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Vessel sizing can be achieved by a number of procedures. The ASME Boiler and Pressure Vessel Code provide several, and the sizing by limit analysis is one of them. With limit analysis, the sizing can be achieved by closed-form formulas, equilibrium relations of free bodies, and finite element lower bound analyses. When coupled with a finite element computer code, a lower bound analysis is an effective tool for the sizing of any vessel or its components. Limit analysis addresses the design objective of preventing gross plastic deformation with an agreed-upon design margin. The procedure is simple and straightforward. If a lower bound to the limit load is established that is equal to or greater than the design loading, the objective is achieved. A design based on limit analysis also protects the vessel against burst by tensile plastic instability (ductile rupture), but with a design margin that depends on geometry, loading, and material. The sizing of vessels by limit analysis is applicable to vessels made of any material that is permitted for Section III-Class 1 and Section VIII-Division 2 construction.