ASME Section VIII, Division 2 code provides or a procedure to analyze the local stresses in vessels and nozzles (Appendix 4-1, Mandatory Design Based on Stress Analysis). Only the elastic analysis approach is discussed here. You should always refer to the applicable code if any of the limits described in this section are approached; if any unusual material, weld, or stress situation exists; or there are non-linear concerns such as operation of the material in the creep range.
The first step in the procedure is to determine if the elastic approach is satisfactory. Section AD-160 contains the exact method and states that if all of the following conditions are met, then fatigue analysis need not be done:
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The expected design number of full-range pressure cycles does not exceed the number of allowed cycles corresponding to a Sa value of 3Sm (4Sm for non-integral attachments) on the material fatigue curve. The Sm is the allowable stress intensity for the material at the operating temperature.
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The expected design range of pressure cycles other than startup or shutdown must be less than 1/3 (1/4 for non-integral attachments) the design pressure times (Sa/Sm), where Sa is the value obtained on the material fatigue curve for the specified number of significant pressure fluctuations.
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The vessel does not experience localized high stress due to heating.
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The full range of stress intensities due to mechanical loads (including piping reactions) does not exceed Sa from the fatigue curve for the expected number of load fluctuations.
Once you decide that an elastic analysis is satisfactory, either a simplified approach—WRC 107 Stress Calculations—or a comprehensive approach—Finite Element Analysis (FEA)—may be taken to the vessel stress evaluation.