Design of Ellipsoidal and Toroidal Pressure Vessels to Probabilistic Criteria

Ellipsoids are frequently used for end closure of cylindrical pressure shells. Toroids of elliptic or circular cross-section, are widely used, e.g., for connecting two parallel legs in a U-shape. This paper presents equations for the means and standard deviations of stresses developed in ellipsoids and toroids with internal pressure. Inherent in these equations are the facts that: (a) design variables are generally characterized by spectra of values, rather than by unique values, and (b) a small, but finite, probability of failure must be recognized in any design. By coupling the stresses due to the applied loading as calculated by the equations given in the paper with the strength available in a material, reliability (or the alternative probability of failure) can be calculated. Conversely, for a given reliability the appropriate size can be determined. Appropriate illustrations of application of these equations are provided through tables and figures. The difficulty of relying on a factor of safety is demonstrated.