Lateral-distortional buckling of frames composed of non-aligned I-members by a simple distortional beam element considering angling effect

Later-distortional buckling may occur in frames composed of non-aligned I-members, for which the buckling resistance may be overestimated if the distortional deformation of the cross-section was ignored. In this regard, the geometric stiffness matrix for a novel straight beam element with nine DOFs per node that incorporates the effect of angling (or concentrated transverse stresses induced by in-plane bending moments) between two non-aligned members via the symmetric and anti-symmetric distortion modes is derived. Specifically, the virtual work done by the induced moments by in-plane bending moments near the angled joints when, in buckling, undergoing the angle of twist and the anti-symmetric distortion, is consistently included in the virtual work formulation. Although the local geometric stiffness matrices appear to be asymmetric, the symmetry of the structural stiffness matrix is ensured in the global assembly process, provided that the compatibility and equilibrium conditions at joints in the deformed configuration are satisfied. The reliability of the present distortional beam element is verified by comparing the present solutions with those by the Abaqus shell element in several well-designed examples, by which the superiority of the present element to the non-distortional beam elements is also demonstrated. Comparison study shows that the effect of distortional deformation is extremely significant when the angled frame is composed of short members, or the arch is of high curvature, and when rigid flanges or flexible webs are adopted. Moreover, the distortional beam element excluding the angling effect will produce significant errors in some particular cases.