Out-of-plane buckling of restrained thin rings of general open section

This paper describes a closed‐form solution based on thin‐walled member theory for the out‐of‐plane buckling of thin rings of an open cross section. The theory considers the practical features of restraint and loading conditions of rings situated at axisymmetric shell intersections, and it is applicable to any thin‐walled open‐section form. Numerical comparisons between the closed‐form solution and a finite‐element shell buckling analysis are then presented to demonstrate the accuracy of the closed‐form solution, and to study the effects on the buckling behavior of angle section rings of various parameters, including the ring width‐to‐thickness ratio, the load position, the restraint position, and the flange size. The effect of secondary warping on the buckling behavior of angle section rings is also discussed in some detail. Finally, a simple expression for use in design is established for the buckling strength of an angle section ring loaded and supported at its inner edge.