Design Coefficients for Rings Loaded Out-of-Plane

This article provides the solution to twelve cases of a ring loaded out of its plane. Each solution may be combined with the others so that many different loading cases may be solved from these twelve. Three sets of nondimensional coefficients are presented in the tables to permit the rapid calculation of forces and deflections as a function of the angle α around the ring circumference. Each set of coefficients is for a different value of the parameter ρ, the ratio of bending stiffness EI to torsional rigidity KG. Therefore, any ring with a value of ρ other than 1.3, 10, and 100 can be analyzed by simply interpolating between the tabular values at any angle α. Two cases (cases 9 and 11) involving sinusoidal torsional moment distributions, several combinations of simpler cases, and some classical out-of-plane cases are included in these tables.