bolted beam-column connection_1961

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June, 1961 203

Bolted Beam to Column Connexions

A.

Synopsis

N. Sherbourne,

Thepaper describes an experimental nvestigationinto he structural behaviour of a particular ype ofbolted eam-column onnexion, in which the con-nexion consists of a plate welded to the end of a beamand astened o he flanges of the column by pre-tensioned high strength bolts. Some recommendationsaremadeas o heplas tic design of the componentparts of such an assembly and general conclusions aredrawnwhich may affect theplastic design of many

Ph.D., M.A., A.M.1.Struct.E.

types of

W , =W =

6 =b =

t =

A =

b y =

M =

L =

B =

T =

f Y =

M , =

fw =-

if =

t, =

E l .=

f Y ' =P , =

A , =

M,r =M f =

M W =

tf =d =

v =I =EI =

bolted connexions.

Notation

plastic collapse load on beams.applied load on beams.vertical deflexion of free end of beam.width of beam flange.thickness of beam flange.yield stress of beam material.net cross-sectional area of bolt.proof stress of bolt material.bending moment.fully plastic bending moment.distarxe between bolts.width of end plate.thickness of end plate.''effective "yield stress of plate material.shear stress.second moment of area of column flange.thickness of web.Poisson's ratio.yield stress of column web.yield load of the column web.area of reinforcement to column web.reduced full plastic moment.full plastic moment of beam flanges.full plastic moment of beam web.flange thickness.distance between flanges.applied shear force.length of heam.bending stiffness of beam.

Introduction

The behaviour of bolted beam to column connexionshas been investigated by Schutz (1959) and Johnson,Cannon and Spooner (1959). Whereaschutz hasdiscussed methods of analysis , he nvestigation ofJohnson et al. has aimed at showing the adequacy ofa ariety of connexionsmployingigh strengthbolts n tension and shear. Recently, Charlton (1960)has shown that boltedoints,usinghigh trengthbolts n tension, will develop ull strength when in-corporated in a portal frame.

In the plastic method of design it is often necessary

to position connexions a t points of high moment. Inconsequence, it is advisable o devise methods orproportioningboltedconnexions odevelop he ullplastic trength of the connectedmembers. It has

been the practice in the past to design the connexionto remain elastic at maximum moment, hus forcingplastic hinges o develop n he connected members,This may be safe design practice , but it is inefficientsince little can be learnt as to the true behaviour ofthe connexion and much wastage of material results,A more rational pproach wouldbe to design thecomponents of the connexion uch that he ntireassembly failed at maximummoment ogetherwiththe connected members.

A second onsideration in theplasticmethod of

design is the requirement of rotation capacity. Sincethe failure of an entire structure is associated with a

mechanism of discrete plastic hinges, the connexionsmust b e sufficiently flexible such that he connected

members may otate a t full plastic momentwhilehingesform elsewhere within hestructure.Inbrief,the connexionmustsatisfy thedualstructural con-ditions of strength and rotat ion capacity.

The current investigation is directed toward exam-ining the behaviourf a single type of bolted connexion.The assembly consists of a plate profile welded t o theends of thebeamsandbolted o he flanges of thecolumn with pretensioned hightrength bolts, tiffeningbeingprovided to he column web in the regions ofthe beam flanges. This ype of assembly has beenselected from the tests conducted by Johnson as beingthe onewhich offers thegreatest economy and sim-plicity.Schutzhas also pointedout thatplasticallydesigned joints which make use of high strength bolts

in tension require a smaller number of bolts and less.fitting material than conventionalplices which employthe bolts in shear only.

Attention has been paid to the strength of the threecomponent par ts of the connexion, viz.,

(A ) The high tensile bolts.

(B) The end plate.

(C ) Column stiffening in he regionof thebeamcompression flange.

TheExperimentalProgramme

All the test specimens were fabricated from ordinary

mildsteel o B.S. 15-1948. Thebeams were 15 X 5R.S.J. and the column stubs 8 X 8 X 35 lb. UniversalColumn Section. A series of five tests were carriedout, the first group of three tests using f in. diameterhigh tensile bolts nconjunctionwith 9 in. diameterblackbolts as shown nFig. 1. Thesecond series of

tests, also shown nFig. l , used 8 in.diameterhightensile bolts, when f in. bolts were found to be inade-quate for the size of beam involved.

Variousombinations of end late nd columnstiffener were employed n the ests.Theendplatewas kept at a constant width of 7 in. and the thicknessranged from l $ in. to 9 in. Stiffening was provided tothe column web in the region of the beam tension and.compression flanges. The stiffeners spanned he ullwidth of the column flange andvaried n hicknessfrom zero to Q in., the nominal thickness of the beam

flange.



204 Th e Structural Engineer

COL F L A N G E STIFFENERS 1 EN D PLATE

1 TEST I STIFFENEREND PLATE] H.T.6Oi..Td T Y P E OF FAILURE!

B 1 LATERAL INSTAB\LITY OF0 N o .a= sf iG

2v6EAMS & LOCAL 8UCKLlt-SOF COL STIFFENER.

B 2 . t ;'l WELD FAILURE AT BEAMo No

I I I I P L A T E , I'NSDN FLANGE 6- END

Fig. -Details of connexions

The bolts used in the est were in. and 8 in.dia-meter X 3 in. long high tensile bolts upplied toA.S.T.M. Standard A.325-55 T with a specified mini-mum proof stress of 37 -9 ons per sq. in. and a mini-mum tensilestrength of 53 - 5 onspersq. n.Theywere used in the"as received "condition with hardenedsteelwashersnder both ut nd ead. Typicalstress-strain curves for these bolts are shown in Fig. 2.These data were selected from tests on several bolts,there being some variation in the mechanical properties

of the specimens tested.Thetressesndtrainswere obtained from readings of the load and extensionusinga 2 in. gauge length and henetarea of theboltat he root of the hread.The gauge length of

2 in. was selected as being nearlyequal to hegriplength nall the tests. The handbook values of thenet areas of the bolts were used to obtain the nominalstress.

A simple torquespanner was used to ighten hebolts, the torque being read off a gauge integral withthe head of the spanner . The spanner was calibratedinitially and found to be correct at torques of 320 lb. ft.and 470 lb. ft., the working torques of the 2 in. and8 in.olts respectively. Thealibrationurve is

shown in Fig. 3 over the entire range of the spanner.All traces of rus t and mill scale were removed fromthecontactsurfacesby wire brushing and heboltswere given an nitial orque of approximately one-



June, 1961 205

th ird of the working value in order to bed the platesdown.The uts were then slackened off in turn,screwed finger-tight and finally brought up to the fullworkingvalue of torque. In all ests he orque wasapplied to henut, he boltheadbeinggripped topreven t slipping. The sequence of tighteningbeganwi th the outermost ension bolt and continued downthe row of bolts along eachflange until the bolt nearestthe compression flange was reached.

STREE

A \'G

t s i

\

Fig. 2-Stress-straincurvesfor 2 in. and in., aH. T.bolts

600 p

I

50G t /

G BSER b ' ED

T C R Q U E

S P A N N E R CORRECT A T 32 0 Ibft.

2001 d

M E A S J R E D T C R Q b E lb ;t

Fig.3-Calibration of torquespanner

The rrangement of the loading and he nst ru-mentation is shown in Fig.4, nd the testswere carriedout in a 500 ton Amsler Hydraulic Testing Machine.The beams were loaded at a distance of 5 ft. from theface of the end plate and the column stub was allowedto otate freely n pace.Thedistance of 5 ft waschosen to avoid premature ateral nstability of thebeams,yetbe sufficiently far from he connexion to

minimise the effect of shear forces and obtain a condi-tion of almost pure moment a t the face of the column.I n computing the plastic collapse load of thebeamsectionnear theendplatedue allowance was made

Fig.4-Testingarrangement

for the hear forces. The modification of the fullplastic moment due to shearwas found o bz negligible.

Theareaaroundeachconnexion was coatedwithordinary plumber's resin to observe the initiation andpropagation of yielding in the specimen.

Before beginning the series of test s on the connexions,a numbx of tension specimens were cut from the beamandcolumnsections in ordero determine the mechanicalpropertiesof thematerial.Theresultsare containedin Table l and averagevalues of the measured yieldstresses were used in predict ing he ultimate load of

the connexion.

Discussion of Test Results

The test results for the five connexions are summar-ized in Fig. 5 in terms of the tot al applied load W an dthe averagevertical deflexion B of theends of thebeams. In all cases theexperimentaldataare com-pared with the idealized load-deflexion characteristicsfor a 15 x 5 x 42 lb. R.S.J. as derived in Appendix I.Also included in Figs. 6 to 10 are photographs showingthe connexions after test and Fig. 11 shows a typicalweld failure which might occur in connexions of thiskind.Thephotographsgive a qualitativepicture of

the yielding in the component parts of the connexionat failure.Throughout the tests the emphasisas on the overall

behaviour of the connexion as typified by strength androtation apacity. N o attempt wasmade to deter-mine the stress or strain distributions in the stiffeners,bolts or end plates.

Before discussing each test in detail, a few generalcommentsmay be made on the esults of the estprogramme as a whole.

0 1.0 2 0 ? O 4 0

V E R T I C A L DEFLEXION S - INS.

Fig. 5-Total load vs end deflexion -series A andB tests



206 Th e Structural Engineer

Table 1.- ension Test Specimens

Avg. Avg.vg.Mark Width U.T.S.ield Stresshickness

Modulus ofElasticity E

Avg.

in. Tonlsq. in.onlsq. in.on/sq. in.n. -AlCFA I CW

1.001

0.661 13,8001. 06.0.001 A2BF

12,8000.300.0010.484

A2CW0.99942CF

12,5000 .55. 8.412.00212,800

A 1B\\:29-6 15-55.668

13,2008 *86.91.002IB F

0.30412,8008.455.8 0.488

1.002

13,000

i\2€3\5' 1.001 0.422 - 30.9 13,800

A3CF 0 .g99 0.464 16.65 29.4A3ClV

12,7000.999 0.297 18.2 28.8

A3BF 0 .g9812,500

0.665A3BW 0.999 0 -426

16.5 29.416.4

13,20030.0 13,800

~ _ _ _- 29.228.37.8

Avg. yield stress for the beams fy =16.0 ton/sq. in.

Avg. yield stressfor th e column web f; =17.63 tonlsq. in.

1

r:

Fig. 6-Test Al. 15 x 5 x 42 beams. 8 x 8 x 35#column. l&n. end plate. No column stiffeners.

fin. dia. H.T.bolts.

Fig. 8-Test A3. 15 x 5 x 42# beams. 8 x 8 x 35#

column. 4 in.end plate. Q in. column tiffeners.2 in. dia. H.T. Bolts.

1

Fig. 7-Test A2.15 x 5 x 42 beams. 8 x 8 x 35#column. 14 in. end plate. in. olumntiffeners.

2 in dia. H.T.bolts.

Fig. 9-Test B1. 15 x 5 x 42# beams. 8 x 8 x 35#column. 1 in. end plate. & in.column tiffeners.

6 in. dia. H.T.bolts.



June, 1961 207

I

Fig. 10-Test B2 .15 x 5 x 42 beams. 8 x 8 x 35 ?+column. 9 in. endlate. in. columntiffeners.

8 in. dia. H.T. bolts.

(a)Thecurves showed the flexibility of this ypeof connexion. Comparing the slopes of theelasticportions of the experimental nd pre-dictedurvesndicates thathe maximumrestraint developed was approximately 70 percent fulligidity.Thisestraint ppearedto be quite independent of the thickness of thecolumn stiffeners, being substantially unchangedfor &in. stiffener (specimen A2) as for a8 in. stiffener (specimen A3).

(b) All the connexions except A1 met the require-ment of strength inasmuch as the plastic collapseload was atta ined and even exceeded. However,it was only connexion B1 which met the require-ment of rotationcapacity in tha t he plasticcollapse load was sustained to large deflexions.Specimens A2 and A3 mighthave qualified assound connexions if larger bolts had been usedand bolt failure avoided. Specimen B2 showedbetter characteristics than specimen B1 until apremature weld failure occurred.

(c) The connexions-except Al-behaved elasticallyto within the vicinity of the working load on thebeams and inelasticbehaviour bxam e evidentonly beyond this load.The working load wasderived using a load factor of l e 7 5 on the plastic

collapse load W,. Specimens A2 and A3, inwhich either heendplate or the column webreinforcement was very stiff, appearohavestrain hardened, whereas specimens B1 and B2,which used anominalamount of column rein-forcementnonjunctionwithmoderatelystiff endplate,exhibited considerable ductilityinsofar ashe curve showed alatter load-deflexion characteristic.

(d) Where the endplates were very stiff, i.e. con-nexions A1 and A2, the distortion of the columnflange suggests an elasticstressdistribution inthe bolts. Where thinner plates were used suchthatbmding of the late was permitted, it

appeared tha t he greatestdistortions of thecolumn flange occurred a t th e bolt mmediatelyabove hebeam tension flange. This suggestsan equalization of the forces in he bolts oneither side of t he beam tension flange,

Fig. 11-TestB2.Weld failurenensionlange

of beam.

(e) Thephotographs show relatively ittle yieldingon the tension side of the beams although con-siderable yielding has occurred in the flange andweb onhe compression side. This wouldindicate that he connexion is fairly stiff toresist compressive forces but fairly flexible inthe column flanges toabsorb he tensile forces

transmittedyhe beam. Clearly the fullplasticmoment is resisted by he compressiveforces in the beam a t th e face of the end plateacting n concertwith the tensile forces in thebolts below the neutral axis.

(f ) In the A series of test s the neutral axis appearsto be located between the second and third boltsfrom the op, i.e. the beam compression flange.In he B series of connexions-which employa different pattern of bolts-the neutral xisappears to coincide with the second bolt romthe boam compression flange.

Test A1

No stiffening was providedohe column andconsequently the failure was by local yielding andbuckling of the column web b2tween the beam com-pression flanges at a total load of 21. 2 tons (0.61 W,).A very heavy end plate was used in his connexion

and it appears that the b-am and end plate rotatedtogether asan integral whole, alldistortionsbcingtaken p yhe column flanges. Themaximumthrust n he column web app2ared to b? centredalong the axis of the column at a point slightly b4 owthe line of baam compression flanges. No yieldingwas noticeable ineither the b2ams or endplates.

Test A2

The effect ofntroducing a nominal amount ofcolumn stiffening can b? observed by comparing thistestwithhe previous specimen Al . Providing astiffener only one half as thick as the b2am flange wasresponsible for ncreasing the loadcapacity of this

connexion to38

ons (1 -1 W,) but the rotation of t heconnexion was curtailed by a failure in tension of oneof the outermost bdt s. This ype of failure may bc

ascrib-d to the stiffness of the end plate n relationto he rest of the assembly. From Fig. 7 it can b?



208 Th e Structural Engineer.

seen that he plate was sufficiently thick o resistbending between the bolts on either side of the beamtension flange, and hismay have had he effect of

inducing an elastic stress distribution in the bolt group.In consequence the higher stresses were carried by theouter line of bolts and no equalization of stress waspossible.

Test A3

This test was designed to observe the effect of heavy

column stiffening and aight ndplate,using thesame pat tern of boltsas n he twoprevious ests.The connexion developed a maximum loadof 42 -8 ons

( l -23 W,) until failure occurred in one of theboltsimmediatelyabove hebeam tension flange (Fig. S ) .I t may be concluded fromsucha ailure that someequalization of the stresses ook place in heboltson either side of thebeam tension flange. It wouldappear from the photograph that considerable yieldingoccurred n theendplate at he junctionwith thebeam tension flange.

TestB1

This connexion developed the most favourable

moment-rotation haracteristics of the ntire seriesinasmuch as he collapse load was sustained o largevertical deflexions of the ends of the beams.Themaximum oad carried was 38 -2 ons ( l - 1 W,) at adeflexion of 4 in. and failure only came about owingto the lateral instability f the beams after onsiderableyielding had set in along the beam compression flangesnearhe endlate. Unlike the previousests,moderately stiff endplate was used in conjunctionwith light column stiffening and this test best demon-strates the plasticbehaviour of this type of connexion.An inspection of Fig. 9 shows that,at failure, con-siderableyieldinghas occurred in all he componentparts of the assembly, viz. the beams, column stiffenerplates and end plate,and considerable distortions of

the bolts have taken place.

TestB2

The connexion was similar to connexion B1 exceptth at a slightly hinner end plate and slightly hickerstiffener was used. The nitial load-deflexion charac-teristics showed a marked improvement over specimenB1, the connexion being slightly stiffer and atta iningthepredicted collapse load a t a smaller deflexion.However, premature failure of this connexion resultedfrom a tea r n he fillet weld at th e junction of thebeam tension flange and end plate at a total load of37 tons (1 -07 W,) and an end deflexion of just under2+ in.Again, asn previousests, considerable

yieldingoccurredn the compression fibres of thebeams andhegreatestdistortions of the columnflange were centred roundhe olts immediatelyabove the beam tension flange.

DesignRecommendations

A few simple rules can be formulated for the plasticdesign of the component parts of the assembly. Ingeneral, these rules have been found to give conserva-tiveestimates of the loadcarryingcapacity of thebolts, the end plates and the column stiffening.

( a ) The High TensileBolts

Atfailure, it is assumed tha t the boltsabove and

below the beam ension flange arestressedequally.Implicit n hisassumption s he act hat heendplate s allowed to deform and so bringabout hisequalization of loadn the bolts. The four olts

Fig. 12-Forces on theendplate.

can thus be designed to develop the strength of thebeam tension flange, i.e.

where b t f y = he load carrying capacity of the beamtension flange.

bt fv =4Aoy - - (1)

A =net cross-sectional area of a bolt,oy=proof stress of the bolt material.

Using handbook values for a 15 x 5 x 4 2 # R.S.J.,the required area of a bolt is given by :

which shows that a 2 inch diameter bolt

is inadequate and a Q inch diameter bolt

is required.

( b ) The End PlateThe size of endplatecan be determined by con-

sidering the bending of theplate between theboltson either side of thebeam tension flange. Assuming

the bolts are spaced an equal distance about the beamtension flange and hat hey completely restrain heplate, then the maximum bending moment developedin the plate is given by (see Fig. 12) :

(Anet=0 -304 in.2)

(Ane t=0-422in.2)

LMext .= y bt 3 * * (2 )

where L is the distance between the bolts.

given by

The nternal resisting moment of the plate can be

where B =width of the end plateT =thickness of the end plate

B ! 2 =plastic modulus4

f =reduced yield stressdue to the presence of

shear stresses in the plate.

Applying a Mises Yield criterion the resisting moment

becomes

where ‘C is the averageshearstress n the endplate

and is given by

. .(4 )

Equatinghenternal nd xternal moments and

substituting for 7 obtain



June, 1961 209

Equation (5) assumes that the yield stresses of theplateandbeammaterialare dentical.Theequationcan be simplified to yield

from which the plate thickness can be obtained.Usinghandbookvalues or hedimensions of the

beam and a value of 7 in. for he width of the end

plate, heendplate hickness of the two series oftests can be deduced as follows :

A series L =3 i in. T =0.89 in.

B series L =5 in. T =1 . 1 in.

(c) Column Stiffeners

For most column sections used in practice, stiffeningbecomesessential n hevicinity of the compressionzones of the column web if general yielding and instab-ility is to be avoided. Parkes (1952)showed that themaximumstress n he web of an I beamunderapoint load was given by

2P

f=3 2 / 3 J t w

. . . . . .(7)

and I f=second moment of area of t he column flange

Thesolution wasderived by reating he columnflange as a finite strip acted upon by a ine oad Pand estingonanelastic oundation ormed of thecolumnweb. The tresses n he column webwereobtained from a stress function solution to the planestress problem and the highest stresses were shown tooccur at he web-flange junction mmediatelybelowthe point of application of the load.

The yield load of the unstiffened column web maybe determined by treating the end plate and columnflange as a single str ip of effective width B =7 in.-the width of the end plate-and total thickness equalto the sumof the thicknesses of the two plate elements

t w= hickness of the column web.

P,= 3 d3 y l t w y(1+v u 3 -4 B(tf +TI32 12tW

. . . . .(8 )

At full plasticity p=0.5 and the measured valuesof the column flange and web thickness are given by

t , =0 -328 in.

ti =0.492 in.

Sxptl. H.T . Bolts

,oad on heor.Cachbm. Bolt dia

V1 2 Tonn.

Exptl.3olt dia

in.

I

The yield stress for the column web is taken from

Simplifying equation (8)obtain for the load capacityTable 1 , fy’ =17 -63 tons/in.2

of the unstiffened columne

P,= -4 y’ (tf +T ) i/tw2B=22 -5 0-492+T )

. . . . .(9)

If the beam flanges are assumed to resist the appliedbendingmoment and hebeam web to resist theapplied shear, then the area of reinforcement requiredcan be derived by providingnoughmaterialodevelop thestrength of thebeam flanges. Assuming .

the yield stress of the reinforcement tobeequal tothat of the beams

btfy =A , f y +1 -4 y’ (tf +T ) V w w (10)-

For the five tests carried out a comparison is madein Table 2 between the heoretical and experimentalload capacities of the connexion as measured in termsof the load pplied on eachbeam. n omputingthe collapse load of the stiffened column web it hasbeen assumed that the yield stress of the reinforcing

plates is 16 tons/in.2 i.e. equal to that for the beams.It should be noted that a slight increase in the yieldstrength of theplatematerial would substantiallyincrease the load capacity of the connexion, especiallyin he case of specimens A2 and B1 which employthin plates

Conclusions

From heresults of this programme of tes ts t ispossible to note certain features which may assist inthe design of bolted connexions generally.

(a) A ominal amount of stiffening is usually requiredacross the column web especially in the region of

the compressionflanges of the beams. The practiceof providing a stiffener of identical thickness asthebeam flanges canbequite inefiicient andwasteful of material. The effect of this stiffeneris wo-fold nasmuch as the connexion gains instrengthndttainsheredictedlasticcollapse load, and instability of the column webplate is avoided.This last tem becomes im-portant if deep column sections are used. Sincethecriterion orpreventing nstability n hecolumn web is one of stiffness, notstrength,athin stiffener mountedorizontallyndncontactwithhe column webwould provideadequate bracing against out f plane movement.

Table2.-Comparison BetweenTheoreticalandExperimentaliResults

1 1 -1En dl.B=7” I

Theor.En d P1.

T n.

0-89

0 e89

0 *89

1.1

1 - 1

Exptl.Capacitynd P1.

Col. Web

Eqn. (9)in .Tons

____

1-232

33.0-975

27.6 0.735

38.8 1.232

38.8

0.735 27.6

Col. Web Stiffeners-Load Capaci ty I Type of Failure.

Area ofReinf.

l.672”x-0.318

0 632

0-318

0 - 529

Reinf.Capacity

=(Ax 16 tsi)Ton

-39.0

77 - 6

39 -0

65 - 0

TotalCapacity

P To n

Theor. Load on each Beam.P x Depth of Beam 15”

Lever Arm 60”-

38.8

77.8

105.2

72 -0

92 - 6

9 - 7

19-45

26.3

18.0

23- 15

Collapse of Col.Web.

Bolt Failure inTension.

Bolt Failure inTension.

Local Buckling of

Col. Stiffener &

lateralnstabil-ity of beams.Weld Fractu re.



The Structural Engineer

Theercentageestraint developed byhisparticular type of connexion appears to be quiteindependent of thehickness of the tiffener

plates. In four of the five testscarriedout hestiffening varied between one-half and full thick-ness of thebeam flanges with ittlevariationin the rigidity of the connexion.By far the most important conclusionconcernstqeplastic design of theentire assembly. Forthe connexion to be most efficient the componentparts must be proportioned so that hey reachthe required strength and allield simultaneously.Only n this way can ulladvantagebe akenof the ductile character of mild steel, and onlyinhis way will the equirement of rotationcapacity be realised.Theetrimental effect of providing a verythick end plate cannot be too stronglymphasisedsince suchplatemay seriously restric t herotation capacity of the connexion by its inabili tyto deform plastically. In some instances a thickend plate may also reduce the strength of a con-nexion by imposing an elastic stress distributionin the bolts with consequent failure in tension of

bolts along the outermost fibres of the end plate.It shouldeemembered that high tensilebolts have brittle mechanical properties and donot possess the bilityo deform lasticallyand thus equalise the forces within a bolt group.This latter effect can only be achieved by pro-portioninghehicknessoermitlasticdeformation of the plate.

Acknowledgements

The work described in this report was carried out intheEngineeringLaboratory of theUniversity ofCambridge, under hegeneraldirection of ProfessorJ. F. Baker. It forms part of a general nvestigation

into he behaviour of bolted and weldedconnexionsbeingcarriedoutwith heassistance of theBritishWelding Research Association.

Theauthor would like to hank members of theworkshop staff forabricatingheest specimens,and Messrs. R. W. Clark, J. W. Gatiss, J. D. H. Morgan,R. A. D. Noble and C. P. Woodcock, undergraduatesin heDepartment of Engineering, orassistance indesigning the experiments and carrying out the tests.

Appendix

Theheoretical load-deflexion relationshipor a15 x 5 x 42 lb. R.S.J. canbe-determinedon hebasis of an idealized elastic-perfectlyplastic tress-strain urve ormild teel.Thepredicted collapseload for the connexion can be obtained from the valueof the ullyplasticmoment of theoist, uitablymodified for the effect of shear forces

. . . . . a) Baker t. l. (1956)

M,r =reduced plastic momentM i=full plastic moment of the flanges alone in the

absence of shear forces=btf(d+ f)fyM , =fullplasticmoment of the web alone n the

t a2absence of shear forces=2 u

t, =web thicknessti =flange thicknessd =depth of section measured between inside edges

of the flangesfy =yield stress

V =applied hear force (see Fig. 4)2

The aboveelationship is derivedrom a MisesYield criterion and assumes that the flanges carry the

bending, that theweb carries the shear and is limited to

Usinghandbookvalues or he section propertiesof a 15 x 5 R.S.J. and a yield stress f v =16 tons/in.2from Table 1 obtain

M f =743 on n.M , =316 ton n.M , =1059 ton in.

Equating the reduced plastic moment to the appliedmoment obtain

(60

7-743)2 =316 6 1 6 - 35*84

fromwhich the otal collapse load W=34 -7 ons.

twdfy W twdf,Check- 52 -9 ons. i.e. -<-3 2 43

Compare with the load required to produce the fullplastic moment MP=1059 ton in.

- 60 =10592

W=35.3 tons.Themodificationdue to shear force is very small.The end deflexion of each beam can be obtained by

assuming the connexion to develop full restraint

W l 3

2 3EI .. -For E =13,400 tons/in.2I =428.5n.Handbook value.)

2=17-35 ons.

obtain 8=0 -22 n.

References

1. Schutz Jr., F. W., “Strength of Moment Connections usingHigh Tensile Bolts,” P r o c. A I S C , April, 1959.

2. Johnson, L. G., Cannon, J. C., and Spooner, L. A., “HighTensile Preloaded Bolts Tested n Joints Designed to Developthe Full Plastic Momentsof the Connected Members, BWRA

Repor t 01/6/58, March, 1959.

3. Charlton, T. M., “Collapse Behaviour of aBoltedFrame,”Engineer ing , February, 1960.

4. Parkes, E. W., “Stresses in Flanged Beams,” P h . 0 . T h e s i s ,University of Cambridge, 1951.

5. Baker, J. F., Horne, M. R., andHeyman, J., “TheSteelSkeleton,” Vol. 11, C.U. Press, 1956.

Discussion

The Councilwould beglad to consider th e publication ofcorrespondence in connexionwith the aboveaper. Com-munications on this subject intended for publication should beforwarded t o reach the nstitutionbySeptember30th, 1961.

bolted beam-column connection_1961

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