1.

A steel cylinder was cooled in liquid nitrogen (72 K) and fitted without play into a nickel-chrome steel shell at room temperature (20^@C). The internal radius of the shell is 25 mm and the external radius is 35 mm. Neglecting deformation of the cylinder find the stress in the shell and the nature of its deformation.

Answer»

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Solution :CONSIDER a segment of the shell subtending a small angle `alpha` and obtain `F = T alpha`where `F = sigma_1 S_1` is the force of pressure of the cylinder on the shell,`T = sigma S_3` is the tensile force in the ring. But `S_1 = h ralpha, S_2 = hd` (FIG.). The pressure on the shell is found in the same way as in Problem 20.10:
`p = sigma_1 = E_1 epsilon= E_1 (Delta r_1)/(r) = E_1 alpha_1 Deltat`
Here `E_1` is the Young modulus for steel, `alpha_1`is the THERMAL expansion coefficient for steel. Hence`E_1 alpha_1 Delta tralpha h = sigma_2 had, ` and the stress in the shell is
`sigma = E_1 alpha_1 r Deltat//d`


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