Parametric study of bonded steel–concrete composite beams by using finite element analysis

Engineering Structures 34 (2012) 40–51

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Parametric study of bonded steel–concrete composite beams by using finite element analysis Yangjun Luo a, Alex Li b,⇑, Zhan Kang c a

School of Mechanics, Civil Engineering & Architecture, Northwestern Polytechnical University, Xi’an 710072, China Laboratoire de Génie Civil, GRESPI, Université de Reims Champagne-Ardenne, Rue des Crayères, BP1035, 51687 Reims Cedex, France c State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China b

a r t i c l e

i n f o

Article history: Received 10 October 2009 Revised 23 August 2011 Accepted 24 August 2011 Available online 2 November 2011 Keywords: Finite element method Bonded Steel Composite beam Structure

a b s t r a c t The steel–concrete composite beam bonded by adhesive has particular advantages over the traditional composite beam. Based on the experimental push-out test, this paper proposes a three-dimensional nonlinear finite element model for the mechanical behaviour simulation of bonded steel–concrete composite beams. The proposed numerical model is validated through comparisons between numerical results and experimental data. The effects of certain parameters, including the elastic modulus of adhesive, the adhesive layer’s thickness, the concrete strength, the bonding strength and the bonding area, are investigated. Numerical results show that the influence of most investigated parameters on the response of the bonded composites is very notable, while that of the adhesive layer’s thickness (variation within 3–15 mm) is relatively small. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction The traditional steel–concrete composite beam composed of concrete slab, steel girder and shear connectors has been widely used in buildings and bridge construction [1–6]. In this type of structure, metal shear connectors such as headed studs and hoops, which are usually welded to the upper flange of the steel girder, are initially placed in fresh concrete and then act as vertical or horizontal stops once concrete has hardened. Thus, the integration of the composite beam is achieved by preventing the relative slip between the concrete slab and the steel girder. However, the traditional composite beam has its weaknesses. First, the metal shear connectors will induce the origin of cracking in concrete because of the stress concentration, which may substantially reduce the durability of the structure. Second, the traditional connection technique will reduce the fatigue life of the structure due to the welding between the connectors and the steel girder. For these reasons, adhesive bonding method was developed as an attractive technique in steel–concrete composite structures at the beginning of the 1960s [7,8]. In this alternative technique, the concrete slab and the steel girder are connected by an adhesive joint. The adhesive joint can tightly combine the concrete slab and steel girder together and ensure the continuity of the stress distribution over the section of composite beams. Therefore, the stress concentration caused by metal connectors is not a concern any ⇑ Corresponding author. Tel.: +33 326918038; fax: +33 326913039. E-mail address: [email protected] (A. Li). 0141-0296/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2011.08.036

more and the welding is also avoided. Furthermore, the adhesive bonding method makes it possible to use a precast concrete slab, which will considerably simplify the manufacture procedure and reduce the construction cost. In fact, adhesive bonding method has become one of the most accepted techniques in strengthening reinforced concrete structures with steel plate [9–11] or fibre reinforced polymer(FRP) [12–15] for more than a decade. However, the studies on applying the adhesive bonding method to steel–concrete composite beams are still limited. Early efforts have been made by Hick and Baar [16], who applied mechanical treatment on the bonding surface of steel and concrete to improve the bonding strength. Recently, Nordin and Täljsten [17] compared the composite beams which connected I-girder and concrete slab in two ways: casting in steel shear connectors and bonding by epoxy adhesive. Their results showed that the adhesive bonded connection works better than the metal shear connection. Bouazaoui et al. [18] carried out the experimental study of adhesive bonded steel–concrete composite beams. The effects of the adhesive nature and the irregular thickness of the adhesive joint, on mechanical performance and ultimate load, were studied. Thomann and Lebet [19] studied a new composite beam consisting of precast concrete slab, cement paste, bonding layer, embossed steel plate and steel beam. Moreover, push-out tests have also been performed by many studies [20,21] in order to evaluate the adhesive resistance and study the failure mechanisms of the bonding joint between the steel and concrete. Since laboratory tests are highly time-consuming and cost demanding, numerical methods, especially the finite element

Y. Luo et al. / Engineering Structures 34 (2012) 40–51

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Nomenclature Ai Dn Ea Ec = fc = fct F Fn F res Fu F u0 NR sn su t

bonding area corresponding to the ith nonlinear spring relative slip value of the nth reference point, see Fig. 6 elastic modulus of adhesive elastic modulus of concrete concrete compressive strength concrete tensile strength force acting on the bonded composite beam load value of the nth reference point, see Fig. 6 residual load of the nonlinear shear spring, see Fig. 6 ultimate load of the bonded composite beam ultimate load of beam P1 total number of the reference points slip of concrete/adhesive interface, see Eq. (1) ultimate slip corresponding with the ultimate shear strength thickness of the adhesive layer

method, have also been resorted for analysis of many practical engineering problems. Si Larbi et al. [20] simulated push-out tests by a linear elastic finite element model. Zhao and Li [22] studied the nonlinear mechanical behaviour and failure process of bonded steel–concrete composite beams by using the finite element method. As the literature survey reveals, although both experimental and numerical studies have been carried out on bonded steel –concrete composite beams, the fundamental debonding failure mechanism is not fully understood yet, and the effects of several important parameters still need to be explored. In this paper, push-out tests are first implemented to determine the shear strength of the adhesive bonding connection. Then, a three-dimensional finite element model is proposed for analysis of the bonded steel–concrete beams. This model takes into account the nonlinearity of the structure as well as the shear resistance of the concrete/adhesive interface. After being validated by existing experimental tests, the proposed model is used to investigate the effects of some important parameters on the mechanical performance of composite beams, including the elastic modulus of adhesive, the thickness of adhesive layer, the concrete strength, the bonding strength and the bonding area. 2. Push-out test The push-out test is widely used to assess the interfacial shear strength of the connection between two different materials. Even though push out tests for various types of adhesive bonding joints have been carried out [20,21], a general bonding stress-slip law is not yet available. Therefore, the push-out test is required in practice to know the bonding behaviour of the specified bonded composite beams and to evaluate the shear strength. 2.1. Push-out specimens A total of three identical specimens (denoted by SPO-1, SPO-2 and SPO-3) were tested. Each push-out specimen consists of two concrete blocks and one steel girder. The concrete parts contain some constructional steel reinforcements. The dimensions of the specimens have been designed according to the requirements of Eurocode 4 [23] and the geometry characteristic of the bonded composite beam. As shown in Fig. 1, the bonding area is 110  350 mm on each face of the steel girder and the required thickness of adhesive layer is 5 mm.

v eau ec e=c cc cm ct rc sn

su su

relative bonding area ultimate tensile strain of adhesive concrete strain concrete strain corresponding with the compressive strength shear transfer coefficient for a closed crack in ANSYS modified material parameter, see Eq. (3) shear transfer coefficient for an open crack in ANSYS compressive stress on concrete shear stress of the concrete/adhesive interface, see Eq. (1) ultimate shear strength average bonding strength of a interface

After the push-out specimens were prepared, a downward load was evenly distributed on the top section of the steel girder by the loading equipment. During the test, the slip between the concrete block and the steel girder was measured by means of a Linear Variable Differential Transformer (LVDT) displacement sensor, which was installed on the web surface at mid location of the bonding length (see Fig. 2) and connected to a desktop PC. The values of the load and the slip were then automatically recorded every 0.1 s by using a data acquisition system. In order to ensure that the specimen are properly seated and to validate that all the instruments worked well, a preload of 20 kN was first applied and then removed gradually. Usually, a careful adjusting and the initialization for instruments were followed. After that, a continuously increasing load at a constant rate of 0.5 kN/s was applied on the push-out specimen up to failure.

2.2. Materials and preparation The concrete slabs were cast at the same time and stored in the same ambient conditions. In this work, high-strength concrete, which was produced by mixing CEM I 52.5 type Portland cement, gravel, sand, water, rolled aggregates, silica smoke and a high water reducer, was used. The compressive mechanical characteristics of the concrete were determined after cure for 28 days by means of standard tests performed on two U16  32 cm cylindrical specimens [24]. The value of the elastic modulus obtained was 36,600 MPa and the compressive strength was 68 MPa. The steel girder used in construction of the specimen was 400 mm in length cut from an IPE 220 rolled beam, having a depth of 220 mm and a flange width of 110 mm. The adhesive layer was made of an epoxy resin which has a rigid behaviour at the working temperature [30, +60 °C]. This epoxy resin can offer a good strength of adhesion but less flexibility. The elastic modulus and ultimate tensile strength measured by standard tests [25] were 12,300 and 19.5 MPa, respectively. Before bonding the steel girder to concrete slabs, the surface treatment was necessary not only for removing any particles and impurities, but also for modifying the microcosmic nature of the surface and thus increasing its surface energy to improve the bonding quality. In this process, the concrete surface was treated by means of a corundum sandblasting to expose the coarse aggregates, and then cleaned by an acetone solvent. Following a covering by the primary adhesive, the steel surface of the flanges was also sandblasted.

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Y. Luo et al. / Engineering Structures 34 (2012) 40–51

Fig. 1. Dimensions of the push-out specimen (unit: mm).

observed in the adhesive layer. This failure mode indicates a good bonding connection between steel and concrete. The evolutions of the relative slip between the concrete slab and the steel girder according to the average shear stress for three specimens were plotted in Fig. 4. Here, the value of the average shear strength equals the applied load divided by the bonding area. It can be seen that measured results for the specimens SPO-1 and SPO-2 are almost identical, and also very close to that of the specimen SPO-3. The stress-slip curves first show a linear relationship at early stages of loading, and then exhibit a distinctly nonlinear behaviour as the loading progressed until a brittle failure. However, the relative slip was rather small and there was no sufficient plastic deformation. Usually, a connection may be referred to as a ductile connector, a semi-rigid connector or a rigid connector depending on the ultimate slip or the stress-slip curve [23,26]. Using the average measured data of the three specimens, the achieved ultimate shear strength is su ¼ 6:36 MPa for this specified adhesive bonding connection, with a corresponding ultimate slip su ¼ 0:0027 mm. It seems to demonstrate that the bonding connection by epoxy adhesive can be regarded as a rigid one. 3. Finite element model of bonded composite beams 3.1. General description

Fig. 2. Experimental setup of the push-out test.

2.3. Push-out results The failure mode of the push-out specimens is shown in Fig. 3. It can be observed that the failure occurred within the first 2–5 mm of the concrete from the concrete/adhesive interface. Although the epoxy adhesive was subjected to a large shear force, no cracks were

Using the finite element package ANSYS [27], a three-dimensional finite element model was developed to simulate the nonlinear material behaviour of bonded steel–concrete composite beams. The concrete slab was modelled by the 8-node concrete solid element (SOLID65). Reinforcing steel bars in concrete were represented by the 3D beam element (BEAM188). The adhesive layer and the steel girder were modelled by the 8-node solid element (SOLID45). When steel and concrete were bonded by the epoxy adhesive, the previous push-out tests showed that the debonding failure

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Y. Luo et al. / Engineering Structures 34 (2012) 40–51

Fig. 3. Failure mode of the push-out specimen. (a) Concrete surface; (b) Adhesive layer surface.

Slip (mm)

0.003

SPO-1 SPO-2 SPO-3

0.002

0.001

0 0

1

2 3 4 5 Average shear stress (MPa)

6

7

Fig. 4. Relative slip versus average shear stress curves.

occurs through a thin layer of concrete near to the adhesive layer, while the adhesive layer itself is not cracking. In view of this special failure phenomenon, a nonlinear spring element (COMBIN39) can be employed to simulate the shear debonding characteristic of the concrete/adhesive interface, whereas the steel/adhesive interface was assumed to be perfectly bonded. 3.2. Concrete/adhesive interface modelling As shown in Fig. 5, the nonlinear springs were added between the adjacent concrete element and adhesive element to model the shear resistance of concrete/adhesive interface, which has zero thickness. In this model, the normal nodal displacements were considered as coincident in the interface. The element COMBIN39 is a one-dimensional element defined by two nodes and a generalised force–deflection curve. In the current study, a damage-type law has been considered to constitute the force–deflection relationship of the spring element. As illustrated in Fig. 6, such law shows an initial linear behaviour, an

Fig. 6. Damage-type constitutive law for the nonlinear spring elements.

ascending curve until reaching the ultimate force su  Ai and then a sharp decrease followed by a plateau residual force F res , that is simply set as 0.1 times the ultimate force. The N R reference points (denoted by (F 1 , D1 ), (F 2 , D2 ),. . ., (F NR , DNR )) on the force–deflection curve represent relative nodal translation versus force for structural analyses. A table of force values Fn and relative slip values Dn for the nonlinear springs can be defined as follows.



F n ¼ sn  Ai ; F n ¼ F res ;

Dn ¼ sn Dn ¼ sn

ðsn 6 su Þ ðsn P 1:5su Þ

ð1Þ

where Ai is the bonding area corresponding to the ith nonlinear spring, sn and sn are the average shear stress and slip value of the nth reference point, respectively. By adopting this damage-type law, the spring element can not only describe the stress-slip relationship as provided by the available push-out tests, but also reproduce the loss of shear strength after reaching the ultimate force. It should be noted that the proposed interface model is strongly dependent on the relation between the shear stress and the slip. If other stress-slip curves are obtained, the values in Table 1 should be remodelled correspondingly. 3.3. Concrete modelling

Fig. 5. Schematic illustration of concrete/adhesive interface modelling.

3.3.1. Compressive behaviour Concrete in compression is considered to be an elastic–plastic and strain-softening material. The elastic modulus and the compressive strength of concrete slab, measured at the 28th day after concreting by means of standard cylindrical specimen tests, are denoted by Ec and fc= , respectively. The stress–strain curve is assumed

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Y. Luo et al. / Engineering Structures 34 (2012) 40–51 =

to be linear up to 0:4fc , and the nonlinear stress–strain relationship for concrete in uniaxial compression can be expressed by the equation proposed by Carreira and Chu [28].

rc ¼

fc= cm



ec =e=c 



cm  1 þ ec =e=c

cm

ð2Þ

where rc is the concrete compressive stress, ec is the concrete strain, e=c is the strain corresponding with the compressive strength fc= , and cm is a modified material parameter defined by

cm ¼

1 1  fc= =ðe=c Ec Þ

ð3Þ

3.3.2. Tensile behaviour Concrete in tension was considered as a linear-elastic material up to the uniaxial tensile cracking stress, which is approximately defined as function of the compressive strength [29], that is qffiffiffiffiffi fct= ¼ 0:6225 fc= MPa. In the model, the presence of a crack at an integration point is represented through modification of the stress–strain relations by introducing a plane of weakness in a direction normal to the cracking face. Thus, the tensile stress decreases to zero immediately after concrete cracking. 3.3.3. Post cracking behaviour During the post-cracking stage, the cracked reinforced concrete will not completely lose the ability of transferring shear forces because of aggregate interlock or friction. In ANSYS, a constant shear transfer coefficient ct is introduced to take into account this shear retention. By appropriately adjusting the concrete material property matrix incorporated in SOLID65 as the crack opens, the shear stiffness of the crack face is reduced to ct times that of the uncracked concrete. Further, if the normal stress in the crack region becomes compressive, the crack will tend to close and the ability of transferring shear forces across the crack face would be restrengthened. Thus another shear transfer coefficient cc for a closed crack is also introduced. The values of shear transfer coefficients are between 0 and 1, where 0 represents a smooth crack (complete loss of shear transfer) and 1 represents a rough crack (no loss of shear transfer). Note that the reasonable values for shear transfer coefficients can be chosen by a trial and error procedure but the relation 0 6 ct < cc 6 1 should hold. In this work, the values of ct and cc estimated from our computational experiences were 0.35 and 0.75, respectively.

3.4. Adhesive and steel modelling The adhesive layer composed of epoxy resin or polyurethane was approximatively assumed to be linear elastic, isotropic material up to failure. Herein, an elastic perfectly plastic constitutive relationship with isotropic hardening has been adopted for the tensile behaviour of the adhesive layer as follows:

r¼



Ea e

ðe 6 eau Þ

Ea eau ðe > eau Þ

ð4Þ

where r, e, Ea and eau are the actual stress, the actual strain, the elastic modulus and the ultimate tensile strain in the adhesive, respectively. For the steel I-girder, the elastic–plastic isotropic hardening rule and the von Mises yielding criterion were considered. A piece-wise linear stress–strain curve was used for steel girder in both compression and tension. The von Mises yield criterion was also used for the internal reinforcing steel in the concrete slab, and an isotropically hardening material is assumed, with perfectly plastic after the elastic limit. 4. Validation of the finite element model Two simply supported bonded steel–concrete composite beams (denoted by beam P1 and beam P2) tested to failure by Bouazaoui et al. [18], were analysed by using the proposed nonlinear finite element model for the validation purpose. The span of the composite beams was 3300 mm and the loads were applied to the midspan of the beams. These two beams, with the only difference in the material properties of the adhesive layer (epoxy resin for beam P1 and polyurethane for beam P2), have the same dimensions as shown in Fig. 7. The material properties for the composite beams are given in Table 1. In the finite element model, a total of 24,374 elements (include 23,200 eight-node solid elements, 819 two-node spring elements and 355 beam elements) are used for modelling a quarter of the bonded composite beam due to symmetry of the problem (Fig. 8). Vertical displacements of the support positions are fixed and symmetric boundary conditions are placed along the two symmetric planes. The curves of load versus mid-span deflection predicted by the proposed finite element model are compared with the corresponding experimental results in Fig. 9. A good agreement between the numerical and experimental results was obtained not only in the initial stiffness but also in the ultimate strength. The ultimate loads obtained by the present model are 230.5 kN for beam P1 and 197 kN for beam P2, which are 3.2% lower and 6.5% higher than

Fig. 7. Sketch of the bonded composite beam. (a) Overall dimension; (b) Cross-section dimensions (unit: mm).

Y. Luo et al. / Engineering Structures 34 (2012) 40–51 Table 1 Material properties of the bonded composite beams. Material

Properties

Value

Concrete slab

Young’s modulus (MPa) Poisson’s ratio Compressive strength (MPa) Strain in compressive strength Young’s modulus (MPa) Poisson’s ratio Yield stress (MPa) Ultimate strength (MPa) Ultimate strain Young’s modulus (MPa) Poisson’s ratio Yield stress (MPa) Young’s modulus (MPa) Poisson’s ratio Ultimate tensile strength (MPa) Ultimate tensile strain Young’s modulus (MPa) Poisson’s ratio Ultimate tensile strength (MPa) Ultimate tensile strain

36,600 0.28 68 0.003 205,000 0.3 470 570 0.1 205,000 0.3 500 12,300 0.34 19.5 0.0016 38.3 0.38 9.2 0.24

Steel girder

Reinforcing steel

Epoxy resin adhesive

Polyurethane adhesive

Fig. 8. Finite element mesh for a quarter of the bonded steel–concrete composite beam.

250

Load(kN)

200 150 100

Experiment P1 Experiment P2

50

Finite element P1 Finite element P2

0 0

5

10

15

20

25

30

35

Deflection at mid-span (mm) Fig. 9. Load–deflection curves by finite element simulation and by experimental study.

the experimental ultimate value, respectively. This small discrepancy may partly be caused by the asymmetric structural behaviour in practical experimental testing or the imprecise simulation for the complicated post-cracking procedure. Usually, the failure of adhesive-bonded composite beams is caused by the steel girder yielding, the concrete slab crushing or the adhesive layer debonding. The occurrence of a certain failure mode is closely related to the material properties, the bonding

45

quality, the boundary and loading conditions, and even the geometrical dimensions. Therefore, the ability to predict the failure mode is also an important criterion to verify the numerical model. Fig. 10a shows the crack pattern of the concrete slab for beam P1 at the moment of failure. In the figure, the red dots indicate that the integration points of the concrete elements have cracks and the blue region denotes the uncracked element. It can be observed that a number of cracks occur through the mid-span section of the concrete slab. The von Mises stress contour of the concrete slab at the failure moment is also plotted in Fig. 10b. The top concrete slab may encounter yielding or crushing since the equivalent stresses in this region reach the concrete compressive strength value. Therefore, the numerical results suggested that the failure of the bonded composite beam P1 was incurred by the concrete’s cracking and yielding at mid-span, which can be confirmed by the experimental observation as shown in Fig. 10c [18]. Therefore, it can be concluded from these comparisons that the finite element model developed in this paper is capable of predicting the nonlinear behaviour of bonded steel–concrete composite beams. In order to investigate the adhesive bonding behaviour of the composite beams, the shear stress (or slip) contours of the adhesive/concrete interface for beam P1 are sequentially given in Fig. 11. At the load of 150 kN for beam P1, the maximal shear stress located near the mid-span is less than the ultimate value of the bonding strength (Fig. 11a). When the ultimate load is applied, the shear stresses in most parts of the interface are still much less than the ultimate bonding strength, although a small part closes to its ultimate value (Fig. 11b). Note that the shear stresses near the mid-span are much lower because concrete cracks in this local region appear. It thus means that a widespread debonding of the adhesive connection in beam P1 does not occur. This conclusion can be further confirmed by the slip contour as shown in Fig. 11c, in which the slips in most parts of the interface are sufficiently far from reaching the ultimate slip value. 5. Effects of parameters In this section, the proposed finite element model will also be applied to investigate the effects of the adhesive’s elastic modulus, the adhesive layer’s thickness, the concrete compressive strength, the bonding strength and the bonding area on the structural behaviour of the adhesive bonded composite beams. Parameters that will influence the structural performance are certainly not limited to these. Nevertheless, the influences of other factors such as geometrical dimensions of the concrete slab and the steel girder are not addressed in this study. It is worth pointing out that the adhesive bonding behaviour has been particularly tested by some existing push-out experiments [16,20,21] under a certain range of conditions. These experiments tend to the common conclusion: the ultimate shear strength depends very slightly on the adhesive’s elastic modulus, the adhesive layer’s thickness and even the concrete compressive strength, but appears to be affected by the concrete tensile strength, the advanced technology of surface treatment and the quality control in construction. Therefore, the same stress-slip constitutive law as shown in Fig. 6 for the concrete/adhesive interface was simply maintained in the process of studying the effects of these parameters on the composite beam. This study would be really significant from the practical point of view. 5.1. Effects of the elastic modulus of adhesive As can be observed in Fig. 9, the initial stiffness and the ultimate strength of beam P2 are much lower than those obtained in beam P1. This shows that the mechanical behaviour of the bonded composites

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Y. Luo et al. / Engineering Structures 34 (2012) 40–51

Fig. 10. Failure mode of the bonded composite beam P1 under ultimate load. (a) Concrete crack pattern; (b) von Mises stress contour; (c) Failure model by experimental study [18].

Fig. 11. Bonding behaviour of the adhesive/concrete interface for beam P1. (a) Shear stress contour under F ¼ 150 kN; (b) Shear stress contour under ultimate load; (c) Slip contour under ultimate load.

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Y. Luo et al. / Engineering Structures 34 (2012) 40–51

250 E a =12300MP E a =100MPa

E a =1000MPa

E a =38.3MPa E a =10MPa

20

Initial stiffness (kN/mm)

Load (kN)

200

150 E a =1MPa

100

50

0

18 16 14 12 10 8 6

0

5

10

15

20

25

Deflection at mid-span (mm)

30

0.1

1

10

100

1000

10000 100000

Elastic modulus E a (MPa)

(a)

(b)

Fig. 12. Behaviour of the composite beam with various elastic moduli of adhesive. (a) Load–deflection curves; (b) Relationship between the initial stiffness and elastic modulus of adhesive.

beam highly depends on the adhesive’s material properties. Since adhesive may have a wide range of achievable stiffness (e.g. an elastic modulus of polyurethane ranging from 20 to 2300 MPa), the proposed model was used to investigate the behaviour of bonded steel– concrete composite beams with various elastic moduli of adhesive, whereas other conditions remained unchanged. The load–deflection curves of the composite beams varying the elastic modulus of the adhesive are shown in Fig. 12a. It can be observed that the initial stiffness and the ultimate strength increase with the increased elastic modulus of the adhesive layer. However, this increase seems to stop at the value of elastic modulus Ea ¼ 1000 MPa. The nonlinear relation between the initial stiffness of the load–deflection curve and the elastic modulus of the adhesive layer is shown in Fig. 12b. According to the correlation level, three regions can be divided in this relation. In the first region (0 < Ea < 1 MPa), the bonding effect by adhesive is much more feeble because it cannot prevent the slip between the concrete slab and the steel girder at all. The mechanical behaviour of the bonded composite beam with adhesive property amongst this part is the same as the composite beam without any connection. In the second region (1 MPa 6 Ea 6 1000 MPa), a relative strong interaction between the initial stiffness and the elastic modulus is observed. In the third region, Ea > 1000 MPa, the initial stiffness is almost not affected by the increased elastic modulus of adhesive. The adhesive bonding can effectively prevent the slip between the concrete slab and the steel girder in this region. Therefore, the elastic modulus of adhesive material should be taken amongst the third region (Ea > 1000 MPa) in order to ensure the desired performance of the bonded steel–concrete composite beams. 5.2. Effects of the adhesive layer’s thickness In the experimental conditions, it is always difficult to keep the steel girder surface or the concrete slab surface flat and to have identical bonded thickness due to the complexity of construction in situ, especially for the long-span beam. Consequently, the thickness of the adhesive layer may not be uniform. In this section, a detailed investigation on the effects of adhesive thickness is carried out by the proposed nonlinear finite element analysis. The investigated composite beams have different adhesive layer’s thicknesses, whereas all other structural and material parameters are identical to those defined for beam P1. The corresponding load–deflection curves of composite beams with adhesive thicknesses of 3, 5, 7, 10 and 15 mm are shown in

Fig. 13a. It is shown from the figure that the initial stiffness of the bonded composite beam is hardly influenced by the variation of the adhesive thickness, but the ultimate load slightly increases with an increase of the adhesive thickness. The relation between the relative ultimate load F u =F u 0 and the adhesive layer’s thickness t is shown in Fig. 13b. A linear expression with a very low growth rate is then obtained as:

Fu ¼ 0:0053ðt  3Þ þ 1; F u0

ð3 mm 6 t 6 15 mmÞ

ð5Þ

where t is in mm, F u is the ultimate load, F u0 is the ultimate load of beam P1 with t ¼ 3 mm. When the adhesive thickness increases from 3 to 15 mm, the ultimate load only increases by 6.3%. It can be concluded that the effect of adhesive thickness on the performance of composite beams is relatively small. 5.3. Effects of the concrete strength In order to investigate the effects of the concrete compressive strength on the beam behaviour, bonded composite beams (similar to beam P1) with different concrete strengths fc= ¼ 20; 30; 40; 50; 60; 68 MPa are analysed, respectively. The corresponding load– deflection curves are plotted in Fig. 14a. It shows that the overall stiffness and the ultimate load decrease obviously for lower levels of the concrete strength. In practice, this behaviour indicates that using a low-strength concrete in this specified composite beam can induce an unexpected yielding or crushing failure of the concrete slab. Fig. 14b presents the relative ultimate load evolution F u =F u0 as a nonlinear function of the concrete compressive strength. Here, the referenced denominator F u0 still represents the ultimate load of beam P1. The observed tendencies show that: for this specified composite beam, the increase of the ultimate load will be more gradual when concrete strength increases from 50 to 70 MPa. Therefore, high-strength concrete (fc= P 60 MPa) was proposed to be used in order to improve the loading capacity of such a bonded composite beam and avoid a premature concrete crushing. 5.4. Effects of the bonding strength The debonding failure of the bonded steel–concrete composite beams depends on the bonding strength of concrete/adhesive interface, i.e. the ultimate shear stress su . In this section, we investigate the debonding behaviour of composite beams with various

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Y. Luo et al. / Engineering Structures 34 (2012) 40–51

250

200

1.05

F u /F u0

Load (kN)

1.10

150

t =15mm t =10mm t =7mm t =5mm t =3mm

100

50

1.00 0.95 0.90

0 0

5

10

15

20

25

3

30

6

9

12

15

Thickness of adhesive (mm)

Deflection at mid-span (mm)

(a)

(b)

Fig. 13. Behaviour of the composite beam with various adhesive layer thicknesses. (a) Load–deflection curves; (b) Relationship between the relative ultimate load and the adhesive layer thickness.

250

1.05

150

/ c / c / c / c / c / c

f =68MPa

1.00

f =60MPa

100

F u /F u0

Load (kN)

200

f =50MPa f =40MPa 50

f =30MPa

0.95 0.90 0.85

f =20MPa 0.80

0 0

5

10

15

20

25

Deflection at mid-span (mm)

(a)

30

20

30

40

50

60

70

Concrete strength (MPa)

(b)

Fig. 14. Behaviour of the composite beam with various concrete strengths. (a) Load–deflection curves; (b) Relationship between the relative ultimate load and the concrete strength.

shear stresses, ranging from 0.5 to 6.0 MPa. The material properties given in Table 1 for beam P1 were used for all cases. In order to study the debonding failure process, the evolution of the shear stress contour for the adhesive-concrete interface when the bonding strength su ¼ 2 MPa was revealed. As shown in Fig. 15a, the shear stress level of the interface is very low at the load of 50 kN. As the applied load increases, the shear stress level increases and then the region with ultimate shear stress gradually expands. At the load of 90 kN, shear stresses in one half of the region reach the ultimate bonding strength (Fig. 15b). When the load increases to 110 kN, almost the whole interface is at an ultimate stress level (Fig. 15c), which means the debonding failure is imminent. In Fig. 16a, the ultimate loads for each case when the debonding failure occurs can be observed from the so-called debonding point. For example, when the ultimate shear stress su of the steel –concrete interface is 0.5 MPa, the ultimate load of the composite

beam is 30 kN. When su equals 4 MPa, the ultimate load is about 200 kN. The debonding failure is a typical brittle destroy process with a catastrophic failure of the composite beams when the debonding point is reached. Thus, an important issue in the design of the bonded composite beams is to avoid the failure in debonding mode. Furthermore, a nonlinear relationship between the ultimate load and the bonding strength for those fully bonded composite beams is plotted in Fig. 16b. It can be observed that the relation between the ultimate load and the bonding strength is divided into three regions: For 0 < su 6 3:4 MPa, the ultimate load, corresponding to the debonding failure, increases linearly according to the increased bonding strength; For 3:4 MPa 6 su < 5 MPa, the ultimate load increases non-linearly and slowly according to the increased bonding strength; For su P 5 MPa, the ultimate load does not increase any more. It reaches its maximal value 230 kN in this study. It means that the

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Y. Luo et al. / Engineering Structures 34 (2012) 40–51

Fig. 15. Interface shear stress contour under various loads when the bonding strength

250

τu=6MPa debonding point

τu=5MPa

200

250

τu=4MPa 150

τu=3MPa

Ultimate load (kN)

Load (kN)

su ¼ 2 MPa. (a) F ¼ 50 kN; (b) F ¼ 90 kN; (c) F ¼ 110 kN.

τu=2MPa

100

τu=1MPa

50

τu=0.5MPa 0

200 150 100 50 0

0

5

10

15

20

25

Deflection at mid-span (mm)

(a)

30

0

2

4

6

8

Bonding strength (MPa)

(b)

Fig. 16. Behaviour of the composite beam with various bonding strengths. (a) Load–deflection curves; (b) Relationship between the ultimate load and the bonding strength.

adhesive bonding connection is sufficient and the debonding failure will not occur for this fully adhesive bonded composite beam. 5.5. Effects of the bonding area In the practical bonding process, the high fluidity of the adhesive combined with imperfections such as inclusions, gas bubbles

and construction errors may lead to an inadequate bonding connection at the interface. Therefore, another key factor that may influence the debonding behaviour of the bonded composite beam is the bonding area. In the present study, a relative bonding area v, which is the percent ratio of the actual adhesive bonding area to the maximal possible bonding area, was used. It is assumed that the actual bonded region is distributed evenly in subsections along

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 The mechanical behaviour of the bonded composite beam depended strongly on the adhesive’s material properties. The elastic modulus of adhesive material should exceed 1000 MPa in order to ensure the desired performance of bonded steel– concrete composite beams.  The ultimate load of the bonded composite beam depends linearly on the thickness of the adhesive layer. However, this influence is relatively small in practical engineering.  The overall stiffness and the ultimate load decrease for lower levels of the concrete strength. High-strength concrete was thus proposed to improve the loading capacity of the bonded composite beam and avoid a premature concrete yielding.  The debonding failure of the bonded steel–concrete composite beam mainly depends on the bonding strength and the bonding area. In view of their effects, an average bonding strength su ¼ vsu  5:0 MPa should be ensured in order to avoid the debonding failure.

Fig. 17. Distribution of the bonded region.

Ultimate load (kN)

250 200 150 100

τ u =6.36MPa τ u =5.50MPa

50 0 50

60

70

80

90

100

Relative bonding area (%) Fig. 18. Relationship curves between the ultimate load and the relative bonding area.

the beam length (Fig. 17). To quantify its influence, simply supported composite beams similar to beam P1 but with various relative bonding areas, ranging from 50% to 100%, were analysed. The curves of the ultimate load versus the relative bonding area are plotted in Fig. 18. For the composite beam with the bonding strength of 6:36 MPa, the higher relative bonding area (v P 80%) resulted in a perfect connection without the debonding failure. However, when the relative bonding area v is lower than 80%, the ultimate load decreases and the composite beam will fail in debonding. For the case of the bonding strength su ¼ 5:5 MPa, a critical relative bonded area v equals to 90%. If the practical relative bonding area is lower than this value, a debonding failure should occur. It is worth noting here that the debonding failure is mainly determined by an average bonding strength, which equals to the relative bonding area multiplying the bonding strength, namely su ¼ vsu . Therefore, by combining the effects of bonding strength and bonding area, an approximate value of average bonding u  5:0 MPa needs to be ensured for this bonded composstrength s ite beam in order to avoid the debonding failure. 6. Conclusions This paper first carried out experimental push-out tests to study the debonding failure mode and determine the bonding strength of the adhesive connection. Then, a validated three-dimensional nonlinear finite element model based on the finite element package ANSYS was proposed to predict the parametric effect of bonded steel–concrete composite beams. From the experimental and numerical results, the following conclusions can be drawn:  The epoxy adhesive bonding connection between the steel girder and the concrete slab provided a bonding strength of 6.36 MPa. The debonding failure takes place within the first 2–5 mm of the concrete from the adhesive/concrete interface.

Numerical investigations in this paper were based on adhesivebonded composite beams with specified steel and concrete sections. We believe that the proposed model as well as the obtained results would also provide meaningful guidance to the design of other composite beams with similar structural characteristics. Further experimental and numerical studies are still needed to cover a broader range of bonded composite beams under multiple loading cases and complex constraint conditions.

Acknowledgements The support from the Natural Science Foundation of China (Grant 51008248), the French Government (scholarship) and the NPU Foundation for Fundamental Research (JC200936) is gratefully acknowledged. The authors would also like to thank the anonymous reviewers for their valuable suggestions.

References [1] Brozzetti J. Design development of steel-concrete composite bridges in France. J Constr Steel Res 2000;55(1–3):229–43. [2] Nie J, Xiao Y, Chen L. Experimental studies on shear strength of steel-concrete composite beams. J Struct Eng 2004;130(8):1206–13. [3] Liang QQ, Uy B, Bradford MA, Ronagh HR. Strength analysis of steel-concrete composite beams in combined bending and shear. J Struct Eng 2005;131(10):1593–600. [4] Ranzi G, Zona A. A steel-concrete composite beam model with partial interaction including the shear deformability of the steel component. Eng Struct 2007;29(11):3026–41. [5] Jurkiewiez B. Static and cyclic behaviour of a steel-concrete composite beam with horizontal shear connections. J Constr Steel Res 2009;65(12):2207–16. [6] Ernst S, Bridge RQ, Wheeler A. Push-out tests and a new approach for the design of secondary composite beam shear connections. J Constr Steel Res 2009;65(1):44–53. [7] Miklofsky HA, Brpown MR, Gonsior MJ. Epoxy bonding compounds as shear connectors in composite beams. Engineering Research Series, RR.62–2. New York: Department of Public Works; 1962. [8] Krieg JD, Enderbrock EG. The use of epoxy resins in reinforced concrete: static load tests. Part II. The University of Arizona: Engineering Research Laboratories; 1963. [9] Swamy RN, Jones R, Bloxham JW. Structural behaviour of reinforced concrete beams strengthened by epoxy-bonded steel plates. Struct Eng Part A 1987;65(2):59–68. [10] Barnes RA, Baglin PS, Mays GC, Subedi NK. External steel plate systems for the shear strengthening of reinforced concrete beams. Eng Struct 2001;23(9):1162–76. [11] Lim YM, Shin SK, Kim MK. A study on the effect of externally bonded composite plate-concrete interfaces. Compos Struct 2008;82:403–12. [12] Yuan H, Teng JG, Seracino R, Wu ZS, Yao J. Full-range behavior of FRP-toconcrete bonded joints. Eng Struct 2004;26(5):553–65. [13] Lu XZ, Teng JG, Ye LP, Jiang JJ. Bond-slip models for FRP sheets/plates bonded to concrete. Eng Struct 2005;27(6):920–37. [14] Ferrier E, Quiertant M, Benzarti K, Hamelin P. Influence of the properties of externally bonded CFRP on the shear behavior of concrete/composite adhesive joints. Compos Part B: Eng 2010;41(5):354–62.

Y. Luo et al. / Engineering Structures 34 (2012) 40–51 [15] Kim YJ, Fam A. Numerical analysis of pultruded GFRP box girders supporting adhesively-bonded concrete deck in flexure. Eng Struct 2011. doi:10.1016/ j.engstruct.2011.07.016. [16] Hick F, Baar S. Structures métalliques collées. Station d’Essais et de Recherches de la Construction Métallique, SERCOM. Belgique: Liège; 1972. [17] Nordin H, Täljsten B. Testing of hybrid FRP composite beams in bending. Compos Part B: Eng 2004;35(1):27–33. [18] Bouazaoui L, Perrenot G, Delmas Y, Li A. Experimental study of bonded steel concrete composite structures. J Constr Steel Res 2007;63:1268–78. [19] Thomann M, Lebet JP. A mechanical model for connections by adherence for steel-concrete composite beams. Eng Struct 2008;30(1):163–73. [20] Si Larbi A, Ferrier E, Jurkiewiez B, Hamelin P. Static behaviour of steel concrete beam connected by bonding. Eng Struct 2007;29(6):1034–42. [21] Berthet JF, Yurtdas I, Delmas Y, Li A. Evaluation of the adhesion resistance between steel and concrete by push out test. Int J Adhes Adhes 2011;31(2):75–83. [22] Zhao G, Li A. Numerical study of a bonded steel and concrete composite beam. Comput Struct 2008;86:1830–8.

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[23] Eurocode 4. Design of composite steel and concrete structures, Part 1-1: General rules and rules for buildings. European Committee for Standardization (CEN), London (UK), 2004. [24] ASTM C 39. Standard test method for compressive strength of cylindrical concrete specimens. Annual Book of ASTM Standards, 2002. [25] ASTM D 882-91. Standard test methods for tensile properties of thin plastic sheeting, Annual Book of ASTM Standards, 1991. [26] Aribert JM. Étude critique par voie numérique de la méthode proposée dans l’eurocode 4 pour le dimensionnement des poutres mixtes acier-béton à connexion partielle. Construction Métallique 1988;1:23–36. [27] ANSYS, Inc. ANSYS theory reference, release 6.1. 2004. [28] Carreira DJ, Chu KH. Stress–strain relationship for plain concrete in compression. ACI J Proc 1985;82(6):797–804. [29] Park R, Paulay T. Reinforced concrete structures. New York: John Wiley & Sons; 1975. p. 16.