Transcription of Thick Walled Cylinders
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Thick Walled Cylinders
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.
needed wall thickness if the factor of safety n is 2.0 and the yield stress is 250 MPa. Use the maximum shear stress theory, i.e. maximum shear stress = yield strength/2n. ( wall = 61.8 mm thick ) 4. A 400 mm OD steel cylinder with a nominal ID of 240 mm is shrunk onto another steel cylinder of 240 mm OD and 140 mm ID. The radial interference δis
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