Piping systems in process industries and nuclear power plants include straight pipe runs and various fittings such as elbows, miter bends etc. Elbows and bends in piping systems provide additional flexibility to the piping system along with performing the primary function of changing the direction of fluid flow. Distinctive geometry of these toroidal shell components result in a structural behavior different from straight pipe. Hence, it would be useful to predict the behavior of these components with acceptable accuracy for design purposes. Analytical expressions are derived for stresses set up during loading and unloading in a toroidal shell subjected to internal pressure. Residual stresses in the component are also evaluated. The proposed solutions are then compared with three-dimensional finite element analysis at different locations including intrados, extrados and flanks.

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