In the mechanics of materials, thin-walled pressure vessel theory analyzes the stress state induced in a vessel wall by internal pressure by treating the wall thickness as negligible relative to the vessel radius (radius-to-thickness ratio greater than about 10) and assuming stress is uniform through the thickness and caused solely by internal pressure. A spherical vessel differs fundamentally from a cylindrical vessel in that, because every planar section through its center is geometrically identical, the wall experiences a single, uniform tensile stress in all directions (σ = pr/2t) rather than the two distinct stresses—circumferential/hoop stress and longitudinal/axial stress—that arise in a cylinder; in both geometries, strains and resulting deformations (e.g., change in diameter) are subsequently obtained from the stresses via the generalized form of Hooke's law, which accounts for Poisson-ratio coupling between orthogonal stress directions.
In the mechanics of materials, thin-walled pressure vessel theory analyzes the stress state induced in a vessel wall by internal pressure by treating the wall thickness as negligible relative to the …