Prebuckling Deformations and Flexural-Torsional Buckling of Arches

When the ratio of the minor axis flexural stiffness to the major axis flexural stiffness is not small, classical analysis may lead to an inaccurate prediction of the flexural-torsional buckling loads of an arch, because prebuckling in-plane deformations change the curvature of the arch. A systematic treatment of the effects of prebuckling in-plane deformations on the elastic buckling of monosymmetric arches is presented in this paper. Nonlinear relationships between the displacements and the strains are obtained using position vectors. Energy equations are formulated for the elastic flexural-torsional buckling of monosymmetric arches, which include the effects of prebuckling in-plane deformations, and closed-form solutions are obtained for arches in uniform bending. The effect of the arch slenderness on flexural-torsional buckling is investigated. Comparisons with the existing theoretical solutions are made.