Finite Element Analysis of 3D Thin-Walled Beam with Restrained Torsion

Abstract

This paper considers a modified formulation of finite element modeling for thin-walled sections with restrained torsion, including the deformation and angle of twisting caused by combined loading conditions. The unknown parameters of thin-walled cross-section are defined as a function of section properties that represent warping behavior along the beam axis. Thin-walled structures are widely used in various structural engineering applications due to their advantage of high bearing strength when compared to self-weight and when subjected to combined loadings. When a thin-walled section is subjected to a combined load with restrained torsion, they are ineffective at resisting, and it leads to reduce the capacity of the beam due to the torsion and additional warping stresses. A finite element calculation can be used to analyze a 3D bar of thin-walled structural sections. Different commercial software and studies commonly consider six degrees of freedom at each node of a member for a space frame without considering the effect of warping restraint at the member's ends. This paper presents a finite element calculation for thin-walled sections with restrained torsion using the 14 × 14 member stiffness matrix, which includes warping as an additional degree of freedom and is commonly used for open thin-walled sections. In this study, we considered two different methods to take into consideration the additional degree of freedom for the stiffness matrix, which are very close to each other for small values of characteristics number.