Optimal Design of Triangular Arches against Buckling

Abstract

This paper is concerned with the optimal design of triangular arches of a given volume of material for maximum buckling capacity. The buckling criteria of triangular arches are derived analytically by using stability functions. Optimal designs of triangular arches with various vertical load positions, base support conditions, and apical joint conditions are obtained based on an optimization procedure involving two decision variables (arch height h and cross-sectional area ratio AA/AB). Based on the optimization results, design recommendations for triangular arches against buckling are (1) the optimal height for triangular arches be taken as L/4 where L is the span length of the arch, and (2) both members of the triangular arch are to take on the same cross-sectional area (i.e., AA/AB=1) when the arch has a rigid joint at the apical point, whereas the cross-sectional area ratio AA/AB should be determined based on the optimality condition that both members should buckle at the same time when the arch has a hinge joint. By changing the base support condition from pinned-pinned to fixed-fixed, the maximum buckling load of the optimal triangular arches is increased by about 2.05 times.