Exact finite element formulation for an elastic hybrid beam-column in partial interaction with shear-deformable encasing component
Résumé
The authors present the exact finite element formulation for partially connected shear-deformable elastic hybrid beam-columns with several embedded sections. Euler-Bernoulli's kinematic assumptions are adopted for the embedded section whereas Timoshenko's kinematic assumptions are considered for the encasing element. The shear connection between the encasing component and the embedded section is modeled through a continuous relationship between the interface shear flow and the corresponding slip. A set of coupled system of differential equations in which the primary variables are the slips and the shear deformation of the encasing cross-section is derived from the governing equations describing the behavior of an elastic shear-deformable hybrid beam-column in partial interaction. 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 into a general displacement-based finite element code, and has been used to investigate the behavior of shear-deformable hybrid beams. Three numerical examples have been considered in order to assess the capability of the proposed formulation and to investigate the effect of the shear connection stiffness and span-to-depth ratios on mechanical responses of the beam-columns. It has been found that the transverse displacements are more affected by the shear flexibility than the slips.