Postbuckling Analysis for the Bending of a Long Beam With a Thin, Open, Circular Cross Section

Abstract

A longitudinal bending moment applied to a thin, open section beam induces limit point buckling, due to a second-order effect that flattens the leaves of the cross section. It is shown here, for the case of a circular cross section, that the leaves themselves may exhibit multiple equilibrium configurations. Thus, the postbuckling behavior of the beam is not uniquely defined, and perturbations may shift the system to an unexpected loading path. In this paper, the various equilibrium configurations are examined and judged for stability. A “perfect” bifurcating geometry is identified, and a form of imperfection sensitivity is observed.