# Magnitude of force within thermally expanding restrained bar

1. Apr 11, 2012

### AnnaWerner

1. The problem statement, all variables and given/known data
A steel rod with a length of l = 1.55 m and a cross section of A = 4.52 cm^2 is held fixed at the end points of the rod. What is the size of the force developing inside the steel rod when its temperature is raised by ∆T = 41.0 K? (The coefficient of linear expansion for steel is α = 1.17×10-5 1/K, the Young modulus of steel is E = 200 GPa.)

2. Relevant equations
F=EA(ΔL/L)
ΔL = L*α*ΔT

3. The attempt at a solution
OK, here is what I have done:
1) Convert GPa to Pa. In my case, 200 GPa = 2*(10^11)Pa. Also, convert A from cm^2 to m^2.
2) Find ΔL: L*α*ΔT (L in m, α, and ΔT in K given).
3) Apply ΔL to F = EA(delta L/L).

Thank you for any assistance.

2. Apr 11, 2012

### truesearch

That looks OK. Put the numbers in and see what you get

3. Apr 11, 2012

### AnnaWerner

Well, I have tried this multiple times, but my answer consistently comes out incorrect. The units are supposed to be Newtons, correct? I'm getting 105,768 N. Seems large . . .

4. Apr 11, 2012

### truesearch

I got ΔL =7.43x10^-4m
Then F = (2x10^11 x 7.43x10^-4 x 4.52x10^-4)/1.55 which came to 43364N
Double check your maths and mine! see if you can spot a difference.