Instances of mixed buckling and post-buckling of steel RHS beams

Simply supported steel beams with rectangular hollow section (RHS) are investigated, taking into account large twist and cross-sections distortions. A closed-form expression for the critical value of the external couple inducing lateral torsional buckling is found; homotopy perturbation method (HPM) is used to investigate the post-buckling non-linear path. The linear and non-linear paths given by HPM are compared to those of: i) a Newton–Raphson algorithm with arc length; and ii) the commercial FEM code Abaqus. Some numerical examples are presented.