For thin-walled cylindrical pressure vessels (defined by the criterion that radius-to-thickness ratio r/t ≥ 10, so through-thickness stress variation is negligible), internal pressure produces two principal tensile stresses on the vessel wall: circumferential (hoop) stress σ₁ = pr/t, derived from equilibrium of a half-cylinder free body, and longitudinal stress σ₂ = pr/2t, derived from equilibrium of a transverse section — with hoop stress always twice the longitudinal stress. This belongs to mechanics of materials / strength of materials, specifically the application of stress analysis to thin-walled pressure vessels, and connects to the broader theory of stress-strain relationships via the generalized Hooke's law, used to compute resulting strains (e.g., circumferential strain and the corresponding change in diameter) from the two principal stresses.
For thin-walled cylindrical pressure vessels (defined by the criterion that radius-to-thickness ratio r/t ≥ 10, so through-thickness stress variation is negligible), internal pressure produces two pr…