An important issue in engineering application of the “design by analysis” approach in pressure vessel design is how to decompose an overall stress field obtained by finite element analysis into different stress categories defined in the ASME B&PV Codes III and VIII-2. In many pressure vessel structures, it is difficult to obtain $PL+Pb$ due to the lack of information about primary bending stress. In this paper, a simple approach to derive the primary bending stress from the finite element analysis was proposed with application examples and verifications. According to the relationship of the bending stress and applied loads or the relationship of the bending stress and displacement agreement, it is possible to identify loads causing primary bending stress for typical pressure vessel structures. By applying the load inducing primary bending stress alone and necessary superposition, the primary bending stress and corresponding stress intensity $PL+Pb$ can be determined for vessel design, especially for axisymmetric problems.

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