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