All of the flange stress computations are defined in ASME Section VIII, Division 1, Appendix 2.
The ASME code requires that the average stress be checkedin 2-8(a)(4) of ASME Sec VIII Div 1.
The bolt stress check is also required, because there should be enough bolt area to withstand the load on the bolts. The ASME code has the check for the bolt areas, so the bolt stress check is implicitly performed.
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Regards,
Richard Ay - Consultant