Numerical large deflection bending and buckling analysis of arches

A numerical procedure for the analysis of slender arch buckling problems for general symmetric loadings is presented herein. Such loadings cause bending moments in the arch which result in significant prebuckling deflections and changes in the arch profile. The problem is nonlinear. The numerical procedure is limited to an inextensible analysis and to elastic behavior. Based on a numerical integration technique developed by Newmark for straight beams, a large deflection bending analysis is combined with small deflection buckling routines to formulate the numerical procedure. The numerical procedure is composed of a combination of the numerical integration and a successive approximations procedure. A computer program was developed from the numerical procedure to obtain useful design data. A study is made of the fundamental buckling loads for a wide range of rise/span ratios for varying combinations of arch geometries, support conditions, symmetric loadings, and antisymmetric and symmetric buckling modes. Results acquired in this study for circular arches are compared to existing exact values and then the numerical procedure is extended to obtain new data on parabolic arches. Comparisons are made between buckling loads computed with the inclusion of prebuckling deflections and buckling loads computed by neglecting all bending deflections