Stress of a material with a core

[joeblow]

If I have a rod with a steel core bonded to an aluminum shell, how can I find the stress in the rod when it is subjected to a temperature change?

I know how to find the stress due to temp change if the tool is made of the same material throughout, but how do I do it if there are two?

I attempted to find the loads induced by the temp changes for the two materials separately, add them, then find the stress that way, but this led to an incorrect answer.

 

[joeblow]

Figured it out. PROTIP: Equate the deformations of both materials.