A steel rod and an aluminum rod of equal length and diameter are placed end to end and secured so that they cannot flex. The rods are heated to the same final temperature, and the steel is found to increase in length by one-tenth of a percent. If the total length of the rods together remains constant, find the increase in temperature for the rods and the mutual stress on the rods.
Ans: 375 oC , 700 MPa
(RATE OF HEAT FLOW)
H = ΔT/R R = L/KA
(LINEAR HEAT EXPANSION)
ΔL = L0αΔT[/B]
F/A = -YαΔT
The Attempt at a Solution
I first solved for ΔT from the linear heat of expansion equation...
Lf(steel) - li(steel) = li(steel)*α*ΔT
1.001*Li(steel) - li(steel) = li(steel)*α*ΔT
0.001 = α*ΔT where α = 1.2 *10^-5
ΔT = 83.33 C
After I find this, I though I would then plug this into the Stress equation for a given metal since they have the same change in temperature. Though this is obviously not the correct answer.
Am I missing something here?