Shell restraint to ring buckling at cone-cylinder intersections

A study is presented of the out-of-plane buckling strength of rings attached to cone-cylinder intersections. Simple formulae which can be used to estimate the stiffness of the rotational restraint provided by adjacent shell walls are first developed from a finite element parametric study. These formulae are then combined with an existing closed-form solution based on thin-walled member theory to predict the flexural-torsional buckling strength of rings with an elastic rotational restraint. Numerical results are obtained for angle section rings from the closed-form solution and a finite element shell buckling analysis which is able to model cross-section distortion. Comparisons between the two approaches show that when the restraint stiffness is small, they agree with each other closely. Beyond a certain level of restraint stiffness, the buckling strength predicted by the finite element analysis falls increasingly below that given by the closed-form solution due to cross-section distortion and approaches the strength of an inner edge clamped ring. The paper concludes with suggestions for safely approximating the stiffness of the shell wall rotational restraint for use in design.