Analytical Solutions for Elastic Shear Buckling of Thin‐Walled Channels with Narrow Flanges

Abstract Thin‐walled channel sections are commonly used as structural beams subjected to bending and/or shear, with a variety of dimensional ratios between web depth, flange width, and lip size. The demand for customising the sectional element sizes in the cold‐forming process arises from different strength optimisation purposes. This results in a significantly wide range of flange width‐to‐web depth ratios, which in turn leads to major changes in the entire section's buckling capacity of buckling modes. This paper presents comprehensive numerical and analytical studies on the elastic buckling of thin‐walled channels subjected to shear, covering a full range of flange width‐to‐web depth ratios and various member lengths. Elastic buckling analyses of lipped and unlipped channels are conducted using both semi‐analytical and restrained semi‐analytical finite strip methods under different modelling conditions, and are benchmarked against finite element models. A new analytical solution for calculating the elastic shear buckling of channel sections across the full range of flange widths is proposed to provide the elastic buckling input for the ultimate capacity design of thin‐walled channel members in shear.