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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:
For cylindrical pressure vessels, the normal loads on a wall element are longitudinal stress, circumferential (hoop) stress and radial stress. 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 ...
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 ...
For example, consider a thin-walled cylinder subjected to an axial compressive load uniformly distributed along its rim, and filled with a pressurized fluid. The internal pressure will generate a reactive hoop stress on the wall, a normal tensile stress directed perpendicular to the cylinder axis and tangential to its surface. The cylinder can ...
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 ...
is the cylinder stress or "hoop stress". 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 one twentieth) of its radius. The cylinder stress, in turn, is the average force exerted circumferentially (perpendicular both to the axis and to the radius of the object) in ...
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This is a special case of a torus for a = 0 (see below), as well as of a thick-walled cylindrical tube with open ends, with r 1 = r 2 and h = 0 Thin, solid disk of radius r and mass m. = = = This is a special case of the solid cylinder, with h = 0