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## Homework Statement

The equation [itex]F/A = -Y\alpha\Delta T[/itex] gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount [itex]\Delta L[/itex] when its temperature changes by [itex]\Delta T[/itex], the stress is equal to [itex]F/A = Y(\Delta L/L_0 - \alpha\Delta T)[/itex].

## Homework Equations

thermal stress:

[itex]F/A = -Y\alpha\Delta T[/itex]

solution:

[itex]F/A = Y(\Delta L/L_0 - \alpha\Delta T)[/itex]

change in length:

[itex]\Delta L = \alpha L_0\Delta T[/itex]

## The Attempt at a Solution

I figure this will have something to do with the area, as that's the only relation to the length I can see in the problem. I tried substituting A0 + deltaA in for A in the thermal stress equation, but that didn't seem to get me anywhere. Would really appreciate some direction with this one.