Free Pressure Vessel Stress Calculator
Calculate hoop and axial stress in a thin-walled cylindrical pressure vessel from internal pressure, diameter, and wall thickness.
Hoop (Circumferential) Stress
250.00 MPa
Hoop (Circumferential) Stress vs Internal Pressure (P)
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).
Example Calculation
A vessel with 1000 mm diameter, 10 mm wall, at 5 MPa pressure.
- 01r = 1000 / 2 = 500 mm
- 02Hoop stress = 5 × 500 / 10 = 250 MPa
- 03Axial stress = 5 × 500 / (2 × 10) = 125 MPa
- 04D/t = 100 (thin-wall assumption valid)
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