To reduce the stress level at nozzle to spherical pressure vessel intersections, reinforcement is generally added to the sphere, the nozzle or both. This paper describes the development of a computer code using closed-form solutions to analyze this problem. Up to seven components can be considered in the model: inner and outer nozzles each connected to pipes; an insert plate; spherical shell; and cylindrical vessel connected to the sphere. All three forces and moments on each nozzle as well as internal pressure and simple thermal loading are considered. Thin shell theory is used for each component. Due to the complexity of the exact solution for the sphere, asymptotic solutions valid for both the shallow and steep regions are used. This solution allows parameter studies to be performed efficiently for various reinforcement geometries.

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