Consider a beach ball on the surface of the water. Consider the same beach ball at a depth of 1000'. The beach ball will be compressed on all sides semi-equally. Technically, the top will be compressed ever so slightly less than the bottom, based on the rho*g*h equation, where in this case, h is the diameter of the ball.

Consider now an extremely long idealized run of pipe, in the horizontal. It, too, will be compressed at the ends, equally, such that the displacement at the center will be 0, however, the ends will displace.

However, let's not assume we're analyzing the entirety of the line. Let's say we're only looking at 1/4th of the line. Ideally, our "partial analysis" will match "ideal analysis of the whole line." Our "partial analysis" should include this compression.

However, I contend that we should not view the compression of the pipe through the lens of "forces added to the ends," but rather an analog that we deal with everyday: temperature.

As we exert pressure to the outside of the pipe, it compresses and shrinks not terribly unlike that of temperature contraction. Do we expect monstrous loads onto supports and the like from a few degrees colder? Not really.

Note that this is only an analog for determining restraint loads.

To my knowledge, I know of no particular guidance of adding external pressure to internal pressure to thermal and occasional loads, except I know of no such inputs in CAESAR. ASME B31.8 might have additional information.