A linear finite element for timber–concrete layered beams with interlayer slip

Abstract

In this paper, a beam theory for linear two-layer beams is presented in the framework of the Finite Element (FE) method. In particular, the beam theory aims to represent the static and dynamic response of timber–concrete layered structures, in which a concrete slab is supported by timber girders. Since the timber layer has a rather low shear stiffness, a shear-flexible formulation of the displacement field is adopted. In general, it cannot be assumed that the layers of such members are perfectly bonded. Therefore, the relative interlayer displacement in the longitudinal direction is considered, which is determined by a linear slip modulus in a smeared approach. Based on these assumptions, the stiffness matrix, mass matrix and load vector of a finite beam element are derived. Modal analyses on a single-span beam with clamped, free and hinged supports are performed and compared to the outcomes of 3D FE simulations to verify the applicability of the proposed beam theory over a wide frequency range. Static analyses on two structural systems illustrate the accuracy of the beam deflection and the interlayer slip, as well as the realistic assessment of normal and shear stresses in the two layers.