This article needs additional citations for verification. (December 2009)
The walls of pressure vessels generally undergo triaxial loading. For cylindrical pressure vessels, the normal loads on a wall element are:
- the longitudinal stress
- the circumferential (hoop) stress
- the radial stress.
The radial stress for a thick-walled cylinder is equal and opposite to the gauge pressure on the inside surface, and zero on the outside surface. The circumferential stress and longitudinal stresses are usually much larger for pressure vessels, and so for thin-walled instances, radial stress is usually neglected.
The radial stress for a thick walled pipe at a point from the central axis is given by
where is the inner radius, is the outer radius, is the inner absolute pressure and is the outer absolute pressure. Maximum radial stress occurs when (at the inside surface) and is equal to gauge pressure, or .