Non-uniform torsional behavior and stability of thin-walled elastic beams with arbitrary cross sections

In this paper, the analysis of the behavior of thin-wa lled beams, derived from Prokić’s work, is carried out by using beam theory with a single warping function valid for arbitrary form of cross sections, without any distinction between open and closed profiles and without using sectorial coordinates. The finite element method is used and numerical examples show the accuracy of the solution by comparison with other numerical or analytical results. For the stability analysis, analytical and numerical calculations of critical loads are given for beams submitted to bending moment and centrally applied forces. Equilibrium equations are established from the principle of virtual work. Critical loads are calculated by considering that a structure already in equilibrium reaches instability if there is one or more than one equilibrium position for the same loading. Results with this formulation are compared to those obtained with classical warping functions.