Thick Cylinders
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1. A steel cylinder with an internal radius of 50mm is designed to carry a maximum stress of 400 MPs. It is subjected to an internal pressure of 80 MPs.
(i) Determine the required wall thickness.
(ii) The outer radius of this cylinder is chosen as 70 mm and the internal pressure is increased to 160 MPa. The cylinder is strengthened by shrinking a steel jacket around it to obtain a compound cylinder.
a) Determine the required outer radius of the jacket noting that the maximum hoop stress is 400 MPa, that is, -400 <= sigma_theta <= 400 Mpa.
b) Determine the interference at the mating surface.
Young's modulus E = 200 GPa.
2. A compound cylinder is manufactured by shrinking a steel cylinder of external radius 110mm and internal radius 90 mm onto another steel cylinder of internal radius 70 mm. Note that there is no internal or external pressure applied on the compound cylinder. Only shrink-fit stresses exist.
a) If the maximum tensile stress in the outer cylinder is 100 MPa, determine the radial compressive stress at the common surface.
b) Determine the interference.
c) Determine the maximum stress in the inner cylinder.
Take E = 200 GPa, v = 0.3 for steel.
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The key to these types of problems is Lame's equation. Based on the information given in these notes, I have worked through the problems that you have provided. This is shown in the attached files.
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