Richard

I can follow your reasoning to evaluating the pressure thrust load (which always exists) and opposing load from restraint, however I would suggest that this is purely a theoretical argument and the pressure thrust can never be completely balanced. I put the following two reasoning forward for discussion:
1. For these loads to balance the restraint would have to be very rigid. The deflection produced by pressure only at the restraint point if the restraint was released would be very small. The restraint would have to counteract the pressure thrust with a deflection much less than the unrestrained deflection. Even a “real” rigid support will be flexible enough to transfer at least part of the pressure thrust back to the nozzle.
2. Even if the restraint were rigid enough to counteract the pressure thrust, any thermal expansion of the pipe would be a far greater than the expansion due to pressure. Therefore practically it would be imposable to balance the pressure thrust against a restraint.

Another case worth considering is case of a manhole in a vessel. Should this WRC calc include the pressure thrust, as there is no restraint to balance? Most low pressure vessel manholes designed in accordance with ASME VIII area replacement method would fail with the pressure thrust alone. Clearly this cannot be correct.

Considering your case where you have a straight run of pipe to an elbow, with an intermediate untied expansion joint. I agree with your point that the shell to nozzle intersection would not see the full pressure thrust (the junction will see the pressure thrust from the difference in area of the pipe ID and exp joint ID). However care must be taken with the loading calculated by Caesar, if the pressure thrust from the expansion joint is included in the piping analysis then the pressure thrust should be included and will balance the WRC pressure thrust.

I would suggest that pressure thrust is not an external loading to be used in the WRC calc, but an internal loading. If this is taken to be the case the allowable stress range (expansion case) should be limited to 2.0 (3.0Sa allowed by ASME for local stresses less 1.0Sa for primary stresses including pressure thrust). Similarly for sustained external loadings the allowable stress should be limited to 0.5Sa (1.5Sa allowed by ASME for local stresses less 1.0Sa).