Stress Distribution Due to a Tangential Concentrated Load in a Thin Cylinder

A solution is shown for stress distribution in an infinite strip with a transverse concentrated load acting at its center. Deformation relations are satisfied to permit this strip to be rolled transversely into an infinite cylinder. Equilibrium conditions are then satisfied by adding a pressure distribution normal to the surface of this cylinder. The stress due to this pressure distribution is solved by methods previously developed for thin cylinders are superposed on the strip stress. Results show that the stresses are nearly the same as those obtained by the elementary methods of strength of materials except near the point of application of the load, where there are localized bending stresses. This bending can be evaluated by the thin cylinder methods, but the process is very involved and a simpler approach is desired. This is found by considering the resultant of the pressure distribution to be a moment applied at the loading point. Two methods of analyzing stress in a thin cylinder loaded with a circumferential couple are shown and deformation curves plotted. The stress criterion is shown to be the normal stress developed near the load in the infinite (unrolled) strip.