Buckling of a Prestressed Circular Ring

A method is presented for determining the critical state of stress, in a prestressed circular ring, at which the ring will buckle. Such rings are used as stiffening rings at the edges of shell domes and as thrust rings at the outer boundaries of ribbed or vaulted domes. The method presented allows prediction of the magnitude of the hoop force in the ring and the magnitude of the tension in the band of prestressing cables that would cause the ring to buckle. A comprehensive mode of buckling is contemplated, such that the cross sections may move radially, tangentially, and normal to the plane of the ring, and may rotate or twist about tangential axes. The case in which the cables are bonded to the ring and the case in which the cables are free to slip in the tangential direction are both treated, and provision is made, in the pertinent formulas, for handling either case. The effect of the attachment to the shell is included through the use of appropriate influence coefficients.