Lateral–torsional elastic buckling of rotationally restrained arches with a thin-walled section under a central concentrated load

An arch often has elastic end restraints provided by the connected structures or elastic foundations. When the arch is subjected to an in-plane central concentrated load, the load produces combined non-uniform axial compressive and bending actions with complicated distributions along the arch length and these actions are significantly influenced by the stiffness of the end restraints. These combined axial compressive and bending actions increase with an increase of external loads and may reach the values, at which the arch suddenly deflects laterally and twists out of the plane of loading, and fails in a lateral–torsional buckling mode. Little research of the lateral–torsional buckling of such arches has been reported in the open literature. This paper derives the analytical solution for the elastic lateral–torsional buckling load of pin-ended circular arches with a thin-walled section and having in-plane elastic rotational end restraints under a central concentrated load, using the principle of stationary potential energy in conjunction with the Rayleigh–Ritz method. The analytical solution agrees with independent finite element results very well, which indicates that the analytical solution can provide accurate predictions for the lateral–torsional buckling loads of arches having in-plane rotational end restraints. The effects of the stiffness of rotational end restraints on the lateral–torsional buckling load are investigated. It is found that the change of the stiffness of rotational end restraints has significant effects on the lateral–torsional buckling resistance of arches.