·Thi~· is

the maximum load the frame can carry and is defined as ultimate

load PUlto

The test results were plotted in Figs 0 ,19.9 20 and 21 as

the load versus horizontal deflection curve at the column top.

,The predicted buckling loads Ppre were shown as dotted lines

on deflection curves of the Southes:!It;- columns of the frames.

-24

,Table 5 provides a summary of all the test results and

of the theoretical analysiso . The ultimate loads obtained

from the tests are 110172~ 100136 and 90160 kips compared

to the predicted buckling loads of Ib0648~ 100181 and 80611

kips for frames W-l~ W=2 and W=3 respectivelyo

Because· of the satisfactory lateral supporting system~

the two frames were acting together as one frame. and no

lateral buckling of the members was observed before the

ultimate loads were reached in any of the three testso

••• - " ._ 0.-'

5 0 2 Comparison of Test Results with Theoretical Frediction=

The ultimate loads Pult obtained from the tests were·

plotted as points W=l~ W=2 and W=3 in Figo ,220 The curves

in the graphs show the predicted inelastic buckling loads

based on the theory given in Hefo 120 For framesW.;.;l and W-3,

the experimental loads are several percent highert~an the

predictedl~ads, while both experimental and predicted: loads

are about equal for frame W=20The average error between the

theoretical prediction and test results is less than 4%0 As

shown in. Figo 22~ a different coefficient of proportionality

.a was used for frame W=3o It was believed from previous test

results that frame W=3 would fail by elastic bucklin~' There­

fore, a was reduced to 108 to assure that the frame would

buckle in the inelastic rangeo

=

The experimental buckling load Pult was compared with

the predicted buckling 10adPpre~ beam-column instability= . =

load. Pum and simple'plastic 10adPu as summarized in Table 5.

503 . Comparison with theAISC Formula

To safeguard against frame instability in plastically

designed one= and two=story rigid frames~ the following rule. (18) '.

is recommended in the AISC Plastic nesign Manual o .

"Columns in continuous frames where'sldesway is not

prevented (a) by diagonal bracing (b) by attachment to an

adjacent structure having ample lateral stability or (c) by'-,

floor slabs or roof decks secured horizontally by walls or

bracing systems parallel to the plane of the continuous frames

shall be so proportioned thatP h <

2 F + 70r -100y

where P = the axial force in the column when the-.frame carries its maximum. ..load 0

Py = the axial yield load of the column

h = slenderness ratio of the column ."r

The justifica~ion of this rule can be found in Refo(~

A frame with a combination of axial load and column slender-

ness ratio within the triangular envelope in Figo 23 'can

carry as much load as a braced frameo Test results indicated

that Frame W-l could carry 9609% of the load ofa braced frame.

The point is very close to the lOO~ line, therefore, the

formula is quite accurate in .the vicinity of the loading

and slenderness ratio of frame W-lo

-26

.'

•

2760,9,,-, -27

60 CONCLUSIONS

. The following conclusions can be drawn from the results

of the investigation presented in this papero

(1) T~e predicted buckling loads are very close to the,

experimental buckling loads and are less· than 4% on the safe

side as could be observed in Table 50 This indicates both

the theory and the test are very satisfactory and successfulo

=

(2) The ultimate load Pult is about 84% of the simple

plastic load o The reduction in load carrying capacity from

simple plastic load is too large to be neglectedo Therefore,

a check against frame stability should be made in plastically

designed frame o

(3) The designs of model frames'and test setup are

very satisfactory as evidenced by the test resultso The

success of this test could be considered asa cornerstone

to a more complicated te.st of multi=story frame 0

(4) The agre~ement of the test results with the AISC

formula for the slenderness of columns in frames not, braced

against sidesway provides confidence that the AISC formula

will.safeguard against the frame stability problem inplasti­

cally designed frameso Since no tests were conducted in the

regions of h~gher. and lower axial load, a more precise design

formula can not be recommended nowo , However, examination of

-28

..

•

these results in the light of the approximate theoretical',:

analysis given in Refo·) suggests that the AISC formula may

be more conservative in these regionso

The fnelastic buckling problem of single story rectangular

frame has been properly solved and future work should be done

on the stability of multi=story frames o

276.9

ACKNOWLEDGEMENTS

2gB.

..

't

..

This report is based on a thesis prepared, bY' Y.· C. Yen

in. partial fulfillment of the requirements for the Master of

Science degree •

. The work contained in this report is. part of an in­

vestigation on "Welded Continuous Frames. and, Their' Components"

being conducted under the direction of Dr. Lynn S. Beedle.

The project is sponsored jointly. by the Welding Research

Council and the Bepartment of the Navy through the Institute

of Research at Lehigh University. ,Funds are furnished by the

. American. Institute of Steel Construction, American Iron and

Steel Institute,. Office of Naval, Research» Bureau of Ships,

and the Bureau of Yards and Dockso The Column·R~search· Council

of the Engineering Foundation,acts in an advisory capacity.

The work was done at Fritz: Engineering Laboratory,. Lehigh

University, Bethlehem, Pennsylvania

The assistance of Mr. Kenneth Ro Harpel"Laboratory

Foreman,.and the' Fritz Lab shop personnel in prep~ring t~e

test setup and in. conducting the tests is greatly appreciated.

The drawings were prepared by Mr. Stanley A., Gawlik and

the manuscript was typed· by: Mrs.· Lillian. Morrow. Their

cooperation is appreciated •

276.9 ' "'1"'29

8. TABLES AND FIGURES

, I

-,

T'ab Ie 1. DIMENSIONS OF TEST FRAMES

Frame Span L Height of' r x h_,No o .: in· - Column h -- r x~in: , in,,:e

-.

W-l 8719

4313

1.095 4032 16,

19 65 11I

W-2 87 1.095 6032 16

. ,_.' ----

W-3 8719 87' 19 1.095 8032 32

_Tab Ie 2 0 SECTIONAL PROPERTIES OF TEST SPECIMENS

"'" Area Depth Flange Flange Web' Ix Sx r x Z f'"-

~of - of Width Thiok= Thi.ok=

S'ection Section ness ness 4in3 in 3

~.~fA in2

d~ in b~ in t p in "IN>, in in in~ :- ., - -- - . - -' --

Nominal 1.085 2.625 1.8,40 0.201 0.156 1.236 0.942 1.062 1.086--_.-

1.121Measured 1 0 043 2.625 1.813 0 0 207 0.156 10251 0.953 1.095 1.067

RWo

Tab Ie 30 SECTIONAL PROPERTIES OF FURLIN..

Area of' Depth of .Flange Flange~ Web I S r x r ySection Section Width Thickness Thickness .x x.

f'A, in2d~ in b· in t~ in w~ in 'in4 in 3 in in~

. --

0 0 34 1.5 0.75 0.188 0.125 0.11 0 0 15 0.56 0.22

Table 4.· SUMMitRY OF COUPON TEST RESULTS

- ~ - .-..

Location (iy QuIt Ey Est E- ,ksi .•·.·~si. . in/in in/tn, ksi

•.

Flange 42~110 54~ 710 0 0 00134 0 0 01336 32,047~000.. .. ..

~,..

n 43,270 54~570 0 0 00125 0 0 01403 31~ 592~OOO,. ... .. .,

Web 48,280 60,350 0 0 00167 0 0 01086 30,483,000

where 6J = Static Yield Level-

GUlt = Ultimate '!Tensile strength

€J = Initial Yield Strain

E~ = Strain at Initiation of Strain Hardening

E = Modulus of' Elasticity

~-E mean = 31,374,000

Tab le .5 0 SUMMARY OF THE TESTS AND COMPARISON WITH. THEORETICAL PREDICTIONS.

.. -. -. -_ .. .-..__... _...-" - - ---

Frame h Experimenta.l- Predicted Cblumn .-- Simple" -- "Per Pult PUlt Pultp ...

urnNo o

r Buekli'ng Loads Buckling Instability 'Plastic>; - - - -,1bs __ 'Load (lbs \ Load ·lbs Load _Ibs '- Ppre 'Ppre Pu Pum Fu= = --

Per '-''P p ,- ~ P r ~ - p r --u1t --

pre um u

_.. ,. .-

W=1 40 9 9~16 , 11 9 172 10 9 648 11 9 533 12 9 433 0 0866 1 0049 00899 00969 0 0928

'- ..W=2 60 8 9 793 10 9 136 10 i 181 11 9 469 12 9 433 00864 0 0996 0 0815 0 0884 00922

fW-3-, ..

80 8 9 194 9 9 160 8 9 611 10 9 437 I 11 9 432 0 0952 1 0064 0 0801 00818 0 0913

I\.UI\)

276.9 -33

•

Load

H' I Case I

Paint of Bifurcation

1------...·~cose2 -n.-- ·I 1 , .-0-........ ' II "... .,, /. ., Case 3

/ .•./

./ 0 Point of instability./

./

Horizontal Deflection of Column Top

FIG.l TYPES OF FRAME INSTABILITY

P

FIG. 2 DIMENSIONS AND LOADING OF FRAMES

PPI PI PI

~ 29 13- 2913a

14JJ:'...."'4 32 64 64 32

L a87!!.-32

- N It)

3 I • •paO( yP,) ~ ~ ~

~ ~ ~0 of... ...P a(l+o) t PI

• a=l!! ~IN!!!I!! -",It) II) ....

oa2 .. CD CD• • •

.""~1 1 1

77r

..

MODEL FRAME

SECTION 0-0

Catler

2 5/8 YF3.725( No. M-2362 of Bethlehem Steel Co.)

o

12' 0"

9' 2",A

50 17 ~2 " =87 19/32'- - 1

14 'IF 314 ase BE am12'-0" Lan -fIi=i===~

I " ~'----- \ / \ / . \ /' 'I~ 0-'S;.6 BI2 with /4 Caver II!. ..L=.L:.. "'l\J h / l<\ I \ lit 't\ii!-:!-If-:A-TI-~+-+_-r'="ll-- 1--,.._,...I

11'.n" _~" ~ 11/ I ~ 81/U~·Yz.~':.if!..~'~-'-;\$::""F~----'==:!===gll;:'-~0~"=;-;::===~~~~~~ -~- '~:I-¥-",? '~H- --f, - .. , - -~- ~

14YF61-II'-4"Lang/ .~/1..-...':::.' IJ \ 'IJ \ I \\ 1 \\ -i-6B/2-3'-2"

\/ \'1 \'

•

5 Y16"x IY16"x ~4' II!. .10~

i61i 11m-:"CXl

~• C\l-to

I 2 V811·I~CD

to

,S

FRITZ ENGINEERING LABORATORY

LEHIGH UNIVERSITY

Drawn by _ _ 'L.."S..:.... If'!::- _;:Ife. .' -HiApproved by 9>~ _

PROJECT NO. 276

TEST FOR FRAME STABILITY

CORNER CONNECTION

/I.

l!'~ ~'~ ,

T 23

5/S'x 15/S" x1/4" II!.

716". - YS" Screw

SECTION S-S

COLUMN BASE CONNECTION

rS

14 'IF 314Base Beam

1'-6"

I

\

\

\

I

/4YF61Base Beam

SECTION A-A

6BI2

n 1'-6"

1-'-I~=-2' 3:....Y4:...."_-t-__--"3!...'.:..--,,,0_"--F--l II" 5"5" II"

O:f5:z:::;t;'J=.=~~:'315.7 Spreader Beam

1/4" ~ Sling ----:I.'i<> 315.7 Magnification Lever

14 'IF 3/4Base Beam

Turnbuckle.I

1/4'. Wire Rope

Loading Basket

Spreader Beam

Dynamometer

C\l.:;:..toI--

Roller Bearing

==-= ---=--=-~--=--==;:,5"0" :

1

ELEVATION

2'-0"

4'IF314 F======== --~-=-=1: I 5' -0"

2'· 1/64"

Model Frame---n",

6BI2 with V4"C.1I!.

Date' Aug. 30, 1961 NO.3-I

FIG. 3 MODEL FRAME AND TEST SET-UP

276.'3 ~35

...so·

40

u.( ksi)

O....._~_---lL....-_...L-_--I__...&.-_......&._--'--~

o 0.002 0.004 0.006 0.008 0.010 0.012 0.014

E (in I in)

FIG. 4 STRESS-STRAIN CURVE FROM STUB-COLUMN: TEST

50

7

L l p

20

40

2 3 4 5 6

• x 10 - 3 (Rod./in.)

FIG. 5 MOMENT-CURVATURE CURVE FROM. CONTROL BEAM TEST

M(kip -in.> 30

•

276.9

------------------------

-36

Fig. 6. SETUP FOR CONTROL BEAM TEST

Fig. 7. FRAME W-l AFTER TESTING

276.9

--------------- ---------

-37

,

Fig. 8 FRAME W-2 AFTER TESTI NG

Fig. 9. FRAME W-3 AFTER TESTI NG

•

276.9

Fig. 10. TESTI NG OF FRAME W-1

Fig. 11 TESTI NG OF FRAME W-2

-38

•

276.9

Fig. 12 TESTI NG OF FRAME W-3

-39

.;.40

•• .§JN _

fter Pin

• •1-- - - N -- - -D

I"" I"

4' 17/16 4 1/4" 17/16b 14

SHAFT·

.. i beop .Screw

7"i'L0n9

.ii Cop SCrew7 b

8 Long

.. .,,~'.:'. PILLOW BLOCK

FIG. 13 ROLLER SUPPORT FOR MULTIPLICATION: BEAM

276.9 -41

Roller Bros. to bePressed Each Endof Shaft Bore of .

r-t--"7'"+-E~---.Bro. 1.250 In. +.0005-.000

3 "V,6 olesd 1i2" I!¥a"

rl an ap I H

1.

!¥ " 1 I" ~16"!.L.

0 I=~ 0s;---$ . ~~ $t- I

IIn' =~;;

1 3/4' 2 "aII

3 "I V4

55/all

SHAFT

7J IIDrill ~6 • Hole

HOle

PI LLOW BLOCK

FIG. 14 COLUMN BASE FIXTURE

276.9

tr~---12 6"----.-1.,

ill~~~~ ~ ~

000--­II II IICD CD CD

~

ill

-4'Z

FIG •. 15 . LOCATION QF DEFLECTION~MEASUREMENT

=

. FIG •. 16 . LOCATION· ©F STRAIN GAGES

276.9 .... 43

,IIIIII

-­.".,.----- ---- --------

N.W. Column N.E.Column

S.E. Column

LEGEND,II1II

- - 9216 1bS.---- P=Pc,= .

---P=IO,720IbS

.( Immediately before Pult)

DEFLECTION SCALE

S.W. Column9 ~ ~ INCHES

"'

FIG.17 . DEFORMED SHAPES,OF W~l

...

'f

276.9

II,,,

II,I,,,

N.W. Column

II,IIIII,,

S.W. Column

LEGEND:

- - 8193 Ib,.----, P=Pcr •

--- p= 9,610 (before isult)

DEFLECTION SCALE'

9 ~ ~ INCHES

,.;.44

,,IIIIIIII,,

N.E. Column

I,,IIIIII,,,

S.E.Column

. FIG. HL., DEFCDRMElD'SHAPES ©F W-2

276.9

12,000

10,000

8,000

PUlt. = 11,172.,.,.---""'-

-45

Pult. =11,172._--- as __

LoadP 6,000

( Ibs)

4,000

2,000

o0./ 0 0./ 0.2 Q3 0.4 0.5

N.W. Column

0.1 0 0.1· Q2 Q3 Q40.5

N.E. Column

Deflection 8 (in.)

Pult . =II, 172--- .--

S.E. Column

0./ 0 0./ Q2 0.3 Q4 0.5

Deflection 8 (in.)

PUlt .= 11,172..-.--------,=------Ppre =10,648

S.W. Column

0.1 0 0.1 02 Q3 Q4 Q5

.. 12,000

10,000

8,000

LqpdP 6,000

(Ibs)

4,000

2,000

0

'J

~

FIG.l9 LOADvs. HORIZ.DEFLECTION AT COL. TOP OF FRAME W-I

}

.,

.'

12,000

8,000

Loadis 6,000

(Ibs,)

4.000

2,000

°

12,00

10,000

8,000

LoadP 6,000

(lbs.)

4,000

2,000

o

0.1 0 0.1 0.20.30.4

N.W. Column

Deflection ·8 (In.)

PUlt 1110,13&

Ppre=10,181

0.1 0 0.1 0.20.30.4

S.W. Column

-46

0.1 0 0.1 0.20.3 0.4

N.E. Column

.PUlt -10,13&..---»'>.....---

0.1 0 0.1 0.2 0.3 0.4

S.E. Column

Deflection 8 (In.)FIG.20 LOAD VS. HORIZ. DEFLECTION AT COL. TOP OF FRAME W-2

276.912,000

10,000

8,000

Loadp 1,000

(lbs)4,000

2,000

o

PUlt =9,160."".----- -~

0.1 0 0.1 02 03

N.W. Column

-47

PUlt. =~160--- .....,,---

01 0 01020.3

N.E. Column

•

'. 12,000

10,000

8,000

LoadJ5' 6,000

(Ibs)

4,000

2,000

Deflection 8 (in.)

PUIt. = ~160-----~.

::::--f~-- -------'-Ppr• I: 8,611

PUIt. = ~160------~~

"

il

o0.1 0 0.1 0.2 0.3

. S.W. Column

0.1 0 0.1 02 0.3

'S.E. Column·''';

Deflection 8 (in.).

FIG.21 LOAD VS. HORIZ. DEFLECTION AT COL. TOP OF FRAME W-3

276.9 ~48

1.0: - - - ~ - - - - - - - - - - - - - - - - - - - \" Simple Plastic Load

oW-I

.8eam Column InstabRity

#

:-,r

Inelastic.6 Buckling

."p '.'.

P "'" Elastic-lSu ."~~.4 3 ......

p=aI PI .h

1'=(1+CI)f PI

~2 L a=2.0

P

0 20 40 60 80 100 120., .her

1.0 . ----- - - - - - - - - - - - - - - -,- Simple Plastic Load" .

\. Beam Column Instability

.8 ~W-3

Inelastic :\

Buckling• 0

.6,.,

PA

P.'-rElastlcis

~I- rl ~I '. BucklinglSu p=aA PI

,

}"

.4 2 ......P=(lta)f PI

0 0 =1.8

.2 L-,)

is P

o 20 40 60 80 100 120h,.

FIG.22 TEST RESULTS AND THEIR COMR WITH THEOR. PREDICTIONS

.. .....'

.'-0

W-2• 88.4 % W-3

• 81.8 %

00 10 20 30 40 50 60 70 80 90 100

h-rI~

~IG.23 COMPARI'SON. OF TEST'-0

RESULTS WITH THE AISC DESIGN RULE

0.3 A I S C Ru Ie.

2;+=10 t = 1.0Y

0.5 --------------------------------.

0.1

0.4

-p-py 02

-50

.,,:. 8. . REFEREN CES

1.'.~' Beedle, L. S.ON THE APPLICATION' OF PLASTIC DESIGN, ,. Proceedings

· of the Second Symposium on Naval StructuralMechanics, p.538, 1960

2. Beedle,. L. S.· PLASTIC DESIGN· OF STEEL FRAMES,. John Wiley &. Sons,

Inc.,_ New York, 1958

3.WRC-ASCE Joint CommitteeCOMMENTARY. ON· PLASTIC DESIGN IN. STEEL, ASCEManualNo. 41,- (1961)

. Puwein, M. G.D~E KNICKFESTIGKEIT DES RECHTECKRAHMENS, .Die Bau~echnik,

Vol. 18, p.32, (1940)

Masur, E. F., Donnell,- L. H., and Chang, I. C.· STABILITY OF FRAMES IN THE PRESENCE OF 'PRIMARY 'BENDING

MOMENTS, Journal of he Engineering Mechanics Division,ASCE,.Vol. 87, No.EM4, (1961) '.

·4•. Chwalla"E.DIE STABILI TAT LOTRECHT BELASTETER. RECHTECKRAHl\ilEN,Der ~auingenieur, Vol. l~, p.69,· (193~)

Chwalla, .IE. , _and Kollbrunner, C. F..BEITR~GE .2UM KNICKPROBLEM DESBOGENTR~GERS' UND DES

· RAHMENS, Der' Stahlbau,. Vol. 11,. p.94,(1938)

5.

~,

6.(\,

7.

8. Bolton,.A.STRUCTURAL FRAMEWORK". Ph.D. Dissertation,- ManchesterUniversity,. (1957)

9. Salem, A.FRAME INSTABILITY IN THEP'LASTIC' RANGE,- Ph·.D •

. Dlssertation, Manchester University,- (195'8)

,)

-L_i.I :

·10.

. ,, .

Gurney, T. R.FRAME INSTABILITY OF PARTJALLY·.P-LASTIC STRUCTURES,British Welding Research Association, Report 'FE 1/56/68'(1957)' .

,....11 •. Low,.M •. W.

·SOME,MODEL TESTS ONMULTI~STORY' RIGID. STEEL. FRAlVlES,· Proceedings~ Institution of Civil Engineering,

Vol. 13, p.287, (1959)

-51

.,

.'

12 0 LU, Lo WoSTABILITY OF ELASTIC AND PARTIALLY PLA~TIC FRAMES,PhoD.o Dissertation, Lehigh UniversitYII (1960)

130 Winter, Go, 'Hsu, Po .To, Koo, Bo, and Loh ll Mo HoBUCKLING OF TRUSSES AND RIGID FRAMES II Cprnelltrniversity, Engineering Experiment Station BulletinN0 0 36, (1948 ) , . .

140 Ojaliro, MoRESTRAINED COLUMNS, Journal of the.EngineeringMechanics Division)) ASeE)) Volo 86, NooEM5, (1960)

150 LU, Lo Wo and Driscoll, Go Co, JroBUCKLING TESTS ON MODEL FRAMES, Fritz Laborator1Report 27603 Lehigh University, '(in preparation)

160 Lee, Go Co, and Galambos,· To VoTHE· POST-BUCKLING STRENGTH, OF WIDE-FLANGE.BElMS,Fritz Laboratory Report 205 Eo12, Lehigh University,(1961)

170 Galambos, To VoINFLUENCE OF PARTIAL BASE FIXITY ON FRAME STABILITY,Journal of the Structural Division, ASCE, VOlo.86,Noo ST5, (1960)

18 0 AISCPLASTIC DESIGN IN STEEL, AISC, 1959