Buckling of restrained monosymmetric rings

Rings are commonly used at junctions between shell segments in pressure vessels, tanks, and silos. Often the ring is in circumferential compression and is susceptible to failure by buckling. This buckling is usually restrained by the adjacent shell segments, which prevent translation and elastically restrain rotation of the point of attachment. The ring is normally not loaded at its centroid or shear center. This paper presents an analysis of the buckling of a monosymmetric ring under these conditions. Four versions of the theory are presented, which make progressively less restrictive assumptions relating to the ring as a "thin ring." The analytical predictions are compared with numerical stability assessments from a finite element shell buckling analysis. The classical thin ring solution is shown to be satisfactory for most practical purposes.