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How to Calculate Hoop Compression in a Pressure Vessel

Hoop stress, or hoop compression stress, is a circumferential mechanical stress of a steel pressure cylinder that is brought on by internal or external pressure. The classic example of hoop stress is the stress applied to metal bands around a wooden barrel. It is a circumferential loading that is a function of the cross sectional radius of the cylinder, the vessel wall thickness and the intensity of the force being applied.

Instructions

- 1
  Determine the vessel wall thickness as measured in inches. For instance, a common thin-walled vessel wall thickness (t) could be 1/8 inch (0.125 inches).
- 2
  Determine the internal radius of the vessel as well as the internal pressure that is to be applied. For a thin-walled vessel, a common radius (r) would be 3 feet, and a reasonable internal pressure (P) would be 10 pounds per square inch (psi).
- 3
  Determine the hoop compression stress using the formula σ = P x r / t. This calculates to be 10 x 3 / 0.125 or 240 psi.

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