Lehigh UniversityLehigh Preserve

Fritz Laboratory Reports Civil and Environmental Engineering

1970

Shear in beam-to-column connections, September1970 (71-21)David J. Fielding

Joseph S. Huang

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Recommended CitationFielding, David J. and Huang, Joseph S., "Shear in beam-to-column connections, September 1970 (71-21)" (1970). Fritz LaboratoryReports. Paper 298.http://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports/298

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Shear in Steel Beam-to-Column ConnectionsThe current AISC design formula is shown to be conservativeby theoretical analysis and tests of a full size beam-to-columnconnection subjected to moment, shear and high axial loadsB Y D. J. FIE L DIN G AND J. S. H U A N G

(4)

(2)

Fig. 2-Exterior beam..to~column connec­tion

de

",II,.T

--..

M V-I

---TAJ'

I-

1, the design formula can be generalizedto include the additional shear forcefrom M l for an interior connection andthe reduction in shear force due to thecolumn shear Va to give2

w ~ y3 (Mr + Ml _ Va) (5)U y de db db

This formula dictates shear stiffeningfor a connection based on a morerealistic value of shear force but inde­pendently of the column loading Pa

in Fig. 1. If Pa is at the ultimate columnload, eqs (4) and (5) still imply,the samecolumn web shear capacity as if Pawere not present. This inconsistencyalong with observed column web sheardeformation in a frame test3 promptedthe current study of the effect of axialload on connection design.

In 1966 a series of seven pilot testswas begun on simulated exterior con­nections. Two of the seven tests weredesigned so that the column wep withinthe connection would yield in shear;however, -in all seven tests, failure

(3)

TT =-

Aw

where Aw is the area of the column webin the connection. If no shear stiffeningis present in the column web then

y3Mw>--­

- cry db de

Actually db and de should be distancesbetween flange centroids. If this formulais used the column web within the con­nection will be prevented from yieldingunder the action of the beam momentM in Fig. 2. However, referring to Fig.

tion under wind or gravity types ofloading. If the moment M in Fig. 2 isreplaced by the forces Twhere

MT = - (1)

db

and db is the beam depth, then the highcolumn-web shear force becomes ap­parent. The design of the connectionshear stiffeners is based on this largeshear force1 ,2 by limiting the shearstress T to the value cryl\/3 according tothe Von Mises yield criterion. This isusually written as

in which de is the column depth and wis the thickness of the web in the con­nection. If shear stiffening is present,an effective web area should be used.Combining eqs (1), (2), and (3) givesthe 1969 AISC design formula from theCommentary of the Specification, Sec­tions 1.5.1.2 and 2.5

D. J. FIELDING and J. S. HUANG arewith the Fritz Engineering Laboratory,Dept. of Civil Engineering, Lehigh Univer­sity, Bethlehem, Pa.

The work described in this paper wascarried out as part of an investigationsponsored jointly by the American Ironand Steel Institute and the Welding Re­search Council-publication of the paperwas sponsored by the Structural SteelCommittee of the Welding Research Coun­cil.

ABSTRACT.-The condition of high shearstress in rigid frame connections and theeffect of high axial force is investigated.A yield condition is derived and verifiedby a test. After yielding in the test speci­men, stable joint deformation was ob­served under monotonic loading and theconnection carried 2.75 times what isconsidered to be the yield strength inshear. The current AISC design formulais shown to be conservative.

Introduction

It is frequent practice in structuralframe analysis to consider that theconnections are the intersections ofbeam and column centerlines and thatthese junctions are rigid. According tothis assumption there is no relativechange in angle of rotation between abeam centerline and a column center­line. Actually a real connection shouldbe considered as a structural memberwith finite dimensions and loading.

Figure 1 shows an interior structuralconnection with an antisymmetricalloading as would be caused by wind orearthquake. The axial forces in thebeams are usually negligible. A similarloading occurs on an exterior connec..

Fig. I-Interior beam-to-column connec..tion

f

I'

Po

Me I"""'--"va

Pl~tlv,-

i ~ )-pr )

Vi. M,

Vb----A'"

t Mb

Pb

fI"

Theoretical AnalysisAssumptions

A beam-to-column connection can be

La-L.Jo 200kip-ft.

Fig. 3-Column moment· and shear diagrams

de - 211 < 70 (6)w -

that the distribution is a parabolicvariation from a constant stress at theedges, the error in assuming a uniformdistribution is smalL This is the sameapproximation that is made concerningthe shear stress distribution in beamwebs. In addition, the experimentalresults reported by Naka ef a/.s showthat the elastic shear stress distributioncomputed from strain gage data ismore nearly uniform than parabolic.Therefore, the assumption of uniformshear stre.':iS in the connection panel ismade.

In order to evaluate the behavior ofthe connection some reference loadsmust be calculated. Considering thestructure in Fig. 3 there are fourpossible failure modes. First, M r canreach the plastic moment for the beambefore the column fails. Second, theplastic moment for the column can bereached at sufficient locations to causea column mechanism. For the fixed-endcolumn in Fig. 3 three plastic hinges arerequired;6 M a , M b, and M L will reachthe plastic moment first. A third failuremode could occur if the column webis thin, that is, shear buckling of theweb. Normally the column web di­mensions are such as to preclude shearbuckling. If the column depth dr., flangethickness If, and web thickness w(including doubler plate thickness) sat­isfy the ratio

""r

p

M ja~Va

"rob1~~D~-0l£b

M;(C7a

)M rVTObIT b

() )

0"0

Va~

f MbP

Ar

Fig. 4-Connection stress states

COLUMNSHEAR

VaCOMectionShear Q

loaded as indicated in Fig. 1 in whichthere is a high moment gradient orshear within the connection. In Fig. 3is shown an assemblage of a column andcantilever beam. The elastic columnmoment and shear diagrams are alsoindicated. The portion of the momentdiagram within the connection is notactually known but can be assumed as alinear transition indicated by the dashedline. This assumption gives rise to theshear diagram in Fig. 3 indicatinguniform shear throughout the columnweb. This is equivalent to saying thatthe beam moment M r enters the. con­nection as shear at the beam flange asindicated in Fig. 2. This is reasonablebecause most of the beam moment iscarried in the flanges for wide-flangeshapes.

Two points are important in thisargument. First, the assumed forcecouple is statically equivalent to thereal moment and, therefore, equili­brium is maintained at the connection.Second, the complexity of an exactsolution of the stress distribution withinthe connection coupled with pastobservations of the pattern and effectof yielding warrants a simplified ap­proach.

It is often implied that this con­nection shear force is carried by thecolumn web as a uniform shear stressas in eq (2). Although an elastic solu­tion5using an Airy stress function shows

COLUMNMOMENT

(At Vr =86kips)

Legend:

-Theory--Measured

Scale:

fP+Vr

STRUCTURE,

P

~....... Mu

.h..2

Mo.........

, Mr -+ left>Mb fVr

11.2

occurred by the formation of plastichinges outside the connection and atloads very much in excess of the pre­dicted failure loads4• In the study it wasconcluded that connection shear de­formations were larger for higher axialload. At that point it was obvious thatthe shear capacity of an unstiffenedconnection should be based on anallowable story drift limit and not onsome imaginary ultimate load expressedby bound solutions using plasticitylimit theorems. 4 A study of the elasticbehavior of connections has beendone,5 and a study of the inelastic be­havior is underway at Lehigh University.The test of a beam and column as­semblage reported herein is part of thelatter investigation. The objective of thetest was to study the influence of axialforce on the behavior of beam-to­column connections that must alsocarry high shear from beam moment. .

In order to attain the test objectives,requireme~ts placed on the assemblagewere:

1. That the connection be very lowin shear resistance.

2. That the column web within theconnection carry large axial force inaddition to high shear force.

shear buckling will not be a problem."The fourth failure mode is that of

general yielding in the column web dueto the high shear force that is present.This mode of failure is stable in nature-that is, there is no unloadfng. AI..though the web of a wide-flange beamis yielded due to shear, the beam willcontinue to carry additional load untilshear deformation becomes excessive.2

This same behavior was observed inthe test of a corner connection8 inwhich the stiffness decreased sub­stantially but with no instability. Thisfourth failure mode is the object ofthis study and, in the following analysis,is assumed to be critical.

mately constant. This means that eq(7) can be solved for any single con­venient point in the connection panelrather than at every point and that theconnection panel yields throughout ata unique loading.

At the center of the connection inFig. 4, (fb can be taken as zero and (fa

can be taken as

(fa = ~ = (~) CJy (8)A c Py

where A c is the column area and Py

= (fyA c is the yield load of the column.From previous discussion2 the shearstress is written:

value. Unlike eqs (4) and (5) currentlyused in design1,2 and which ignoreaxial force, eq (10) indicates that Tab

must be zero when P = Py (columnfully yielded by axial load).

The equations derived can be used topredict general yielding of a connection.Although such information is inade..quate to predict ultimate capacity, itis useful in predicting the point at whichinelastic action begins. This will bediscussed again in light of experimentalresults.

Equations 9 and 10 can be combinedto give an interaction equation similarto eq (5):

Von Mises Yield Criterion

The Von Mises Iyield criterion or themaximum distortion energy theory offailure 9 for biaxial stress state as existsin a joint panel is written:

U (12 - Ua(jb + (jb2 .+ 3rab2 = (f y2 (7)

where a and b refer to the coordinateaxes in Fig. 4. In one test,4 strain gageswere applied on the column web withinthe connection and the principal stress..es were calculated and recorded. Fromthese data for a connection with noadded shear stiffening it can be seen thatthe left hand side of eq (7) is approxi..

Tab = 1- (Mr + M~ - Va) (9)A w db db

Substituting eq (8) into eq (7) gives:

(10)

This equation can be solved forTab = T y ', a reduced yield stress in shear.When Tab in eq (9) is equal to ry' theentire column web will yield due tocombined axial load and shear. Equat­ing the right hand side of eq (9) to Ty',any of the interrelated moments andshear can be calculated as a limiting

(11)

This formula specifies the columnweb thickness required to preventgeneral yielding under the action ofantisymmetrical beam moments M r

and M 1 and column load P.Conversely, eq (11) can be used to

compute the moment M r that will causeyielding of a column web with thicknesslV. All the moments and shears in eq(11) are related by the equations ofstatic equilibrium.

r

Column Top PkJte2"x 2411

X30"

W24x 160

See Fig. 8

Horizontal Stiffen,er

p,'--+t-........-..+t----...-......----<. TC" U4 (Some at Other End)

I III rh=IS"2V2 I 1F=~V;::::j========:=::::f

~11 IZ"0"74 I

IIL

(b)

(0 )

D. ,= y ~ (Bending Neglected)

ct­/

// /(f-:t---~ ~---=----JI I --II V

. dbI1=2:

--+-,~-"--"'-r-')""""-"~_

Rigid Link

(c) tP+V

Edge Preparation

Column Bose Plate3"x 24"x 2411

Fig. 5-Connection loading and equivalent cantilever Fig. 6-Co-nnection assemblage-Bl

Q = T - V (12)

and, from r = G'Y, the elastic sheardeformation of the column web withinthe connection can be computed as:

Elastic Connection Behavior

The shear force in the connection ofFig. 5(a) is:

Qy = ru'A w (15)and

T I

(16)'Y I - .-JL11 - G

much lower than the loads to causefailure of the column or beam outsidethe connection. A beam section with alarge plastic modulus was required;however, this plastic modulus had to berealized in the thickness of the flangesrather than in the depth of the beam. Anincrease of the beam depth would in­crease the strength of the connectionregion proportionally, so that the dangerof a failure outside the connection is notdiminished. Therefore, of beams withequal depths, only those with thegreatest thickness of the flanges hadbeen considered. Unless the beams andcolumns were designed in this way, ashear failure within the connectionwould not occur. Further, by omittingthe required shear stiffening, the ob­jective of obtaining a connection shearfailure should be realized.

A second consideration was that thecolumn and beam sections should forma connection of a realistic size andshape-that is, the beam depth shouldbe greater than the column depth andthe plastic moment of the beam shouldbe approximately twice that of thecolumn.

Interaction curves for combinationsof sections were used to finally select anassemblage consisting of a W14 X 184column and a W24 X 160 beam ofASTM-A36 steel. 13 The interactioncurves for the assemblage are shown inFig. 7. This is a plot of the non-dimen­sional column force ratio PjPl/ and thecolumn moment Me defined in Fig, 3and non-dimensionalized by the fullplastic moment of the column. Thesecurves are dependent upon geometryand boundary conditions. The assump­tion was made that the column endswould be fixed against rotation. Thebeam section failure curve representsthe value of M a when a plastic hingewould form at the end of the beam. Thecolumn failure curve shown is Formula(2.4-3) of the AISC specification! forcolumns bent in double curvature. Theother three interaction curves refer togeneral yielding of the connection usingeq (4), (5), and (11) and equations ofstatics to relate beam moment tocolumn moment M a • At high axial loadthe interaction curves for the connec­tion and the column outside the con­nection are very close. Obviously, themargin between connection yield fromeq (11) and'member failure outside thejoint is a maximum when PjPy = 0.5.

The geometry of the specimens of theprevious test series4, called the A-series,was adopted in this test as shown inFig. 6. That geometry was satisfactoryexcept for the following points:

1. Local buckling occurred in boththe beams and the columns.

2. The length of the column was tooshort. As a result, the shear force in thecolumn was high and cancelled out a

(19)Q- = GA w'Y

This is obtained from eq (14) as­suming that the flange contribution Q/is negligible. When the column webyields, the elastic shear modulus Gwill become zero as evidenced by tests. tO

However, the flange contribution fromeq (17) gives:

Description of TestThe single test described in this

section was proposed to study thebehavior of steel frame connectionsunder antisymmetrical moment loadingand axialloading. 12 Pilot tests4 indicatedthat axial load has some effect onyielding and deformation of connec­tions and so special emphasis wasplaced on" these factors.

Q! _ 24 Elf (20)'Y - db

2

where ehas been taken as half the beamdepth db.

The stiffness of the connection for aninelastic web is still based on the elasticmodulus and section dimensions aslong as the flanges have not fully yielded.This appears to be reasonable if oneconsiders the large shear strains thatare required before the connection panelcan strain harden. It is not implied thatstrain-hardening does not occur locallybut that the shear stiffness immediatelyafter yielding of the column web isprovided by the remaining elasticmaterial in the column flanges. Atlarger strains eq (20) will not be reliableas the flanges too become yielded.However, at larger strains it is possiblefor the entire connection web to strainharden. This strain-hardening effect hasnot been included in this analysis norhas the limit of flange contribution in theinelastic range.

The limiting shear for this behaviormust theoretically correspond to theformation of a plastic mechanism. 2

However, tests have indicated increasedcapacity due to the occurrence of strain­hardening in regions of moment grad­ient.ll

elastic,

Of particular importance in com...puting connection deformation is thestiffness, or the ratio of shear force to

. Q h ..shear straIn, -. When t e connectIon IS'Y

Design of Assemblage

The assemblage shown in Fig. 6,designated BI, represents an exteriorcolumn and the left hand portion of abeam from a multistory frame. Theparticular beam and column sectionswere chosen with two objectives in mind.First, the loads that cause failure withinthe connection web panel were to be

(14)

(13)Qr =-A w

The shear stress r is

Q'Y =~

GA w

The bending deformation within theconnection has been neglected but canbe included as others did. s The sheardeformation 'Y from eq (14), measuredin radians, will be the relative anglechange from the right angle betweenthe beam and column centerlines. Thisdeformation is normally neglected inframe analysis. The angle 'Y is not astrain at a point but rather the grossaverage panel shear deformation.

It is apparent that the connection inFig. Sea) can be represented by thecantilever in Fig. 5(b) whose length isone-half the beam depth. Equations(13) and (14) are the same for thecantilever and the connection. Thelimit of elastic behavior will be atr = r/ when there is general yieldingof the web in shear. At this point:

Post-Yield Behavior

The preceeding equations predictgeneral yielding of a connection panel.It is not necessarily true that the columnflanges bounding the joint are alsoyielded. If they are elastic there will besome remaining elastic stiffness of theconnection until these flanges too arefully yielded by the monotonic loading.This elastic stiffness can be computedfrom the model in Fig. 5(c) in whichthe flanges, connected by a rigid link,bend independently of the web.

Qj t 3

~ = 3£ (2Ij

) = 'YI (17)

where Qf is the portion of Q carriedby the flanges and If is the moment ofinertia of each flange (hf X 1f).

1If = 12 bl t/

3 (18)

For this model, the interaction be...tween the web and flanges after yieldinghas been neglected since it is assumedthat the web will deform freely. Thismodel is used only after the connectionDanel is yielded.

Fig. 8-Connection pa nel deta iIs

b

I I

5 10in.

Section b-b

o

-la

~21 Dia. ErectionBolts ~I Holes

Backing StripY411X~4xJ4Va

If(Typ.)

These jacks were arranged in a planeperpendicular to the plane of the assem­blage, the center jack being vertical andthe outside jacks being slanted awayfrom the beam toward the floor. Thisloading scheme provided stabilityagainst lateral...torsional buckling of thecantilever beam.

The column ends were made flat­ended. This provided greater stiffnessto the assemblage so that jack strokewould be conserved; however, thestructure was more indeterminate as aresult. The observed column end rota..tions are indicated in Fig. 11. Thebending moment M u in Fig. 3 couldbe applied to the testing machine cross­head with no distress to the system;however, the upper column shear Vawould cause the crosshead to drag onits guide rails. This condition waseliminated by providing a W36 X 194beam to accept the column shear (seeFig. 9). The beam was connected to thecolumn top plate through thirty 1Uin. A325 high-strength bolts, and restedon its side, supported by two smallermembers. The smaller members werebolted to the testing machine columns,and the stiff beam reactions weredelivered to the sides of the testingmachine through special bearing padsof mild steel. No lateral bracing wasprovided for the column.

In many respects this investigationwas a pilot test to determine the feasi­bility of testing such assemblages under

R=It5te'

Stiffener Both Sides4 !. !14

M

XS"x 12!1sM

Section a-a

a

1.0

welds were single bevel groove weldswith U in. root opening.

The horizontal stiffeners on the col­umn web were designed according tothe AISC specification1 to resist thecolumn web crippling force from thebeam flange. The ~ 6 in. fillet weldsconnecting the stiffeners to the columnflanges were the minimum allowed bythe thickness of the parts joined.1 How­ever, these welds tore during the test(see Appendix) and were built up to ~in. fillet welds for completion of thetest.

Section a-a in Fig. 8 shows that thestiffener was narrower than the beamflange width. There are no design guidesconcerning this detail, and the widthof stiffener was governed by the limitingwidth~thickness ratio.1

Test Setup

A special arrangement was devised toapply loads to the assemblage of Fig. 6.This setup is shown in Fig. 9. The axialload in the column was. applied by a5,000,000 lb capacity hydraulic uni­versal testing machine. The crossheadof the testing machine through whichthe applied column load was measuredis indicated. The base of the assem­blage was bolted to the floor with four1~ in. bolts.

The beam load was applied throughthree 100,000 lb capacity hydraulicjacks in tension as shown in Fig. 10.

tg~t0.=

Column Failure

II

" ~ Test 81

" " Beam Section" Failure

",~I

0.5

p,Ma~}Mr

Mb .

t~Eq.11

/ ~Eq.4

Eq.5

o

to.5

Ma{Mp}c

Fig. 7-lnteraction curves for the assemblage consisting ofW14X184 (column) and W24X160 (beam)

large part of the shear force in the con­nection.

These two factors caused failures· inthe A-series specimens outside the con­nection. The AISC design formulas1

have been used to check for localbuckling in this test. It was expectedthat the shear force in the columnwould be reduced sufficiently by takinga length of the column between in­flection points of ten feet.

The length of the beam in Fig. 6 wasdetermined by the capacity and strokeof the available hydraulic jacks, theavailable testing space, and the allow­able difference between the axial loadsin the top and bottom parts of thecolumn. As shown in Fig. 3, the axialload in the bottom part of the columnwas P + Vr where Vr was the beamload. The objective here was to keepP + Vr approximately equal to P toavoid premature column failure due toexcessive reduction of M pc at thesection below the connection.

The details of the connection be­tween the beam and column and thestiffening are shown in Fig. 8. Althoughthe fabrication was completely done inthe shop, the details are those of awelded field connection. An erectionplate was fillet welded to the columnflange. This plate had holes for erectionbolts and was to be used as the backingstrip for the beam web groove weld.The beam flange to column flange

Fig. IO-Beam load applied by threehydraulic jacks

+V

5

~P=O.5Py

8u

The absolute rotations of both thetop and bottom end plates of thecolumn and of the- support end of thebeam were measured with level barsattached to the member webs directlyinside the flanges. The locations of thelevel bars are indicated in Fig. 12.

The column load was applied andmeasured through the hydraulic uni..versal testing machine. The beam loadwas measured using three dynamo..meters located in series with thehydraulic jacks in Fig. 10. The dynamo­meters were each calibrated before thetest.

Before testing, the assemblage waswhitewashed so that yielding patternscould be observed and photographed.

Mechanical Properties

Over-all dimensions of the assem..blage as well as cross..sectional dimen..sions of the beam and column weremeasured. The over..all dimensionsagreed with those in Fig. 6 to withinX 6 in. so those dimensions are nottabulated. The measured cross-sectionaldimensions of the beam and columnsections are given in Table 1 along withthe corresponding dimensions from theAISC Manual.1

Tensile tests were performed onspecimens taken from the beam andcolumn flanges and webs. Two speci..mens were cut from the flanges and twofrom the webs of each section. The testresults in Table 2 are the static yieldstress, the tensile strength, and thepercent elongation in 8 in. Test resultsreported for the web are the averageof two tests. The static yield stress is

2 3 49 (RADIANS)

Legend:

---Theory--Measured

• 8uo 8L

4

o

200

240

160

V(KIPS)

Fig. 11--Column end rotations

gages on the beam web, Section boob.Stiffener strains were measured usingfour gages on each stiffener and onegage on the beam flange just outside theconnection and directly in line with thestiffener gages. These strain gage loca­tions are indicated in Fig. 12 Sectionc..c. Strains were automatically read andrecorded.

Dial gages were employed to measureover..all column shortening, beam de..flection, and lateral movement of thecolumn midpoint. The arrangement ofeight dial gages in the panel zone isshown in Fig. 13. This pattern wasduplicated on the opposite side of thespecimen so that measurements couldbe averaged, thereby excluding out ofplane behavior.

Each dial gage was mounted on a postwhich in turn was tack welded normalto the column web. A wire was thenstretched between the dial gage postand another post. The gage length, thedistance between the two posts beforestraining, was recorded prior to thetest. Two of the dial gages were used tomeasure diagonal deformation of thepanel zone, one gage being mountedalong each of the tension and compres­sion diagonals. The other six gages wereused to measure relative movementbetween the sections indicated in Fig. 12.

Translation and rotation was meas..ured between sections c..c and d-d, d-dand e-e, and f-f and g..g. Sections d-dand f..f are the centerlines of the con..nection. Sections c..c and e-e were located1 in. outside the connection boundaries.Section g-g was 4 in. away from thecolumn flange.

Dynamometers

HydraulicJocks

Testing MachineCrosshead

,-- 5,000,000 lb.Testing Mo:hineColumn

W6x20

Fig. 9-Test setup

W6x20

antisymmetrical loading condition. Thesetup was designed for reuse and hasthe following limiting conditions:

1. Maximum column load: 5,000,000lb (Load tested to 819,000 lb)

2. Maximum beam load: 270,000 lb(Load tested to 216,000 lb)

3. Maximum stroke at end of beam:11% in. (Tested to 11~ in.)

4. Maximum column dimensions:15~ in. X IS%" in. (Limitation is dueto floor bolt hole pattern.)

Instrumentation

Strain gages and dial deflection gageswere used to check forces and dis­placements. Four strain gages werelocated at each of four column crosssections as indicated in Fig. 12 Sectiona-a. These gages provided sufficientinformation to enable computation ofthe resultant axial force, bending mo­ment, and shear in the column aboveand below the connection. The beamload was monitored by two strain

Column Shortening

The response of the column, as it wasloaded to 0.5 Py , was in good agreementwith elastic theory as indicated in Fig.14. The abscissa is the column shorten..ing as measured by a dial gage. Theordinates are, first, the column load Pand then the beam load V. The columnshortening increased elastically due tobeam load until Vv', the load thatcauses connection yielding, was reached.(V/ is the beam load corresponding tothe condition expressed by eq (15) andby eq (11) plotted in Fig. 7.) Beyondthe load Vy ', inelastic column shorten..ing was observed.

Beam Load and Deflection

Figure 15 shows the response of theassemblage in terms of the deflection Llat the end of the cantilever beam.Deviation from elastic behavior wasnoted at 86 kips. The three referenceloads VI, -V2, and Vy ' indicated on Fig.15 were computed by solving eqs (4),(5), and (11) respectively for the assem­,blage. In eq(4):

M = V1£ (21)

Fig. 13-Panel zone deformation meas­ured by dial gages (V == 117 kips)

Test Results And Discussion

vent any sharing of the column load bythe cross beam. After this precautionwas taken, the beam loading was begunin 10 kip increments. During the entirebeam loading phase the column loadwas maintained at 819 kips. Beforeinstruments were read, all readings werepermitted to stabilize under constantload; this required between ten andfifteen minutes for each increment ofload.

Frequent visual inspections of thespecimen and setup were made. As anadded precaution, a transit was used todetermine any possible lateral move..ment at the free end of the cantileverbeam.

Fir

~-- ..8"-

Section -b~b

2. Column loading up to 819 kip~

(PfPy = 0.5).3. Tightening transverse shear...pick

up beam at top of column.4. Beam loading to failure.The column was considered to be

aligned when the strain gages measuringaxial strains in the column were inagreement within 10% at a column loadof 100 kips. During the second step(column loading) a close watch waskept on the axial strains to ensure thatthe column was in fact receiving oqlyan axial load. The column load of 819kips was applied in five increments. Atthe end of each increment all instru..ments were read.

After the column loading was com..pleted, the cross beam in Fig. 9 wastightened in place. This was delayeduntil after the column loading to pre-

t2"

21/~·I

2 1'2

1'1 l

Section C·.c

b---;-

I

Legend:

- SR--4 Strain Gages

-- Lever Bars for RotationMeasurMWnt

,}13"Section a-a

tiT I3..1 ...

'A

f ~Q

I II

-Icd

I rI

I

If Q

to

3'II~

a

Fig. 12-lnstrumentation

Test Procedure

The testing sequence was as follows:1. Column alignment.

determined by reducing the testingspeed to zero in the plastic region of thestress..strain relationshipl4. This pro..cedure eliminates the effect of strainrate in the plastic region.

The mechanical properties from themill report for the W14 X 184 aregiven on the bottom line of Table 2. Thenotable difference in yield strength ismore than one might expect as a resultof the difference in testing speed.

The yield stress from the web testswas used to compute VI, V2, and Vy '.

Py was calculated as the sum of theproducts of web area and web yieldstress and flange area and flange yieldstress.

fl Top flange of column is on the beam side.

Table 2-Measured Mechanical Properties From Tensile Tests

of full yield. It is evident from this testunder substantial axial load that thisbasis is conservative and that there isa considerable reserve of strength. Thisreserve is due first to the strength of theflanges and stiffeners that surround theweb panel and act as a rigid frame.Second, it is due to subsequent strain­hardening of the connection web panel.

If the connection web had not yieldedin shear, the simplified plastic theorycould be used to predict a failuremechanism at the load Vp l'.2 The posi­tions of plastic hinges for such amechanism are indicated on the sketchin Fig. 15. Three hinges are required fora fixed-end column. The third hinge atthe column base is not req uired if theends are pinned. A second mechanismis possible: the formation of a singleplastic hinge at the end of the beam.The predicted load levels at which eachof these mechanisms would form areindicated in Fig. 15 by Vpc and Vp ,

respectively. The dashed lines in Fig.15 represent the elastic-perfectly plasticbehavior of the assemblage, the initialslope taking into account elastic sheardeformation within the connection zone.

In the analysis it was assumed thatno movement along the longitudinalaxis of the beam was possible. Thiscondition was only approximatelyachieved as shown by the data in Fig. 16.The maximum lateral movement at thebeam level of the assemblage was 0.2 in.After the formation of three yieldedzones the lateral deflection reversed indirection as would be expected for themechanism indicated in the upper partof Fig. 16.

As the beam load V increased to 16kips, flaking of the whitewash on thespecimen in the connection panel was

The member depths db and de havebeen taken as the distances betweenflange centroids (db - tb and d(: - te).2The condition that was assumed toobtain eqs (22c) and (23c) was that thecolumn ends were fixed.

There is very little difference amongVI, V2 , and Vv' for the specific axialload P/Py = 0.5 applied in this test.From Fig. 7 it is clear that V2 calculatedfrom eq (5) is equal to Vy' from eq (11)when P = O. When the beam loadexceeded the value Vy', inelastic be­havior was observed.

The basis for eq (4) (VI), upon whichthe provisions of Part 2 of the AISCSpecification rest, is a limit condition

14.091 14.069 15.660 15.7821.135 1.128 1.378 1.3690.656 0.676 0.840 0.890

14.091 14.131 15.660 15.8051.135 1.135 1.378 1.38924.72 24.75 15.38 15.49

...-------- Beam --------., ,.-------- Column --------.,

.------- W24 X 160 --------.,r---- W14 X 184 -------....Elongation Elongation

O"y, ksi <Tu, ksi % in 8 in. <T y , ksi (Tu, ksi % in 8 in.

28.9 57.3 35.3 29.9 66.4 31.233.3 62.4 31.7 31.4 63.9 32.230.2 57.5 36.6 28.8 65.2 30.1

45.1 67.7 26.2

M r = V2{ (22a)

M z = 0 (22b)

3 L(22c)Va = 2" V2 /;

M r = Vy'l (23a)

M z = 0 (23b)

3 ,LVa = 2Vy It (23c)

Element

a Top flange of column is on the beam side.

Table I-Specimen Dimensions (In.)

Member ...------ Beam -. ...----- Column ---------.....---- W24 X 160 ----.., ..---- W14 X 184 --------

AISC AISCmanual Measured manual Measured

Member

Element

Top flange n

WebBottom flangeMill report

Topn Widthflange ThicknessWeb thicknessBottom Widthflange ThicknessDepth

where t is indicated on the sketch inFig. 15. In eq (5):

where Land h were defined in. Fig. 3.In eq (11):

Failure Modes

p= a.spyt

Vu=216-- r'l------{)

Vp =203-­

r Extensive Yielding at/ Locations 1,2 and 3

-~_....-/

240

200

Vpc=1732,3,- - - --

I160 IT-159

V ,(KIPS) 1

120 IIJ

I

Leoend:

---Theory

--~easured

tV

tP+V

100

V(KIPS)

h

p

J

200

a-+--:a~o~ot=--- P=a19 (0.5 E='y)

600

p(KIPS) 400

200

o 0.1 0.2

be (IN.)

Fig. 14-Column shortening measured by over-all dial gage

o 5 10

6 (IN,)

Fig. I5-Load-deflection curve of the connection assemblage­8!

Fig. 17-Panel zone at V == 117 kips

this time photographs were taken of theyielding at the plastic hinge locations.Figure 20 shows this yielding above andbelow the connection and Fig. 21 showsthe plastic region above the base plate.

The beam compression flange in Fig.22 shows yielding and possible incipientlocal buckling. The beam moment ex..ceeded the theoretical plastic momentfor the W24 X 160 by 6%. Figure 23shows the permanent plastic deforma­tion of the assemblage. The totalamount of beam deflection of 11.5 in.was limited by the maximum jackstroke.

Although considerable deformationin the connection panel was observedtoward the end of the test and despiteits yielded condition, the panel wasable to transmit the moments and forcesapplied to it. The tendency of axial loadto accelerate the onset of yielding wasobserved.

Connection Shear Deformation

The connection panel shear stress wascomputed using eq (13). The columnshear forces needed in that equationwere computed from the moment

Fig. 19-0ver-all view of ·connection as..semblage 81 before repair of stiffenercracks (V == 149 kips)

0.2

Legend:'

---First Order Theory--Measured

Loading continued to 149 kips. Atthis point cracks were observed at theends of the top horizontal stiffenersdirectly behind the beam tension-flange.These cracks occurred at the toes of thefillet welds. A later check of the designshowed that these welds had beenunderdesigned. The original design ofthe fillet welds did not permit develop..ment of the full yield strength of thestiffener plates.

.The specimen was unloaded and thesefillet welds were burned out to thebottom of the cracks and replaced withlarger welds that could develop theyield strength of the stiffener plates(see Appendix) although this may havebeen an overly conservative procedure.After the repair, there was no furtherdifficulty with the stiffeners. The appear­ance of the panel zone and assemblageis shown in Figs. 18 and 19.

The assemblage was reloaded to 136kips at which point the beveled grooveweld of the top beam flange-to-columnflange cracked. This crack was re­paired by burning and rewelding (Ap­pendix) but ultrasonic testing showedlack of fusion between the repair weldand base metal. A second repair of thiscrack was shown to be sound by ultra­sonic testing and again the assemblagewas reloaded. Extensive yielding beganat the three locations indicated in Fig.15 at 176 kips. Finally at 216 kips themaximum jack stroke was reached.Deflections increased at constant loaduntil the jack stroke was depleted. At

Fig. 16-Column lateral deflection i

v(KIPS) 100

Fig. 18-Panel zone before repair ofstiffener cracks (V == 149 kips)

200

noticed. At 46 kips flaking of white­wash was observed on the exteriorcolumn flange along a horizontal banddirectly behind the top pair of hori­zontal stiffeners. This yielding raises,some doubt concerning the validity ofthe flange bending model used toestimate the post-yield stiffness. At 86kips excessive flaking in the connectionpanel was observed. At the same loadFig. 15 shows a definite decrease ofstiffness. The appearance of the panelzone is shown in Figs. 13 and 17 atV = 117 kips.

-,-~~-------------_ ..- - - -- - -- -

Fig. 21-Plastic region above base plate(V == 216 ki ps)

(26)

Stiffener Strains

Strain gages were mounted on allhorizontal stiffeners. The two plots in,Fig. 27 show the variation of strainalong a compression stiffener and atension stiffener. The locations of thestrain gages are indicated below theplots. The stiffener strains are indicatedfor four different beam loads V. Above

(27)D,.J = d3 (1 - cos "I)

Beam Support End Rotation

The rotation at the connection endof the cantilever beam plotted in Fig.26 indicates the large rotations that areencountered after the connection panelyields. The rotation f)b is absolute rota­tion measured with a level bar. Thetheoretical curve was calculated as­suming a fixed-end column taking intoaccount elastic shear deformation withinthe connection zone. After Vy ' = 85kips, a second theoretical slope, cal­culated using the connection stiffnessexpressed by eq (20), is shown. Theindication here is that the approxima­tions used in eq 20 are acceptahIe forloads in excess of Vy ' and that the rota­tion f)b becomes larger than the pre­dicted value as yielding becomes ex­tensive in the connection.

where d3 is the distance between meas­urement pins. Using the first two termsof an infinite series for cos "I gives:

D.j = dB (f) (28)

This relationship has been graphed inthe upper portion of Fig. 25 and sohave the experimental results from dialgage measurements of D,.J. The shear

.strain values used in eq (28) .were themeasured values indicated in Fig. 24.Evidently, the second order effect oflarge shear strains expressed by eq (28)can Decome quite substantial.

Connection Compression

The column shortening indicated inFig. 14 agreed with theory until thebeam load exceeded Vv' at which theconnection yielded. After V y ', thecolumn outside the connection wasstill unyielded so the shortening shouldnot be ascribed to those parts of thecolumn. Furthermore, the column loadabove the connection remained con­stant and below the connection in..creased only slightly so that furtherelastic column shortening was small.The connection panel compression,then, must be an allied effect to thejoint shear deformation 'Y. The rela..tionship between the connection short­ening ~J and 'Y is indicated in the sketchin Fig. 25:

Fig. 23-0ver-all view of connection as­semblage 81 after testing

(25)

Fig. 2o-Plastic regIons below and aboveconnection panel zone (V == 216 kips)

The shear stress-strain curve soobtained is plotted in Fig. 24. It shouldbe remembered that this is not a shearstress-strain curve for a pure shearcondition but rather for high shear inthe web of a particular wide-flangesection, the W14 X 184. The elasticregion of this curve agrees well with theelastic shear stress-strain curve usingthe elastic shear modulus G = 11,500ksi. The inelastic region predicted byeqs (13) and (20):

~ _~ _ ?:4ElfI' - Awl' - A wdb

2

is dependent upon the elastic propertiesof the web boundary.

The stresses T y and T y ' in Fig. 24 areobtained from eq (10) assuming P = 0and P = 0.5 P'y respectively. The stressry' more accurately defines the experi­mentally observed yield stress. The postyield stiffness is predicted by accountingfor the flange-stiffener boundarystrength.

where

gradients given by strain gage measure­ments. Shear deformation was obtainedby measuring the extension and con­traction of the diagonals of the panelzone. The extension 07 and the con­traction 08 are averaged to eliminate thecomponents due to column axial load.This average deformation is directlyproportional to the connection shearstrain. The proportionality is dependentupon the distances between the meas­urement points d1 and d2 in the sketchin Fig. 24:

'Y = (Vd12 + d22) 0 (24)

d1d2

0.2

TENSIONSTIFFENER

COMPRESSIONSTIFFENER

46 ~ips

tp+V

105kips 86 kips

'-86kips

------46 kips

Dial GogeMeasurementsof !J.j

V= /42 kips

105 kips

V=142 kips

y2.L\j cd 3 (I-cosY) ~d3 (2)

( Y From Measurements in FiO.24)

- - - ~~- - ---

----~--- -

010..------------ _

oL-_~~===:::='_------

1000

o

100

200

.. ( 1000(/-, IN/IN.)

v(KIPS)

0.1

6j (IN.)

Fig. 25-Column and beam loads versus connection shortening

P(KIPS)

+E

\ (JL IN.lIN,)

0.08

Measured

0.06

0.10

Measured(Eq.24)

1'"

dIIM~~Y----

0.04

0.05

Y (RADIANS)

0.02

~ .... With~ Web

o

20

30

40

o

160

P:cO,5 Pyt

200

Fig. 24-Panel zone shear stress versus shear strain deter­mined by diagonal gages 7 and 8

v(KIPS)

120

r(KS!)

8b (RADIANS)

Fig. 26-Beam load versus beam support end rotation

Fig. 27 (right)-Stiffener strains

v = 86 kips the strains measured inthe beam flanges at location 1 becameextremely large. This was due to theproximity of the gage and the beamgroove weld, an area of high residualstress and a certain degree of stressconcentration.

The strains in. the stiffeners de­creased from a maximum at the beamconnection end to zero at the other end.This would seem to indicate that thestiffener force is transferred to the webwithin its length and that welds are notqeeded where the stiffener joins the

exterior column flange. Such a possi­bility must be more fully studied.

Strains exceeded the yield strain(€y = 1200 J.L in.jin.) at location 2 in thecompression stiffener for V = 105 kipsand in the tension stiffener for V = 142kips. This indicates that the stiffenersdeveloped their full yield strength.Furthermore, because the strains de­creased to zero along the stiffener, thetransfer of the full yield strength of thestiffener to the column web was effected.

These results suggest that the stiff­ener welds be sized to transmit a force

equivalent to the yield load of thestiffener plate.

Maximum Load

A defined ultimate load for the con­nection was not observed. The observedmaximum load Vu at 216 kips waslimited by jack stroke; however, asufficient number of yielded zones hadformed to permit the structure to deformplastically without further increase inload. The predicted ultimate load Vpc

from simplified plastic theory was 173kips. The difference between Vu and Vpc

Table 3-Tests Results of 81 And A Series a

p ,----..~ Experimental --------------- Reference -------. Vu Vo Vo

Test Column size Py Vu Vo Vpc Vy' V2 Vpc Vy' V2

W2 81 W14 X 184 0.50 216.0 86 173.0 85.0 99.0 1.25 1.01 0.87

I~ Al W6 X 25 0.60 39.2 26 30.4 25.1 31.4 1.29 1.03 0.82

L1l A2 W6 X 25 0.80 35.6 22 12.9 18.9 31.5 2.76 1.16 0.70

rztt A3 W6 X 20 0.60 29.1 23 17.5 1.66

~ A4 W6 X 20 0.80 22.8 15 10.2 2.23

t$ A5 W6 X 20 0.80 17.4 13 13.3 1.31

t$ A6 W6 X 20 0.60 27.1 22 19.5 1.39

tU A7 W6 X 25 0.80 35.0 20 12.7 2.75

II All beam sections of A series are M12 X 16.5; all loads listed are beam loads (V) in kips.

is evidently due to strain-hardening inthe plastic zones outside the connection.This effect has been explained inprevious work. ll

The onset of inelastic behavior atV/ was clearly observed. The inelasticcolumn web deformation was pre­dicted by theory in the range of plasticdeformations.

A table containing the experimentaland reference loads discussed above isgiven as Table 3. The first row of thislist contains the data for the test re­ported herein, Specimen Bl. The testsdesignated Al to A7 were reported byPeters and DriscoIl.4 A sketch of thejoint detail is given in the column tothe left of the specimen designation. Thecolumn sizes are given for the assem­blftges all of which were similar to thatin Fig. 3. Axial load ratios PIP]} arelisted for the column segment havingthe smaIIer axial load. (Refer to Fig. 3.)

The experimental ultimate loads VIl

and the observed yield loads Va aregiven next. Va is taken as the load atwhich deformations deviate from anelastic prediction. The reference loadVp (: is the predicted ultimate load com­puted using the mechanism method ofthe simplified plastic theory.2 V/ andV2 are calculated from the equationspresented previously.

The ratio VlIlVpc shows the reservestrength of the assemblages over theprediction from simplified plastic theory.For connections with no shear stiff­ening AI, A2, and B1 there 'was noreduction in ultimate load. The finalcolumns in Table 3 are the ratios of theobserved yield load to the calculatedyield loads Vo/V/ and Vo/V2• Theseratios are listed only for connectionswith no shear stiffening with V/ con­sidering axial load. The data, indicatethat the equations for V3' can be usedto predict connection yielding due toshear and axial load.

The above predictions of connectionbehavior have been achieved withoutconsidering strain..hardening. Thismeans that connection web deformationfollows elastic-perfectly plastic behav­ior fairly well rather than to lead toimmediate strain-hardening. To utilizethis knowledge in design (through per­mitting higher allowable shear in webs)will require evaluation of the effect ofthe deformations on frame behavior.If the consequences of connectiondeformation are tolerable, then noconnection shear stiffening is necessary.In addition, where stiffening is re­quired the amount of such stiffeningmust be based on the -required con­nection rigidity rather than on thecriterion defining connection yielding­eq (ll)-since post yield stiffness hasbeen demonstrated.

Conclusions

1. Yielding of the connection waspredicted with accuracy using the VonMises yield criterion to account forthe axial load effect-eq (11).

2. The ultimate load of the assem..blage occurred after the formation ofyielded zones outside the connection­Fig. 15.

3. Column web deformations withinthe connection can be predicted satis­factorily in the elastic range and theinitial portion of the inelastic range­Fig. 24.

4. There was a large margin ofreserve strength in the connection thatshould be considered in design. Thestrength of the assemblage exceeded alltheoretical ultimate loads-Table 3.

5. Any revision of connection shearstiffening requirements must be basedon required rigidity because shearcapacity exceeds that given by the yieldcriterion-eq (11).

6. The horizontal stiffeners, designed

according to the 1969 AISC Specifica­tion, behaved satisfactorily.

7. Weld detail and quality wereshown again to be important factors injoint design. Welds approved by ultra..sonic tests were satisfactory.

Acknowledgements

This work was sponsored by theAmerican Iron and Steel Institute andthe Welding Research Council. Theauthors are grateful for their financialsupport and the technical assistanceprovided by the WRC Task Group, ofwhich J. A. Gilligan is Chairman.

The project under which this reportwas written is directed by Dr. L. S.Beedle with Dr. G. C. Driscoll, Jr. andDr. W. F. Chen as advisors. The workwas carried out at the Fritz EngineeringLaboratory, Department of Civil En­gineering, Lehigh University. Dr. L.S. Beedle is Director of the Laboratoryand Dr. D. A. VanHorn is Chairmanof the Department.

The authors are especially thankfulto Messrs. J. A. Gilligan, C. F. Diefen..derfer, and C. L. Kreidler for theirparticular assistance in the fabrication,testing, and inspection phases of thiswork. Messrs. 1. J. Oppenheim and C.Bennett contributed their time to testingand reduction of data. Thanks are alsodue Mr. W. E. Edwards for his valuablecomments on this report.

References1. Manual of Steel Construction, Speci­

fication (and Commentary) For the De­sign, Fabrication, and 'Erection of Struc­tural Steel For Buildings, 7th Edition,American Institute of Steel Construction,1970.

2. Plastic Design in Steel, ASCE Man­ual 41, 2nd Edition, The Welding ResearchCouncil and The American Society of CivilEngineers, New York, 1971.

3. Yura, J. A., "The Strength of BracedMulti-Story Steel Frames", Fritz Labora­tory Report 273.28, Lehigh University,Bethlehem, Pa. 1965.

Repair of Connection Assemblage Bl

1. Crack no. 1 caused by under­designed fillet weld·-Fig. A. Crackburned out and fillet weld replaced

4. Peters, J. W. j and Driscoll, G. C., Jr.,"A Study of the Behavior of Beam-To­Column Connections", Fritz LaboratoryReport 333.2, Lehigh University, Bethle­hem, Pa. 1968.

5. Naka, T., Kato, B" and Watabe, M.,"Research On The Behavior of Steel Beam':To-Column Connections", Laboratory forSteel Structures, Dept. of Architecture,University of Tokyo, 1966.

6. Beedle, L. S., "Plastic Design of SteelFrames", John Wiley and Sons; Inc., NewYork, 1958.

7. Lyse, I., and Godfrey, H . .I., "Investi­gation of Web Buckling in Steel Beams",Fritz Laboratory Report 155.1, Lehigh Uni­versity, Bethlehem, Pa, 1933.

B. Beedle, L. S., Topractsoglou, A. A.,and Johnston, B. G" lIConnections forWelded Continuous Portal Frames", Prog­ress Report No.4, WELDING JOURNAL, 30(7), Research 'Suppl" 359-8 to 384-s (1951).

9. Seely, F. B., and Smith, J. 0 .. lfAd­vanced Mechanics of Materials", 2nd Edi­tion, John Wiley and Sons, Inc., New York,1932.

10. Ros, M., and Eichinger, A., "Experi­mental Investigation of Failure Theories(Versuche Zur Klaerung Der Frage DerBruchgefahr), Diskussionsbericht Nr. 34,Eidgenoessische Materialpruefungsanstaltan Der E. T. H. in Zurich, 1929.

11. Lay, M. G., and Galambos, T. V.,lflnelastic Steel Beams Under MomentGradient", Journal ASeE, 93 (STI) , P. ·381(February 1967).

12. Van Zuilen, L., Fielding, D. J" andDriscoll, G. Cot Jr., lIProposal for Test ofFull Size Beam-To-Column Connection Sub­jected to Moment, Shear, and High AxialLoads", Fritz Laboratory Report 333.4,Lehigh University, Bethlehem, Pa., 1968.

13. Standard Specification For StructuralSteel, American Society for Testing andMaterials, Philadelphia, 1967.14. Beedle, L. S.. and Tall, L" "BasicColumn Strength", Journal ASeE, 86(ST7) , p. 139, (July. 1960).

AppendixNomenclature

A c Profile area of columnA w Area of column webE Modulus of elasticity of steelG Shear modulus of elasticity of

steelIf Moment of inertia of individual

flanges of a beam or columnL Distance between column cen-

terline and load point in beamM Moment (kip-feet)M a Moment above connectionM b Moment below connectionM L Moment in assemblage at floor

base plateMz Moment at the left-hand side of

a connection

CriticalWeld

T

v

v,.

Plastic momentPlastic hinge moment modifiedto include the effect of axialcompressionMoment at the right..hand sideof a connectionMoment in assemblage at col..umn top plateApplied column loadColumn load above connectionColumn load below connectionAxial load in beam to the leftof a connectionAxial load in beam to the rightof a connectionPlastic axial load; equal to pro..file area times yield stress (kips)Shear force within a cOhnectionPortion of shear force whhina connection carried by thecolumn flangesPlastic connection shear force;equal to web area times shearyield stress (kips)Force system statically equiva­lent to bending momentStatical shear in any member;also beam load (kips)Shear force above connectionShear force below connectionShear force in the member tothe left of a connectionBeam load at observed yieldBeam load causing plastic hingeat support end of cantileverBeam load causing columnmechanismShear force in the member tothe right of a connectionStatical shear. (or beam load)produced by "ultimate" loadin plastic design (kips)Statical shear (or beam load)at connection yield accordingto Von Mises yield criterionStatical shear (or beam load)at connection yield neglectingaxial load and column sheareffectsStatical shear (or beam load)at connection yield neglectingaxial load effectFlange width of rolled sectionDepth of beam

h

e

Ou

'T

Tab

'Ty

Tv'

Depth of columnDistances between deflectionmeasurement pinsAssemblage column height be­tween fixed endsDistance between cantileverbeam support end and loadingpointBeam flange thicknessColumn flange thicknessFlange thickness, in generalColumn web thicknessDeflection at free end of canti­lever beam (in.)Axial column deflectionAxial connection deflectionDeflection in the direction ofthe beam axisShear strain (radians)Shear strain at shear yieldstress; Ty'/GDiagonal connection deflection(in.)Dial gage deflection where "n"refers to a particular gagenumberStrains measured by SR-4 straingagesAbsolute joint rotation (radians)Rotation of column base (ra­dians)Rotation of column top (ra­dians)Normal stress on an element(ksi)Normal stress along a-axisNormal stress along b-axisStatic yield stress from tensiontestUltimate tensile stress fromtension testShear stress on an element (ksi)Shear stress on element inplane of axes "a" and "b"Shear yield stress in ~e absenceof axial stress; (jy/y3Shear yield stress in the pres­ence of axial stress

~Fig.D

~ Crack No.1

) 314'1' ..... ~~6~

Crack No.2·

Fig. A

Backing' .$t~ipk;IX314"xI4~i"

1'6'JfV~I'

Fig. 8

Fig. C

with ~ in. fillet weld-Fig. B.2. Crack no. 2 caused by stress con­

centration at intersection of flanges­Fig.A.

(a) Arc-air out to bottom of crackchecking for bottom of crack by

magnafluxing.(b) Reweld with E7018 electrodes.

Add a contouring fillet weld (72in. leg)-Fig. B.

(c) Ultrasonic inspection: Weld re­jected due to lack of fusion as

indicated in Fig. C.3. Crack no. 2 re-repaired by re­

moving backing strip and burning outfrom bottom of flange-Fig. D. Re..weld approved on the basis of ultra..sonic inspection.