Stress of a material with a core

AI Thread Summary
To determine the stress in a rod with a steel core and aluminum shell under temperature changes, it's essential to equate the deformations of both materials. Simply calculating the stress for each material separately and adding them may lead to inaccuracies. The correct approach involves understanding how the different thermal expansions affect the overall stress distribution. By ensuring that the deformations match, one can accurately assess the induced stresses. This method provides a reliable solution for composite materials under thermal stress.
joeblow
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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.
 
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Figured it out. PROTIP: Equate the deformations of both materials.
 

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