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It gives the contact stress as a function of the normal contact force, the radii of curvature of both bodies and the modulus of elasticity of both bodies. Hertzian contact stress forms the foundation for the equations for load bearing capabilities and fatigue life in bearings, gears, and any other bodies where two surfaces are in contact.
Bearing pressure for a cylinder-cylinder contact. In the case of a revolute joint or of a hinge joint, there is a contact between a male cylinder and a female cylinder. The complexity depends on the situation, and three cases are distinguished: the clearance is negligible:
They are free of stress when entering the contact patch, then stick to a particle of the opposing surface, are strained by the overall motion difference between the two bodies, until the local traction bound is exceeded and local slip sets in. This process is in different stages for different parts of the contact area.
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.
(It may be necessary to calculate the stress to which it is subjected, for example.) On the right, the red cylinder has become the free body. In figure 2, the interest has shifted to just the left half of the red cylinder and so now it is the free body on the right. The example illustrates the context sensitivity of the term "free body".
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 ...
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Functions of the principal stresses, such as the yield function, can be represented by surfaces in 'stress space. In particular, the surface represented by von Mises yield function is a right circular cylinder, equiaxial to each of the three stress axes.