Spatial Stability of Nonsymmetric Thin-Walled Curved Beams. I: Analytical Approach

Abstract

An improved formulation for spatial stability of thin-walled curved beams with nonsymmetric cross sections is presented based on the displacement field considering both constant curvature effects and the second-order terms of finite-semitangential rotations. By introducing Vlasov's assumptions and invoking the inextensibility condition, the total potential energy is derived from the principle of linearized virtual work for a continuum. In this formulation, all displacement parameters and the warping function are defined at the centroid axis so that the coupled terms of bending and torsion are added to the elastic strain energy. Also, the potential energy due to initial stress resultants is consistently derived corresponding to the semitangential rotation and moment. Analytical solutions are newly derived for in-plane and lateral-torsional buckling of monosymmetric thin-walled curved beams subjected to pure bending or uniform compression with simply supported conditions. In a companion paper, finite-element procedures for spatial buckling analysis of thin-walled circular curved beams under arbitrary boundary conditions are developed by using thin-walled straight and curved beam elements with nonsymmetric sections. Numerical examples are presented to demonstrate the accuracy and the practical usefulness of the analytical and numerical solutions.