A hollow cylinder is located between two rigid plates. There is a presurized gas inside that exerts tangential and longitudinal stress. We also rise temperature so that the cylinder experiences thermal stresses.

When we calculate the stress in the longitudinal direction on a plane differential element of the cylinder, do we have to add both thermal and longitudinal stress of the fluid, or do we only consider the thermal stress?

I say this because thermal stress is supposed to compensate for the difference in length, and that the total longitudinal stress should be one so that it does compensate for it. I think if we also include the longitudinal stress by the fluid, we cause another uneeded deformation, so thermal stress should be the total. Please clarify me that. Thanks in advance!