Radial stress is stress towards or away from the central axis of a component.
The walls of pressure vessels generally undergo triaxial loading. For cylindrical pressure vessels, the normal loads on a wall element are:
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 is given by σr = [(pi ri2 - po ro2) / (ro2 - ri2)] + [ri2 ro2 (po - pi) / r2 (ro2 - ri2)] where ri is the inner radius, ro is the outer radius, pi is the inner absolute pressure and po is the outer absolute pressure.