Elastica Solution of Braced Struts

Abstract

An exact formulation is derived for the buckling of structs supported elastically at the midspan. The formulation is based on the large deflection theory of the beam column. Two coupled nonlinear equations involving definite integrals govern the postbuckling solution. The equations are solved numerically with an iterative scheme. The postbuckling solutions are found for the range of support stiffness of interest. The load‐deflection history of the postbuckling path, as well as the postbuckling shape, is traced. As the support stiffness increases from zero, the postbuckling path changes from stable to unstable. This finding confirms the results of a previous study using a static perturbation method. The current results, however, also reveal the rate of change of the load‐carrying capacity along the postbuckling path away from the buckling load. For the range of support stiffness that renders the postbuckling path unstable, the rate of reduction of the load‐carrying capacity along the path is found to be small.