Shear bond mechanism of composite slabs — A universal FE approach

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 Shi School of Civil Engineering, Tongji University, Shanghai 200092, People's Republic of China

a r t i c l e

i n f o

Article history: Received 4 March 2010 Accepted 17 March 2011 Available online 25 May 2011 Keywords: Composite slabs Shear bond slip Cohesion Friction Contact analysis Finite element analysis

a b s t r a c t The strength of concrete slabs composited with cold-formed profiled steel decks is normally governed by the longitudinal shear bond failure at the steel concrete interface. The design methods for the longitudinal shear bond strength adopted in the current construction practice such as the m-k method and partial interaction method all based on the full-size tests, which are expensive and time consuming, however are also semiempirical. A universal FE approach of composite slabs is presented, in which the shear bond interaction between 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 is verified in simulation of the pull-out tests as far as the cohesion and the frictional bond of the contact interface are considered. The fine FE analysis using the contact model is further carried out in study of the composite slabs in flexural bending. The FE analysis based on the nonlinear contact concept is verified and validated by comparing the test results for both the pull out and bending tests of the composite slabs. Comparisons of the experimental 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 of composite slabs. © 2011 Elsevier Ltd. All rights reserved.

1. Introduction Composite slabs consisting of profiled steel sheeting and concrete are widely used in buildings nowadays. The use of the cold-formed steel profiled sheeting or steel deck in combination with concrete results in an optimum solution bringing with it great advantages such as no form work, quick installation, and reduced dimensions and weight to the construction of building floors. Essentially, behavior of composite slabs is governed by the horizontal shear bond at the interface of the steel deck and the concrete. To achieve the desired and efficient composite action, shearing forces have to be transferred between the concrete slab and the steel deck, normally being accomplished by mechanical interlocking devices like embossments rolled onto the surface of the steel sheeting. The shear bond distribution and the failure mechanism of composite slabs are rather complex. In many cases, the load carrying capacity of composite slabs depends on the shear–bond resistance at the interface of the steel profiles and the concrete. Design procedures for composite floor slabs consisting of profiled steel sheeting and concrete based on the ultimate strength concepts were recommended by Porter and Ekberg [1], in which the design equations for the shear bond capacity were derived from the data collected from a series of full scale performance tests on one-way single span slabs and

⁎ Corresponding author. Tel.: + 86 21 65986183; fax: + 86 21 65982668. E-mail address: [email protected] (S. Chen). 0143-974X/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2011.03.021

developed by establishing the linear regression relationship. The method was further verified and supported by many other researchers [2–4]. The current design procedures of longitudinal shear for these steel deck reinforced composite slabs, namely the m-k, and the partial interaction methods are also based on the data from the full scale bending tests [5,6]. Using these methods, however, makes the number of tests needed to determine the behavior of the various existing commercial products under the service and the ultimate loading rather significant and testing programs become very expensive. Besides, due to the semi-empirical nature of these two methods, neither model can be said to result in a clear picture of the physical behavior of the steel–concrete connection. The design shear bond strength V, in terms of the vertical shear force, adopted in the m-k method also includes the contribution of cross section area of steel sheet, so that it is not simply a shear bond resistance inherent at the interface. Experimental investigations demonstrated that the load carrying characteristics of composite slabs with certain cold-formed steel profiled decks would be unique. Over the last decade, attempts have been made to develop new design methods for composite slabs based on the idea of using experimental values from small-scale tests instead of the standard large-scale tests. The aims of these developments are to move away from the use of expensive large-scale tests, and to take into account parameters which have been ignored by the existing methods. Element tests are the alternative method to reveal the shear bond– slip relationship between the profiled steel sheeting and the concrete.

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In element shear bond tests, the pull-out tests are designed to investigate the interaction between the steel deck and the concrete, and the push-off tests are designed to investigate the behavior and the strength of end anchorage between the steel section, the deck, and the concrete slab at supports [7]. But the major weakness of the element shear bond tests is that the effect of bending is not incorporated because of the test arrangements. A new element test method for composite slab specimens under bending was presented by Abdullah and Easterling [8], in which the narrow specimen cutting from a whole composite slab specimen had a width equal to one rib of a typical trapezoidal deck profile, while the other dimension of this narrow specimen was the same as the that in the full scale tests. End anchorages at the supports of a composite slab also have contribution to its shear bond strength. Chen [9] tested seven simply supported one-span composite slabs and two continuous composite slabs, using different end restraints in the simply supported slabs. The slabs with the end anchorage of steel shear connectors were found to bear higher shear–bond strength than that of slabs without end anchorage. To enable an effective end anchorage, however, it is the shear–bond slip rather than the strength of anchored studs that governs the contribution of the end restraints to the shear–bond resistance in composite slabs. The finite element (FE) analysis method is popular for its advantage 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 beam elements for analyzing single and continuous span composite slabs, in which nonlinear behavior of materials was considered, and the shear interaction property was obtained from a pull out test. Veljkovic [11] performed 3D FE analysis using software DIANA to study the behavior of steel concrete composite slabs. The shear interaction between the steel deck and the concrete was modeled using a nodal interface element and its property was obtained from a push test. Abdullah and Easterling [7] developed a calculation procedure to generate the shear bond property from bending tests. The shear bond property or shear– bond slip curves were then applied to connector elements of finite element models to model the horizontal shear bond behavior in composite slabs. Widjaja [12] used two parallel Euler–Bernoulli beam elements to simulate the bending test of composite slab, however only one single typical longitudinal slice of the slab was considered in the model, and the vertical nodal displacements of the two parallel beam elements were forced to be the same. The main deficiency of these FE methods is that the connection property of the interface between the steel deck and the concrete has to be predefined. Besides, it is likely that the bearing mechanism at the shear bond interface of a push-out specimen test would be different from that of a bending specimen, and influences of the support friction and the natural clamping due to curvature under bending on the shear bond–slip property would also be no more negligible. The shear bond connection between the concrete and the profiled steel sheeting in composite slabs is a highly nonlinear contact problem where sticking, sliding and frictional phenomena are present at the interface. Ferrer et al. [13] simulated the pull-out tests of composite slabs using the FE method, in which contact elements were implemented between the steel deck and the concrete, and various coefficients of friction were analyzed. The failure of concrete, however, was not considered by replacing concrete block with a rigid surface, resulting in a much simpler model. More recently, the shear bond interactions of the composite slabs were treated as a unilateral contact problem and simplified as a two dimensional contact model by Tsalkatidis and Avdelas [14]. This paper aims to study the shear bond behavior and mechanism of composite slabs consisting of concrete and profiled steel sheeting using a universal FE approach. The universal FE model of composite slabs is presented, in which the shear bond interaction between the steel deck and the concrete is treated as a contact problem

considering adhesion and friction. Coulomb friction model is used to describe the shear bond–slip property at the contact interface, and both geometrical and material nonlinearities are considered in the FE analysis model. The numerical results such as the shear bond–slip curves, the load–deflection curves, the end slippage, and the shear stress distributions and characteristics at the steel–concrete interface are presented and compared with those results of the full-size pullout and bending tests. It is illustrated that the numerical simulations of composite slabs using this universal FE approach agree well with the test results. A parametric study is further carried out and factors like shear span length that influence the strength and the behavior of the composite slabs are discussed. 2. Contact mechanism of composite slab The shear bond connection between the concrete and the profiled steel deck in composite slabs is a highly nonlinear problem as far as boundary conditions, material and geometrical shapes are concerned. The shear bond resistance of the steel to concrete interface is provided by profiled steel sheet, embossments and end anchorage of the composite slabs. Suitable shape of the profiled steel deck and embossments can provide resistance to the vertical separation and the horizontal slippage. End anchorage and similar construction measures would also increase the shear bond resistance of the composite slabs. When the loading of a composite slab which is transferred to concrete exceeds the tensile strength of the concrete, the concrete will initiate cracks and results in the mechanical interlock mainly due to the embossments of the profiled steel sheeting, to hold the concrete and steel deck together. When a critical loading is achieved, the shear bond is broken and sliding would occur at the interface of the two materials that form the composite slab, and further increase of the loading will lead to shear bond failure of the composite slab, normally characterized by the development of an approximate diagonal crack under or near one of the concentrated load, followed by an observable end slip between the steel deck and the concrete. It is recognized that chemical bond, frictional bond and mechanical bond are the three main shear transfer mechanisms contributing to the shear bond resistance between the steel deck and the concrete. The chemical bond is a bond resulting from the chemical adherence of cement paste to the steel sheeting. Once this bond is broken, slip is initiated and the chemical bond strength will reduce to zero and does not reform. The frictional bond is a direct result from and also directly proportional to the normal force, which act perpendicular to the steel–concrete interface. Mechanical bond exists due to the physical interlocking between the profiled steel sheeting and the concrete. The interlocking is developed as a result of clamping action caused by bending of steel deck, and from the friction between the steel deck and the concrete, due to the surface roughness such as indentation or embossment on the steel surface. Under loading, there would be three states for arbitrary points of the concrete and the profiled steel deck with a coincident position, described as follows: adhesion, slippage and disconnection, as illustrated in Fig. 1. It is defined that adhesion contact is the state when at the position where the steel deck and the concrete are continuous in displacement in all directions; slippage situation is the state when at the position relative displacement between the steel deck and concrete appears only in the tangential direction; and disconnection situation is the state when relative displacements occur in arbitrary direction. Based on the Coulomb friction concept, the tangential shear bond stress–displacement relationship of the steel–concrete interface can be described as: if τ b μP then u = 0

ð1Þ

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

Fig. 1. Contact states at the interface.

if μP ≤ τ b μP + τc then u = ½0; us 

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 the prescribed cohesion, which is used to indicate the action of sticking at the interface, μ is the constant coefficient of friction, and P is the normal stress at the interface of the composite slab. While u is the tangential displacement, us is the displacement at the point when the sticking between the bodies at the interface of the composite slab excesses into sliding. Eqs. (1)–(3) represent the case of sticking contact and Eq. (4) is for the case of sliding contact. When the shear stress is more than the summation of frictional bond and cohesion, relative slip will initiate at the interface between the steel deck and the concrete. As shown in Eq. (4), the shear force at the interface is the result of a constant coefficient of friction after the initiation of a relative slip. The cohesion τc represents the inherent property of sticking contact and has nothing to do with the normal stress and the coefficient of friction. 3. Description of the FE model A FE model was proposed based on the contact analysis of program ANSYS [15]. The contact analysis with the adhesion and the friction was selected for modeling of interface between the steel deck and the concrete of composite slabs. The interface between the two parts was considered to be deformable. Both geometrical and material nonlinearities were considered. The concrete was treated as a multi-linear isotropic hardening material. William–Warnke failure criterion with five parameters was used. The constitutive material law for the steel deck was multi-linear Kinematic Hardening using the von Mises yield criterion. The concrete slab was modeled with 8-node solid element (solid 65) capable of cracking in tension and crushing in compression, while the steel deck was modeled with 4-node shell element (shell 181).

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The contact pair (element target 173 and element contact 170) was constructed by using the surface-to-surface contact elements defined with the same real constant. As illustrated in Fig. 2, the interface between the steel deck and the concrete was modeled by contact elements, where the surface of the concrete was selected as the target surface, and the surface of the steel deck was set as the contact surface accordingly. Since the high nonlinear property exists in the contact analysis, in this study, the profile steel sheeting was modeled as un-embossed deck. Effect of the embossment was simulated by introducing the reliable contact modes and parameters. In the library of ANSYS [15], various contact modes among which the “bonded” contact and standard unilateral contact are developed according to the degree of interaction. As the relative displacement between the target and the contact surfaces could be either bonded or free in one or more directions, the “No separation” contact mode in which the vertical separation is restricted was selected. A small value for the stiffness factor applied when the contact opens was specified, so that the “weak spring” effect was adopted to maintain the connection of the contact surfaces as well as to prevent rigid body motion. Based on the Coulomb friction model, the restriction to horizontal slippage was acquired by the friction at the interface between the steel deck and the concrete. The nonlinear FE analysis was performed on both the pull-out composite slabs and the composite slabs in bending, and experimental data from the pull-out tests and the bending tests were used to validate and calibrate the proposed FE models.

3.1. Pull-out tests Pull-out tests are one option to obtain the shear bond slip curves which could reflect the shear transfer interaction between the steel deck and the concrete of composite slabs. However, the clamping effect due to curvature on the shear bond–slip property which would be no more negligible in the bending tests is not included in the pullout tests. The objective of the FE calibration and validation is to justify whether the contact problem approach considering the adhesion and the friction could be applied in analyzing the longitudinal shear bond at the interface of composite slabs. The preliminary analysis is aimed at the FE model calibration with the appropriate contact parameters. Pull-out test results reported by Daniels [10] were selected for the FE study. Geometric shape and dimensions of the profiled steel decks are shown in Fig. 3. The 3D-DECK type was used in the pull-out model. Length and width of the steel deck are 300 mm, and one rib width of the profiled sheeting is selected in the FE study. Symmetry was used to simplify the FE model as illustrated in Fig. 4. The displacements along the Z axis of the cover concrete are fixed. The prescribed displacements in the slip direction (Z) are exerted on the steel sheeting to simulate the relative slip in the test. The lateral force is exerted to represent the self-weight of concrete, defined in direction Y in the model.

Fig. 2. Analytical model of steel deck–concrete interface.

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(a) 3D-DECK sheets

Fig. 5. Set up of the bending test.

(b) Holorib-2000 sheets Fig. 3. Geometric shapes of the steel profiled sheeting: trapezoidal and dovetail rib profiled sheeting.

The shear bond resistance–slip curves derived from the FE approach are drawn in Fig. 7 and are compared with the Daniels' test results [10]. Different cohesion values were adopted in the FE analysis. It appears that the shear resistance at the interface between steel and concrete increases with the cohesion in the contact model analysis.

3.2. Bending tests 4.2. Bending tests The set up of bending tests are shown in Fig. 5. Two profile shapes were selected in the FE validation and calibration for the bending tests. Dimensions and geometric shapes are shown in Fig. 3. The symmetrical model is illustrated in Fig. 6. The three translation degrees of the nodes locating at the hinged support were fixed. Loads were applied at the upper nodes of the concrete slab at the location of the 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 Daniels based on a series of pull-out tests [10]. The classic Coulomb friction model with cohesion is applied in the FE modeling of the pull-out tests. It would be logically reasonable that if the contact FE results of pull-out specimens agree well that of the tests, the longitudinal shear bond properties such as the adhesion and the friction for the pull-out composite slabs should also be used in the FE analyzing of composite slabs in bending.

(a) Daniels’ test set up[10]

The FE numerical analysis of pull-out tests demonstrates that both the contact model and the shear bond parameters like the shear bond cohesion value are crucial in simulation of the composite slab behavior. To better understand parameter influence on the numerical outputs, a simplified FE model of elemental bending tests is analyzed firstly, in which both the profile shapes and the failure mode of concrete crushing are not considered. A fine FE model including the profile shapes and concrete crushing failure is further established and the FE results of the full-scale bending specimens are then compared with those derived from tests. 4.2.1. The simplified FE model The geometric shape and test set up are selected based on the elemental tests presented by Abdullah and Easterling [7]. To illustrate influence of the selected parameters on the FE analysis results, both the slender and compact slabs are analyzed, in which the slender slab is defined as one with long span and thin concrete depth and the compact 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, the concrete slab is modeled as a rectangular section with the moment of

(b) The FE model

Fig. 4. Pull-out test and the FE model. (a) Daniel's test set-up [10]; (b) the FE model.

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

(a) the trapezoidal deck

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(b) the dovetail rib deck

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

inertia and the area of the section identical to the original concrete section. Since the bending stiffness of the steel deck is much smaller than that of the concrete section, the steel deck is modeled as a plane with the same area as the original sheeting section. Fig. 8 shows simplification of the cross section, where beq and heq are the equivalent width and height of the section respectively. A symmetrical model is depicted in Fig. 9. Transformation in bending stiffness of the concrete section is expressed by:

that the load carrying capacity of the composite slabs increases with μ for both the slabs with compact and slender sections. In both the states when the mid-span deflection equals to l/250 and l/50, slip and shear stress do not uniformly distribute along the span. Slip decreases from the end to the central of the span for the composite slabs, and the maximum slip occurs at the end of the specimens. It is also verified that the shear stresses over the pure bending region are much smaller than that in the shear span.

Ec Ix = Ec Ix′

4.2.2. The fine FE model analysis A fine FE model considering shape of the steel profiles is further studied. The composite slabs with trapezoidal rib profiled sheeting tested by Chen [9] and the composite slabs with dovetail rib profiled sheeting tested by Marčiukaitis [11] are selected for the FE simulation. Relevant dimensions and parameters of the specimens are given in Table 2. The contact model with the adhesion and Coulomb friction was used in the fine FE analysis to simulate the interface interaction of composite slabs. The cohesion selected for the contact analysis was 0.06 MPa for the trapezoidal deck and 0.08 MPa for the dovetail rib deck respectively as proposed by Widjaja [10]. The friction coefficient adopted was 0.3 for all analysis. The elasticity modulus for all structural steel is 210 GPa. The yield stress of the steel deck for Chen's specimens [9] is 275 MPa, and 317 MPa for Marčiukaitis' specimens [11]. Both cracking and crushing failure modes were included. In the FE analysis, when concrete initiates cracking, the shear transfer coefficients for an open crack and for a closed crack were 0.2 and 0.9 respectively. A default value of the stress relaxation

ð5Þ

where Ix and Ix′ are the moment of inertia of concrete section before and after the simplification, and Ec is the elasticity modulus of concrete 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 various situations at the steel–concrete interface. Two states of distribution of slippage between the concrete and the steel deck along the span of the composite slabs with different μ are illustrated in Fig. 11. It appears

shear resistance /MPa

0.25

0.20

0.15

0.10 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

0.05

0.00

0

0.5

1

1.5

2

2.5

3

Concrete

x

3.5

x’ heq

h

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

Steelsheeting 305mm

Table 1 The parameters for elemental tests. Number of specimens

Deck type

Span length Slab depth Shear span Concrete strength fc′ (mm) (mm) (mm) (MPa)

27 [7] 30 [7]

3–16 3–16

2440 4270

190 125

810 1320

31 31

(a) Original section

beq

(b) Simplified section

Fig. 8. Simplification of cross section.

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Fig. 9. The symmetrical simplified FE model.

(a) specimen 27[7] (compactsection)

(b) specimen 30[7] (slender section)

25

9 u=0.1

8 20

u=0.3

7

u=0.6

load/kN

load/kN

6 15 u=0.1 u=0.3

10

2

u=0.6

l/250 0

0

10

20

l/50 30

40

50

4 3

u=0.4 5

u=0.8

5

1

u=0.8

l/250

0 60

70

deflection /mm

0

10

20

l/50 30

40

50

60

70

80

90

100

deflection/mm

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).

coefficient, 0.6 was adopted. The measured modulus and strength for concrete were used in accordance to the reported values [9,11]. Comparisons of the FE analysis results against the test results are given in Figs. 12 and 13. Fig. 12(a) shows the load–deflection curves of A-5, the composite slab with the trapezoidal rib profiles. The corresponding 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. 13(b) shows the load–deflection curves of specimen P2-2. It appears that the test results generally agree well with the FE analysis results, and the fine FE analysis using the contact model is capable of predicting the structural responses of composite slab. Failure development in the composite slabs could also be illustrated in the load–deflection curves, characterized by two crucial points in the curves. As shown in Fig. 13(a) and (b), point A indicates

(b) mid-span deflection = l/50

Fig. 11. Distributions of slippage at the concrete–steel interface of slabs (specimen 30 [7]).

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

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Table 2 Parameters 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] P1-2 [11] P2-2 [11]

3D-DECK Holorib-2000 Holorib-2000

2600 1800 1800

165 75 98

650 600 600

20.1 21.6 28.6

275 317 317

(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]).

35

30 concrete crushing

25

B

concrete crushing

25

load/kN

20

load/kN

B

30

15 10 A

experimental analysis

5 concrete cracking in tension

5

10

15

20

25

A

15 10

concrete cracking in tension

5

numerical analysis

0 0

20

30

deflection/mm

(a) specimen P1-2

0

experimental analysis numerical analysis

0

5

10

15

20

deflection/mm

(b) specimen P2-2

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

the situation when cracking of concrete in tension initiates, and point B corresponds to the initiation of concrete crushing. Positions of the crack and crush of concrete all occurred in the constant moment region. As depicted in Figs. 12 and 13, there is also a sudden drop in the load when concrete reaches its tension strength and crack initiates. The fine cracks in concrete will then result in local shear debond leading to a shear slip between the concrete and the steel deck. The slip distributions when concrete initiates cracking and crushing derived from the FE analysis of specimen A-5 are shown in Fig. 14. One can find that slip is not uniformly distributed over the full span of the composite slab. Slip decreases gradually from the end to the midspan of the slab. To illustrate the shear bond mechanism better, the longitudinal shear forces derived from summation of the longitudinal shear stress at the steel–concrete interface are drawn against the mid-span deflections as shown in Figs. 15 and 16. It is found that at the early stage of loading, the longitudinal shear force at the interface was provided with the shear span region. As the

load continued to increase, cracks initiated in the concrete, and local shear debond occurred and the shear bond stress would develop beyond the shear span and distribute over the full span of the composite slab. Major part of the shear bond existed in the shear span region, while the shear bond resistance would also develop in the pure bending region. The ratios of the total shear span to the full span of the composite slabs studied are 1/2 f or slab A-5 and 2/3 for slabs P1-2 and P2-2 respectively. But, at the ultimate state, fraction of the longitudinal shear forces within the shear span region is 58.4% of the total longitudinal shear along the span for A-5, and 75.8% for slabs P1-2 and P2-2. It appears that the greater the shear span region, the larger the proportion of shear longitudinal shear forces. 5. Parametric study and discussions In an effort to gain a fundamental understanding of the behavior of composite slabs, by varying shear span length of the composite slab, while keeping the span length the same, a parametric study was further

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(a) concrete cracking

(b) concrete crushing

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

90

within shear span full span

200

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

80 70

load/kN

longnitudinal shear force/kN

250

150 100

60 50 40 30 20

50

10 0

0 0

10

20

30

40

50

60

0

10

20

30

70

40

50

70

60

deflection/mm

deflection/mm

Fig. 17. Load–deflection curve: specimen A5 in different shear span length. Fig. 15. Longitudinal shear forces at the interface for slabs with open rib shape profiles.

carried out on specimen A5. The load–deflection curves of the slabs are illustrated in Fig. 17. Table 3 shows the numerical results and the corresponding parameter of the shear span length adoptedwhere de is the effective depth of the concrete, a distance from the top fiber of concrete slab to the centroid of the steel deck, accordingly. In Table 3, Vu is equal to the maximum shear force at the support, Nf is the longitudinal shear force at the interface between the concrete and the steel deck at the shear bond failure when the maximum load is reached, and Nmax is the maximum longitudinal shear force at the interface. The

longitudinal shear forces Nf and Nmax are calculated by integration of the longitudinal shear stress over the steel concrete interface. The FE analysis shows that the all composite slabs failed in longitudinal shear bond failure. From Table 3, it is illustrated that the maximum vertical load Vu exerted on the slabs which equals to the vertical shear force at the support or in term of the nominal design shear bond force adopted in the m-k method [5,6] increases with the decrease of the shear span length. At the onset of the shear bond failure, the longitudinal shear force Nf at the interface between the concrete and the steel deck also increases when the shear span length

160

within shear span full span

160 140

longnitudinal shear force/kN

longnitudinal shear force/kN

180

120 100 80 60 40 20 0

within shear span

140

full span

120 100 80 60 40 20 0

0

5

10

15

20

25

30

0

5

10

deflection/mm

deflection/mm

(a) specimen P1-2

(b) specimen P2-2

Fig. 16. Longitudinal shear forces at the interface for slabs with dovetail rib shape profiles.

15

20

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Table 3 Analysis 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

300 500 650 1000 1300

L/8.7 L/5.2 L/4.0 L/2.6 L/2.0

2.4 3.9 5.1 7.9 10.2

80.72 48.31 37.06 25.64 16.96

24.22 24.16 24.09 25.64 22.04

82.85 85.00 70.47 65.10 34.89

92.43 89.69 101.14 99.33 79.99

0.896 0.948 0.692 0.655 0.436

decreases, while the maximum longitudinal shear forces Nmax along the 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 shear span 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 longitudinal shear force is an inherent property for each specific composite slab as far as the steel profiles and the concrete are the same, and the longitudinal shear bond resistance is influenced inversely by shear span length. It is also noticed that all the composite slabs failed in the longitudinal shear bond failure, at which concrete crush occurs in the steel deck while yielding does not, and the maximum flexural moments attained in all the composite slabs (A5, for a parametric study) are around 24 kN·m, a value much less than the full plastic moment of the composite section. The profile steel sheeting was modeled as un-embossed deck in the FE analysis, the effect of the embossment was simulated by introducing the reliable contact modes and parameters, which were calibrated by the push out tests. The cohesion selected for the parametric FE analysis is 0.06 MPa and the friction coefficient adopted is 0.3. As shown in Fig. 10, shear bond resistance would increase with the friction coefficient adopted. It seems necessary to normalize the test conditions of standard rules to the worst case, for example near to null coefficient. Depth and embossing slopes are also significant parameters affecting the shear resistance as found by Ferrer and Marimon [17] recently. Burnet and Oehlers [18] found that the main variable that controlled the shear bond strength was the shape of the profiled sheeting rib. The variation of shear bond strength with the shape parameter was found to be linear and independent of the surface treatment, embossment conditions and plate thickness. Ferrer et al. [13] pointed out that the contribution of embossment on the shear bond resistance of composite profiled slabs is limited by the brittle peel-off failure of concrete. After the initiation of relative slip between

30 25

concrete and profiled steel sheeting, the longitudinal shear resistance of composite slabs mainly depend on the friction bond between the interface of concrete and profiled sheeting. According to the surface treatment, the values of friction coefficient are variable from 0 to 0.6 [13]. However, the moderate value 0.3 maybe reliable for most of the profiled sheeting with common surface treatment as the suggestion by Tsalkatidis and Avdelas [14]. To further calibrate the proposed FE model, other thirteen fullscale tested composite slabs were studied using the fine FE analysis. Details of the experimental study are reported in the paper [20] to be published. The FE analysis approach developed in this paper was used to simulate the shear bond characteristics of composite slabs. Results and comparison between tests and FE analysis are shown in Fig. 18. The cohesion selected for the further FE analysis is still 0.06 MPa and the friction coefficient adopted is 0.3. Fig. 18 shows slight difference between the tests and the FE analysis results. This may partly be due to the material law of concrete used in the FE model proposed by Saenz et al. [19] which would differ from the concrete used for the specimens. Difference in the load procedures between tests 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 and from the finite element analyses are all listed in Table 4. The mean value of Ptest/PFE ratio is 1.00 with the standard deviation of 0.10. The finite element analysis appears to agree well with the test results in predicting the stiffness and the longitudinal shear resistance for the composite slabs. 6. Conclusions A FE analysis approach for study of behavior and failure mechanism of composite slabs has been presented. The approach is based upon the nonlinear contact analysis with the frictional contact

test(slab3)

35

test(slab6)

FE(slab3)

30

FE(slab6)

25

load/kN

load/kN

20 15 10

20 15 10

5

5

0

0 0

10

20

30

40

50

60

0

20

40

60

80

100

deflection/mm

deflection/mm

(a) slab3(span length 2.5m)

(b) slab6(span length 4.0m)

Fig. 18. Comparisons between tests and simulation results.

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

Table 4 Comparison of load carrying capacity obtained from tests and finite element analysis. No.

Ptest/kN

PFE/kN

Ptest/PFE

2 3 5 6 7 8 9 10 11 12 13 Mean Standard deviation

35.00 24.81 31.24 30.03 48.52 33.97 84.53 91.28 85.92 47.49 60.91

35.34 20.88 28.03 29.71 57.47 36.11 90.43 102.88 90.01 42.08 62.74

0.99 1.19 1.11 1.01 0.84 0.94 0.93 0.89 0.95 1.13 0.97 1.00 0.10

at interface between the profiled steel deck and the concrete. Both adhesion and friction at the interface are considered. In the fine FE analysis, the cohesion selected for the contact analysis is 0.06 MPa for the trapezoidal deck and 0.08 MPa for the dovetail rib deck respectively, and the friction coefficient adopted was 0.3 for the all analysis. Conclusions drawn from this study include: 1. The FE analysis based on the nonlinear contact concept is verified and validated by comparing the test results for both the pull out and bending tests of composite slabs. Comparisons of the experimental and the FE analytical results indicate that the FE analysis results agree well with the test results, and the fine FE analysis using the contact model is capable of predicting the load behavior of composite slabs. 2. The FE study shows that all the composite slabs failed in the longitudinal shear bond failure, which is initiated by fine cracks in concrete which result in local shear debond leading to shear slip between concrete and steel deck, then a sudden drop in the load. 3. Slip is not uniformly distributed over the full span of the composite slab, and it decreases gradually from the end to the midspan of the slab. 4. Major part of the shear bond existed in the shear span region, while the shear bond resistance would also develop in the pure bending region. 5. It is likely that the maximum capable longitudinal shear force is an inherent property for each specific composite slab as far as the steel profiles and the concrete are the same, and the longitudinal shear bond resistance is influenced inversely by shear span length. 6. Further calibration of the finite element model is carried out against thirteen full scale composite slab tests. The finite element analysis appears to agree well with the test results in predicting the

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