ABSTRACT
This chapter is concerned with the out-of-plane flexural-torsional buckling of planar arches, curved beams, and rings which are loaded in-plane. It explores the energy method to the flexural-torsional buckling of arches and rings. The chapter discusses the in-plane behaviour of arches under other loadings than those of uniform compression and uniform bending is best analysed by the finite element method. Closed form solutions are developed for circular arches and rings in uniform compression or bending. Arches whose ends are prevented from moving apart are often used structurally because of their high in-plane stiffness and strength, which result from their ability to transmit most of the applied loading by axial force actions, so that the bending actions are reduced. Curved beams ends are free to move apart have much more significant bending actions, and are less stiff and strong in-plane. Rings are self-reacting, and have high in-plane stiffness and strength with respect to uniform radial loading.
