TESTING AND ANALYSIS OF COMPOSITE STEEL-CONCRETE · PDF file90 Int. J. Struct. & Civil Engg....

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Int. J. Struct. & Civil Engg. Res. 2013 Jeffrey A Laman and David Leaf, 2013

TESTING AND ANALYSIS OF COMPOSITESTEEL-CONCRETE BEAM FLEXURAL STRENGTH

David Leaf1 and Jeffrey A Laman2*

*Corresponding author:Jeffrey A Laman, [email protected]

ISSN 2319 – 6009 www.ijscer.comVol. 2, No. 3, August 2013

© 2013 IJSCER. All Rights Reserved

Int. J. Struct. & Civil Engg. Res. 2013

Research Paper

INTRODUCTIONComposite concrete slab on steel beam is awidely used construction with proven benefitsof increased ultimate strength and stiffness.The predictions of both strength and stiffnesshave become routine on the basis of methodsprescribed in the American Institute of SteelConstruction Steel Construction Manual

(2010) and American Concrete Institute 318-11 (2011). The most common composite beamconsists of a W-shape steel beam madecomposite with a concrete slab through headedshear studs (see Figure 1). The headed studstransfer horizontal shear forces between thesteel and concrete causing the two elementsact as one composite member under load.

Composite steel-concrete beams are common structural members used in floor systems andare evaluated by well known procedures. Evaluation of composite member flexural strengthrequires an expectation of strain transfer between the two materials, however, perfect transferdoes not occur, therefore, predictions of flexural strength may not be consistent with measured.Composite beam test demonstrations conducted at the Pennsylvania State University onidentically constructed members have revealed that composite beams fail before reachingpredicted strength. Observations of failed composite beams include longitudinal cracking of theconcrete slab and interlayer slip between the concrete slab and the steel beam. This paperpresents laboratory test results and analyzes the ultimate flexural strength of the tested compositebeams using currently available methods and compares to observed behavior. Additionally,simplified finite element models of the composite beam were developed with results alsocompared to the data obtained from the tests. Based on the results of these analyses,recommendations for design are made that allow accurate determination of composite beamflexural strength.

Keywords: Composite-beam, Shear studs, Steel-concrete

1 Bridge Designer, HDR, Inc. 1016 W. 9th Avenue, Suite 110, King of Prussia, PA 19406-1331.2 Professor of Civil Engineering, The Pennsylvania State University, Department of Civil and Environmental Engineering, 231J Sackett

Building, University Park, PA 16802.

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Two composite beam test demonstrationsare conducted each academic year (one persemester) at The Pennsylvania StateUniversity for educational purposes.Composite beams are designed according tothe provisions of AISC, Part 16, Chapter I forfull composite action and constructedidentically each semester. All composite beamtests were conducted on an A992, Gr. 50, W10× 17 with a solid concrete slab and a singlerow of headed shear studs. In each test, thebeam is loaded to failure with load anddeflection recorded. In nearly all cases it hasbeen observed that the predicted load carryingcapacity is lower than the measured capacity.Ten complete sets of data have been recordedwith the predicted flexural strengthoverestimated as compared to tests by anaverage of 7%.

Observations of the failed compositebeams have commonly revealed a longitudinalcrack along the center of the concrete slabdirectly above the headed shear studs asshown in Figure 2. In most tests, the crack wascontinuous and propagated the entire lengthof the beam. In some cases the longitudinalcracks were not continuous, and developedabove and in the vicinity of the shear studs only.In addition to the longitudinal slab crack,interlayer slip between the slab and the steelbeam top flange was observed.

The demonstrated and consistent over-prediction of strength reveals that current andwidely accepted method of determiningcomposite beam strength is inaccurate andthe method may benefit from knowledgegained through the experimental investigation.The presence of interlayer slip indicates thatthe beam experiences partial composite actionand assuming full composite action isincorrect. A better understanding andincorporation of a suitable level of partialinteraction between the two elements andmodeling of the behavior of the shearconnection in the method is warranted.

The primary objective of this study is tounderstand and more accurately predict thebehavior of a concrete slab on steel compositebeam. This includes an evaluation of thelongitudinal slab cracking on the behavior of acomposite beam and the interface slip tobetter understand the degree of interactionbetween steel and concrete in a compositebeam with headed shear studs. Theconcluding objective of the study is to developa simple model and corresponding analyticalmethod to predict flexural strength of acomposite beam.

PREVIOUS STUDIESThere are many analytical studies in thepublished literature, however, there are veryfew studies based on laboratory tests. Theconsensus of published literature generally isthat the behavior of a composite beamdepends primarily on the behavior of theconnection between the slab and beam. Alongwith theories to explain the behavior of theconnection there are complex methods ofexact analysis, simplified approximate

Figure 1: Typical CompositeBeam Cross Sections

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analysis methods, and methods that use finiteelement analysis.

TESTSA l imited number of composite beamlaboratory studies have been conducted toconfirm prediction models currently in use.Naithani and Gupta (1988) tested threecomposite beams to compare measured topredicted strength. The three beamconfigurations tested the effect of shearconnection type and transverse reinforcementplacement. One configuration failed byconcrete crushing with a longitudinal crack.The ultimate strength of the beams exceededthe predicted strength by 8%, 4%, and 45%.The configuration that exceeded predictedstrength by 45% utilized double, but smaller,shear studs. These tests demonstrate that theshear connection significantly affects theultimate strength of a composite beam. Rammand Jenisch (1997) investigated interfacelongitudinal shear forces and recognized thatadditional transverse bending in the concreteslab affects composite beam strength. Fullscale beam tests were performed to study theeffect of transverse bending. It was observedthat negative transverse bending momentsreduced the ductility of the composite beamsand longitudinal cracks and transverse bendingmoments significantly influence capacity.

ANALYTICAL MODELSA number of theoretical/analytical studies havebeen conducted. Leon and Viest (1997)conducted a review of elastic and inelasticcomposite beam theories based onincomplete interaction. Assumptions forinelastic analyses include no friction or bond

at the interface, no uplift, and linear straindistributions. Finite element models werefound to be very accurate, however, are mostoften used for academic purposes and specialcases. Leon and Viest (1997) conclude thattwo concerns require development: (1)develop a refined shear connection model;and (2) simplify finite element models.Sapountzakis and Katsikadelis (2003)presented an analog equation method as asolution to the case where deformable shearstuds are used. The method neglects uplift, butconsiders in-plane shear forces anddeformation of the slab and axial forces anddeflection of the steel beam. The results showthat as the stiffness of the connectiondecreases, the interface slip increases, theshear forces at the interface decrease, andthe lateral deflections of the beam increase.Liu et al. (2005) investigated strain differencesbetween the steel and concrete in a compositebeam using partial interaction and the theoryof elasticity. Taking slip and curvature intoaccount, it was demonstrated that the straindifference affects the displacement and loadcapacity of a beam. In comparing fullinteraction and partial interaction, thecalculated deflection difference was 11% inone case, therefore, it was suggested that thefull interaction assumption should not be usedfor design. Girhammar et al. (1993) proposeda complex composite beam-column analysisof partial interaction to determine internalactions and displacements. The analysisincorporates a first- and second-order analysisthat accounts for interlayer slip. Girhammar etal. (2007) proposed a refined composite beamor beam-column static analysis with partialinteraction that accounts for interlayer slip

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where more accurate boundary conditions areincluded. The methods of exact analysispresented by Girhammar et al. (2007) are,however, extremely long, intensive, anddetailed resulting in a need to simplify.

APPROXIMATE ANALYTICALPREDICTION METHODSGirhammar et al. (2009) presents anapproximate strength prediction method thatis simpler and more readily applied. Theapproximate, simplified method incorporatesan effective bending stiffness that was usedfor buckling in the more exact analysis. Thisanalysis uses a differential element to defineequations for moment, section shear, interfaceshear, deflection, and axial force for a fullycomposite member. For approximation ofthese terms for a partially composite beam,the bending stiffness for the full compositemember is replaced with the effective bendingstiffness for the partially composite member.While this method is much simpler than thepreviously proposed methods by Girhammaret al. it is suitable for approximation only andnot for codified design. Effective stiffness:

1

02 2

0

/ 11

( / ) ( )eff

EI EIEI EI

EI L

...(1)

where EI = bending stiffness of the fullycomposite section, EI

0 = bending stiffness of

the non-composite section, K = slip modulusof shear connection, r = distance between thetwo centroids, L = length of composite beam,= buckling length coefficient (for a simplysupported beam, = 1), L = the partialcomposite action parameter (defined belowin equation (2)) obtained from the generalsolution, in terms of displacement, to the

differential equation for a partially compositebeam loaded transversely as discussed byGirhammar et al.

2

1 oo

KrL L

EIEI EI

...(2)

Fabbrocino et al. (1999) also proposed ananalysis method to predict composite beamflexural strength. Their results demonstrate thatactual behavior of a composite beam differsfrom predictions based on a full interactionassumption. The Fabbrocino analysisrecognizes that composite beam behaviordepends on slip distribution and the resultingforces at the interface. In this model, slip isrelated to the rotation of the beam anddisplacement of the centroids of the twosections. By defining this relationship, thederivative of the slip is shown to be a functionof the curvature and strains at the centroids ofthe two sections. The dependency of therelationships causes the solution to be involvedand non-linear, however, the method predictedultimate load to within 1% of experimentalresults.

Qiongxi Lui (2011) proposed a compositebeam ultimate load prediction method thataccounts for reduced flexural rigidity due tocracking of the concrete and slip strain. Totalslip is determined by integrating the slip strainalong the beam length. In addition, as the slipis greatest at beam ends, end slip iscompared to shear connector strength. Themethod is lengthy, but accuracy was notevaluated against experimental results.

Other researchers have proposedcomposite beam flexural strength prediction

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methods involving longitudinal shear stressesin the composite beam. Segura (1990)proposed a method to evaluate the shearstresses at the steel and concrete interface.Gara et al. (2010) proposed a strengthprediction method based on the effects ofshear lag. Along with others, these methodsare long and complex, and are not practicalfor codified design.

FINITE ELEMENT MODELINGA number of finite element studies have beenconducted in the recent several years that haveinvestigated a number of issues relating tocomposite flexural members with shear studs.Mirza and Uy (2008) describe the effects ofstrain profiles on the headed shear studconnection in composite beams. Becauseshear studs are subjected to both flexure andshear, Mirza and Uy emphasize the importanceof evaluating the combined effect. Thepresence of both moment and shear causesa nonlinear response, therefore ABAQUS wasused to create a 3D solid element shear studmodel. A push test analysis under differentstrain regimes was performed to determinethe shear stud load limit. The finite elementmodel predicted the strength of the shear studsto within 0.7% of the experimental data andconcluded that strain regimes in a solidconcrete slab do not significantly affect theshear stud performance. Ranzi and Zona(2011) compared three different numericalmodels incorporating a uniformly deformableshear connection to link the concrete slab andsteel beam. Ranzi and Zona evaluated themodel using two Euler-Bernoulli beams, acombination of an Euler-Bernoulli beam(concrete) and a Timoshenko beam (steel),

and two Timoshenko beams. All three modelspredicted the ultimate load to within 2%,however, where beams were controlled byshear, none of the three models providedaccurate results. In this case, the models usinga Timoshenko beam provided much closerfailure load predictions than the model usingtwo Euler-Bernoulli beams. Earlier work byRanzi and Zona (2007) presented a detailedanalysis using an Euler-Bernoulli beam for theconcrete and a Timoshenko beam for the steelto include shear deformation. He et al. (2011)used an element between the steel beam andconcrete slab to represent the shearconnection in a composite beam. The elementwas assigned a stiffness to model the averageeffect of the shear connectors along the beam.The results of this finite element model werecompared to two different experimental teststhrough the ultimate load. The model predictionoverestimated the ultimate load by 5.5% and3.5%. da Silva and Sousa (2009) presenteda family of interface elements to account forinterlayer slip in a composite beam. Vertical,horizontal, and rotational displacement fieldswere considered. Different degrees offreedom were used in the different elementswith some elements considering shear strain.Da Zilva and Sousa determined that aTimoshenko interface element with quadraticdisplacement accounting for shear strain is themost reliable.

AISC STRENGTH PREDICTIONIt is presumed that the reader is familiar withAISC strength prediction of composite beamson the basis of both full and partial compositeaction and, therefore, the method is onlydescribed conceptually here. In general the full

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concrete strength and plastic yield strength ofthe materials is expected to develop and theinternal moment is computed as M

n. In the case

of partial composite action, the shearconnector strength is less than the controllinginternal, longitudinal shear force developed byeither the steel or concrete.

LABORATORY TEST BEAMAND NUMERICAL ANALYSISPhysical Test

The tested beam geometry and loadingconfiguration under the present study ispresented in Figure 3. Each beam wasconstructed with 24 identical and equallyspaced, ¾ inch diameter headed shear studs.The test data sets are presented in Figure 6and Figure 7. The AISC, Part 16, Chapter Icomposite beam strength prediction for af'

c = 4,000 psi, solid concrete slab and W10×17

A992 steel beam is Mn = 158 ft-kips with a

corresponding center point load of 31.7 kips.

Finite Element Model

To better study the composite beam behaviorof the tests, the tested beam was modelednumerically using a very simple, 3D, SAP2000with shell elements for the slab and frameelements for the beam and studs (see Figure4). To incorporate material nonlinear behavior,hinges that allow yield were assigned atdiscrete locations along the steel beam.Modeled concrete material is f '

c= 4000 psi

on a 1" × 2" grid. To model the shear studs,frame elements were used with the crosssection of the shear stud and the properties ofASTM A108 steel. Shear stud length wasequal to half the thickness of the concrete slabis used, 17/16", which is less than the actuallength of the shear stud, however, the shear

area remained the same. The model wassubjected to an incrementally increasing pointload at mid-span to study the loadconcentrations at the shear studs, the shearlag development in the concrete slab, thelongitudinal distribution of force in the shearstuds, and composite beam load versusdeflection relationship.

MEASURED AND SIMULATEDRESULTSLaboratory Test Results

A number of behavior observations from boththe laboratory tests and numerical results werecollected. Longitudinal cracks often developedin the concrete slab of a composite beamdirectly above the headed shear studs aspresented in Figure 2. In addition, the slab wasautopsied to examine the headed studcondition after loading. The four studs at theend of the beam were examined (see Figure5) and deflection of each of the four end studswas measured to be 1/8" toward the end of

Figure 2: Observed LongitudinalCracking of Test Beam Slab

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the beam—an indication that distortion of thestud and interface slip occurred during the testto failure. The relative movement between theconcrete slab and steel beam flange was alsomeasured to be 1/8", providing evidence thatpartial, but not full composite action,developed. After inspection of the exposedstuds, a single, 20 ounce hammer impactbroke the studs free from the steel beam,indicating near failure of the weld during loadtesting. A deformed and broken stud is shownin Figure 5.

Numerical Analysis Results

Both linear static and nonlinear analyses wereconducted in the present study. To determinethe load that corresponds to steel first yield(F

y = 50 ksi), the stress in the extreme tension

Figure 3: Test Beam Drawings

a) Cross Section of Test Beam

b) Composite Beam Lab Test Configuration

Figure 4: SAP2000 Finite Element ModelViews of Composite Beam Numerical

Model

a) SAP2000 Finite Element Model Schematic

b) SAP2000 Extruded View of Basic Elements

Figure 5: Shear Studs with ConcreteRemoved after Failure

of Composite Beam

a) Shear Stud at End of Beam

b) Stud Failure after Low Impact

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Figure 6: Percent Predicted MaxMid-span Load vs. Deflection – All Tests

Test Beam (Typical), SAP2000 Mode

fiber must be calculated. The analyticallypredicted elastic limit occurs at a concentratedload equal to 21.3 kips with f '

c = 4,000 psi.

Observation of the test data load versusdisplacement graphs (Figures 7a through 7j)indicates the elastic limit occurs at a mid-spanload between 20 kips and 25 kips, dependingon the f '

c for the ten sets of test data.

Although considered conservative fordesign, the theoretical maximum deflectionpredicted by the AISC lower bound stiffnesswas in no case conservative as shown inFigures 7a through 7j. The actual stiffness of acomposite section is affected by the degreeof interlayer slip as well as the concretestiffness, which is dependent on f '

c. Full

composite action, which is assumed for theAISC lower bound moment of inertiacalculation, was not achieved by the testbeams.

In comparing the numerical modelpredicted deflections in the elastic range, AISCelastic deflection predictions, and measureddeflections, the numerical model predictions

compare more closely with measured load-deflection behavior than does AISC; however,neither provide an accurate or conservativeestimate for deflection as compared to the testbeams. Although a portion of the test concreteslab developed cracks, causing a loss instiffness, this is not accounted for in thenumerical analysis because the concrete slabis analyzed was a linear material in SAP2000.For analytical purposes, the concrete slabstress distribution is assumed to be uniform;however, the numerical model concrete slabstress distribution is far from uniform aspresented in the results of Figure 8. The stressdistribution presented reflects the compositebeam nonlinear stage under the predictedmaximum 31.7 kip load. It can be readilyobserved that a concentration of compressivestress develops around the studs and isparticularly apparent at the stud near the endof the beam. The end studs experience thisstress concentration because the transferredshear forces are largest at the support. Inaddition, longitudinal forces (in the plane of theslab) concentrate at the stud as resented inFigure 9 where the force distributions atselected studs are presented. Studs arenumbered, starting at mid-span with 1 and 12being the end stud. The numerical analysisdemonstrates that the slab compressive stressis concentrated over a width of 2" to 3". Inaddition, tensile stresses develop directlyadjacent to the end stud in the model, whichare indications of the observed longitudinalslab cracks.

Uniform shear stud shear force along thebeam is normal ly assumed, however,numerical modeling demonstrates that shearforces are concentrated at the end studs.

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Figure 7: Load vs Deflection of the Ten Laboratory Composite Beam Tests

Mid

-Spa

n L

oad

(kip

s)M

id-S

pan

Loa

d (k

ips)

Mid

-Spa

n L

oad

(kip

s)M

id-S

pan

Loa

d (k

ips)

Mid

-Spa

n L

oad

(kip

s)

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Figure 10 presents the magnitude of shear

force in each stud along the beam as a result

of applying four load levels at mid-span: (1)

the predicted ultimate load (31.7 kips); (2) the

load at which yield was experienced in the

nonlinear analysis (28 kips); (3) the load at

which the elastic limit was observed from the

linear analysis (21.3 kips); and (4) a load in

the elastic range (15 kips). Within the elastic

range, the ratio of maximum calculated shear

to the assumed uniform shear magnitude

(Vmax

/Vassumed

) is constant. After the steel beam

has yielded, however, the maximum stud shear

force approaches the uniform force predicted

value. On this basis it can be observed thatthe actual maximum stud shear force may beas much as 1.25 times the predicted, uniformforce. Considering the f '

c = 4,000 psi case:

kips369in)in)(3psi)(2800(0.85)(4,0

85.0

87

seffcc tbfV

...(3)

kips502ksi))(50in(4.992

yss FAV

...(4)

kips852kips)(12)(21.5 nq QV ...(5)

studkips8.20

studs12kips250

nV

...(6)

Increasing this uniform shear force by theratio discussed above to account for end studeffects results in an expected applied shearforce of approximately:

kips5.21stud

kips2625.1

studkips8.20

studs12kips5.249

nQ

nV

...(7)

Figure 8: Numerical Analysis Results ofConcrete Slab Force Stress Distribution

Figure 9: Force Distributionsacross Concrete Slab at Four

Selected Stud Locations

Figure 10: Shear Forces in Studsalong Axis of Composite Beam

(1 = mid-span, 12 = end)

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The predicted end stud shear force of 26kips loads the stud beyond capacity. Studshear forces of this magnitude results in studdeflection, slab to beam slip, and ultimatelypremature failure. Additionally, for thisf '

c = 4,000 psi example, the stud shear force

is only slightly below the value at which thesurrounding concrete is expected to fail.

The composite beam laboratoryobservations of the studs after load areconsistent with this analysis. However, thisevaluation so far is limited to a W10×17 beamwith a 37/

8" concrete slab and 24 headed shear

studs. To evaluate the effect of slab thicknessand width on the distribution, two more modelswere constructed and evaluated.

The initial numerical model was modifiedto create two additional models: (1) W10×17beam with a 60" wide by 37/

8" concrete slab

and 24 headed shear studs; and (2) W10×17beam with a 28" wide by 2¾" concrete slaband 24 headed shear studs. The b

eff used for

these two models is the AISC maximumallowable, taking span/8 on each side of thebeam. Because V

max/V

assumed was observed to

decrease after first steel yield, the mid-spanload corresponding to the elastic limit wasused. Based on this study, it was determinedthat V

max/V

assumed increases as the effective slab

width increases. Also, a decrease in Vmax

/V

assumed is observed with a decrease in slab

thickness. In the case of a large effective slabwidth, increasing the expected shear by 1.25may not provide a conservative estimate.However, V

max/V

assumed for the numerical models

with effective widths equal to 60" and 28" arewithin 2%. Also, V

max/V

assumed is expected to

decrease after the steel yields. For a slab

thickness of 2¾", Vmax

/Vassumed

decreases,therefore, expecting a shear of 1.25 timesgreater than predicted by AISC remainsconservative.

To compare this method to other typicalcomposite beams, two additional models werecreated. The fourth and fifth numerical modelswere assigned the same material propertiesas all previous models. The models includeda single row of shear studs and loaded with aconcentrated load at mid-span. The fourthmodel consisted of a W18×35 beam and a64" wide by 37/

8" thick concrete slab with

headed studs spaced at 8" and a span lengthof 32 ft. The fifth model consisted of a W14×26beam and an 80" wide by 3" thick concreteslab with headed studs spaced at 10" and aspan length of 30 ft. The simulation resultsdemonstrate that these beams alsoexperience end shear stud forces that were20.2% and 17.7% higher than a uniformdistribution would predict, respectively. Itappears, based on this limited study, thatlarger steel beams will experience larger thanpredicted end shear stud forces.

DISCUSSION ANDEVALUATIONComposite beam tests demonstrated thatneither the steel beam nor the concrete slabattained full plastic strains despite loading tofailure, indicating that full composite action, asnormally assumed, did not develop. The errorin predicting ultimate flexural capacity rangedfrom –0.30% (under prediction) to +19.2%(over prediction) with an average overprediction of 6.6%.

To evaluate the degree of composite actionthat did develop in the test beams, a partial

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composite analysis was conducted. FromEquation 8, the flexural capacity of a partiallycomposite section with the PNA in the topflange of the steel is determined.

2)(2

22x

xFba

tCd

TM yfscsn ...(8)

Because the calculated total shear studstrength has been shown to be sufficient, C

c

becomes an unknown variable of interest.Equation 8 can be rearranged by makingseveral substitutions and C

c can be calculated

from the quadratic Equation 9:

0442

241

')85.0(21

2

2

PLb

FAdFA

bA

tCbFbf

C

f

ysys

f

ssc

fyeffcc

...(9)

which is valid when the PNA is in the steelflange. For the f '

c = 4,000 psi example

examined here, the actual Cc that was

experienced is calculated to be 189 kips.Knowing the value of x, the tensile forcecomponent of the flexural moment at failure canbe calculated. This evaluation demonstratesthat 86% of the steel plastic tensile strengthwas coupled against the concrete at the timeof flexural failure. Among the ten sets ofmeasure beam response data, the developedtension ranged from 64% in one test to twotests of 100% with an average of 87%.

Load versus deflection plots are alsopresented for measured composite beamresponses. Figure 6 presents a compilationof all data sets normalized to predictedultimate flexural strength due to differentmeasured concrete strengths with each test.

Figures 7a through 7j present the measurecomposite beam response as compared tothe analysis methods suggested byGirhammar et al. (2009) and AISC (2010). Alower bound moment of inertia (I

LB) is used to

develop the AISC load vs. deflectionrelationship. I

LB is an AISC, theoretical

minimum moment of inertia including only thatportion of the concrete slab within Whitney’sstress block and is therefore consideredconservative. For many of the data sets,however, it can be observed that thisseemingly conservative approach is actuallyvery accurate other than for data sets 1, 2, and3 where the measured elastic deflections werenotably greater than deflections predictedusing I

LB.

The deflections predicted util izingGirhammar et al. (2009) are presented inFigures 7a though 7j. Girhammar et al. usesan effective bending stiffness that accounts forpartial composite interaction involving anestimated slip stiffness, K. For a non-composite section, the slip stiffness is zeroand increases with higher degrees ofcomposite interaction. The slip stiffness, K, isdifficult to estimate because the slip is smalland concrete properties are nonlinear. It wasdetermined that using a slip stiffness of 9 ksifor every test data set provided an accurate orsomewhat conservative estimate. While theGirhammar et al. method is attractive and canprovide accurate predictions, a reliablemethod to quantify the slip stiffness is notavailable.

SUMMARY ANDCONCLUSIONSComposite steel-concrete beams tested to

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failure have been observed to consistently failbefore the nominal flexural strength predictedby AISC is reached, indicating a deficiency incurrent design standards. For the complete setof data, the numerical prediction error inaccordance with AISC ranged from –0.30%to +19% with an average of a 6.6% overprediction. Several observations during thesetests have highlighted problem areas. Theseobservations include:

• The presence of interlayer slip, indicatingthat full interaction is not achieved.

• Longitudinal cracking of the concrete slabin the vicinity of the shear studs, indicatingthat stress concentrations are experiencedin the slab at the shear stud locations.

• Shear forces in the end shear studs werehigher than predicted, based on post-testexamination.

A finite element model was developed usingSAP2000 to analyze the test beam behavior.The results of the model show consistency withobservations made during full-scale beamtesting. The numerical model indicates highstress concentrations in the plane of the slabat the shear stud locations. As a result, tensilesplitting forces in the concrete slab areexperienced adjacent to the shear studs. Alongthe axis of the beam, shear distributions aresubject to the effects of shear lag, causing theend studs to experience shear forces as muchas 25% higher than predicted. On the basis ofthe results presented here, further research isnecessary to determine the distributions ofshear forces both in the concrete slab andalong the beam in a larger sample ofspecimens.

REFERENCES1. American Institute of Steel Construction

(2010), Steel Construction Manual, 14th

ed., American Insti tute of SteelConstruction, Chicago, Illinois.

2. American Concrete Institute (2011),Building Code Requirements forStructural Concrete (ACI 318-11) andCommentary , American ConcreteInstitute, Farmington Hills, Michigan.

3. da Silva A R and Sousa J B J (2009), “Afamily of interface elements for theanalysis of composite beams withinterlayer slip”, Finite Elements inAnalysis and Design, Vol. 45, No. 5, pp.305-314.

4. Fabbrocino G, Manfredi G and CosenzaE (1999), “Non-linear analysis ofcomposite beams under posit ivebending. Computers and Structures, Vol.70, No. 1, pp. 77-89.

5. Gara F, Ranzi G and Leoni G (2010),“Short-and long-term analytical solutionsfor composite beams with partialinteraction and shear-lag effects”,International Journal of Steel Structures,Vol. 10, No. 4, pp. 359-372.

6. Girhammar U A (2009), “A simplifiedanalysis method for composite beamswith interlayer slip”, International Journalof Mechanical Sciences, Vol. 51, No. 7,pp. 515-30.

7. Girhammar U A and Gopu V K A (1993),“Composite beam-columns with interlayerslip - exact analysis”, Journal of StructuralEngineering, New York, Vol. 119, No. 4,pp. 1265-1282.

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8. Girhammar U A and Pan D H (2007),“Exact static analysis of partial lycomposite beams and beam-columns”,International Journal of MechanicalSciences, Vol. 49, No. 2, pp. 239-255.doi:10.1016/j.ijmecsci.2006.07.005

9. Gupta V K, Okui Y, Inaba N and Nagai M(2007), “Effect of concrete crushing onflexural strength of steel-concretecomposite girders”, Doboku GakkaiRonbunshuu A, Vol. 63(3), pp. 475-485.

10. He S, Li P and Shang F (2011), “Threedimensional simulation of steel-concretecomposite beams with an interface-slipmodel”, Paper presented at the 2011International Conference on Structuresand Building Materials, ICSBM, January7, 2011 - January 9, 163-167, pp. 1520-1524.

11. Leon R and Viest I (1997), “Theories ofincomplete interaction in compositebeams”, In Buckner C and Shahrooz B(Eds.), Composite construction in steeland concrete III , p. 858, AmericanSociety of Civil Engineers.

12. Liu H, Liu W and Zhang Y (2005),“Calculation analysis of shearing slip forsteel-concrete composite beam underconcentrated load”, Applied Mathematicsand Mechanics (English Edition), Vol.26(6), pp. 735-740.

13. Mirza O and Uy B (2011), “Effect of strainprofiles on the behavior of shearconnectors for composite steel-concrete

beams”, Paper presented at the 6thInternational Conference on CompositeConstruction in Steel and Concrete, July20, 2008 - July 24, pp. 160-172.

14. Qureshi J, Lam D and Ye J (2011), “Effectof shear connector spacing and layout onthe shear connector capacity incomposite beams”, Journal ofConstructional Steel Research, Vol.67(4), pp. 706-19.

15. Ramm W and Jenisch F (1996), “Load-bearing behaviour of composite slabs asa part of composite beams”, In BucknerC and Shahrooz B (Eds.), Compositeconstruction in steel and concrete III, pp.673, American Society of Civil Engineers.

16. Ranzi G and Zona A (2007), “A steel-concrete composite beam model withpartial interaction including the sheardeformability of the steel component”,Engineering Structures, Vol. 29(11), pp.3026-3041.

17. Sapountzakis E J and Katsikadelis J T(2003), “A new model for the analysis ofcomposite steel - concrete slab andbeam structures with deformableconnection”, Mechanics, Vol. 31, pp.340-349.

18. Segura J M (1990), “An approximatemethod of determination of shearstresses due to flexure in compositebeams”, International Journal ofEngineering Science, Vol. 28(8), pp.735-50.

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