Post-buckling analysis of nonlinear shear-deformable prismatic columns using a GBT consistent energy formulation

The post-buckling analysis of shear-deformable prismatic columns under uniform compression is studied using the Generalized Beam Theory. The member's deformed shape is described by a linear combination of three modes of deformation: axial elongation, bending and the shear deformation. The total potential energy is computed, based on the relevant relations of the theory of elasticity, and is rendered discrete through the Rayleigh-Ritz method. The buckling behaviours of the pinned-pinned columns are validated by comparison with available critical load formulae. The post-buckling behaviours, for three representative lengths, are computed by searching nontrivial equilibrium points in the neighbourhood of the critical state. The results, described by the load-displacement plots of the equilibrium paths, are symmetric and stable. Furthermore, the stability of the post-buckling paths, measured by the magnitude of their concavity in the neighbourhood of the critical state, increases with increasing values of cross section shear stiffness and of the member's length.