Pressure Vessel Stress Calculator

Calculate hoop and axial stress in a thin-walled cylindrical pressure vessel from internal pressure, diameter, and wall thickness.

MPa
mm
mm

Hoop (Circumferential) Stress

250.00 MPa

Axial (Longitudinal) Stress125.00 MPa
D/t Ratio100.0

Hoop (Circumferential) Stress vs Internal Pressure (P)

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Formula

## Thin-Walled Pressure Vessel Stresses For a cylindrical vessel where the wall thickness is much less than the diameter (D/t > 10), the stresses can be calculated using simplified thin-wall formulas. ### Formulas **Hoop stress: sigma_h = P × r / t** (circumferential, the larger stress) **Axial stress: sigma_a = P × r / (2t)** (longitudinal, half the hoop stress) The hoop stress is twice the axial stress, which is why pressure vessels fail along longitudinal seams (circumferential stress governs).

Esempio Risolto

A vessel with 1000 mm diameter, 10 mm wall, at 5 MPa pressure.

  1. 01r = 1000 / 2 = 500 mm
  2. 02Hoop stress = 5 × 500 / 10 = 250 MPa
  3. 03Axial stress = 5 × 500 / (2 × 10) = 125 MPa
  4. 04D/t = 100 (thin-wall assumption valid)