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Magnitude of force within thermally expanding restrained bar

  1. Apr 11, 2012 #1
    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. jcsd
  3. Apr 11, 2012 #2
    That looks OK. Put the numbers in and see what you get
     
  4. Apr 11, 2012 #3
    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 . . .
     
  5. Apr 11, 2012 #4
    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.
     
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