flexural strength of steel and concrete composite beams

8/12/2019 Flexural Strength of Steel and Concrete Composite Beams

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Lehigh University

Lehigh Preserve

Fritz Laboratory Reports Civil and Environmental Engineering

1-1-1963

Flexural strength of steel and concrete compositebeams,

R. G. Sluer

G. C. Driscoll Jr.

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Recommended CitationSluer, R. G. and Driscoll, G. C. Jr., "Flexural strength of steel and concrete composite beams, " (1963). Fritz Laboratory Reports. Paper1806.hp://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports/1806
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THE FLEXURAL STRENGTH OF STEEL

N CONCRETE COMPOSITE BEAMS

byR G Slutter

G C Driscol l Jr

This is a f inal report of ani n v e s t ~ g t i o n of c o m p o s i ~ e beams forbuildings sponsored by th e American nsti tute of Steel Construction

Fri tz Engineering Laboratory e p r t ~ e n t of Civil ~ ~ g i n e e r i n g

~ h i h UniversityBethlehem Pennsylvania

March 963

Fri tz Engineering Laboratory Report NOr 279 15


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279 5


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L IS T o F T: A B L E S AND IG U R STable Page

1 SUMM RY OF BEAM TESTS 272 SUMM RY OF E M TEST RESULTS 283a ULTIMATE STRENGTH OF STUD CONNECTORS 293b ULTIMATE STRENGTH OF SPIRAL CONNECTORS 293c UL+IMATE STRENGTH OF CHANNEL CONNECTORS 30

4 COMPARISON OF TEST RESULTS WITH ND 31

Figure

11

12

456789

1011

121314

DErAILS OF TEST E MS B1 THROUGH B13SUMM RY OF LOADING CONDITIONSDELAILS OF PUSHOUT SPECIMENS

STRESS DISTRIBUTION AT ULTIMATE MOMENTSHEAR ~ O N N E T O R FORCES AT ULTIMATE M O M E N ~ULTIMATE STRENGTH OF STUD. SHEAR CONNECTORSULTIMATE STRENGTH OF SPIRAL SHEAR CONNECTORSULTIMATE STRENGTH OF CHANNEL SHEAR CONNECTORSMOMENT-DEFLECTION CURVES. FOR E MS B1 TO B6MOMENT-DEFLECTION CURVES FOR E MS B7 TO B12RELATIONSHIP BETWEEN SHEAR CONNECTOR STRENGTHND MOMENT CAPACI TYMEASURED STRAINS ON MEM ERS AT MIDSPANSTRESS D I S T R I U T ~ O N AT MODIFIED ULTIMATE MOMENTMOMENT DEFLECTION CURVES FOR TESTS OF B10 BllND B12

323334

3536

3738394041

424344

45


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L I T L E S N F IG U RES continued

i i i


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S Y N P S S

The resul ts of a research program to invest igate the ultimatestrength of composite s teel and concrete members are reported. Theseresul ts along with informa tion on the 4ltimate strength of various typesof mechanical shear connectors are used to develop cr i te r ia for minimumshear connector requi rements for composite building members The effectof s l ip between concrete slab and s tee l beam is shown to have no measurable effect on the ultimate moment of a member A method of determiningthe ultimate strength of members ~ i ~ very weak shear connectors isdeveloped and applied to the a naly sis o f tes t resu l t s This method of

iv

analysis is used to establ ish a defini te minimum number of shear connectorsto be useq in pesign. t is shown that the redis t r ibut ion of load on shear

o n n ~ t o r s a t high load makes unnecessary to space shear connectors inaccordance with the shear diagram. One t e s t of a continuous member ispresented to show that not only ultimate strength th eo ry but plas t icdesign theory can be applied in a l imited way t o composite members


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A research program was i ni tia te d a t

279.15 -1

I N T ROD U C T lOoN

Prior to the adoption of the Specification for the DesignFabrication and Erection of S t ruc tu r al S t ee l f or Build ings l by theAmerican nst i tu te of Steel Construction in 1961 the design of compositebeams con si st in g o f a s tee l member and a concrete slab was based upon thee las t ic approach developed for the 1957 revision of AASHO StandardSpecifications for Highway Bridges Lehigh University in 1959 under the sponsorship of the American nst i tu teof Steel Cons truc ti on to develop a more sui table design approach forbuilding members where the problem of fatigue does not exis t For buildingmembers the solution need not be res t r ic ted to e las t ic concepts There-fore the test ing program was planned so that the u l t ~ t strength ofmembers could be careful ly invest igated

Elast ic design has been found to possess cer tain shortcomings inboth reinforced concrete design and s tee l design. These shortcomings s t i l lexis t when the two ma te ri als a re combined into a composite member Oneaddi t ional disadvantage of e las t ic design occurs with regard to th e d esig nof shear connec to rs Elast ic design concepts are not able to provide ananswer to the question of what is the minimum number of shear connectorsrequired in a composite member which wil l carry only s t a t i c loading

Efforts to solve the problem of shear connector design resul tedin refinements of simple beam th eo ry as pertains to composite members.Theories for incomplete interact ion in composite members were developed by


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3i nve st ig at or s i n America and abroad The concept of incomplete in terac t ipnhas added great ly to the understanding of composite act ion and has been in -valuable as a research tool . The effect of s l ip between s t ee l section andslab in the elas t ic range can be evaluated by this theory. Unfortunatelythe eva lu ation o f s t resses considering incomplete in terac t ion is very in-volved and requires information which is not available to the designer.For these reasons i t has never re su lte d in an economical shear connectordesign approach.

The semi-empirical formulas for loads on shear connectors whichf i r s t appeared in the 1957 S O Standard Specifications for Highway

2Bridges were based upon l imiting the s l ip between s t ee l member and slabto a certain value which has been found to be safe for fatigue loading.These same valu es w it h a more l i e ~ l factor of safety have been used in

3other specif icat ions for building design However because of the originalmethod of determining these values was not p os sib le to determine in arat ional manner how l iberal a factor of safety could be used in buildingdesign.

t was therefore necessary to consider the ultimate strength ofthese members to find an answer to the problem of what is the l eas t numberof connectors that is adequate for a composite member The method of cal-culation of the ult imate strength of composite members is not new but theuse of this approach for the design of shear connectors was developed fromthe research program described in this paper.

The experimental work for this program consisted of test ing twelvesimple span composi te members of 5 -0 span one continuous two-span member


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also having 15 -0 spans, and nine pushout specimens . All members con-sis t of a concrete slab 4 inches thick by 4 feet wide connected to

~ 7 beam with mechanical shea r connectors. None of the conclusions ofthis r epo rt nece ssa ri ly pertain to encased composite members. The ult imatestrength of m ~ m r s tes ted by other invest igators has been considered inorder to present additional date in support of the conc lus ions reached .


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.2 . E X P R M E N TAL PRO G RAM

The twelve 15 feet simple span members te ste d a re described inFig. 1, and are d e s i g n a t ~ d ~ s ~ through B12 The continuous member

-4

d e s i g n a t ~ d B consi st ed o f two spans of 15 -0 with the same crosssection. The shear connectors provided in each beam are l isted in Table 1along with the concrete strength for each ~ e m b e r Tests performed in thisinvestigation w h ~ h th e resul ts qave not been previously published areident if ied by an aster isk in the Reference Number columns of Tables 1, 3a,and 3c T ~ e l o ~ 4 i n g conditions for the tests of these members and thetests performed.by o th er in ve stig ato rs a re given in Fig. 2 and Tab le 2.The data o b t ~ i n ~ d for maximum applied moment type of f a i l u r ~ maximumcpnnector force, and maximum end s l ip are also given in Table 2.

will be ~ o t i c ~ that some of the twelve members in this prQgramwere tes ted several times. The procedm;e in these tes,ts was to load themember up to a point a t which strains on the tqP of th e concret e slab a tmidspan indicated t h a ~ r u s ~ i n g of the concrete was imminent. Then th emember was unloaded and loaded again with the load points further apart .The ultimate moment data for only the las t of such tests is used in the

a n ~ l y s i s t is not known to what e x t ~ ~ t previous loadings may haves l ight ly reduced final. ultimate moment.attained. However the resultsfor ultimate moment from these tests are conservative.

N e a ~ u l ~ i m a t e l ~ a d i t is imposs ib le to determine the loads theshear c o n n e ~ t o r s by m ~ a s u r e m e n t s such as s l ip between beam and s lab.


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279.15

easurements of strain on the s urf ac e o f the connector

r ~ s i n c e5

m x mum load per connector m y occur ft r y ie ld in g o f the connector materialTherefore ~ o t h e r means of determining the m x mum force which a connector canr s is t must be u ~ e d o ~ t investigators have used a pushout specimen such asth e one used in this i n v e s ~ i g t i o n and shown in Fig 3. Nine of these weretested in this investigation. he resul ts of these tests will be discussedin a l t r s ec tio n o f th e report .


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3. U L T I M A T E S T R E N G T H O F ME M B E R S

Assuming t h a t a suff icient number o f s he a r connectors have beenprovided the sta t ic ul t i m at e s tr en gt h o f th e member may be determinedfrom a fam i l i ar s i m p l i f i e d s t ress d i s t r i b u t i o n . s shown in Fig .. 4 t h i ss tress d i s t r i b u t i o n is s i m i l a r to t h a t assumed in determining th e u l t i m a t es t r e n g t h o f r ei nf or ce d c onc r e te members. In Fig. 4 is th e 28-dayc onc r e te s t r e n g t h f y is the y i e l d s t r e n g t h o f the s tee l an d a is thedepth o f the compressive s t ress block in t he c on cr et e when tha t depth i s

-6

less than th e s l a b t hi ckness. The dimensions o f sla b w idth s l a b t hi cknessan d beam depth a re b t an d d r e s p e c t i v e l y . The to ta l compressive f or c ein t he c on cr et e s l a b is designated by C and the to ta l tensile f or c e i.n th ebeam by T Any compressi.ve f or c e which may exis t i n th e s t ee l beam isdesignated by C . The moment arms from T to C and C a r e e an d e .

Composite members may be c o nv e ni en tl y d i vi d ed into two cases asi ndi cat ed in Fig. 4. Case I includes a l l members in which th e a r e a o f th econcrete s l a b i s suff icient to re s i s t the entire compressive force Crequi red f or e qu il ib ri um . Case I I includes a l l members in which th e con-c r e t e area is n o t suf f ic ien t an d the top flange o f th e s t ee l beam iss t r e s s e d to f y in compression. The s tee l member may c o n s i s t of a r o l l e ds e c t i o n b u i l t - u p s e c t i o n o r a s t ee l j o i s t Regardless o f th e dimensionso f the cr os s s e c t i o n the ul t i m at e moment may be c a l c u l a t e d by th e followingequations:


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Case I : C = 0. 85fd 1T = s f y 2C = T f y s 3a = 0 8 5 f ~ c

~ t a 4= -2 2Cd D 5u = = s f y t

Case I I : C = 0.85 btT = C C 1

2M u = C e C e

6

7

8

In these equations i s the ultimate moment and s i s the t o t a l area ofthe s t e e l sect ion. For Case I I , th e valu es of e and e are dependent uponth e shape of the cross s e c t i o ~

The assumption that th e concr ete does npt act in tension has beenmade for t hi s ca lcu la ti on . Hence a t sections where negative moment occurs,only the s t e e l member plus the slab reinforcing s t e e l r e c o n ~ i d e r e d I fslab s teel i s neglected, the ultimate moment of th e sect ion reduces to theplast ic moment of the s t e e l member.

The ultimate s t ~ e n g t h has been determined assuming that a sufficientnumber of shear connectors has been provided to completely develop the con-crete slab. I t ~ h p ~ l d be noted that e l a s t i c design methods do not neces-s a r i l y i n s ~ r e that th is condition i s s at is fi ed . ht b d {

t v s se.t:- / )Y[


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In tests of mem ers w s found that some m ~ m e r s reached theu l t i ~ t ~ load predicted y ~ above t heory whi le qthers did not the

d i f f e r ~ n e between these mem ers being only difference in the num er ofshear connectors . Obviously me ns of finding tqe minimum num er ofshear connectors requireq w s needed.

8


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U L TIM T S T R NG T Ho F SH R NN C TOR S

The minimum shear connector r e q u i r ~ m e n t may be d e f i n ~ d by cons i d e r ~ n g a free body of a portio n o f t he concret e slab between the crosssection t ultimate moment and th e end of the member as shown in Fig. 5.The force C is resisted by the f o r c e s ~ A u or the sum of the u 1 t i ~ t es tre ng th s o f shear connectors in the ~ e n g t h of slab Ls This provides

9

a means of determining the force on a shear c o n ~ e c t o r in a beam t ultimateload only when th e member has more than the minimum number required. twill be shown that th e ultimate strength of a member with less than theminimum requirement can be determined once the m i n i ~ u m n u m b ~ r is ~ n o w nfor that member.

Ev en though previous investigators had ignored the ultimatestrength of c o n n e ~ t o r s their work produced some rel iable data on thisproperty. Pushout tes t data was more r ead il y avai lab le t an beam tes tdata because beam tests of ~ e m ~ e r s with minimum numper of connectors

h ~ d not been made by o t h e r ~ Unfortunately not l l of the pushout t es tdata v i b ~ ~ c o u d be ~ s e d because the true ultimate strength qf a con-nector was not obtained i f the concrete slab was not adequately ~ ~ ~ ~or t he ooncr et e s t r n s ~ h was not adequate. The data t h t ~ d ~ tJl f 1afe f h ~ f A or 4JMt.- hrl.~ s been a r r a n g ~ d in Table 3 in the order of decreasing magnitude ofthe ultimate loa4 per cQnnector for welded studs s p ~ r a 1 and channelconnectors. The scat ter in the ~ a t a is in part due to the lack of a


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standard pushout specimen. Also was found that considerable care inalignment of a specimen was necessary to obtain consistent results

The data for welded studs was analyzed by f i t t ing a semi-empiricalcurve of the form previously used to specify allowable loads on shear con-nectors. t was generally observed that a concrete strength of 3 psiwas sufficient to develop the ful l s tre ng th o f those types of connectorstested. h e r e f ~ r e concrete strengths higher than 3 psi do not increasethe ultimate strength o f c onne ctors, but c on cre te strengths lower than3 psi m y r educe connector strength.

The ultimate stress in ksi for welded studs is plot ted as ordinatewith the height divided by diameter of studs as a b s c i s ~ a in-Fig. 6. The

t

maximum values for a concrete strength pf 3 psi are given. The empiricalformulas derived in this invest igat ion for the ultimate load per connectorare:

qu Rds for studs with i s less than 4.1 and: 9)10)

for studs with i s greater than 4.1, where R is the height of the studand ~ the diameter of the connector. In no case should qu be taken greater than the ultimate tensi le strength of the connector material. Forconcrete strengths of 3 psi or higher, the tensi le strength of connectormaterial is a convenient value to use.

In a similar manner the ultimate strength for spira l connectorsm y be determined. Available tes t resul ts are given in Table 3b and


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p lo tte d in Fig. 7 and an empirical formula for the ultimate strength of oneturn of spira l is given as:

, ,4f71qu = 8000ds J fc 11This fo rmula is of th e same form as used for spira l connectors in elas t icdesign. The value of a turn of spira l should never be taken as higherthan twice the tensi le strength of the spiral material .

The treatment of channel connectors i s r es tr ic te d to an empiricalapproach using a formula similar to the familiar elas t ic design formulafor allowable load on this type of connector. Data points are given inTable 3c and t e s t resul ts and formula are plotted in Fig. 8. The formulawrit ten in the form fo r u lt ima te strength of one connector becomes:

qu = 550 h = 0.5t w 12.where h is the average flange thickness, t is the web thickness, and w isthe len gth of channel.

The values given in the Speci f icat ion for the Design, Fabricationand Erection o f S tr uc tu ra l Steel for Bui ldings of the American Ins tuteof Steel Construction ,for a concrete strength of 3 p si are indicated bythe dashed l ines in Figs. 6, 7, and 8. The dashed l ines were obtainedusing a factor of 2.5 with respect to the u lt ima te value s.

Three formulas given above were used to determine th e ultimatestrength of shear connectors in the beam tests w ith th e exception that theconcrete strength a t the time of t e s t rather than th e 8 day strength wasused for The tensi le strength of the connector material was taken asthe l imiting value for studs and spira ls . The tensi le s tr engt h o f studswas taken as 7 ksi and the tensi le strength of spirals as 6 ksi .


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5. A N A L Y 0 F B E A M T S T S

The importance of bond and f r ic t ion in transmitt ing s he ar f or ce swas f i r s t evaluated. by test ing two beams, designated Bl and B2 which had

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no shear connectors . In both members shrinkage of the concrete caused bondfa i lure and the only sh ear fo rce acting was due to fr ict ion caused byapplied loads on the top flange. These f r ic t ional forces i nc re as ed th eultimate moment of member B by approximately above the plas t ic momentof the s t ee l beam This amount of shear t ransfer was assumed to benegligible in the analysis of beam tes t resu l t s I t was also assumed thatslipwhich is the basis of elas t ic analysis could be ignored in ultimates t rength analysis .

I t is therefore not neces sa ry to c on sid er whether or not theinteract ion between s t ee l beam and concrete slab is complete or incompleteas defined in the l i te ra ture on elas t ic analysis . To avoid confus ion withelas t ic analysis the terms lIadequate and l Iinadequate were adopted torefer to the sh ear connection. The shear connection is lIadequate i f thesum of the u ltim ate s tre ng th s o f the shear connectors in the shear spanis equal to or greater than the maximum compressive force in the slab a tthe point of maximum moment or s ta ted by formula:

1 3The term lIinadequate is used whenever the sum of the u lt ima te s tr eng th sof the shear connectors i s less than the maximum compressive force in thes lab, or s ta ted by formula:

qu = < 14


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All avai lable t es t resul ts of composite beams were evaluatedusing Equations 3 and 14. These resul ts are plotted in Fig. 9 with themaximum t es t moment M divided by the theoret ical ultimate moment asordinate and the sum of the ultimate strength of connectors qu dividedby the compressive force in the slab C as abscissa. The data plot ted inFi.g. is gi.ven in Table 4.

The curves of Fig. show that the condition qulc ::: 1.10 issuffi ient to insure tb at the theoretll cal ult:i.mate moment is at ta ined.The points plot ted in Fig. include tests with l l three types of con

=

nectors. This clear ly shows that the minimum shear connector requirementis I qu = C for an y composite e m ~ and that thi.s requirement is dependentonly upon the ultimate strength of the shear connectors. This requirementshould be s tis fie d t every poi.nt on the span.

t p


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6. U L T IM TE S T R ENG THO F . M E M B E R SWIT H I N A D E QUA T E CON: N E C TOR S

I t is p o s s i b l ~ to write an empirical equation 9 the sloping l inein th e l e f t portion of Fig 11 w h i ~ h WOUld g ~ v e a good approximation forth e ultimate strength of members with iqadequateshear connectors asfollows:

u= qu 98C 15This equation helps to evaluate th e degree of seriousness of a weak s h e ~ rconnection upon the u 1 t i m a ~ e strength of a member. However this equationcan not be e x t ~ n d e d to c o m p a ~ i t e sections and a m o ~ e basic u n ~ e rstanding of this problem is necessary

In ~ e s t s of members with inadequate sqear fonnectors i t was ob-serveq that generally c o n n ~ c t o r s failed 9n1y after the maximum moment hadbeen attained In cases w h e ~ ~ the connector s t r e ~ g t h was greater than 8of a d e q ~ a t e a flexural fai lure resulted without connector f a i ~ u r e .

T y p i c ~ l s t r ~ i n m ~ s u r m n t s m ~ on two members are shown in Fig. 12.Compared in Fig 12 are i d e n ~ i c a l members except that member B3 hadsl ight ly less than adequate cqnnectors whi le B6 had approximately halfthat number. ~ t u d y of these straiq diagrams and types of failures in-dicated that the stress block in th e concrete a t maximum load was similarto the concrete s t r e s ~ b l o c ~ in members with an adequate number of connectors.


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A theory for the c a l ~ u l a t i o n of tqe m a x i m ~ m b e n d i n ~ strength,when shear c o n n ~ c t o r s are i n ~ d e q u a t e referred to as modified ultimateIstrength d e v e l o p ~ d which exhibited good cqrrelation with t s t resul ts . This theory is based upon the stress distribution shown in Fig.

-15

From previous discussion, i t is obvious that the compressive force inthe slaQ can not exceed the sum of the ultimate strengths of the shearconnectors. Equiliprium 9f the horizontal forces is established as inCase of Fig. 4 a s s u ~ i n g that s tee l is stressed to f y either intension or c o m p r e ~ s i o n The modified ultimate moment may t h ~ n be cal-culated by the following f o r ~ u l a s :

qu 16)a 2 qu 170.85 fdb

As f s quC 2 18) C Ie 19)~ u Ce The values of e and ~ u s t be ~ e t e r m i n e d by considering the geometry ofthe seCtion .

The value o f ~ has peen c a l c ~ l a t e d for the t s t ~ e m b e r s qayinginadequate shear connectors and is given in Table 2. The q u a n ~ i t y M / M ~or m a x ~ m u m test momrnt d i v ~ d e d by the m o d i f i ~ d ultimate strength for

member is given in Table 4. The test results considered from thepoint of view of M / M ~ ~ n s t e a d of M Mu show better agreement with theoty

many of the members ~ was less than 1.0. The ~ o l l o w i n greasons are offered to exp lain this:

1. M e ~ b e r s B3, B6, B7, B8, and B9 were tested


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several times and cumulative damage from previoustests may have reduced the f inal resul t .

2. In m ~ m b e r s B6 B10 Bll , B shear connectorsact ua ll y f ai led t maximum load.

3. Because of the scat ter in the t es t results foru l t i m ~ e s tr engt h o f connectors, the value assumedfor a tes t member may have been too large.

4. No allqwance was made for fact some ofthe connectors may have peen infer ior Qr previously

5. Connector fai lure may have been premature becauseof cracks in the concrete slab produced in p r ~ v i o u stests

6. The p e r c e n t ~ g e of reinforcing s tee l in the slabinfluences crack width and also connector s t r e ~ g t hhe percentage of slap reinforcement in tes t m e ~ e r s

c o r ~ e s p o n d s only to ACI temperature s tee l requirements.

Members B10 Bll, B must be treated separately because of the typeof loading.

Elastic design of members supporting uni form loads resulted invariable s h e ~ r connector spacing between the end of the member and mid-span because horizontal shear per inch is determined by:

v VQ/I 20where v is th e horizontal shear per unit length, V is total appliedshear ,Q is the s t t ic l moment of the transformed, area of th e slab, and


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279 15 ; 7

I is the moment of iner t ia of composite sect ion When consideringthe ultimate moment condition spacing connectors in accordance with theshear d i g r ~ m does not seem to be necessary Beams B1D an d Bll weretested with five equally spaced concentrated loads and w ith s he ar con-nectors equally spaced Beam B12 was ident ical except that i t had anequal number of connectors spaced in accordance with the shear diagramResults of the tests of these members in the form o f ap plied m o m ~ n tversus midspan deflection are shown in Fig 14 The difference betweenth e curve for B12 and the curves for B1D and Bll is so s l ight as to beof no p r t i ~ l importance t can therefore be concluded that the shear connectors may be spaced uniformly regardless of the shape of the sheardiagram

Members B1D Bll and B1Z did not reach th e theoret ical ultimatemoment primarily qecause of inadequate shear connec tors Also i t shouldbe pointed out that th e cr i t i ca l point in these members was not th epoint of maximum moment but the section a t the second concentrated loadAt this point the applied moment is 89 of midspan moment and the com-pressive force in slab is only sl ight ly less than a t midspan n th i scase the compressive force is r e s ~ s t e d by the s hea r connectors in theshear span plus th e t e n s i ~ e strength of th e slab stee l This sectionr ~ h e r than midspan cr i t i ca l in beams B1D and Bll


25/57

279.15

7. I N L U N e E 0 F S P

18

Previously investigators have been great ly concerned about theeffect of s l ip on the completeness of interaction between slab an d beam, 1- - f rtl f v ~ S h + OThis factor has ~ e n i g n o r e ~ i n considering the ultimate strength ofmembers The maximum sl ip measured a t th e end of the beam wil l be usedin the i l lus t ra t ions which follow to show that s l ip is not a s ignif icantparameter when consi de ri ng t he ultimate strength of members

A careful reco rd o f s l ip was made on the three members B10 Blland B12 Maximum end s l ip for these members is plot ted as abscissa inFig 15 with applied moment divided by theoret ical ultimate momentplot ted as ordinate. The curves for these members with midspan deflect ioninstead of s l ip plot ted as abscissa nearly coincided. However there isconsiderable d if fe re nc e i n Fig 15 between th e curve for B 2 and the curvesfor BlO an d Bll. At M Mu of 0 80 th e maximum end s l ip for members BlO an dBll is n ea rl y t hr ee times the value of B12 However a t a higher load theconnector forces in the three members become redis t r ibuted an d the sl ipof the three members becomes more nearly equal. This is somewhat analgousto the redistribution of load which takes place in a r iveted jo int af te ry ie ld in g o f the r ivets occurs This further i l lust ra tes that the spacingof connectors need not be in accordance with the shear diagram.

To further i l lust ra te that s l ip is not an important factor a tultimate l oad consider t he load versus maximum end sl ip curves of membersBI BII an d BIll given in Fig. 16. In Fig. 16 the maximum en d sl ip is


26/57

279.15

plot ted as abscissa and th e applied moment divided by the theoreticalultimate m o m ~ n t is p ~ o t t e d as ordinate. All three of these members areident ical in cross section concrete strength and loading condition.The members d i f f ~ r e d only in n ~ m b e r of shear connectors in the shearspan although l l members had more than a d ~ q u a t e shear connectors twill be n q t ~ c e d that l l t h r e ~ members reached the theoretical ultimatestrength. However the maximum end s l ~ p of the member with the leas tnumber of c o n n e c t o r ~ was approximately four times the maximum sl ip of themember with the most c o n n ~ y t o r s t should aleo noted that the tot lamount of sl ip shown up to about 60 of ultimate moment in both Figs 15and 16 is less than 0 02 inch This is ~ e s s th an tw ice the thicknessthe le t te r 1 on ~ h i s page an amount which cal . not be considered as

19

disastrous structural d ~ m g e fp e engineer need not pay any at tent ion ~to this because i t would nqt affect the strength of beam. The sl ip t working load in a n o n c o m p o s i t ~ beam could be ten times this amount.

The midspan deflection is plot ted as ~ b s c i s s a for the samemembers BI ~ I I and BIll Fig 17 with the applied moment divided by

t h e o r e t i c ~ l ultimate moment as ordinate The t h r e ~ moment versus deflection curves n e a r ~ y coincide throughout the loading range andfact do coincide t loads near ultimate. This further i l lust r tes thatsl ip does not a f f ~ c t magnitude of the u l ~ i m a t e moment provided thatthe number of shear c


27/57

279.15

8 CON T U 0 U S M E M B E R S

The design of comppsite construction might be made even moreeconomical by applying the concepts of plast ic analysis along with ultimate strength design. To i n v e ~ t i g a t e whether this application ofplast ic design is feasible one two span continuous member designated asB 3 was tested. This member was ident ical to members Bl through B incross section and c on sis te d o f two f i f t e ~ n foot spans

The ultimate strength of this member d ~ t e r m i n e d using bothplast ic analysis and ultimate s t r ~ t h theory. The ultimate moment ofthe posi t ive moment region was taken as Mu of the composite section

w h r ~ s the ultimate moment of the negative moment region was taken as the s tee l member plus t he loqgi tud inal slab reinforcement.

The m e ~ b e r was tested f i r s t by l oa ding only one span a t a timeand stopping the loading below u l t i ~ t e Final ly the member was testedto fai lure with two concentrated loads on each sp an Fig 18 s h o ~ s themidspan deflection of both spans plotted as abscissa with th e total applied load P divided by theoret ical load a t collapse Pp The loadPp was exceeded in the t es t even though the value of ~ q u was only0.888 for the ends and 0.978 for the in te r ior portion of the two spanmember

t was observed d u r i n ~ the tests of this member that wide cracksformed in t he n eg at iv e moment region even a t loads below working load.


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279.15 21

A means of controlling this cracking should be employed in the designei ther in the form of an expansion jo int or suff ic ien t slab reinforcementto distr ibute cracks along the member However in members where th enegative plast ic hinge forms f i r s t appears that composite members couldbe designed by plast ic analysis . f buil t up members were employed inwhich the positive plast ic hinge formed f i r s t the rotat ion capacity ofthe posi t ive h in ge c ou ld be insuff ic ient to allow a mechanism to form.


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279.15 22

9. CON LUS I ON S

The ultimate strength of composite beams was carefully investigated and this was used as a basis for the determination ofminimum shear connector requirements for composite members The following c o n c l u s ~ o n s may be reached as a r sul t of th e testing program:

1. III t imate s t r ngth analysis p1P Viaea defini te1 k ~ d r J J O r J f . h c . o . . f e ~ o t N J - N 1 -minimum shear connector r e q u i r e m e n t ~ b s e d upon

the ultimate strength of shear connectors.2. The ultimate moment of a member wil l be attained

provided the ultimate strength of the shear connectors in th e shea r span equals or exceeds th e

3.compressive force in t he concret e slab.The shear connectors may be spaced uniformly ~ O _ j ~

/4. gardless of th e shape of the shear diagram.

4. The ultimate strength of a member may be determined i f the number of shear connectors is inadequate.

5. f number of shear connectors is adequatesl ip does not affect the load versus deflectioncurve within pract ical l imits .

6. Composite members may be designed by plasticanalysis on a i m i t e ~ basis.


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279,15 -23

10. C KNOW LED G MEN T S

.This study is part of a research project ent i t led Investigationof Composite Design for Buildings being carried out a t the Fri tz En-gineeringLaboratory of Lehigh University under th e g enera l d ir ec tio n o fDr. L S Beedle. The investigation is sponsored by the AmericanInst i tute of Steel Construction, and guidance for the p r o j e c ~ is supplied by the ISC Committee on Composite Design Dr. T R Higgins,

C h a i r ~ n The original p l a n n i ~ g of the program was conducted under thesupervision of Dr Bruno Thurlirnann.

W e ~ d e d stud shear connectors for the experimental investigationwere supplied and welded by KSM Products, Inc Moorstown, New Jersey.

The tests were planned and conducted by Messrs . Charles G C ~ l v e rand Paul J. Zarzeczny as a part of their programs for the Master of ScienceDegree. The authors wish to express their t n ~ s to Mrs. Dorothy Fieldingwho did the typing and for Mr Richard Sopko for his assistance with thedrawings.


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279.15

11. A P P N D I X NOT T I ONI /

24

following symbols have been d o p ~ e d for use in this paper:

a depth of concrete s t r e s ~ ~ l o ~ k at ultimate momentAsbc

of s t ~ e l member of composite beam - I I ) w i d ~ h of th e ~ o n ~ r e t e slab compressive force in t he concrete slab at ultimate moment I

c D c o ~ p r e s s i v e force in steel beam a t ultimate momenttd depth th e steel memberIds diameter of stud or ~ p i r l s h e ~ c o n n ~ c t o re d ~ s t n c e between compressive force in slab and tensile

force a t ultimate moment, e l distance between compressive force in the beam and t e n s ~ l eI I

force a t ultimate momentI - Ify y ie ld stre ngth of ~ t e e l

concrete compressive strength 8 daysh t h ~ c ~ n e s s of f l ~ n g e pf a ~ h n n e l shear connectorH height of a stud ~ h e r connectorI moment of i n e r t i ~ of th e c o m p o s ~ t e sectionLs length of span from point of m ~ i m u m ~ n t to point of z e ~ o

mome ntM applied o ~ n tI

plastic ~ m e f l t of a s teel s e c t i ~ n theoretical ultimate momentI


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279.15

P P N D I . X NOT T ON continued

-25

theoret ical ult imate moment for member with inadequateushear connectors

P to ta l applied loadPp theoret ical plast ic collapse loadqu ult imate strength of a shear connectorqu sum o f u ltim ate strengths of a l l shear connectors in shear

spanQ s ta t i ca l moment of transformed slab areat thickness of concrete slabT tens i le force in the .gteel memberv horizontal shear per uni t len gth o f member to ta l applied shearw length of channel shear connector


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279 15 26

2 TAB L S F GU RES


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279.15.-

TABLE 1. SUMM RY OF E M TESTS

-27

Specimen Reference Steel Size Test Type of Connector ConcreSection Concrete Span Connectors Spacing StrengSlab(in. (psiB1 * 12 27 4 x 48 15 -0 11 None --- 360B2 * 12 27 4 x 48 15 -0 11 None 360B3 * 12 27 4 x 48 15 -a 1/2 11 studs 2 @ 7.5 360B4 * 12 27 4 x 48 15 -0 1/2 11 studs 2 @ .7.5 360B5 * 12 27 4 x 48 15 -0 3 C 4.1 4 @ 20 360B6 * 12 27 4 x 48 15 -0 11 1/2 studs 1 @ 7.5 360B7 * 12 27 4 x 48 15 -0 J/2 11 studs 2 @ .7.5 333\B8 * 12 27 4 x 48 15 -0 1/2 11 studs 2 @ 7.5 333B9 i t 12 27 4 x 48 15 -0 1 3/4 11 studs 2 @ 15 333B10 * 12 27 4 x 48 15 -a 1/2 11 studs 2 @ 9 359B11 * 12 27 4 x 48 15 -0 11 1/2 11 studs 2 @ 9 359B12 * 12 W 27 4 x 48 15 -0 1/2 studs Variable 359

BI 5 Vf 17 3 x 24 to -a 1/2 studs 3 @ 5.5 556BII 5 17 3 x 24 10 -0 1/2 studs 2 @ 5.5 556BIll 5 17 3 x 24 10 I -0 1/2 studs 2 @ 7 556B21S 6 21 If 68 6.25 x 7 37 -6 11 4 C 5.4 I 6 @ 14.5 648B21W 6 21 If 68 6.17 x 37 -6 11 4 C 5.4 4 @ 36 558B24S 6 24 If 76 6.25 x 7 37 -6 11 41: 5.4 6 @ 14.5 562B24W 6 24 76 6.11 x 7 37 -6 11 4 [ 5.4 6 @ 18 550

Bridge 7 18 5 6 x 65.5 30 -0 1/2 11 studs 3 @ 14 328

1 8 If 17 7.5 x 30 21 -0 Spirals Variable 7382 8 17 7.5 x 30 21 -0 Spirals Var:iab1e 7043 8 17 7.5 x 30 21 -0 Spirals Variable 7384 8 17 7.5 x 30 21 -a Spirals Variable 704

*Tests performed in th is in ve stig atio n


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279.15TABLE 20 SU RY OF BEAM IEST RESULTS

-28

Member Test Type of Maximum Theoretical Values Apparent Maximum MaximuFailure Test Mu Mu Connector Force End SlMoment(*) f (kip-in. (kip-ino) (kip-ino) (kips per Connector) (ino)

B3 T2 A 2708 2880 -- 1204 (per 1/2 stud) 0.040I4 A 2636 2880 -- 12.9- 0.077T7 D 2514 2880 2647 1507 0.092

B4 T2 A 2571 2750 -- n .7 (per 1/2 11 stud) 00015I4 A 2546 2750 1205 00020T8 D 2614 2750 2490 16.6 00126

B5 T2 A 2695 2880 -- 5401 (per 4 11 channel) 00029T4 A 2758 2880 -- 7005 00046I I I B 2418 2880 2401 7204 0.207

B6 I2 D 2416 2880 2440 1708 (per 1/2 stud) 0.120B7 T2 A 2506 27.30 -- 11.2 (per 1/2 11 stud) 0.059

T4 C 2554 2730 2691 1300 0.139B8 T2 A 2618 2730 1204 (per 1/2 stud) 0.035T4 A 2.6.34 2730 -- 1400 0.063

T9 C 2491 2730 2557 1504 00129T2 A 2586 2730 -- 22.1 (per 3/4 11 stud) 0.040I5 A 2514 2730 -- 2604 0.039flO B 2514 2730 2626 31.4 0.198

B10 T13 D 2596 2760 271.7 1302 (per 1/2 11 stud) 0.268B11 I13 D 2556 2760 2717 1208 (per 1/2 stud) 0.199B12 . I13 2626 2760 2717 1306 (per 1/2 11 stud) 0.170B1 I3 1178 1141 700 (per 1/2 11 stud) 0.004B11 T3 A 1164 1141 -- 1006 (per 1/2 stud) 00008

1 4 12.14 1141 -- 1201 0.044.BIll T3 A 1154 1141 -- 1304 (p er 1/2 stud) 00021I4 A 1146 1141 -- 15.4 00071I6 D 1085 1141 1051 1606 0.092

B21S Tl C 12678 11920 -- 50.8 (per 4 11 channel) 0.010B21W I1 10057 11480 9589 91.7 (per 4 channel) 00077B24S I l A 14100 13600 -- 54.3 (per 4 channel) 0.006B24W T1 A 13690 13710 -- 51.4 (per 4 11 channel) 0.009

Bridge Tl C 16740 16455 -- 1304 (per 1/2 stud) 0.028IFl Il2 C 2572 2.150 -- 17.0 (per 1/2 spiral) 0.006 . T12 A 2362 2i50 -- 15.6 (per 1/2 spiral) 00007 . T12 A 2272 2150 -- 1500 (per 1/2 spiral) 00004Ift T12 A 2402 2150 \ 15.9 (per 1/2 11 spiral) 0.009*See Figo 2f Test stopped before fai lureB Failure to carry addit ional loadC Crushing of concrete slabD Tensile fai lure of connectorsE Failure by tensi le cracking of slabF Failure by connectors pulling out of concrete


36/57

279.15TABLE 3a. ULTIMAtE SIRENGTH OF STUD CONNECWRS

Specimen Reference Stud type of H/d Type of Concrete Max. Qu1t. SDiameter Test Failure Strength Slip S in . ) psi) in . ) 2 9 1/2 Pushout 4.5 D 5000 -- 14.54A 10 1/2 Pushout 8.0 D 3840 0.163 14.44B 10 1/2 Pushout 8.0 D 4390 0.170 13.9

B12-T13 * 1/2 Beam 4.5 D 3595 0.170 13.6 6Bridge 7 1/2 Beam 3.8 C 3280 -- 13.4

.BlO-I13 1/2 Beam 4.5 D 3595 0.198 13.2B7-T4 * 1/2 Beam 4.5 C 3337 0.139 13.0

3 9 1/2 Pushout 4.5 D 5000 -- 12.9B11-l 13 1/2 Bea m 4.5 D 3595 0.199 12.8

P5

1/2 Pushout 4.5 D 3600 0.265 12.1P6 * 1/2 Pushout 4.5 D 3680 0.290 12.1

. P8 1/2 Pushout 4.5 D 3063 0.335 12.1Pl * 1/2 Pushout 5 D 3600 0.200 11.0P4 * 1/2 Pushout 4.5 D 3600 0.190 10.4SA 10 .5/8 Pushout 6.3 D 3790 0.319 23.85B 10 5/8 Pushout 6.3 D 4250 0.279 22.56F 10 3/4 Pushout 6.7 D g 0.364 34.86B 10 3/4 Pushout 5.2 D 4240 0.246 32.56A 10 3/4 Pushout 5.2 D 3870 0.382 32.06G 10 3/4 Pushout 9.3 D 4590 0.276 31.57H 10 7/8 Pushout 10.0 D 3440 0.278 45.0

*Performed this ~ n v s t ~ g t i o n

TABLE 3b . ULTIMA IE STRENGTH OF SPIRAL CONNECTORSSpecimen Reference Spiral Type of Type of Concrete Max. Qu1t. SDiameter Iest ,Failure Strength Slip S in . ) ps i)

4A 10 1/2 Pushout D 2990 0.250 34.54B 10 1/2 Pushout D 2990 0.247 29.35B 10 5/8 Pushout E 3520 0.1395A 10 5/8 Pushout E 3520 0.190 43.72-1 11 5/8 Pushout 4540 0.047 42.92-2 11 5/8 Pushout D 3080 0.068 38.51 1 ,3/4 Pushout D 5120 0.023 58.36B 10 3/4 Pushout E 3250 0.075 54.96A 10 3/4 Pushout E .3250 0.088 52.31-2 U 3/4 Pushout E 2965 0.034 .51.1


37/57

279.15 -30

fABLE 3c. ULTIMATE STRENGTH OF CHANNEL CONNEC ORS

Specimen Reference Size of Type of Type of Concrete Load perChannel Test Failure Strength in.B5 3 t 4.1 Beam C 3600 18.13C 3H3 6 3 t 4.1 Pushout D 3920 14.93C 3H2 6 3 C 4.1 Pushout D 3310 12.6P2 3 C 4.1 Pushout E 3600 11.93C 3H 6 3 C 4.1 Pushout D 2810 10.5

B2 W 6 4 C 5.4 Beam C 558Q 22.94C 3W2 6 4 [ 5.4 Pushout D 4430 20.44C 3ell. 6 D 6320 19. 4C 3C9 6 D 5340 19.44C 3e10 6 D 5740 18.74e 3e7 6 D 4140 17 .14C 3eB 6 D 4770 16.44C 3F4 I ]}I 4690 16.24C 3e 6 6 l 3500 15.84C 3C5 6 D 3470 15.24C 3F3 6 D 4600 15.14C 3S2 6 E T970 15.04C 3W 6 D 2810 15.04C c 6 D 3140 13.24e 3e1 6 D 2010 12.54C 3F2 6 2650 12.44C 3F5 6 D 3080 12034C 3C2 6 D 2300 12.14C 3D2 6 D 3310 11.64C 3e3 6 D 2510 11.24e 3D 6 D 2990 9.94e 3Fl 6 it D 2580 9.64C 381 6. E 1340 8.04C 5 8 6 4 [ 1.25 Pushout .I 1. 5050 21.8.4C 5 I7 6 D 4360 17.14C 4T 6 D 4010 16.44C 5F 6 D 2110 16.44e 5T6 6 D 3530 15.84C 5 f3 6 D 3130 15.14e 5 2 6 D 2910 14.54C 5 I4 6 D 3190 14.24C 5 5 6 D 3310 14.14e 5S 6 D 2720 14.04C 5 6 D 2300 13.25C 3H2 6 5 [ 6.7 Pushout D 3260 15.25C 3H 6 5 L 6.1 Pushout D 3110 14.9 Performed in this investigation


38/57

279.15 -31

ITABLE 4. COMPARISON OF TEST RESULTS WITH AND Mu

Beam Test Type of Fai lure quiC M M IMuB3-T7 D 0.772 0.873 0.950B4 T8 D 0.722 0.951 1.049B5-T11 B 0.437 0.838 1.006B6 T2 D 0.473 0.838 0.991B7 :T4 C 0.897 0.936 0.950B8 T9 C 0.717 0.913 0.976B9 TlO B 0.807 0.922 0.958BlO-T13 D 0.888 0.941 0.956B11-T13 D 0.888 0.926 0.944B12-T13 D 0.888 0.952 0.968BI-T3 C 2.04 1.030 BII-T4 C 1.21 1.061 BIII-T6 C 0.760 o 9 51 1.032Bridge C 1.045 1.020 B21S C 1.95 1.062 B2 W C 0.50 0.877 1.050B24s A 1.59 1.036 B24W A 1.41 0.998 No. 1 A 1.57 1.090 No. 2 C 1. 75 1.110 No. 3 A 1.72 1.052 No. 4 A 1.60 1.032

\


39/57

~ ~ r ~ T : ~ : ; : : i L4N=

I SECTION ELEVATION 8 TO 8 2

ELEVATION 8 3

ig DETAILS OF TEST BEAMS l THROUGH B


40/57

279 15 33

I

L8b4

L

1 188L8 tP4 4

l t

L L2 2I It L \ I

Test TI Test TI

L b b b L Lp5

L I L Test x in inches Test TIT2 9T3 2T4 8T5 2T6 23T7 28T8 30T9 33TIO 36Til 38

Fig 2 SUMMARY OF LOADING CONDITIONS


41/57

v \J

ELEVATION

Spherical Bearing

612 6Mesh

Plywood

r1~ i = A l I ~ =: Ii f -

1

. . :: 1;; . ...

SECTION B BFig DET ILS OF PUSHOUT SPE IMENS


42/57

e

c - . - -

r _ y Ie

T

O 8 f ~tCN Ae

c

T

L 0 8 5 f ~N.A.-T-

b : .p l 10 :1

4 A. , I I , J

y SE

y SE

Fig STRESS DISTRIBUTION AT ULTIMATE K>MENT

IW\Jl


43/57

x x p l

M

I J-p P P _onnector orces qu

ig SHE R ONNE TOR FOR ES T ULTIM TE MJMENT


44/57

80o

o

o

12

oooo

Beam Testo Pushout Test

D Recent Lehigh U Tests AISC Design t res _

930 /3000 ~ L ~ ~ = = ~ ; -As

8eight iameter of Stud HId

20

220Hds 300060 AS

c40

ig ULTIMATE STRENGTH STUD SHEAR CONNECTORS


45/57

8

o

6

oo

9o

4

o Pushout Tests

----- o O ~S o ~ q ~ -~------------

60

40 fc.=

Q) 20 0

J

ds i[ for SpiralFig 7 ULTIMATE STRENGTH OF SPIRAL SHEAR ONNE TORS


46/57

3 o Pushout Tests Beam Tests b Recent Lehigh U TestsenC

c. 2Qccs ;U

0s ; 1c

QC00 J

q u = 5 5 0 h + O . 5 t v 1 ~

o oo oo cPc9 to

o o

2 3

o

4h+O.5t for hannel Section

Fig 8 ULTIMATE STRENGTH OF CHANNEL SHEAR CONNECTORS


47/57

279 15 40

M/Mu 1 Loads Suspended fromSteel Beam BlT2 - o -Slab and Beam Separated

2 3 4 5 in

1 0 BT2 - o -

80n

0 2 3 4 5 8 inc B3E T2 - o - T ~T ~

; -. 0 0 4 5 8 in~ > Loads Suspended+ from Steel Beam B4 Tc T ~E T 8 ~0 0 2 3 4 5 80n-0Qa B5a TT ~ ~

0 4 5 8 in

1 0 B6T

Midspan Deflection in InchesFig 9 MOMENT DEFLECTION CURVES FOR BEAMS l TO B6


48/57

4

279 15

M Mu 1 87T2 T4

2 3 4 5 8 in

88T 2 oT4 T9

2 3 4 5 8 in:QE 89Q T2

T5 TIO O::J-I- 2 3 4 5c: 81E T13 0Qa. 2 5 8 in.


49/57

o o1 0 o

c 0 8E0Qc 0 6E=

l:qu CQ 0 4E M Mu0 TE 0 Recent Lehigh U Tests J 0 2

E lc Lse

o 0 2 0 4 0 6 0 8 1 0 1 2Total Connector Strength Compressive Force

1 4 l:qu/CFig 11 RELAnONSHIP BETWEEN SHEAR CONNECTOR STRENGTH AND MOMENT CAPACITY


50/57

M/M =0 846 M Mu =0 9088

o qu =0 944

86 T2

qu =0 473

M/Mu =0 744 M M =0 858

Strain Distri bution at Midspan ig MEASURED STRAINS ON M M RS AT MIDSPAN


51/57

' , >i : ' ' : :: .,.'.'-: :....,:: .;.:-: ::;'. .F : ~ c o ~ 8 5 f ~ _N _

I

d

_

ig STRESS DISTRIBUTION T MO IFIE ULTIM TE MOMENT

I I ~ T . . . .


52/57

M Mu1

cQ 0 8E:EQ0 0 6E

I qu C=0 888 for all MemberscQ 0 4E 812 Variable Connector Spacing:E C 0 Uniform Connector SpacingQa 0 2 81 Uniform Connector Spacing

o 0 5 1 1 5 2 0 2 5 3.0 3.5 4 0Deflection at Midspan in Inches

Fig 14 MOMENT DEFLECTION CURVES FOR TESTS OF Bl0 Bll ND B12


53/57

M Mu t1Q 0 8

Q

E 0.6::>QE 0.4 CQ.aa

0 2

Lqu C 888 for all Memberso B 12 Variable Connector Spacingo B II Uniform Connector Spacing B 1 Uniform Connector Spacing

o 0 05 0.10 15 0 20Maximum End Slip in Inches

Fig 15 MOMENT END SLIP CURVES FOR TESTS OF ID Bll and B 2


54/57

M/Mu1

-cQEo 0.8Qo~ 0.6

cQE o0Q

~ 2


55/57

M M1

.IVI

o Test S I T3 Iqu C = 2 4 Test SIT T3 Iqu C = 1 36 Test Sm T3 I C= 1 06

cQ)E0Q) cE

cQ)E00Q)Q 0 2

o 0.2 4 0.6 0.8 1 1 2 1 4 1 6Deflection at Midspan in Inches

Fig. 17 MOMENT DEFLECTION CURVES FOR TESTS OF BlO, ll an d B12Ico


56/57

2 00

P/Pp

3 000

P/Pp ... - - ,

1 : 0 8 1 : 8c c0 0 J JQ Qc cE 6 E 6

-1 : 1 : p p p pc c 4 4 4 40 4 3 4 J

rY : 1 :Q Q Aa. a.a. a.


57/57

279 15 50

13 REF E R EN C S

1 American Inst i tute of Steel ConstructionSPECIFICATION FOR THE DESIGN FABRICATION AND ERECTIONOF STRUCTURAL STEEL FOR BUILDINGS. New York New York 1961

2 American Association of State Highway Officials STANDARD SPECIFICATIONS FOR HIGHWAY BRIDGES 7th

e d i t i o n ~ Div I Sect 9 19573.. TENTATIVE RECOMMENDATIONS FOR THE DESIGN AND CONSTRUCTION

OF COMPOSITE BEAMs AND GIRDERS FOR.BUILDINGSProceedings ASCE Vol 8S No. ST12 December 19604 Siess C. P Viest I M Newmark N. M.STUDIES OF SLAB AND BEAM BRIDGES PART I I I SMALLSCALE TESTS OF SHEAR CONNECTORS AND COMPOSITE T BEAMSUniversity of I l l inois Bulletin No. 396 19525 Culver G. and Coston R.TESTS OF COMPOSITE BEAMS WITH STUD SHEAR. CONNECTORSProceedings ASCE Vol 87 No. ST2 February 19616 Viest 1 M Siess C. P Appleton J H Newmark N. M.

FULL SCALE TESTS OF CHANNEL SHEAR CONNECTORS ANDCOMPOSITE T BEAMSUniversity of Il l inois Bulletin No. 405 19527. Thurlirnann B.COMPOSITE BEAMS WITH STUD SHEAR CONNECTORSHighway Research Board National Academy of ScienceBulletin No. 174 19588 REPORT OF TESTS OF COMPOSITES TEEL AND CONCRETE BEAMSFritz Engineering Laboratory May 19439

10

Thur lirnann B.FATIGUE AND STATIC STRENGTH OF STUD SHEAR CONNECTORSACI Journal Vol 30 June 1959Viest 1 M.

flexural strength of steel and concrete composite beams

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