Geometrically nonlinear analysis of perforated rack columns under a compression load by means of Generalized Beam Theory

Abstract

This paper presents a simplified methodology to take perforations in rack columns into account by means of a geometrically nonlinear Generalized Beam Theory (GBT) analysis. A new GBT formulation, which considers perforation effects through the addition of supplementary terms in the finite element internal force and tangent stiffness matrices during the member analysis, is developed and evaluated. The critical loads, ultimate elastic loads, equilibrium paths and displacement fields obtained by the GBT formulation with perforations are successfully compared using a shell finite element analysis for distortional and global dominant failure modes. Furthermore, the possibility to extend an equivalent thickness approach to handle rack columns perforations in a nonlinear buckling analysis is assessed. Finally, the influence of deformation modes and limitations of the presented GBT formulation are discussed.