A key problem in engineering applications of “design by analysis” approach is how to decompose a total stress field obtained by the finite element analysis into different stress categories defined in the ASME Code III and VIII-2. In this paper, we suggest a two-step approach (TSA) of stress classification and a primary structure method (PSM) for identification of primary stress. Together with the equivalent linearization method (ELM), the stress classification problem is well solved. Some important concepts and ideas discussed by Lu and Li [Lu, M. W., and Li, J. G., 1986, ASME PVP-Vol. 109, pp. 33–37; Lu, M. W., and Li, J. G., 1996, ASME PVP-Vol. 340, pp. 357–363] are introduced. They are self-limiting stress, multi-possibility of stress decomposition, classification of constraints, and primary structures. For identification of peak stress, a modified statement of its characteristic and a “1/4 thickness criterion” are given. [S0094-9930(00)00201-8]

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