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Being that for thick-walled cylinders, the ratio is less than 10, the radial stress, in proportion to the other stresses, becomes non-negligible (i.e. P is no longer much, much less than Pr/t and Pr/2t), and so the thickness of the wall becomes a major consideration for design (Harvey, 1974, pp. 57).
The radial stress for a thick-walled cylinder is equal and opposite to the gauge pressure on the inside surface, and zero on the outside surface. The circumferential stress and longitudinal stresses are usually much larger for pressure vessels, and so for thin-walled instances, radial stress is usually neglected.
All formulae mentioned above assume uniform distribution of membrane stresses across thickness of shell but in reality, that is not the case. Deeper analysis is given by Lamé's theorem, which gives the distribution of stress in the walls of a thick-walled cylinder of a homogeneous and isotropic material. The formulae of pressure vessel design ...
In certain situations, a gently curved thin plate may also be assumed to have plane stress for the purpose of stress analysis. This is the case, for example, of a thin-walled cylinder filled with a fluid under pressure. In such cases, stress components perpendicular to the plate are negligible compared to those parallel to it. [1]
Autofrettage is a work-hardening process in which a pressure vessel (thick walled) is subjected to enormous pressure, causing internal portions of the part to yield plastically, resulting in internal compressive residual stresses once the pressure is released. The goal of autofrettage is to increase the pressure-carrying capacity of the final ...
As an example, the stress state of a steel beam in compression differs from the stress state of a steel axle under torsion, even if both specimens are of the same material. In view of the stress tensor, which fully describes the stress state, this difference manifests in six degrees of freedom , because the stress tensor has six independent ...
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Barlow's formula (called "Kesselformel" [1] in German) relates the internal pressure that a pipe [2] can withstand to its dimensions and the strength of its material.This approximate formula is named after Peter Barlow, an English mathematician.