ENGINEERING – MECHANICAL ENGINEERING CALCULATOR
Pressure Vessel Hoop Stress
A precise tool.
What is the Pressure Vessel Hoop Stress & How does it work?
Hoop stress, also known as circumferential stress, is the tensile stress that acts around the circumference of a pressure vessel. It arises because the internal pressure tries to expand the vessel, pulling the walls apart in the hoop direction. For thinβwalled vesselsβwhere the wall thickness is less than about oneβtenth of the inner radiusβthe stress distribution can be approximated as uniform across the wall thickness. This simplification leads to a straightforward analytical expression that engineers use for preliminary design and safety checks. The hoop stress is calculated using the internal pressure, the vesselβs inner radius, and the wall thickness. Keeping the stress below the materialβs allowable limit ensures the vessel can safely contain the fluid without yielding or rupturing.
\sigma_{h} = \frac{P \cdot r}{t}
\sigma_{h} = hoop stress (Pa), P = internal pressure (Pa), r = inner radius (m), t = wall thickness (m)
Parameters
Result
β
Frequently Asked Questions
What is hoop stress in a pressure vessel?
Hoop stress is the circumferential tensile stress that occurs when internal pressure tries to expand the vessel, pulling its walls apart.
When is the thin-walled approximation valid for pressure vessels?
The thin-walled approximation is valid when the wall thickness is less than about one-tenth of the inner radius of the vessel.
How do I calculate hoop stress in a pressure vessel?
Hoop stress can be calculated using the formula Ο_h = (P * r) / t, where P is internal pressure, r is inner radius, and t is wall thickness.
Why is hoop stress important in engineering design?
Hoop stress is crucial for ensuring the structural integrity of pressure vessels, preventing failure due to excessive expansion from internal pressure.
Can this calculator handle non-thin-walled vessels?
This calculator is specifically designed for thin-walled vessels. For non-thin-walled vessels, a more complex analysis is required.
What units should I use when inputting values into the calculator?
Use consistent units throughout: typically, pressure in Pascals or PSI, radius in meters or inches, and thickness in meters or inches.
How does hoop stress differ from longitudinal stress in a pressure vessel?
Hoop stress acts circumferentially around the vessel, while longitudinal stress acts axially along the length of the vessel.
Results are for informational purposes only and do not constitute professional advice.