Deformation equations of thin-walled open-profile members considering distortion and its application

In order to simplify the analysis of thin-walled open-profile bars, a method is presented in which the analysis is split into two parts, dominated by in-plane and out-plane loading effects respectively. This article focuses on the out-plane loading effects. Based on bending theory of thin plate with small deflection, each slab or strip is analyzed separately and the results are integrated into vectors, in which, the deformation shapes and equilibrium conditions are simplified appropriately, thus leading to the slabs' out-plane bending resistance system of thin-walled bars, which reflects the properties of the bar's distortion and torsion. By composing the slabs in-plane tension-bending resistance system and the slabs' out-plane bending resistance system, deformation equations of thin-walled open-profile bars considering distortion are deduced. In order to set up the finite bar element method, stiffness equation and equivalent nodal forces of internode loadings are deduced. Comparative analysis with finite shell element method indicates the high efficiency and accuracy of this method.