Let me try to explain what would be the correct procedure IMHO:
1) Assume you need to comply with ASME VIII Div.1
2) Check your flange design per Div.1 App.2 with no account of expansion stresses from external piping
3) Expansion stresses give rise to secondary stresses and these are not required to be accounted for in Div.1 (this is by the way the main and very basic difference between Div.1 and Div.2): se also below, however.
4) As your expansion stresses seem a bit high (though for sure not really excessive) you can check them, still staying within the frame of Div.1, hence using Div.1 allowables, but going to Div.2 for the checking method, as Div.1 doesn't provide one.
5) App.3 of Div.2 is of no use here: it is in fact the same as App.2 of Div.1 and uses the same type of loads (pressure only).
6) App.4 of Div.2 is what you need, and with 4-141 you should be OK. However note that the service stress in bolts should be determined including the effect of preload (of course by accounting also the effect of preload stress going towards zero under flange loads) and the effect of torsion in tightening, if any.
7) Of course under the provisions of Div.2 the material could plasticize (though not really in your case it seems) and this is not normally a good thing for flanged joints. The limit set forth by Div.2 insures that no accumulation of plastic strain will occur across load cycles, but in my opinion this is not fully insured if you repeatedly retighten the bolts in service (though of course you could replace them when needed).
8) Now a much more complicated consideration need be made. Secondary stresses are by definition self limiting: so the classification I made above for expansion stresses to be secondary is based onto the assumption that, when the bolts will eventually deform under load, causing the flange to act as a partial hinge, the expansion load should go to zero (or, better said, when the expansion loads are increased due to increased temperature, the loads in the flange calculated as a plastic hinge should stay stationary). If this condition is not met (and may well not be, especially if the expansion load is mainly an axial load, not a bending moment), then point 3 above is no more true: you should classify the stresses coming from the external loads as primary, hence transform those loads into an equivalent pressure for the flange, and fully check it per Div.1 (I understand that in this case you wouldn't satisfy the limits, but that's it...).
9) As a closing comment I should also recall that the normal procedure to account for external loads, be them of mechanical or thermal origin, is as at the end of point 8: this is safe, and does not require any special consideration on the interaction between the piping and the vessel. I mentioned the procedure above (points 2 to 7) only because you have a problem and this could well be your escape lane. prex
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