Hoop Stress Calculator

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Cylinders have different hoop and longitudinal stresses. Spheres have equal hoop stress in all directions.
Gauge pressure inside the vessel above the external (atmospheric) pressure.
MPa
Inside diameter of the pressure vessel or pipe.
mm
Thickness of the vessel wall. The thin-wall assumption is valid when t/r is less than 0.1 (d/t greater than 20).
mm
Weld joint efficiency factor (0 to 1). Use 1.0 for seamless or fully radiographed welds, 0.85 for spot-examined, 0.70 for standard fillet welds.
Yield strength of the wall material. Used to compute the safety factor. Leave at zero to skip.
MPa
Elastic modulus of the wall material. Used to compute the change in diameter. Steel is about 200 000 MPa (29 000 000 psi).
MPa
Ratio of transverse to axial strain. Steel is about 0.3; aluminium about 0.33; rubber near 0.5.
Hoop stress (sh)Adequate safety factor
125

Circumferential stress in the vessel wall - the largest stress component

Longitudinal stress (sl)62.5
Radial stress (sr)-2.5
Safety factor2
Change in diameter (dd)0.2656
Diameter-to-thickness ratio (d/t)50
Stress unitMPa
Dimension unitmm
Hoop stress125
Longitudinal stress62.5

Hoop stress: 125.00 MPa

  • The hoop stress is 125.00 MPa, which is the largest stress component and governs design for cylindrical pressure vessels.
  • Longitudinal (axial) stress is 62.50 MPa, exactly half the hoop stress - a key characteristic of thin-walled cylinders.
  • The diameter-to-thickness ratio is 50.0, confirming the thin-wall assumption is valid (ratio above 20).
  • Safety factor is 2.00 based on yield strength vs hoop stress. A minimum of 2.0-3.0 is typically required for pressure vessels (consult ASME Boiler and Pressure Vessel Code).
  • Under this pressure the inner diameter expands by approximately 0.2656 mm.

Next stepFor final design, verify compliance with the applicable pressure vessel code (e.g. ASME BPVC Section VIII, EN 13445, or PD 5500) and account for corrosion allowance, fatigue, and external loads.

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