Derivation of the exact stiffness matrix of shear-deformable multi-layered beam element in partial interaction

• Shear-deformable multi-layered beams in partial interaction.
• Solution strategy of the coupled governing differential equations.
• Derivation of the exact finite element model.
• Shear-deformable model versus the shear-rigid model.
• Influence of shear-connection stiffness and the span-to-depth ratio on the overall structural response.

This paper presents the exact finite element formulation for the analysis of partially connected shear-deformable multi-layered beams. Timoshenko׳s kinematic assumptions are considered for each layer or component, and the shear connection is modeled through a continuous relationship between the interface shear flow and the corresponding slip. The effect of possible transversal separation of the two adjacent layers has not been considered. The governing equations describing the behavior of a shear-deformable multi-layered beam in partial interaction consist of a set of coupled system of differential equations in which the primary variables are the slips and the shear deformations. This coupled system has been solved in closed form, and the “exact” stiffness matrix has been derived using the direct stiffness method. The latter has been implemented in a general displacement-based finite element code, and has been used to investigate the behavior of shear-deformable multi-layered beams. Both a simply supported and two continuous beams have been considered in order to assess the capability of the proposed formulation and to investigate the influence of the shear connection stiffness and span-to-depth ratios on mechanical responses of the beams. It has been found that the transverse displacement is more affected by shear flexibility than the interlayer slips.