Journal of Constructional Steel Research 67 (2011) 1475–1484

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Journal of Constructional Steel Research

Shear bond mechanism of composite slabs — A universal FE approach

Shiming Chen ⁎, Xiaoyu ShiSchool of Civil Engineering, Tongji University, Shanghai 200092, People's Republic of China

⁎ Corresponding author. Tel.: +86 21 65986183; fax:E-mail address: chensm@tongji.edu.cn (S. Chen).

0143-974X/$ – see front matter © 2011 Elsevier Ltd. Adoi:10.1016/j.jcsr.2011.03.021

a b s t r a c t

a r t i c l e i n f o

Article history:Received 4 March 2010Accepted 17 March 2011Available online 25 May 2011

Keywords:Composite slabsShear bond slipCohesionFrictionContact analysisFinite element analysis

The strength of concrete slabs composited with cold-formed profiled steel decks is normally governed by thelongitudinal shear bond failure at the steel concrete interface. The design methods for the longitudinal shearbond strength adopted in the current construction practice such as the m-k method and partial interactionmethod all based on the full-size tests, which are expensive and time consuming, however are also semi-empirical. A universal FE approach of composite slabs is presented, in which the shear bond interactionbetween the steel deck and the concrete is treated as a contact problem considering adhesion and friction.Both geometrical and material nonlinearities are all considered in the FE model. The preliminary FE analysis isverified in simulation of the pull-out tests as far as the cohesion and the frictional bond of the contact interfaceare considered. The fine FE analysis using the contact model is further carried out in study of the compositeslabs in flexural bending. The FE analysis based on the nonlinear contact concept is verified and validated bycomparing the test results for both the pull out and bending tests of the composite slabs. Comparisons of theexperimental and the FE analytical results indicate that the FE analysis based on the interface contact model,agree well with the test results, and is capable of predicting the performance and the load carrying capacity ofcomposite slabs.

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1. Introduction

Composite slabs consisting of profiled steel sheeting and concreteare widely used in buildings nowadays. The use of the cold-formedsteel profiled sheeting or steel deck in combination with concreteresults in an optimum solution bringing with it great advantages suchas no form work, quick installation, and reduced dimensions andweight to the construction of building floors. Essentially, behavior ofcomposite slabs is governed by the horizontal shear bond at theinterface of the steel deck and the concrete. To achieve the desired andefficient composite action, shearing forces have to be transferredbetween the concrete slab and the steel deck, normally beingaccomplished by mechanical interlocking devices like embossmentsrolled onto the surface of the steel sheeting.

The shear bond distribution and the failure mechanism ofcomposite slabs are rather complex. In many cases, the load carryingcapacity of composite slabs depends on the shear–bond resistance atthe interface of the steel profiles and the concrete. Design proceduresfor composite floor slabs consisting of profiled steel sheeting andconcrete based on the ultimate strength concepts were recommendedby Porter and Ekberg [1], in which the design equations for the shearbond capacity were derived from the data collected from a series offull scale performance tests on one-way single span slabs and

developed by establishing the linear regression relationship. Themethod was further verified and supported by many other re-searchers [2–4]. The current design procedures of longitudinal shearfor these steel deck reinforced composite slabs, namely the m-k, andthe partial interactionmethods are also based on the data from the fullscale bending tests [5,6]. Using these methods, however, makes thenumber of tests needed to determine the behavior of the variousexisting commercial products under the service and the ultimateloading rather significant and testing programs become veryexpensive. Besides, due to the semi-empirical nature of these twomethods, neither model can be said to result in a clear picture of thephysical behavior of the steel–concrete connection. The design shearbond strength V, in terms of the vertical shear force, adopted in them-k method also includes the contribution of cross section area ofsteel sheet, so that it is not simply a shear bond resistance inherent atthe interface.

Experimental investigations demonstrated that the load carryingcharacteristics of composite slabs with certain cold-formed steelprofiled decks would be unique. Over the last decade, attempts havebeen made to develop new design methods for composite slabs basedon the idea of using experimental values from small-scale testsinstead of the standard large-scale tests. The aims of these de-velopments are to move away from the use of expensive large-scaletests, and to take into account parameterswhich have been ignored bythe existing methods.

Element tests are the alternative method to reveal the shear bond–slip relationship between the profiled steel sheeting and the concrete.

1476 S. Chen, X. Shi / Journal of Constructional Steel Research 67 (2011) 1475–1484

In element shear bond tests, the pull-out tests are designed to inves-tigate the interaction between the steel deck and the concrete, and thepush-off tests are designed to investigate the behavior and thestrength of end anchorage between the steel section, the deck, and theconcrete slab at supports [7]. But the major weakness of the elementshear bond tests is that the effect of bending is not incorporatedbecause of the test arrangements. A new element test method forcomposite slab specimens under bending was presented by Abdullahand Easterling [8], in which the narrow specimen cutting from awhole composite slab specimen had a width equal to one rib of atypical trapezoidal deck profile, while the other dimension of thisnarrow specimen was the same as the that in the full scale tests.

End anchorages at the supports of a composite slab also havecontribution to its shear bond strength. Chen [9] tested seven simplysupported one-span composite slabs and two continuous compositeslabs, using different end restraints in the simply supported slabs. Theslabs with the end anchorage of steel shear connectors were foundto bear higher shear–bond strength than that of slabs without endanchorage. To enable an effective end anchorage, however, it is theshear–bond slip rather than the strength of anchored studs thatgoverns the contribution of the end restraints to the shear–bondresistance in composite slabs.

The finite element (FE) analysis method is popular for itsadvantage of higher efficiency and lower costs. For composite slabs,various models have been proposed. Daniels and Crisinel [10]developed a special purpose FE procedure using the plane beamelements for analyzing single and continuous span composite slabs, inwhich nonlinear behavior of materials was considered, and the shearinteraction property was obtained from a pull out test. Veljkovic [11]performed 3D FE analysis using software DIANA to study the behaviorof steel concrete composite slabs. The shear interaction between thesteel deck and the concrete was modeled using a nodal interfaceelement and its property was obtained from a push test. Abdullah andEasterling [7] developed a calculation procedure to generate the shearbond property from bending tests. The shear bond property or shear–bond slip curves were then applied to connector elements of finiteelement models to model the horizontal shear bond behavior incomposite slabs. Widjaja [12] used two parallel Euler–Bernoulli beamelements to simulate the bending test of composite slab, howeveronly one single typical longitudinal slice of the slab was considered inthe model, and the vertical nodal displacements of the two parallelbeam elements were forced to be the same. The main deficiency ofthese FE methods is that the connection property of the interfacebetween the steel deck and the concrete has to be predefined. Besides,it is likely that the bearing mechanism at the shear bond interface of apush-out specimen test would be different from that of a bendingspecimen, and influences of the support friction and the naturalclamping due to curvature under bending on the shear bond–slipproperty would also be no more negligible.

The shear bond connection between the concrete and the profiledsteel sheeting in composite slabs is a highly nonlinear contactproblemwhere sticking, sliding and frictional phenomena are presentat the interface. Ferrer et al. [13] simulated the pull-out tests ofcomposite slabs using the FE method, in which contact elements wereimplemented between the steel deck and the concrete, and variouscoefficients of friction were analyzed. The failure of concrete,however, was not considered by replacing concrete block with arigid surface, resulting in a much simpler model. More recently, theshear bond interactions of the composite slabs were treated as aunilateral contact problem and simplified as a two dimensionalcontact model by Tsalkatidis and Avdelas [14].

This paper aims to study the shear bond behavior and mechanismof composite slabs consisting of concrete and profiled steel sheetingusing a universal FE approach. The universal FE model of compositeslabs is presented, in which the shear bond interaction between thesteel deck and the concrete is treated as a contact problem

considering adhesion and friction. Coulomb friction model is used todescribe the shear bond–slip property at the contact interface, andboth geometrical and material nonlinearities are considered in the FEanalysis model. The numerical results such as the shear bond–slipcurves, the load–deflection curves, the end slippage, and the shearstress distributions and characteristics at the steel–concrete interfaceare presented and compared with those results of the full-size pull-out and bending tests. It is illustrated that the numerical simulationsof composite slabs using this universal FE approach agree well withthe test results. A parametric study is further carried out and factorslike shear span length that influence the strength and the behavior ofthe composite slabs are discussed.

2. Contact mechanism of composite slab

The shear bond connection between the concrete and the profiledsteel deck in composite slabs is a highly nonlinear problem as far asboundary conditions, material and geometrical shapes are concerned.The shear bond resistance of the steel to concrete interface is providedby profiled steel sheet, embossments and end anchorage of thecomposite slabs. Suitable shape of the profiled steel deck andembossments can provide resistance to the vertical separation andthe horizontal slippage. End anchorage and similar constructionmeasures would also increase the shear bond resistance of thecomposite slabs. When the loading of a composite slab which istransferred to concrete exceeds the tensile strength of the concrete,the concrete will initiate cracks and results in the mechanicalinterlock mainly due to the embossments of the profiled steelsheeting, to hold the concrete and steel deck together. When a criticalloading is achieved, the shear bond is broken and sliding would occurat the interface of the twomaterials that form the composite slab, andfurther increase of the loading will lead to shear bond failure of thecomposite slab, normally characterized by the development of anapproximate diagonal crack under or near one of the concentratedload, followed by an observable end slip between the steel deck andthe concrete.

It is recognized that chemical bond, frictional bond andmechanicalbond are the three main shear transfer mechanisms contributing tothe shear bond resistance between the steel deck and the concrete.The chemical bond is a bond resulting from the chemical adherence ofcement paste to the steel sheeting. Once this bond is broken, slip isinitiated and the chemical bond strength will reduce to zero and doesnot reform. The frictional bond is a direct result from and also directlyproportional to the normal force, which act perpendicular to thesteel–concrete interface. Mechanical bond exists due to the physicalinterlocking between the profiled steel sheeting and the concrete. Theinterlocking is developed as a result of clamping action caused bybending of steel deck, and from the friction between the steel deckand the concrete, due to the surface roughness such as indentation orembossment on the steel surface.

Under loading, there would be three states for arbitrary points ofthe concrete and the profiled steel deck with a coincident position,described as follows: adhesion, slippage and disconnection, as illus-trated in Fig. 1. It is defined that adhesion contact is the state when atthe position where the steel deck and the concrete are continuous indisplacement in all directions; slippage situation is the state when atthe position relative displacement between the steel deck andconcrete appears only in the tangential direction; and disconnectionsituation is the state when relative displacements occur in arbitrarydirection.

Based on the Coulomb friction concept, the tangential shear bondstress–displacement relationship of the steel–concrete interface canbe described as:

if τ b μP then u = 0 ð1Þ

Fig. 1. Contact states at the interface.

1477S. Chen, X. Shi / Journal of Constructional Steel Research 67 (2011) 1475–1484

if μP ≤ τ b μP + τc then u = 0; us½ � ð2Þ

if τ = μP + τc then u = us ð3Þ

if u N us then τ = μP: ð4Þ

In the above equations, τ is the tangential shear stress, τc is theprescribed cohesion, which is used to indicate the action of sticking atthe interface, μ is the constant coefficient of friction, and P is thenormal stress at the interface of the composite slab. While u is thetangential displacement, us is the displacement at the point when thesticking between the bodies at the interface of the composite slabexcesses into sliding. Eqs. (1)–(3) represent the case of stickingcontact and Eq. (4) is for the case of sliding contact.

When the shear stress is more than the summation of frictionalbond and cohesion, relative slip will initiate at the interface betweenthe steel deck and the concrete. As shown in Eq. (4), the shear force atthe interface is the result of a constant coefficient of friction after theinitiation of a relative slip. The cohesion τc represents the inherentproperty of sticking contact and has nothing to do with the normalstress and the coefficient of friction.

3. Description of the FE model

A FEmodel was proposed based on the contact analysis of programANSYS [15]. The contact analysis with the adhesion and the frictionwas selected for modeling of interface between the steel deck and theconcrete of composite slabs. The interface between the two parts wasconsidered to be deformable. Both geometrical and material non-linearities were considered.

The concrete was treated as a multi-linear isotropic hardeningmaterial. William–Warnke failure criterion with five parameters wasused. The constitutive material law for the steel deck was multi-linearKinematic Hardening using the vonMises yield criterion. The concreteslab was modeled with 8-node solid element (solid 65) capable ofcracking in tension and crushing in compression, while the steel deckwas modeled with 4-node shell element (shell 181).

Fig. 2. Analytical model of stee

The contact pair (element target 173 and element contact 170)was constructed by using the surface-to-surface contact elementsdefined with the same real constant. As illustrated in Fig. 2, theinterface between the steel deck and the concrete was modeled bycontact elements, where the surface of the concrete was selected asthe target surface, and the surface of the steel deck was set as thecontact surface accordingly.

Since the high nonlinear property exists in the contact analysis, inthis study, the profile steel sheeting was modeled as un-embosseddeck. Effect of the embossment was simulated by introducing thereliable contact modes and parameters. In the library of ANSYS [15],various contact modes among which the “bonded” contact andstandard unilateral contact are developed according to the degree ofinteraction.

As the relative displacement between the target and the contactsurfaces could be either bonded or free in one or more directions, the“No separation” contact mode in which the vertical separation isrestricted was selected. A small value for the stiffness factor appliedwhen the contact opens was specified, so that the “weak spring” effectwas adopted to maintain the connection of the contact surfaces aswell as to prevent rigid body motion. Based on the Coulomb frictionmodel, the restriction to horizontal slippage was acquired by thefriction at the interface between the steel deck and the concrete.

The nonlinear FE analysis was performed on both the pull-outcomposite slabs and the composite slabs in bending, and experimen-tal data from the pull-out tests and the bending tests were used tovalidate and calibrate the proposed FE models.

3.1. Pull-out tests

Pull-out tests are one option to obtain the shear bond slip curveswhich could reflect the shear transfer interaction between the steeldeck and the concrete of composite slabs. However, the clampingeffect due to curvature on the shear bond–slip property which wouldbe no more negligible in the bending tests is not included in the pull-out tests. The objective of the FE calibration and validation is to justifywhether the contact problem approach considering the adhesion andthe friction could be applied in analyzing the longitudinal shear bondat the interface of composite slabs.

The preliminary analysis is aimed at the FE model calibration withthe appropriate contact parameters. Pull-out test results reported byDaniels [10] were selected for the FE study. Geometric shape anddimensions of the profiled steel decks are shown in Fig. 3. The 3D-DECKtype was used in the pull-outmodel. Length andwidth of the steel deckare 300 mm, and one ribwidth of the profiled sheeting is selected in theFE study. Symmetry was used to simplify the FE model as illustrated inFig. 4. The displacements along the Z axis of the cover concrete are fixed.The prescribed displacements in the slip direction (Z) are exerted on thesteel sheeting to simulate the relative slip in the test. The lateral force isexerted to represent the self-weight of concrete, defined in direction Yin the model.

l deck–concrete interface.

(a) 3D-DECK sheets

(b) Holorib-2000 sheets

Fig. 3. Geometric shapes of the steel profiled sheeting: trapezoidal and dovetail ribprofiled sheeting.

Fig. 5. Set up of the bending test.

1478 S. Chen, X. Shi / Journal of Constructional Steel Research 67 (2011) 1475–1484

3.2. Bending tests

The set up of bending tests are shown in Fig. 5. Two profile shapeswere selected in the FE validation and calibration for the bendingtests. Dimensions and geometric shapes are shown in Fig. 3.

The symmetrical model is illustrated in Fig. 6. The three translationdegrees of the nodes locating at the hinged support were fixed. Loadswere applied at the upper nodes of the concrete slab at the location ofthe loading. The bending specimens tested by Abdullah and Easterling[7], Chen [9] and Marčiukaitis [16] were selected for the FE validation.Details of the specimens are referred to the tests [7,9,16].

4. The FE analysis: calibration and validation

4.1. Pull-out tests

The typical shear resistance-slip behavior was proposed by Danielsbased on a series of pull-out tests [10]. The classic Coulomb frictionmodel with cohesion is applied in the FE modeling of the pull-outtests. It would be logically reasonable that if the contact FE results ofpull-out specimens agree well that of the tests, the longitudinal shearbond properties such as the adhesion and the friction for the pull-outcomposite slabs should also be used in the FE analyzing of compositeslabs in bending.

(a) Daniels’ test set up[10] (b) The

Fig. 4. Pull-out test and the FE model. (a) Da

The shear bond resistance–slip curves derived from the FEapproach are drawn in Fig. 7 and are compared with the Daniels'test results [10]. Different cohesion values were adopted in the FEanalysis. It appears that the shear resistance at the interface betweensteel and concrete increases with the cohesion in the contact modelanalysis.

4.2. Bending tests

The FE numerical analysis of pull-out tests demonstrates that boththe contact model and the shear bond parameters like the shear bondcohesion value are crucial in simulation of the composite slabbehavior. To better understand parameter influence on the numericaloutputs, a simplified FE model of elemental bending tests is analyzedfirstly, in which both the profile shapes and the failure mode ofconcrete crushing are not considered. A fine FE model including theprofile shapes and concrete crushing failure is further established andthe FE results of the full-scale bending specimens are then comparedwith those derived from tests.

4.2.1. The simplified FE modelThe geometric shape and test set up are selected based on the

elemental tests presented by Abdullah and Easterling [7]. To illustrateinfluence of the selected parameters on the FE analysis results, boththe slender and compact slabs are analyzed, in which the slender slabis defined as one with long span and thin concrete depth and thecompact slab is a slab with short span and thick concrete depth.Relevant data of test specimens are shown in Table 1.

In the simplified FE model of composite slabs in bending, theconcrete slab is modeled as a rectangular section with the moment of

FE model

niel's test set-up [10]; (b) the FE model.

(a) the trapezoidal deck (b) the dovetail rib deck

Fig. 6. FE models of composite slabs with steel profiled sheeting.

1479S. Chen, X. Shi / Journal of Constructional Steel Research 67 (2011) 1475–1484

inertia and the area of the section identical to the original concretesection. Since the bending stiffness of the steel deck is much smallerthan that of the concrete section, the steel deck is modeled as a planewith the same area as the original sheeting section. Fig. 8 showssimplification of the cross section, where beq and heq are theequivalent width and height of the section respectively. A symmet-rical model is depicted in Fig. 9. Transformation in bending stiffness ofthe concrete section is expressed by:

EcIx = EcI′x ð5Þ

where Ix and Ix′ are the moment of inertia of concrete section beforeand after the simplification, and Ec is the elasticity modulus ofconcrete section.

Fig. 10 shows the load–deflection curves of the composite slabs [7]with different μ, varying from 0.1 to 0.8 to simulate the varioussituations at the steel–concrete interface. Two states of distribution ofslippage between the concrete and the steel deck along the span of thecomposite slabs with different μ are illustrated in Fig. 11. It appears

0 0.5 1 1.5 2 2.5 3 3.5

slip /mm

0.00

0.05

0.10

0.15

0.20

0.25

shea

r re

sist

ance

/M

Pa

typical shear resistance-slip behavior by Daniels

valuse used in the numerical analysis by Daniels

numerical analysis with cohesion 0.1MPa

numerical analysis with cohesion 0.2MPa

Fig. 7. Shear bond resistance to slip curves: comparisons of the FE analysis and the tests[10] for pull-out specimens.

Table 1The parameters for elemental tests.

Number ofspecimens

Decktype

Span length(mm)

Slab depth(mm)

Shear span(mm)

Concrete strength fc′(MPa)

27 [7] 3–16 2440 190 810 3130 [7] 3–16 4270 125 1320 31

that the load carrying capacity of the composite slabs increases with μfor both the slabs with compact and slender sections. In both thestates when the mid-span deflection equals to l/250 and l/50, slip andshear stress do not uniformly distribute along the span. Slip decreasesfrom the end to the central of the span for the composite slabs, and themaximum slip occurs at the end of the specimens. It is also verifiedthat the shear stresses over the pure bending region are much smallerthan that in the shear span.

4.2.2. The fine FE model analysisA fine FE model considering shape of the steel profiles is further

studied. The composite slabs with trapezoidal rib profiled sheetingtested by Chen [9] and the composite slabs with dovetail rib profiledsheeting tested byMarčiukaitis [11] are selected for the FE simulation.Relevant dimensions and parameters of the specimens are given inTable 2.

The contact model with the adhesion and Coulomb friction wasused in the fine FE analysis to simulate the interface interaction ofcomposite slabs. The cohesion selected for the contact analysis was0.06 MPa for the trapezoidal deck and 0.08 MPa for the dovetail ribdeck respectively as proposed by Widjaja [10]. The friction coefficientadopted was 0.3 for all analysis.

The elasticity modulus for all structural steel is 210 GPa. The yieldstress of the steel deck for Chen's specimens [9] is 275 MPa, and317 MPa for Marčiukaitis' specimens [11]. Both cracking and crushingfailure modes were included.

In the FE analysis, when concrete initiates cracking, the sheartransfer coefficients for an open crack and for a closed crack were 0.2and 0.9 respectively. A default value of the stress relaxation

Concrete

Steelsheeting

heq

x’x

h

(a) Original section (b) Simplified section

beq305mm

Fig. 8. Simplification of cross section.

Fig. 9. The symmetrical simplified FE model.

u=0.1

u=0.3

u=0.4

u=0.6

u=0.8l/250 l/50

u=0.1

u=0.3

u=0.6

u=0.8

l/250 l/500

5

10

15

20

25

load

/kN

0 10 20 30 40 50 60 70

deflection /mm0 10 20 30 40 50 60 70 80 90 100

deflection/mm

0

1

2

3

4

5

6

7

8

9lo

ad/k

N(a) specimen 27[7] (compactsection) (b) specimen 30[7] (slender section)

Fig. 10. Load–deflection curves for slabs with different μ for coefficient of friction at the interface. (a) Specimen 27 [7](compact section); (b) specimen 30 [7](slender section).

1480 S. Chen, X. Shi / Journal of Constructional Steel Research 67 (2011) 1475–1484

coefficient, 0.6 was adopted. The measured modulus and strength forconcrete were used in accordance to the reported values [9,11].

Comparisons of the FE analysis results against the test results aregiven in Figs. 12 and 13. Fig. 12(a) shows the load–deflection curves ofA-5, the composite slab with the trapezoidal rib profiles. Thecorresponding load–end slip curves are illustrated in Fig. 12(b).Fig. 13(a) shows the load–deflection curves of specimen P1-2, and

(a) mid-span deflection = l/250

Fig. 11. Distributions of slippage at the concrete

Fig. 13(b) shows the load–deflection curves of specimen P2-2. Itappears that the test results generally agree well with the FE analysisresults, and the fine FE analysis using the contact model is capable ofpredicting the structural responses of composite slab.

Failure development in the composite slabs could also beillustrated in the load–deflection curves, characterized by two crucialpoints in the curves. As shown in Fig. 13(a) and (b), point A indicates

(b) mid-span deflection = l/50

–steel interface of slabs (specimen 30 [7]).

Table 2Parameters for full-scale tests.

Number of specimens Deck type Span length(mm)

Total concrete thickness(mm)

Shear span(mm)

Conc. comp. strength fc(MPa)

Steel yield stress fy(MPa)

A-5 [9] 3D-DECK 2600 165 650 20.1 275P1-2 [11] Holorib-2000 1800 75 600 21.6 317P2-2 [11] Holorib-2000 1800 98 600 28.6 317

(a) load-deflection curves (b) load-end slip curves

Fig. 12. Comparison of the test and the FE analysis results for open rib shapes (specimen A-5 [9]).

experimental analysis

numerical analysis

concrete crushingB

A

concrete cracking in tension

experimental analysis

numerical analysis

concrete crushing

concrete cracking in tension

A

B

0

5

10

15

20

25

30

load

/kN

0

5

10

15

20

25

30

35

load

/kN

0 5 10 15 20 25 30

deflection/mm0 5 10 15 20

deflection/mm

(a) specimen P1-2 (b) specimen P2-2

Fig. 13. Comparison of test and FE analysis: load–deflection curves for the dovetail rib shapes (test specimens [11]).

1481S. Chen, X. Shi / Journal of Constructional Steel Research 67 (2011) 1475–1484

the situation when cracking of concrete in tension initiates, and pointB corresponds to the initiation of concrete crushing. Positions of thecrack and crush of concrete all occurred in the constant momentregion. As depicted in Figs. 12 and 13, there is also a sudden drop inthe load when concrete reaches its tension strength and crackinitiates. The fine cracks in concrete will then result in local sheardebond leading to a shear slip between the concrete and the steeldeck.

The slip distributions when concrete initiates cracking andcrushing derived from the FE analysis of specimen A-5 are shown inFig. 14. One can find that slip is not uniformly distributed over the fullspan of the composite slab. Slip decreases gradually from the end tothe midspan of the slab. To illustrate the shear bond mechanismbetter, the longitudinal shear forces derived from summation of thelongitudinal shear stress at the steel–concrete interface are drawnagainst the mid-span deflections as shown in Figs. 15 and 16.

It is found that at the early stage of loading, the longitudinal shearforce at the interface was provided with the shear span region. As the

load continued to increase, cracks initiated in the concrete, and localshear debond occurred and the shear bond stress would developbeyond the shear span and distribute over the full span of thecomposite slab. Major part of the shear bond existed in the shear spanregion, while the shear bond resistance would also develop in thepure bending region. The ratios of the total shear span to the full spanof the composite slabs studied are 1/2 f or slab A-5 and 2/3 for slabsP1-2 and P2-2 respectively. But, at the ultimate state, fraction of thelongitudinal shear forces within the shear span region is 58.4% ofthe total longitudinal shear along the span for A-5, and 75.8% for slabsP1-2 and P2-2. It appears that the greater the shear span region, thelarger the proportion of shear longitudinal shear forces.

5. Parametric study and discussions

In an effort to gain a fundamental understanding of the behavior ofcomposite slabs, by varying shear span length of the composite slab,while keeping the span length the same, a parametric studywas further

(a) concrete cracking (b) concrete crushing

Fig. 14. Slip distribution for open rib shapes (specimen A-5).

0

50

100

150

200

250

0 10 20 30 40 50 60 70

within shear span

full span

long

nitu

dina

l she

ar f

orce

/kN

deflection/mm

Fig. 15. Longitudinal shear forces at the interface for slabs with open rib shape profiles.

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60 70

shear span 300shear span 500mmshear span 650mmshear span 1000mmshear span 1300mm

load

/kN

deflection/mm

Fig. 17. Load–deflection curve: specimen A5 in different shear span length.

1482 S. Chen, X. Shi / Journal of Constructional Steel Research 67 (2011) 1475–1484

carried out on specimen A5. The load–deflection curves of the slabs areillustrated in Fig. 17. Table 3 shows the numerical results and thecorresponding parameter of the shear span length adoptedwhere de isthe effective depth of the concrete, a distance from the top fiber ofconcrete slab to the centroid of the steel deck, accordingly. In Table 3, Vuis equal to the maximum shear force at the support, Nf is thelongitudinal shear force at the interface between the concrete and thesteel deck at the shear bond failurewhen themaximum load is reached,and Nmax is the maximum longitudinal shear force at the interface. The

0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30

within shear span

full span

long

nitu

dina

l she

ar f

orce

/kN

deflection/mm

(a) specimen P1-2

Fig. 16. Longitudinal shear forces at the interfac

longitudinal shear forces Nf and Nmax are calculated by integration ofthe longitudinal shear stress over the steel concrete interface.

The FE analysis shows that the all composite slabs failed inlongitudinal shear bond failure. From Table 3, it is illustrated that themaximum vertical load Vu exerted on the slabs which equals to thevertical shear force at the support or in term of the nominal designshear bond force adopted in the m-k method [5,6] increases with thedecrease of the shear span length. At the onset of the shear bondfailure, the longitudinal shear force Nf at the interface between theconcrete and the steel deck also increases when the shear span length

0

20

40

60

80

100

120

140

160

0 5 10 15 20

within shear span

full span

long

nitu

dina

l she

ar f

orce

/kN

deflection/mm

(b) specimen P2-2

e for slabs with dovetail rib shape profiles.

Table 3Analysis results for specimen A5 with different shear span length.

Shear span Ls(mm)

Shear span ratio Ls/de Maximum load Vu

(kN)Maximum moment(kN·m)

Nf

(kN)Nmax

(kN)Nf/Nu

300 L/8.7 2.4 80.72 24.22 82.85 92.43 0.896500 L/5.2 3.9 48.31 24.16 85.00 89.69 0.948650 L/4.0 5.1 37.06 24.09 70.47 101.14 0.6921000 L/2.6 7.9 25.64 25.64 65.10 99.33 0.6551300 L/2.0 10.2 16.96 22.04 34.89 79.99 0.436

1483S. Chen, X. Shi / Journal of Constructional Steel Research 67 (2011) 1475–1484

decreases, while the maximum longitudinal shear forces Nmax alongthe interface with different shear span length are almost the same.

In the present case, the ratio of Nf to Nmax is 0.436 for a larger shearspan length, Ls=L/2.0 and 0.948 for a small shear span length, Ls=L/5.2 respectively. It is likely that the maximum capable longitudinalshear force is an inherent property for each specific composite slabas far as the steel profiles and the concrete are the same, and thelongitudinal shear bond resistance is influenced inversely by shearspan length.

It is also noticed that all the composite slabs failed in thelongitudinal shear bond failure, at which concrete crush occurs inthe steel deck while yielding does not, and the maximum flexuralmoments attained in all the composite slabs (A5, for a parametricstudy) are around 24 kN·m, a value much less than the full plasticmoment of the composite section.

The profile steel sheeting was modeled as un-embossed deck inthe FE analysis, the effect of the embossment was simulated byintroducing the reliable contact modes and parameters, which werecalibrated by the push out tests. The cohesion selected for theparametric FE analysis is 0.06 MPa and the friction coefficient adoptedis 0.3. As shown in Fig. 10, shear bond resistance would increase withthe friction coefficient adopted. It seems necessary to normalize thetest conditions of standard rules to the worst case, for example near tonull coefficient.

Depth and embossing slopes are also significant parametersaffecting the shear resistance as found by Ferrer and Marimon [17]recently. Burnet and Oehlers [18] found that the main variable thatcontrolled the shear bond strength was the shape of the profiledsheeting rib. The variation of shear bond strength with the shapeparameter was found to be linear and independent of the surfacetreatment, embossment conditions and plate thickness. Ferrer et al.[13] pointed out that the contribution of embossment on the shearbond resistance of composite profiled slabs is limited by the brittlepeel-off failure of concrete. After the initiation of relative slip between

0

5

10

15

20

25

30

0 10 20 30 40 50 60

test(slab3)

FE(slab3)

deflection/mm

load

/kN

(a) slab3(span length 2.5m)

Fig. 18. Comparisons between t

concrete and profiled steel sheeting, the longitudinal shear resistanceof composite slabs mainly depend on the friction bond between theinterface of concrete and profiled sheeting. According to the surfacetreatment, the values of friction coefficient are variable from 0 to 0.6[13]. However, the moderate value 0.3 maybe reliable for most of theprofiled sheeting with common surface treatment as the suggestionby Tsalkatidis and Avdelas [14].

To further calibrate the proposed FE model, other thirteen full-scale tested composite slabs were studied using the fine FE analysis.Details of the experimental study are reported in the paper [20] to bepublished. The FE analysis approach developed in this paper was usedto simulate the shear bond characteristics of composite slabs. Resultsand comparison between tests and FE analysis are shown in Fig. 18.

The cohesion selected for the further FE analysis is still 0.06 MPaand the friction coefficient adopted is 0.3. Fig. 18 shows slightdifference between the tests and the FE analysis results. This maypartly be due to the material law of concrete used in the FE modelproposed by Saenz et al. [19] which would differ from the concreteused for the specimens. Difference in the load procedures betweentests and finite element analysis could be another reason. In the test,the load procedure was controlled by load increment, while,displacement control mode was used in the finite element analysis.The ultimate load of the specimens, P, obtained from the tests andfrom the finite element analyses are all listed in Table 4. The meanvalue of Ptest/PFE ratio is 1.00 with the standard deviation of 0.10. Thefinite element analysis appears to agree well with the test results inpredicting the stiffness and the longitudinal shear resistance for thecomposite slabs.

6. Conclusions

A FE analysis approach for study of behavior and failuremechanism of composite slabs has been presented. The approach isbased upon the nonlinear contact analysis with the frictional contact

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120

test(slab6)

FE(slab6)

deflection/mm

load

/kN

(b) slab6(span length 4.0m)

ests and simulation results.

Table 4Comparison of load carrying capacity obtained from tests and finite element analysis.

No. Ptest/kN PFE/kN Ptest/PFE

2 35.00 35.34 0.993 24.81 20.88 1.195 31.24 28.03 1.116 30.03 29.71 1.017 48.52 57.47 0.848 33.97 36.11 0.949 84.53 90.43 0.9310 91.28 102.88 0.8911 85.92 90.01 0.9512 47.49 42.08 1.1313 60.91 62.74 0.97Mean 1.00Standard deviation 0.10

1484 S. Chen, X. Shi / Journal of Constructional Steel Research 67 (2011) 1475–1484

at interface between the profiled steel deck and the concrete. Bothadhesion and friction at the interface are considered. In the fine FEanalysis, the cohesion selected for the contact analysis is 0.06 MPa forthe trapezoidal deck and 0.08 MPa for the dovetail rib deckrespectively, and the friction coefficient adopted was 0.3 for the allanalysis. Conclusions drawn from this study include:

1. The FE analysis based on the nonlinear contact concept is verifiedand validated by comparing the test results for both the pull outand bending tests of composite slabs. Comparisons of theexperimental and the FE analytical results indicate that the FEanalysis results agree well with the test results, and the fine FEanalysis using the contact model is capable of predicting the loadbehavior of composite slabs.

2. The FE study shows that all the composite slabs failed in thelongitudinal shear bond failure, which is initiated by fine cracks inconcrete which result in local shear debond leading to shear slipbetween concrete and steel deck, then a sudden drop in the load.

3. Slip is not uniformly distributed over the full span of the compositeslab, and it decreases gradually from the end to the midspan of theslab.

4. Major part of the shear bond existed in the shear span region, whilethe shear bond resistance would also develop in the pure bendingregion.

5. It is likely that the maximum capable longitudinal shear force is aninherent property for each specific composite slab as far as the steelprofiles and the concrete are the same, and the longitudinal shearbond resistance is influenced inversely by shear span length.

6. Further calibration of the finite element model is carried outagainst thirteen full scale composite slab tests. The finite elementanalysis appears to agree well with the test results in predicting the

stiffness and the longitudinal shear resistance for the compositeslabs.

Acknowledgments

This research was made possible through the financial supports ofthe National Science Foundation of China (50678132, 51078290). Thefunding, cooperation and assistance of many people from the organiza-tion are gratefully acknowledged.

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