Bending and Buckling of Thin-Walled Open-Section Rings

The Wagner theory for the bending and buckling of straight bars of thin-walled open section is extended to circular curved bars and rings. The differential equations of equilibrium are determined by a summation of force components, whereas the natural boundary conditions are derived by the minimum potential energy principle. The effects of nonuniform torsion, unsymmetrical loading, elastic foundation, and axial extension are included. The buckling of a ring subjected to a uniform external pressure is treated. The critical pressure is found to be the root of a cubic characteristic equation. Simplified solutions are found by restricting the generality, thereby reducing the characteristic equation to the first order.