A GENERAL THEORY FOR IN-PLANE NONLINEAR ANALYSIS OF CIRCULAR ARCHES

Current theories for arch buckling analysis have great differences. Based on the Bernoullis assumption, a new theory for nonlinear analysis of circular arches is proposed. The finite displacement theory for strain-displacement relation is adopted. The nonlinearity of the shear and the transverse stresses is considered. It is believed that the nonlinear effects of various stresses, which are in equilibrium prior to buckling, will cancel each other partially, so neglecting any one of these stresses will lead to unwanted terms in the equilibrium equations. Employing the internal forces in linear analysis, a set of linearized equations suitable for buckling analysis of arches are derived. A detailed analysis of the buckling of circular arches under uniform radial load is conducted. The results of the linear analysis are substituted into the nonlinear equations to obtain a set of equations which are solved using Galerkin technique. The effect of pre-buckling deformation is included. Various assumptions often used by previous researchers, especially the inextensional assumption of the arch axis, are discussed. A comprehensive comparison of various theories is provided.