Analytical solutions for buckling of space frames subjected to torsional loadings

Abstract

The paper presents analytical solutions for the buckling of single beams as well as two- and three-member frames subjected to torques at the supports. The governing equations and their solutions are stated, including boundary conditions and continuity conditions at connections between members, and buckling solutions are provided for a wide range of support conditions and frame geometries. The cross-section is assumed to be solid or hollow and accordingly, warping effects are ignored. The presented solutions are for a solid rectangular cross-section, and different aspect ratios are analysed to investigate the effect of changing the ratio between the minor and major second moments of area on the buckling torque and associated buckling mode. Solutions are provided for both the critical mode and higher-order modes, allowing mode-changes between symmetric and asymmetric modes to be identified.