Hoop stress pr/t is twice the longitudinal stress pr/2t in a cylinder.
In a cylinder of radius r, wall t and pressure p, hoop stress σ_h=pr/t and axial stress σ_a=pr/(2t); a sphere has σ=pr/(2t). The thin-wall approximation needs r/t>10. Failure occurs along a longitudinal split first.
A 1 m diameter boiler at 2 MPa and 10 mm wall has σ_h=100 MPa.
Pressure vessels and pipes are common in process plants, and hoop stress is usually the governing check in the cylinder wall.
Hoop stress pr/t is twice the longitudinal stress pr/2t in a cylinder.
Pressure vessels and pipes are common in process plants, and hoop stress is usually the governing check in the cylinder wall.
The pressure acts on the end cap area to give axial load, which is spread over twice the wall area of the circumference, so the hoop stress is larger.
Usually hoop stress, which needs the thickest wall. The axial stress is used to check end closures and joints.
Typical applications include sizing the wall of a pipe carrying high-pressure steam, checking the boiler shell for the required plate thickness and designing a gas cylinder with a given working pressure.
Study "Principal stresses" first (topic 62 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Hoop stress is double axial. Spheres are twice as efficient. Thick walls use Lamé equations.
A 1 m diameter boiler at 2 MPa and 10 mm wall has σ_h=100 MPa.
The next topic is "Failure theories", which builds directly on this one.
It is classed as Intermediate in Engineering Mechanics (topic 63 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.
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