A new analytical solution for lateral-torsional buckling of arches under axial uniform compression

A circular arch with a uniform open thin-walled cross-section that is subjected to a radial load distributed uniformly around the arch axis may suddenly displace laterally and twist out of its plane of loading by buckling in a lateral-torsional mode. The classical solution for the elastic lateral-torsional buckling load of such an arch is based on the assumption that the uniform radial load produces a uniform axial compressive force in a circular arch without in-plane bending. This assumption is approximately correct for deep arches. However, the uniform radial load may produce substantial bending actions in shallow arches, and so the assumption does not hold for shallow arches. Hence, it is doubtful whether the classical solution can correctly predict the lateral-torsional buckling load of shallow circular arches under a uniform radial load. The prebuckling behavior of a pin-ended circular arch under a uniform radial load is investigated in this paper. It is found that circular arches under a uniform radial load are subjected to combined axial compressive and bending actions, and that the bending action in shallow arches is substantial. It is also ascertained that the axial compressive force in shallow arches is much smaller than the nominal axial compressive force used in the classical buckling analysis. This paper derives a new unified analytical solution for the lateral-torsional buckling load of pin-ended arches by accounting for the combined bending and axial compressive actions. Comparisons with finite element results show that the new solution can accurately predict the lateral-torsional buckling load of both shallow and deep circular arches under a uniform radial load, while the classical solution predicts incorrect lateral-torsional buckling loads for shallow arches. The effects of the in-plane boundary conditions on the lateral-torsional buckling load are also investigated. The analytical solution for the lateral-torsional buckling load accounting for the effects of in-plane fixed boundary conditions is also derived. It is found that the in-plane fixed boundary condition greatly increases the lateral-torsional buckling load of shallow arches. In addition, the effects of the height of application of the load on the lateral-torsional buckling are studied, and the analytical solution for the buckling load including the effects of the height of the load application is derived. The agreements of these analytical solutions with finite element results are very good.

► New solution for lateral-torsional buckling load of arch in uniform compression.
► Classical solution underestimates lateral-torsional buckling load of shallow arches.
► New solution accounts for combined axial compressive and bending actions.
► Solutions accounting for in-plane fixed supports and load height are derived.
► Effects of in-plane fixed supports and load height on buckling loads are significant.