Stresses From Local Loadings in Cylindrical Pressure Vessels

Abstract

Abstract A short discussion is given of the possible methods for computing the stresses caused in cylindrical shells by local loadings. It is concluded that the method of developing the loads and displacements into double Fourier series leads to formulas which are best suited for numerical evaluation. With this method the pertinent expressions for the displacements caused by radial loads are found by reducing the three partial differential equations of the shell theory to an eighth-order differential equation in the radial displacements, which is similar to, but not identical with, those derived by Donnell and Yuan. Insertion of the Fourier series for the radial displacements and the external loading in this equation leads directly to a double series expression of the radial displacement w in terms of the load factors Zmn of the radial load. This results in the pertinent expressions for the other displacements and for the bending moments and membrane forces. The cases of radial loading considered here and those which can be reduced to it are (a) a load uniformly distributed within a rectangle, (b) a point load, (c) a moment in the longitudinal direction, uniformly distributed over a short distance in the circumferential direction, (d) a moment in the circumferential direction, uniformly distributed over a short distance in the longitudinal direction. For all these loadings the load factors Zmn, which have to be used in the pertinent formulas for the displacements, bending moments, and membrane forces, are computed. For the case of tangential loading an eighth-order differential equation is derived in terms of the radial displacement and the tangential load. Using this equation, formulas for the displacements, bending moments, and membrane forces for tangential loading within a rectangle are found.