Transcription of Thick Walled Cylinders - UW Courses Web Server
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Thick Walled Cylinders - UW Courses Web Server
Thick Walled CylindersConsider a Thick Walled cylinder with open ends as shown above. It is loaded by internal pressure Piand external pressure Poas seen below. It has inner radius riand outer radius r r r+ d rNow consider and element at radius r and defined by an angle increment d and a radial increment dr. By circular symmetry, the stresses and rare functions of r only, not and the shear stress on the element must be zero. For an element of unit thickness, radial force equilibrium gives:Ignoring second order terms gives:Assuming that there are no body forces.()()drdrdddrrdrrr +=++)1(0 LLL=++rdrdrr aba b cdc d Now consider strains in the element. By symmetry there is no displacement v. there is only a radial displacement u given by line aa . Point c is displaced radially by (u + du) given by line cc.
occurs at the inside surface. (c) Press and shrink fits When a press or shrink fit is used between 2 cylinders of the same material, an interface pressure p i is developed at the junction of the cylinders. If this pressure is calculated, the stresses in the cylinders can be found using the above equations. The pressure is:
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