Pressure Vessel Design

Hoop Stress — Thick-Walled Cylinder

Lamé equations for tangential, radial, and longitudinal stress distribution through a thick-walled pressure vessel, with Von Mises equivalent stress.

Inputs

same unit as inner radius

Key Results

Max tangential σθ (inner)

—

psi

Max radial σr (inner)

—

psi

Longitudinal σL

—

psi

Max Von Mises σVM

—

psi

Stress distribution through wall thickness

Tangential (σθ)
Radial (σr)
Von Mises (σVM)

Stress Distribution Table

Location Radius Tangential σθ Radial σr Longitudinal σL Von Mises σVM

Lamé Equations — Thick-Walled Cylinder

σθ = P·rᵢ² / (ro²−rᵢ²) · (1 + ro²/r²)  [tangential] σr = P·rᵢ² / (ro²−rᵢ²) · (1 − ro²/r²)  [radial] σL = P·rᵢ² / (ro²−rᵢ²)  [longitudinal, closed ends] σVM = √(σθ²+σr²+σL²−σθσr−σθσL−σrσL)  [Von Mises]
P = internal pressure rᵢ = inner radius ro = outer radius r = radius at point of interest Sᵧ = material yield strength (for safety factor)