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The in-plane and the out-of-plane buckling theory of rings exposed to external pressure is presented. A ring is considered as a segment of a toroidal shell. The governing ring equations are obtained by deducing the toroidal shell energy equations for the linear and the nonlinear strain. The obtained formulae for critical load are compared with those known in relevant literature. The critical load depends on the assumption concerning the load behaviour during buckling. Illustrative examples are solved numerically by means of several commercial FEM computer programs in order to investigate which assumptions are introduced in the ring buckling analysis.

Ring Buckling Analysis Based on the Toroidal Shell Theory