Buckling solutions for compression members with end restraints defined along non-principal directions

Abstract

The classical flexural-torsional buckling solution for compression members with asymmetric cross-sections is intended for members with end fixity conditions defined along the principal directions. In a number of practical situations, member ends can be rotationally restrained about a non-principal direction and rotationally free about the orthogonal non-principal axis. This may occur, for example, when one of the legs of a compression member with an angle or the web of a zed cross-section is connected to a gusset plate. The buckling loads in such cases cannot be determined from the classical solution. Within this context, the present study formulates the variational principle, governing neutral stability conditions, and associated boundary terms based on general non-principal directions, and then develops analytical solutions for the resulting coupled equations. The validity of the solutions is then demonstrated though comparisons with shell and thin-walled beam-based finite element solutions. The solutions are then used to investigate the influence of the orientation of the restraining axes on the buckling load capacity and associated buckling modes for single angles and zed shaped compression members with common end conditions.