Displacement-based formulations for composite beams with longitudinal slip and vertical uplift

This paper describes three novel displacement-based formulations for the analysis of composite beams with a flexible connection which is capable of deforming along the longitudinal axis of the member as well as vertically, i.e. transverse to the interface connection. For completeness, the analytical model which forms the basis of the proposed modelling technique is presented in both its weak and strong forms. The three novel finite element formulations are derived and tested using different structural systems; their nodal freedoms include the vertical and axial displacements as well as the rotations at each element end of both layers. Curvature locking problems are observed to occur for one of these elements and the origin of this behaviour is demonstrated analytically. Two applications are then proposed adopting a bi-linear constitutive relationship for the vertical interface connection to reflect the more realistic case in which, already in the linear-elastic range of the materials forming the cross-section and of the longitudinal interface connection, two vertical connection stiffnesses are required, i.e. one to model the event of separation between the layers and one when one bears against the other one.