Deflection of Hinged Rings Under Uniform Pressure

The deflection and stresses in a ring having two or three hinges, spaced evenly along the circumference, and subjected to a uniform external pressure are derived on the basis of small-deflection ring theory. The effect of extensional strain is not ignored but is found to be negligible. The results indicate that the ring bends out of round from the onset of loading. The deflection is a nonlinear function of the loading and reaches a point of instability defined by deflections exceeding all bounds. In some respects, the problem is analogous to the bending of an eccentrically loaded column. The hinges may be placed offset from the centroidal axis and thereby eliminate the displacement out of round. The problem then reduces to an eigenvalue problem for the critical buckling load.