Spatial stability of nonsymmetric thin-walled curved beams. I: Analytical approach

An improved formulation for spatial stability of thin-walled curved beams w ith nonsymmetric cross sections is presented based on the displacement fiel d considering both constant curvature effects and the second-order terms of finite-semitangential rotations. By introducing Vlasov's assumptions and i nvoking the inextensibility condition, the total potential energy is derive d from the principle of linearized virtual work for a continuum. In this fo rmulation, 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 initi al stress resultants is consistently derived corresponding to the semitange ntial rotation and moment. Analytical solutions are newly derived for in-pl ane and lateral-torsional buckling of monosymmetric thin-walled curved beam s subjected to pure bending or uniform compression with simply supported co nditions. In a companion paper, finite-element procedures for spatial buckl ing analysis of thin-walled circular curved beams under arbitrary boundary conditions are developed by using thin-walled straight and curved beam elem ents with nonsymmetric sections. Numerical examples are presented to demons trate the accuracy and the practical usefulness of the analytical and numer ical solutions.