Buckling analysis of thin-walled box beams under arbitrary loads with general boundary conditions using higher-order beam theory

When a higher-order or generalized beam theory is used for the buckling analysis of thin-walled beams, the analysis accuracy critically depends on the number and shapes of the cross-sectional modes associated with warping and distortion. In the study, we propose to use the hierarchically-derived cross-sectional modes consistent with the higher-order beam theory for the analysis of pre-buckling stress and buckling load. The proposed formulation is applicable to any box beams subjected to arbitrary loads and general boundary conditions. We demonstrate the effectiveness of the proposed method by performing buckling analyses for axial, bending, torsional, and general loadings. Length-to-height ratios of the beams are also varied from 1 to 100. If up to fifty cross-sectional and rigid-body modes are employed, the calculated buckling loads are found to match favorably those predicted by the shell finite element analysis. In that a unified buckling analysis under general loads is developed for box beams, the present study is expected to contribute towards new possibilities for the efficient buckling analysis of more general box beam structures involving several joints.