Cylinder stress
Cylinder stress patterns include: These three principal stresses- hoop, longitudinal, and radial can be calculated analytically using a mutually perpendicular tri-axial stress system.
In thick-walled pressure vessels, construction techniques allowing for favorable initial stress patterns can be utilized.
[2] The hoop stress is the force over area exerted circumferentially (perpendicular to the axis and the radius of the object) in both directions on every particle in the cylinder wall.
It is usually useful to decompose any force applied to an object with rotational symmetry into components parallel to the cylindrical coordinates r, z, and θ.
For the thin-walled assumption to be valid, the vessel must have a wall thickness of no more than about one-tenth (often cited as Diameter / t > 20) of its radius.
[4] This allows for treating the wall as a surface, and subsequently using the Young–Laplace equation for estimating the hoop stress created by an internal pressure on a thin-walled cylindrical pressure vessel: where The hoop stress equation for thin shells is also approximately valid for spherical vessels, including plant cells and bacteria in which the internal turgor pressure may reach several atmospheres.
In practical engineering applications for cylinders (pipes and tubes), hoop stress is often re-arranged for pressure, and is called Barlow's formula.
Inch-pound-second system (IPS) units for P are pounds-force per square inch (psi).
When the vessel has closed ends, the internal pressure acts on them to develop a force along the axis of the cylinder.
that is developed perpendicular to the surface and may be estimated in thin walled cylinders as: In the thin-walled assumption the ratio
is large, so in most cases this component is considered negligible compared to the hoop and axial stresses.
) the thin-walled cylinder equations no longer hold since stresses vary significantly between inside and outside surfaces and shear stress through the cross section can no longer be neglected.
Therefore, by definition, there exist no shear stresses on the transverse, tangential, or radial planes.
The shearing stress reaches a maximum at the inner surface, which is significant because it serves as a criterion for failure since it correlates well with actual rupture tests of thick cylinders (Harvey, 1974, p. 57).
This means that the inward force on the vessel decreases, and therefore the aneurysm will continue to expand until it ruptures.
[7] The first theoretical analysis of the stress in cylinders was developed by the mid-19th century engineer William Fairbairn, assisted by his mathematical analyst Eaton Hodgkinson.
