Elastic lateral–torsional buckling of circular arches subjected to a central concentrated load

An arch under an in-plane central concentrated radial load is subjected to combined axial compressive and bending actions. When these combined axial compressive and bending actions reach a certain value, the arch may suddenly deflect laterally and twist out of its plane of loading and fail in a lateral–torsional buckling mode. This paper derives analytical solutions for the elastic lateral–torsional buckling load of pin-ended circular arches that are subjected to a central concentrated load, using the principle of stationary potential energy in conjunction with the Rayleigh–Ritz method. Analytical solutions of the buckling load for in-plane fixed and out-of-plane pin-ended arches and for the case of the load acting above or below the shear centre are also derived. The analytical solutions are compared with results of a commercial finite element package ANSYS and a finite element code developed by authors elsewhere for arches with different slendernesses, included angles, and cross-sections. The agreement between the analytical solutions and the finite element results is very good.