ABSTRACT
The more common forms of pressure vessels involve spheres, cylinders, and ellipsoids, although conical and toroidal configurations are also found. When such components have small thickness compared with the other dimensions and offer a limited resistance to bending, the stress can be calculated with the aid of the membrane theory. Such stresses, taken as average tension or compression over the thickness of the vessel wall, act in the direction tangential to the surface. Since themiddle surface of the wall extends in two dimensions, the analysis can become complicated where more than one expression for the curvature is required to describe the displacement of a particular point. In a more rigorous sense, it would be necessary to define a normal force, two transverse shearing forces, two bending moments, and a torque in order to describe the entire state of stress. Fortunately, membrane theory allows us to neglect the bending, shearing, and twisting effects. In a number of elementary but practical cases, the simple equations of equilibrium of forces are sufficient for deriving the necessary design formulas.
