Out-Plane Buckling of Arches with Variable Cross-Section

The variable cross-section arch is widely used in practical engineering because of its beautiful arc and excellent mechanical properties. However, there is still no systematic and comprehensive study on the out-plane buckling of variable cross-section arches. In view of this, this paper is focused on the elastic analytical research of out-plane buckling of arches with variable cross-sections under a uniformly distributed radial local load. The pre-buckling and out-plane buckling behavior of a variable cross-sectional arch under an external load is quite different from that of an arch with a uniform cross-section. Castigliano's second theorem is used to establish pre-buckling force method equilibrium equations for variable cross-sectional arches under a uniformly distributed radial local load, and corresponding analytical solutions of normal stress, axial compression, and the bending moments are obtained. Based on the energy method and the Ritz method, analytical solutions of the critical load for the elastic out-plane buckling of arches with variable cross-sections are derived. Comparisons with ANSYS results indicated that the analytical solutions are able to accurately predict the pre-buckling internal forces and critical out-plane buckling load of variable cross-section arches subjected to a uniformly distributed radial local load. It is found that the internal forces and the out-plane buckling load of an arch are significantly affected by the variation of cross-sectional height. As the ratio of the arch's cross-sectional height increases, the bending moment decreases, and the axial force and critical out-plane buckling load increase. Analytical solutions of pre-buckling internal force and critical out-plane buckling load problems for arches with variable cross-sections have a wider significance since they can provide an effective explicit analytic method for the optimal design of arch structures.