Stress in open-end cylinder due to temperature change

[we23sd]

Homework Statement

An open-end cylinder with inner and outer diameters of 2a=30 and 2b= 60 mm, respectively, is subjected to a uniform temperatures change from 25 oC to 45 oC. Assuming the cylinder is rest on a table and free to move, determine the stress and the final dimensions (i.e. length, outside diameter and inside diameter) of the cylinder. Length 20 cm; α=0.0000117 per oC.

Homework Equations

Linear thermal expansion: ΔL = (ΔT*α)*L

The Attempt at a Solution

Is it safe to assume that the change in length as well as the diameters will be found using the linear thermal expansion equations? If so that part is simple.

I am stuck trying to find the stress though. I cannot remember any stress equations where the change in temperature is incorporated, without having to know the material property - Elastic Modulus & Poisson's ratio.

Any help is appreciatd, thanks!

 

[Chestermiller]

If the cylinder is unconstrained, then the traction stresses on the surfaces of the cylinder will be unchanged when it is heated. Each small element of the cylinder material will expand the same amount in all directions. There will be no thermal stresses developed.