How this calculator works
The membrane model treats stress as uniform through a thin wall at the mean radius. A closed cylinder has hoop and axial stress; a sphere has equal tangential stresses. Joint efficiencies scale the stress resisting the relevant membrane load. Elastic dimensional changes use those averaged effective stresses, a small-strain approximation rather than a local seam model. Inner radial stress is approximated as minus internal gauge pressure and falls toward zero at the outer wall. The thickness check requires t/r no greater than 0.1. External-pressure buckling and pressure-vessel code design are outside this membrane calculation.
Formula
Cylinder: sigma_h = p r/(t eta_h), sigma_z = p r/(2t eta_z). Sphere: sigma_t = p r/(2t eta). epsilon_h = (sigma_h-nu sigma_z)/E.
Worked example
For a seamless cylinder with p = 1 MPa, r = 0.5 m and t = 5 mm, hoop stress is 100 MPa and axial stress is 50 MPa. A sphere with the same dimensions has 50 MPa tangential stress.
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Frequently asked questions
Why is cylinder axial stress half hoop stress?
Force equilibrium acts over different resisting areas for longitudinal and circumferential cuts in a closed thin cylinder.
Can I use outside radius?
The page uses mean radius. For a sufficiently thin wall the difference is small; thicker walls need a thick-cylinder solution.
Does this calculate a code-required wall thickness?
No. Corrosion allowance, weld rules, load combinations and code safety margins require a design-standard calculation.