The limit pressure for a flush cylindrical nozzle in a spherical pressure vessel

Using a simple circumscribing yield surface for Nθ, Nф, Mф, the limit pressure has been calculated for a flush cylindrical nozzle in a spherical pressure vessel for a range of parameters rR, RT, tT. A lower bound and upper bound to the limit pressure have been derived using approximations similar to those used in other limit analyses of shells of revolution. In spite of the approximations, which are discussed, the analysis gives a useful insight into the plastic behaviour of nozzle/spherical shell intersections.