3D formulation of mono-symmetrical composite beams with deformable connection

Abstract

This paper deals with a 3D linear formulation for mono-symmetric composite beams with deformable connection, taking into account non-uniform torsion. To simplify the development of the analytical solution, it is assumed that the warping of each layer of the composite section has no contribution on the stress resultants of each layer. Therefore, the warping function obtained with the classical St-Venant beam theory can be used for each subsection. As a result, the variables associated to both connection shearing plans become uncoupled. Using the virtual work principle, the governing equations are derived, and solved in closed-form. Based on the analytical expressions of the displacement fields, the exact stiffness matrix of the composite beam is computed. In addition, a displacement-based formulation is suggested. Appropriate polynomial interpolation functions are selected to circumvent slip-locking phenomenon. It has been shown that the slip-locking can be avoided by using quadratic shape function for axial displacement interpolations, by providing an additional middle node in each layer. Four examples are investigated in this paper. The prediction as well as the performance of the proposed direct stiffness method, are compared against an existing solution from the literature. In addition, slip-locking problem is addressed and the performance of the displacement-based method against the exact formulation is evaluated. The influence of warping effects on the composite beam response is assessed. Finally, a parametric study is conducted to evaluate the influence of connection rigidity and the coupling of the displacement fields on slip distributions.