| doi:10.3850/978-981-08-6218-3_CC-Fr010 |
 Final Paper PDF
|
CLOSED-FORM SOLUTION FOR TWO-LAYER COMPOSITE SHEAR DEFORMABLE BEAMS WITH INTERLAYER SLIP
Q-H. Nguyen1,a, M. Hjiaj1 and E. Martinelli2
1Structural Engineering Research Group, INSA de Rennes, 20 avenue des Buttes de Coësmes CS
70839 F–35708 Rennes Cedex 7, France.
aquang-huy.nguyen@insa-rennes.fr
2Department of Civil Engineering, University of Salerno, Via Ponte don Melillo - 84084 Fisciano (SA),
Italy
EXTENDED ABSTRACT
This paper presents a closed-form solution for linear elastic steel-concrete composite beams with partial interaction (cf. Figure 1). In the literature, several analytical solutions have been proposed for steel-concrete composite beam with deformable shear connection where the section shear deformation is ignored [1], [2], [3]. In this paper, the later is taken into account by using separately the Timoshenko’s beam theory for concrete slab and the steel beam. It should be noted that the slip can occur at the interface steel-concrete but there is no separation (cf. Figure 1a).
Figure 1: Two-layer composite shear deformable beam
By using the equilibrium equations, the compatibility equations and constitutive relationships, the governing equations of the problem can be expressed in two differential equations with two main unknowns: shear and uplift forces at the interface. These differential equations can be analytically solved from which the exact expression of displacements and forces fields can be derived. This analytical solution is not straightforward. Based on these expressions, the exact stiffness matrix is deduced for a generic composite beam element. The proposed exact stiffness matrix may be used in a classical finite element program for the analysis of shear deformable steel-concrete composite beams with partial interaction [4]. The present formulation requires a minimum number of elements depending on the support and loading conditions. Finally, a numerical application dealing with a simply-supported steel-concrete composite beam is presented in order to validate the solution and compare the steel-concrete composite shear deformable beam with steel-concrete composite Bernoulli beam.
References
[1] N. M. Newmark, C. P. Siess, and I. M. Viest, Tests and analysis of composite beams with incomplete interaction, Proceedings Society for experimental stress analysis, 8(1): 75-92, 1951.
[2] C. Faella, E. Martinelli, E. Nigro, Steel and concrete composite beams with flexible shear connection: “exact” analytical expression of the stiffness matrix and applications, Computers & Structures 2002; 80(11), 1001-1009.
[3] Q-H. Nguyen, Modélisation du comportement non-linéaire des poutres mixte acier-béton avec pris en compte les effets différés, PhD thesis, INSA of Rennes and University of Wollongong, 2009.
[4] Q-H. Nguyen, E. Martinelli and M. Hjiaj, F. E. analysis of two-layer composite shear deformable beams with partial interaction based on the exact stiffness matrix, European Journal of Mechanics- A/Solids (submitted).