Welded Continuous Frames and Their Components

Column Research Council Project B.2.D

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By

Lynn S. Beedle

These are the notes written following

presentation of a description of the

Lehigh program at the Technical Session

of the Column Resear ch Council

MaY 11, 1951

Fritz Engineering LaboratoryDepartment of Civil ~n~neering and Mech.

Lehigh University

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205A.5 5/11/51

INTRODUCTION

1

In 1946 the AISC canm.enced sponsorship at Lehigh Universityunder the direction of Dr. Bruce G. Johnstm the current investi­gation of columns loaded 'IIvi th combined axial force and end man ent.

The ohjectives at that time were:

(a) to determine the plastic behavior of steel columns ofthe type used in bUilding frames with continuousconnections, and

(b) it was also sought at that time to determinecarry-over and stiffness factors.

The program is now part of a larger investigation sp nsoredby WRC, And ONR with funds furnished by the AISC, AISI, BUSHIPS,BUY&D,. ONR.

I represent a conaiderable number of people who have workedon this project, commenced by Drl Johnston. Joseph Ready,Mr. C.H. Chen, Mr. Jan Ruzek and Robert Ketter have in thatsequence been Besearch Assistants on the project. Mr. Ketter isnow actively carrying out the investigation.

moth analytical and experimental phas.s of the investigationare proceeding ~zXh±sX1RZBgXtgnZt~xx simulbaneously. In thisbrief presentation, the experimental attack will be described,followed by a discussion of the theory. The comparison betweentheory and the exper&ments carried out up to the present timeis given and certain appropriate conclusions are drawn.

EXPERDIlENTAL EFFORT

The load-carrying capacity of steel columns is of coursea function of many variables. SLIDE 1 shows a program of rtests and indicates the variables being examined in this program:

(a) Loading condition (5 are being studied) )[(b) Size effect (4WF13 and 8~~3l)(c) Flexure Axis(d) Slenderness Rati~ (27 to 120)(e) Magnit~de of Axial Load (ratio of P to M)(f) End Condi tion(g) Shape of cross-section.

This latter variable is not evident in the slide, since the twosections have almost identical shp,pes. At some future time someexperimenta should be carried out with this variable in mind.

. Some of the methods bhat have been used by preVious investi­gators to attack some of the above problems are shown in SLIDE NO.2

205A.5 5/11/51 2

In each of these it is either difficult or ~possible to indepen­dently vary axial load and end moment ••••menti oned above as oneof the unique features of the investigation.

A second feature is, of course, the size of the member, sincecommercially-available as-delivered columns are being tested inthis program.

SLIDE 3 shows the test apparatus being used in the experi­mental program at ~ehigh University. The test column is weldedto a base plate at each end, these plates in turn being boltedto end fixtures with moment arms.

Axial load is applied with a a.crew-type machine of 8009000#capaci ty. The,knd bending moment,s are applied wi th the help ofa frame shown in the slide as a "test frame". Forces appliedhydraulically by pumps and jacks deliver the m:mrziit» moment tocolumn ends. By virtue of the adjustable cross-beams the testframe carries the moment.

Horizontal ties carry the shear force. By reversing eitherthe direction of the moment arm or the posi tio n of the jack anddynamome~ter assembly the directions of end moments may beneversed. In those tests where a "fixed-end" condition isdesired, this is accomplished with the aid of level bars.

Among the test methods ~ossible, two have been used. In theone case, the full magnitude of axial load has been applied, andsUb3equently bending moments have been applied to collapse. Ina few cases the reverse procedure has been used.

ANALYSIS AND THEORY

Considering sketch (a) on the blackboard,when no endbending momen t is applied the member is a column whoseultimate strength is predicted by the tangent modulus theorywith satisfactory engineering accuracy. This critical loadi.PE for an elastic column or P~ for an inelastic column if theidealizaed stress-strai n diag!'am of ske tch b is ass:umedresulting in the column curve of sketch d.

On the other hand, as is evident in sketch (£1 for zeroaxial load t)J.e member is a beam wi th the predicted My and Mpbeing shown.

If now these two curves are put together then for certaincombinations of axial loadand bending moment there will be a locUSof pointBo! initial yield and a a.ocus of points for collapse.

205A.5 5/11/51...

,-

SLIDE 4 shows such an "'interactin curve It • Two curves areobtained (as alrea~ mentioned). For this part.icular case theintial yield condi tion is given by ,

piA .. Mc/I g.fy ·

The method of test is also indic'ated.· The collapse curve isalso shown and the curve is derived on 'the basis of 'the theoryoutlined by the' second set of sketches on the blackboard.

(discuss~d formation of eiastic limit and collapse curves)

SLIDE 5 shows the influence of ,axial load. When L/r iszero (or approaches zero) the influence of axial lo~d is onlyto decrease in linear proportion the stress at which the yieldpoint is reached in ,bending.

o

Fo~ L/r not zero under combfu. ~d bending and axial loadthe Illoment at a section will be made up, of two parts: that dueto-moment and that due to axial load. .

" In .the first combined diagram the critical section foryielding is at the end, the load P being less than PL to bedefined. As the axial load is increased there will De reached.a load at which the moment.diagram.indicates zero slope· at theend. This ~.xial load is called fL' the, limit axial load forthis condition. As the load is increased further the point ofmaximum momen, t (and thus ~aximum stress) kX moves away from ~the end and occurs at some interior point.

The phenom~non just described is a function of,L/r, since,for a more slender column .it is logical.that this ~mR~ZmDBEXX

P value be lowered. It is also a function of load condition,,f1)r ItCll there would never be a moment maximum at the ends.

Interaction curves are drawn throughout this investigationin terms of Mo , the moment at' the end of theco~umn•.

. . ~ .

The;e curves shaw the influence of slenderness ratio (SLIDE i).Notice fb r L/r of 112 1h e successive decrease.' ~n capacity (intialyield) as the load condition is changed f~om a-b-d-c.

SLIDE 7 shows Zbtb somewhat more clearly the influence'of condition of loading on the initial yield strer.gth~ Forone particular member the allowable fDomthe AlSO formulais also shown in this slide. For the different load conditionsthe PL value is reached as follows:

a: p'b- ~5~PE.•c: 0d: .27PE

• <.

205A.5 5/11/51

A three-dimensional interaction curve (developed in thisprogram at Lehigh) is shown in hgx SLIDE S. By adding az-coordinate with units of in/in a more complete picture of JIbtheoretical column behavior is obtained. In the load-L/r '.cdordinate system we see the familiar column curve (plottedof course to the opposi te hand :i:r.0mZ to that whi ch we areaccustomed) • In the horizonhal plane is the familiarlateral buckling curve f or members loaded in bending only.The interaction curves are evident in the third coordinatesystem.

The surface in space traced out by the initia~ yield andcoll@ se conditions may be grasped.

The AISC formula is again shown as a basis for comparison.

One point of interest is the plane surface generated l1Tbby the initial yield condition. If confirmed experimentally ~this might eliminate the possibility of separate considerationof· L/r •••.• for a particular range. .

COMPARISON OF THEORY AND EXPERIMENT

Formulas have been developed for the various load conditionsto pr.edict the initial yield strength. Other theories are partiallydeveloped for the collapse condition.

SLIDE 9 e mpares experiment with theory for load conditionb~ 8WF31, Ljr : 56, KL/r = 0.7 X 56. Observation of the firstyield line is shown by the short line. The circles indicate"yield strength" according to the BJ criterion EP'!d the maximumstrength is indicated by the squares.

Tests 3 and 4 develop the strength. T5 failed by lateralco1.lap se and the evidence indicates that this is due to residualstress. A residual stress level of about 12 kai is evident fromthe curves.

A ddtiona1 tests at low P/Pcr were condllLcted (13 and 14)for load conditions d and a respectively. No difficulty wasexperienced in reaching-the predicted values. In the case,of14, two tests were run, the column being tested aga n underhigher axial load after completing the lower point.

Strain-hardening probably accounts for a considerableportion of the increase above the predicted co1l~se value.

c..

205A.5 5/11/515

SLIDE 10 shows the other extremex in loading condition••••the same Llr, an S" column, but loaded inslgnle curvature.

The column does not develop even its elastic limit strength,let alone the predicted collapse value. Again, the formation ofz:mZiibzX¥:bdx first yield line,' the developement of Yield Strength,and the collailse P9ints are indicated. ' .

T12; shows a reduction of,25% alone due to load condition.(Compare with T4 on Slide 9).

The Jezek solution is plotted. There is a range, of course,where the result is impossible, indicating collapse below thepredicted yield point. The same solution has been attemptedon 4WF13 members but the results are impossible: and indicatethat real study needs to be given the factor whiCh depends upmcross-sectional form in the Jezek procedure.

This slide also shows the other method of test used.

SLIDE 11 is for load condition b, the four tests indicatingthe influence of slenderness ratio. F~ the increased slendernessratio of 112 (double that of slide 9) the column has furtherdifficulty in developing its yield strength.

Nome of these columns tested developed the predictedcollapse strength according to the plastic theory due tocollapse by combined bending and twist.

For these proportions, restraint, and loading, the theoreticalmaximum load ~~xp~emeEax with zero end moment is 104 klpss

TO and T7 gave identical results, TO having beenX initiallydeformed plastically under axial load alone. T7 was a "pure" test.The influence of the prior plastic deformatio n was negligible.

SLIDE 12 plots a stress functlon ~ against carry-over factor.IJ:Ihe theoretical elastic value for this particular axial loadis given byxRXx the dotted line. The observed points are shownby the circles. The dot-dash line gives the ratio of end anglechanges for load condition d •••.•valid only to the elastic limit.

Stiffness and carry-over factors are geing determined in allthe tests. While of value to confirm our theories in the elasticrange, the value of the plastic results has not yet been eatabliahed.

205A 5/11/51 6

Earlier was mentioned the mode of failure of some of thecolumns tested. Some of these will now be pictured.

SLIDE 13 shows Tl2 which failed by combined bending and tw~st.

This is typical of a,ll condition II C Il tests and ,for those columns \\which do not develop their predicted ~BEZXZ~EHEg~ collapse ~strength. L/~ for this test is 56. IJ.'he moment is not a !.l.maximum at the end •.

SLIDE 14 shows the type of failure tha t occurs when thecolumns do successfully carry the predicted strength. In this ~

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has reached tre yeild condition.

SLIDES 15, 16, and 17 show local buckling of beams andof a connection Ii

lJ.1hetheareThe

The frame of SLIDE 18 was tested under 3/8-point loading.condi tion of the central SEan is shown in SLIDE 19 and ofconnections in SLIDE 2(0'. 'l'he other members in each case8WF40, the frame previously shown having been 8B13 shape.influence of local buc kling in this case is quite severe.

SUMMARY AND DISCO'SSION--

1. In single curvature the column does not develop its yield&trength unless axial load is relatively low.

-vL)

2. Residual stress accounts for s'ome of the reduc tio n in load capacity

3. There appears to be a residual stress level of about 12 ksi in I 'the column material tested (8").

, '

4. Whenever the moment is not a maximum at the end then thecolumn is in a mer e serious condition.

"

5. For other load conditions, than single curvature the column-either w,ill· or will ,not ,develop tb,e pre2l.ieted collaps e strengthdepending on L/. and P. "

"

6. So long as axial loadis such that the maximum moment is atend, then .the column will 'at 'least devill10p its yield strength.

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205A . 5/11/51

ADDITIONAL NOTES NOT INCLUDED IN TALK

7

The purpose of this study is to determtne the Plastic'behavio4of columns. E.:olumns in bUildings are occassionally restrained . Icolumns and the program treated thus far in this talk has not ~dealt with this subject. However, the work is important isnce Iit provides an indication of the abili~y of. columns to carrymoments assumed.

For example .the tests show that, if these were members in \111a truss, bent in the same directionJ as that used in these tests, 1Jthe influence of secondary bending stresses may be quite pro- -­nouneed.

Since these columns will no t even carry c ondi tion "c"loading to the predicted yield point, it is extremely doubtfulwhether or not the strengths predicted by the Winter-Bijlaardtheory may be realized.

ACKNEWLEDGE~.ENTSAND REFS

The assittance of various individuals indicated earlierin the text.

rp"'hi s mater ial has been taken in part from:

Progress Report No. 2" " .K" " L

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TESTS OF COLUMNS UNDER COMBINED THRUST AND MOMENT *

by LYNN S. BEEDLE, JOSEPH A. READY, and BRUCE G. JOHNSTONFritz Engineering Laboratory,Department of Civil Engineering

and Mechanics, Lehigh University, Bethlehem, Pa.

ABSTRACT

Under sponsorship of the American Instituteof Steel Construction, test equipment has beendeveloped in which various desired combina­tions of axial load and end moments may beapplied to metal columns. Lengths of 8, 12, and16 feet may be accommodated in the apparatus,which is designed to test steel columns up toan 8WF40 rolled section size.

Axial load is applied by a universal testingmachine of 800,000 pound capacity. The endmoments are applied separately through leverarms with tension-compression hydraulic jacksmounted in series with dynamometers whichmeasure the thrust.,

The behavior of test columns under load isdetermined by the use of four measuring tech­niques: (1) taut-wire and mirror deflectiongages, (2) level bars, (3) SR-4 strain gages,and (4) whitewash. In addition, the moment­producing thrust is measured by aluminumtube dynamometers.

The test program is currently being spon­sored by the Welding Research Council. Some

. of the test results obtained are presented todemonstrate the effectiveness of the apparatus.The ohjectives of the program are described,the principal one being to determine the ulti­mate strength of steel columns under varyingcombinations of end moments and direct load.

INTRODUCTION

For a number of years the American Insti­tute of Steel Construction has sponsored re­search on the general column problem at theFritz Engineering Laboratory of the LehighUniversity Civil Engineering Department. Astudy of the local buckling of the flanges of WFcolumns was completed in 1942.(1) This wasfollowed by an investigation of tile behavior ofeccentrically-loaded columns. (2) The pre­vious work contains rather complete referencesto other theoretical and experimental studiesof the column problem.

In 1946, the AISC commenced sponsorship of

the current investigation of columns loadedwith combined axial force and various end mo­ments' simulating the loads acting on a columnin a rigid frame. Two principal objectives 'are:

(1) to determine the ultimate strength of col­umns under combined axial load and end mo­ment, and

(2) to determine the moment distributioncarry-over and stiffness factors of steel col­umns in both the elastic and plastic range. Avariation in the magnitude of compressive loadwill influnece these factors.

Some similar tests have been conducted onsmall specimens. So far as is known to theauthors, none approaching column sizes usedinstructures have been made in which a cons­tant axial load could be maintained while theapplied moment was varied, or in which theapplied moment could be maintained constantduring change in axial load. These, then, arethe essential features of this investigation:

(a) the use of rolled structural steel mem­bers, and

(b) the ability to independently vary axialload and end moment.

The program is now coordinated with a five­year investigation of the ultimate strength ofwelded continuous frames sponsored by theWelding Research Council with financial sup­portfrom the American Institute of Steel Con­struction, The American Iron and Steel Insti­tute, the U. S. Navy bureau of Yards and Docks,and the U. S. Navy Bureau of Ships through acontract with the Office of Naval Research.The Column Research Council also supports thework in an advisory capacity.

In Fig. 1 are shown the forces applied by thetest apparatus used in the current investigation.It will be seen that it is possible to apply axialload to the test specimen independently of endmoments. The concentric force, P, is appliedthrough knife edges with an 800,000 lb. Rhieletesting machine. Thrusts, F, applied hydrauli­cally to lever arms, deliver the moment. La­teral support, H, is provided. Previous investi­gators have used some of the testing arrange­ments shown in Fig. 2, since their study was

.'

*Progress Report No.2 on the "Ultimate Strength of Welded Continuous Frames and Their Components"

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TEST OF COLUMNS UNDER COMBINED THRUST AND MOMENT 115

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116 EXPERIMENTAL STRESS ANALYSIS

Fig. 5. Frame and column under

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column are separately centered between thevertical screws of the testing machine.

The knife edge seats, being rigidly attachedto the end fixtures, act to automatically posi­tion the knife edge blocks which are supportedwith wedge blocks and cylindrical bearings,enabling them to shift to the proper position.The moment arm is centered in the test frame

by adjustment of lateral tie rods.Thus with the equipment described, the col­

umn is placed squarely in line with the testingmachine axis, and the moment arm is positionedin the intended plane of bending, normal to theaxis of knife edges.

Prior to an actual test, the alignment ischecked usingSR-4 gages and level bars at theends. The SR-4 gages indicate the eccentricityat the ends (Fig. 7 is a typical arrangement),whereas the measured rotations tend to averageall the eccentricities and constitute a moregeneral indication of alignment. Thus far inthe investigation, centering under load, (theprocess by which the column is shifted withrespect to the machine screws or supports)has been used to a limited extent.* Extremeaccuracy of alignment of the vertical axis is notnecessary since a moment of considerablemagnitude is applied at one or both ends in alltests.

Hydraulic Pumps, 1acks, and Dynamometers

As previously mentioned, the application ofend moment is accomplished with tension-com­pression jacks in series with load measuringdynamometers. Two pumps are connected withhigh pressure tubing to each jack, one for usein tension, the other for use in compression.**The pumps, high pressure tubing. and jackswere procured commercially***, the dynamo­meters having been designed and constructed atthe Fritz Engineering Laboratory making useof SR-4 gages under license from Baldwin­SouthwarkCorporation. Fig. 6 shows the sys­tem in operation in the pilot test.

The dynamometers shown in the photographsconsist of aluminum tubes with heavy endsthreaded to receive the jack and pin connectors.Four SR-4 strain gages, type AD-I, were in­stalled on each unit.

The arrangement of strain gages on the dyna­mometers is one in which both the active, "A",and compensating, "D", gages are mounted onthe aluminum tubing, the "D" gages being* The use of this process by others has beendescribed by Osgood.(4)** Inorder to use the system at high compres­sive loads it is necessary to provide lateralsupport to the jacks. Thus far it has beenpossible to run tests using tension alone.***Messinger Bearing Co. Philadelphia, Pa.

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AXIAL·LOAD

200

150

100

""

"yA.l.S.C.""

p

p

o INITIAL YIELD

o COLLAPSE

200 400 600 800 1000 1200

END MOMENT

....

... ..

... ..

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o 50 100 150 200 250

20

40 l-----------t---,t----1

END MOMENT

- ,I ,., ._

~, .... _~ / .. .,J

1.1

,(d)

\.0.9.8.7

.6

r:AXiOI load not constant -: I

gradually reduced fromI 40 k. to 38.5 k.I

I.0 I---'·II-·~v----=-:...L-:t=:-:.::::::C¢:-:===---:o-=---T_------t---~

'/ ' --I (j '-r-: { ----- -I-- "----1o,

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It I " ' I '~ 'z: -Theoretical value (for elastic behavior onh )

I r-I I .: ~ j42...-Value observed in conditionI did test (~Ie)1° I I I.41---~1-h-llJrtt----+------;.---l-/~-A--+---.l.lr-------l

I : I ' '1'

,I I

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1

-1'--1-,---t'----f-- '«V'T- B(J'y ,~Iower yield (b)

point stressI '

" I (J =PIA + MISo '-------<_-'-__--,----J''-- --'--- -l- ---J

.6

()

cry,

r:: Carry - Over Factor (M lower I Mupper)

FIG.18.- CARRY-OVER FACTOR; ITS VARIATION WITH STRESS

II

L1.- ---~ --~------------------------------

Fig.~ ·Yielding lines· on column after test.

•

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:~~7

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F Ft

FIG. IS - BEHAVIOR OF RESTRAI NED COLUMNSLoads onStructure

+F P

T 1P F Loading Moment Diagrams

>Z>t""-<en­en

(+F ==t=~*=~)

tJ1' (t~='===t!::::=~t)

( b)

F!:Opoe::: Per

(d)

NearCollapse

(a)

Fixed EndBeam

TEST OF COLUMNS UNDER COMBINED THRUST AND MOMENT 127• I

.Fig. 15 Column Deflection At Midheight--pilot test.

ment distribution at any load as well as thebuckling load of the entire Jrame.

Consider the illustrative case shown in Fig.16*. For an infinitely rigid column, case (a),the beam is "fixed" at the ends. For a morerealistic column, case (b), the end moments inthe beam are reduced over their "fixed-end"values. As the loads F are applied and in­creased, case (c), the moment at the ends ofthe column will decrease and finally beComezero at the load which would produce bucklingif it were not for the factthal the beams willtend to prevent end rotation. At higher loads,case (d), the column "tries" to puckle but isrestrained from doing so by adjoining mem­bers. Note that greater than simple beam bend­ing'{"moment is developed at the center of thebeam span. Finally, when the combined bend­ing stiffness of the columns and b~ams framinginto a particular joint reaches zero, the entireframe will buckle.

The foregoingprocedure of analysis has beenrestricted principally to the elastic range. Oneof the purposes of this investigation is to de­termine to what extent similar procedures areapplicable in the inelastic range.

The preceding discussion has been pre­sented as a background for consideration of theexperimental methods of obtaining collapseloads and stiffness factors of framed columns.*The case described is one in which the col­umn is initially deformed in single curvature.

...

Thus far in the experimental program theseloads and factors have been determined for thecase where the total axial load is less than Pcr(Fig.16band16c). This is also the type of load­ing acting on single span rigid frames or on the .top floors of industrial buildings. In both in­stances the principal axial force comes fromloads in the beams. Consideration of specificframes shows thata condition of negative stiff­ness would almost never be reached in prac - .tice tmless additional load is applied directlyto the column. Whether or not negative stiff­ness develops is determined as follows: com­pute the critical axial load under pin-end con­ditions for the column; then distribute this loadto the beam and determine the maximum mo­ment under simply-supported conditions. Thebeam will not provide restraint to the columnifthismomentis greater than the plastic hingevalue of the beam.

Although no tests under restrained conditionshave been conducted as yet, collapse loads un­der this type of loading can be dete rmined withthe apparatus, simulating different degrees ofend restraint (variation in beam stiffness) anddifferent magnitudes of initial load due to bend­ing moment. As was mentioned previously, thisis a situation approached in the lower floors ofa tier building or in any case where the totalload on the compression member exceeds thecritical buckling load for a pin ended column.

In England, Professor J. F. Baker and hisassociates are' conducting a program at Cam­bridge University entitled, "Investigation Intothe Behavior of Welded Rigid Frame Struc­tures" under the auspices of the British Weld­ing Research Association. Numerous interimreports have been published by this group, ageneral report describing the work up- to thepresent time having appeared recently. \6) Thebehavior of the restrained column has re­ceived particular emphasis in their work andforms a basis for any future studies.

The Interaction Curve

The carrying capacity of the type of memberunder investigation is a function of applied axialforce and end moment. Such an "interaction"curve is shown in Fig. 17. For zero axial load,P, the member is a beam and initial yield andultimate collapse are determined from elasticand plastic beam theory. For zero moment,

1.0.8.6

Deflection ~ inches

2

~~-- 745 obseMdy-- . IIlCIlliTum

/

f~

I P

~'''''''Mmeasurement

I P

oo

90

30

60

kips

P

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