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What Is Hoop Stress? | Piping Engineering Glossary
What Is Hoop Stress?
In piping engineering and process engineering, hoop stress is the circumferential stress that internal pressure creates in the wall of a pipe or cylindrical vessel. The pressure tries to expand the pipe’s diameter, and the wall resists by carrying tension around its circumference, much like the steel hoops on a wooden barrel. Hoop stress is the main stress used to set the minimum wall thickness of pressure piping.
How Hoop Stress Is Calculated
For thin-walled pipe, hoop stress is commonly estimated with Barlow’s formula: stress equals pressure times outside diameter divided by twice the wall thickness. Hoop stress is about twice the longitudinal stress produced by the same pressure, which is why pipes under excessive pressure tend to split lengthwise. Codes such as ASME B31.3 build on this relationship and compare the result with the material’s allowable stress.
As an example of scale, a 6-inch Schedule 40 carbon steel pipe with an outside diameter of 168.3 mm and a wall of 7.11 mm sees a hoop stress of roughly 118 MPa at an internal pressure of 100 bar. Doubling the pressure doubles the stress, while doubling the wall thickness halves it.
Applications
Wall Thickness Design
Designers calculate the pressure design thickness from hoop stress, then add corrosion allowance and mill tolerance before choosing a pipe schedule. The calculation is repeated at the design temperature, because the allowable stress drops as temperature rises.
Pressure Ratings
Hoop stress limits underlie the pressure rating of pipe, fittings, and components at a given temperature.
Integrity Assessment
When corrosion thins a pipe, engineers use thickness measurements and hoop stress calculations to determine whether it can still hold its operating pressure.
Benefits
Simple and Reliable Basis
The calculation is straightforward and well proven for sizing pressure piping.
Conservative Design
Combined with code allowable stresses, it provides a clear margin against bursting.
Supports Fitness Decisions
It gives a quick way to judge whether thinned or degraded pipe remains safe. Engineers can quickly estimate the minimum wall needed before a corroded line must be repaired or replaced.
Limitations
Thin-Wall Assumption
Barlow’s formula becomes less accurate for very thick-walled pipe, where codes require more detailed equations.
Pressure Only
Hoop stress covers internal pressure but not weight, thermal expansion, or vibration, which require a full pipe stress analysis.
Local Effects Not Included
Openings, branch connections, and localized corrosion create stress concentrations beyond the basic calculation. These areas need separate checks or reinforcement calculations.
FAQ
Is hoop stress larger than longitudinal stress?
Yes. For a closed-end pipe under internal pressure, hoop stress is roughly twice the longitudinal pressure stress.
How does a hydrostatic test relate to hoop stress?
A hydrostatic test raises pressure above the design value, which raises hoop stress and demonstrates that the wall and welds can contain it safely.
Does temperature affect hoop stress limits?
Temperature does not change the hoop stress produced by a given pressure, but it lowers the allowable stress, so hotter lines need thicker walls for the same pressure.
What happens to hoop stress under external pressure or vacuum?
Under external pressure the hoop stress becomes compressive, and the main concern shifts from bursting to buckling or collapse. Vacuum lines and jacketed piping are therefore checked with separate external-pressure design rules rather than the internal-pressure formula.
Reference
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