Effects of prebuckling analyses on determining buckling loads of pin-ended circular arches

Conventionally, when a circular arch is subjected to uniform radial loading, the difficulty in performing an accurate prebuckling analysis is usually circumvented by considering that the uniform radial loading produces axial compression, but no bending, in the arch. However, the transverse loading may produce bending as well as axial compression in the arch, particularly in shallow arches, and the arch may deform considerably prior to buckling. Treating the prebuckling stresses in the arch as being trivial is therefore questionable, and the prebuckling analysis should be carried out with caution. This paper investigates the prebuckling response of the classical analysis and its effects on determining the out-of-plane and in-plane elastic buckling loads of circular arches that are subjected to uniform radial loading. It is found that the current solutions based on the classical prebuckling analysis overestimate the in-plane buckling loads of shallow arches and underestimate the out-of-plane buckling loads of shallow arches significantly. Proper prebuckling analyses for out-of-plane and in-plane buckling are presented and new analytical solutions for the out-of-plane and in-plane buckling loads of arches are derived accounting for both axial compressive and bending actions.