Three‐Dimensional Stresses in Short Cantilevered Cylinders

Abstract

A three‐dimensional stress analysis for a short cantilevered cylinder subjected to a partial shear load on one end is presented based on the theory of elasticity. A solution to three‐dimensional elasticity problems proposed by the writer is used for the analysis. Boundary conditions on the fixed end are rigorously prescribed by three components of displacement. Basic and additional solutions are determined to satisfy boundary conditions. Numerical results for stresses and displacements in the short cantilevered cylinder, with a length‐to‐radius ratio of 2.0, are illustrated and are compared to those obtained by Saint‐Venant's method. A criterion of applicability of Saint‐Venant's method to this problem is proposed. The values of three components of stress at the loaded end become infinite at the boundary of the loaded area. The values of four components of stress at the fixed end show a tendency for stress concentration at the circumference of the end.