Buckling analysis of curved beams by finite-element discretization

Recently, an extensive theoretical investigation on the buckling and large-displacement behavior of thin-walled circular beams was reported in a two-paper series. Equilibrium equations governing the linear, bifurcation buckling, and large-displacement behaviors were derived using the principle of minimum total potential energy. This paper first presents the transformation process for finite-element stiffness relationships for a spatial curved beam element with a total of 14 degrees of freedom. It then presents numerical data demonstrating the applicability of the method for the lateral buckling of arches and the lateral-torsional buckling of horizontally curved beams. A numerical comparison between the present formulations and those presented by others is made, along with a comparison to results obtained from using three-dimensional finite-element models. Based on results from the lateral bifurcation buckling of horizontally curved beams, a regression equation is formulated representing the reduction in critical moment due to the simple addition of curvature. A comparison of results from using this regression equation to ultimate strength experimental test results of horizontally curved girders by others resulted in an unexpected excellent correlation.