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Thermal Concrete Physics

  1. Nov 30, 2006 #1
    1. The problem statement, all variables and given/known data
    Two concrete spans of a L = 270 m long bridge are placed end to end so that no room is allowed for expansion (Fig. P10.55a). If the temperature increases by T = 21.0°C, what is the height y to which the spans rise when they buckle (Fig. P10.55b)

    [​IMG]




    2. Relevant equations
    change in L/L= average coefficient of expansion(change in T)

    average coefficient of concrete= 12 X 10^-6

    3. The attempt at a solution

    I tried doing

    change in L/270= 12 X 10^-6 (21)

    I got change in L, and now I dont know what to do. HELP
     
  2. jcsd
  3. Nov 30, 2006 #2

    Kurdt

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    Once you work out how much the concrete expands by its really just a case of pythagoras theorem to work out the height they raise when they buckle.
     
  4. Nov 30, 2006 #3
    how?

    I got change in L as 0.06804
     
  5. Nov 30, 2006 #4
    This is so frustrating
     
    Last edited: Nov 30, 2006
  6. Nov 30, 2006 #5
    anyone care to help?
     
  7. Nov 30, 2006 #6

    FredGarvin

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    If you assume that the break is in the middle as the picture points out, you have the original length and the new length which is the original plus the change in length. Divide each number in half and that will give you the hypotenuse and the base sides of a right triangle. You need to find the opposite side's length, which I am assuming you can do.
     
  8. Nov 30, 2006 #7
    ^ the height should be around 3.0, I am not getting that number
     
  9. Nov 30, 2006 #8

    OlderDan

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    What calculation have you done and what is your result?
     
  10. Nov 30, 2006 #9
    L= 270
    change in L/270= 12 X 10^-6 (21)= 0.06804
    270+0.06804= 270.06804

    270/2= 135
    270.06804/2= 135.03402

    now according to u I should do pythagorean theorum, which I did and got 190.9

    thats not right

    I got it though finally, when I do L/2, which is 270/2= 135, take the change in L, which is .06804

    135 X .06804 and take its square root, I get 3.03, which is the answer
     
    Last edited: Nov 30, 2006
  11. Nov 30, 2006 #10

    OlderDan

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    Your Pythagorean calculation is incorrect. You added the square of the long leg (135) to the square of the hypotenuse. You need to subtract the square of the long leg from the square of the hypotenuse and take the square root to find the short leg.
     
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