Radial stress

Pressure vessels

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.

Formula

The radial stress for a thick walled pipe is given by σ_r = [(p_i r_i² - p_o r_o²) / (r_o² - r_i²)] + [r_i² r_o² (p_o - p_i) / r² (r_o² - r_i²)] where r_i is the inner radius, r_o is the outer radius, p_i is the inner absolute pressure and p_o is the outer absolute pressure.