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.