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Homework Help: Finding the force exerted on a beam when the temp of the aluminum beam is increased

  1. May 6, 2010 #1
    1. The problem statement, all variables and given/known data
    An aluminum beam 79 m long and with a cross-sectional area of 0.095 m2 is used as part of a bridge. The beam is clamped rigidly at both ends.

    (a) If the temperature of the beam is increased by 29°C, what is magnitude of the extra force exerted by the beam on one of its supports?

    (b) What is the magnitude of the force if the temperature of the beam is decreased by 43°C?


    2. Relevant equations
    delta L = alpha of alum (a constant) * L * temp
    Force = Young's Modulus of alum * area * delta L / L

    3. The attempt at a solution

    For a)
    delta L = (22.2x10^-6)*(79m)*(302 K) = .53m

    F= (7.0x10^10)*(.095m^2)*(.53m)/(79m) = 4.46x10^7

    Unfortunately, that was incorrect.

    Because I couldn't get the first part correct, I haven't been able to attempt b, but I'm assuming you do the same thing but change the temp in the first equation.

    Any help?
     
  2. jcsd
  3. May 6, 2010 #2

    Mapes

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    Re: Finding the force exerted on a beam when the temp of the aluminum beam is increas

    Check your first equation; it should include the change in temperature.
     
  4. May 6, 2010 #3

    rl.bhat

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    Re: Finding the force exerted on a beam when the temp of the aluminum beam is increas

    delta L = (22.2x10^-6)*(79m)*(302 K) = .53m
    ΔT = 29 degrees, not 302 K
     
  5. May 7, 2010 #4
    Re: Finding the force exerted on a beam when the temp of the aluminum beam is increas

    I thought I did that..
    Although I did convert the celsius to Kelvin, but 29+273 = 302 K.
    Am I not supposed to convert it to K?
     
  6. May 7, 2010 #5

    Mapes

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    Re: Finding the force exerted on a beam when the temp of the aluminum beam is increas

    A temperature of 29°C is a temperature of 302 K, but a temperature change of 29°C is a temperature change of 29 K. A degree Celsius is equivalent to a Kelvin, but their reference points, their zeros, are different. Does this make sense?
     
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