I think the whole issue here (and the fact that I didn't see when I made my first post) is that there is no rational piping geometry where pressure can cause gross axial displacement without first producing a hoop stress failure.

So it seems that axial pressure stress can be considered to be self-limiting. And your methodology would be correct.

It looks like you are going to have to do a lot of hand calculations in order to perform this analysis effectively. If I was forced to choose between the CAESAR II "Bourdon case" and an analysis where the axial elongation was modeled as a synthetic temperature increment, I am not sure which way I would go.