Elastic buckling of ring-stiffened cone–cylinder intersections under internal pressure

Abstract Cone–cylinder intersections are commonly found in pressure vessels and piping. Examples include conical end closures to cylindrical vessels and conical reducers between cylinders of different radii. In the case of a cone large end-to-cylinder intersection under internal pressure, the intersection is subject to a large circumferential compressive force. Both the cone and the cylinder may be thickened near the intersection to resist this compression, but it is often convenient and necessary to augment further the strength of the intersection using an annular plate ring stiffener. Under this large circumferential compression, the intersection may fail by elastic buckling, plastic buckling or plastic collapse. This paper describes an investigation of the elastic buckling strength of ring-stiffened cone–cylinder intersections. Two buckling modes are identified: a shell mode for thin intersections with a shallow cone (a cone with its apex half angle approaching 90°) and/or a relatively stocky ring stiffener, and a ring mode for other cases. An existing elastic buckling approximation for annular plate rings in steel silos is found to be applicable to the intersection when it buckles in the ring mode. New approximate design equations are also established for the shell mode. In addition, simple expressions are identified which relate the number of circumferential buckling waves to the geometric parameters of the intersection.