Hi,
I suggest to follow the Project Specification/Procedure - you are "covered", since, as you said, the Bending Stress at Flange-Pipe joint node is bellow the prescribed allowed limit.
I met several times on past projects this kind of approach for flanged joint load check.
You should be aware that Equivalent Pressure Method is generally conservative. If your calculations by this method indicate flange overload not exceeding 25...30%, then most probable, the detailed calculation as per ASME VIII Division 1 BPV Code (Caesar II flange module) will yield to acceptable results.
You may do also a check with "flange leakage" key words on this Forum, there are several interesting discussions about this subject.
Another important issue: Which is the relation between your DESIGN PRESSURE and ALLOWABLE WORK PRESSURE AS PER ASME B16.5 (OR B16.47 as aplicable)? Generally, a good and sound engineering approach should limit DESIGN PRESSURE at maximum 75...80% from ASME B16.5 WORKING PRESSURE values (according to your Material class and Design Temperature). In this way, a part pf the flange loading capacity remains available to withstand the external piping loads (bending moment and axial force).
If your DESIGN PRESSURE is equal to ASME B16.5 WORKING PRESSURE value, then you are wasting your time trying to apply Equivalent Pressure Method, all calculations will indicate overload. I've met several times this case, when people from Process Discipline did not understand these correlations and prescribed the Design Pressure equal to ASME B16.5 Pressure Rate (e.g. for them, the external piping loads doesn't matter...)
Best regards,
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Dorin Daniel Popescu
Lead Piping Stress Engineer