Pressure Vessel Stress Calculator — Formule
## 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).
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).
Exemple Résolu
A vessel with 1000 mm diameter, 10 mm wall, at 5 MPa pressure.
- r = 1000 / 2 = 500 mm
- Hoop stress = 5 × 500 / 10 = 250 MPa
- Axial stress = 5 × 500 / (2 × 10) = 125 MPa
- D/t = 100 (thin-wall assumption valid)