Compatibility Equations

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  1. ViralRiver's Avatar
    • Overlord in Training
    • Posts: 2,408
    Compatibility Equations
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    Hi, I have been working on a question for 3 hours now and keep getting the signs wrong in my final answer. I can now see why, but I don't understand it. Basically, the question is to do with working out the displacement of a node in a truss structure when one of the bars is subjected to a temperature change.

    The crux of the problem is that I have the following contradiction when finding the bar force:

    \epsilon = \dfrac{e}{L} + \alpha \Delta T

    E = \dfrac{\sigma}{\epsilon}

    \sigma = \dfrac{F}{A}

    Method 1:

    E = \dfrac{\dfrac{F}{A}}{\dfrac{e}{L  } + \alpha \Delta T}

    \dfrac{e}{L} + \alpha \Delta T = \dfrac{F}{AE}

    F = \dfrac{AE}{L}\big( e + L\alpha \Delta T \big)


    Method 2:

    e = \epsilon L + L\alpha \Delta T

    e = \dfrac{F}{AE} L + L\alpha \Delta T

    F = \dfrac{AE}{L}\big( e - L\alpha \Delta T\big)

    As you can see, there is a difference in sign when comparing the final answer from both methods. Can someone tell me what's the problem here?


    Nevermind, got it.
    Last edited by ViralRiver; 09-04-2012 at 19:15. Reason: Solved it.
  2. Coursework.info's Avatar
    • Retired TSR Help Bot
    • Location: That galaxy over there
    Compatibility Equations
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