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Deflection simply supported beam

  1. Oct 4, 2013 #1
    1. The problem statement, all variables and given/known data
    How do I find an expression for the deflection at midspan of this beam? The beam is simply supported and there is two triangular loads on each side of the beam.

    Illustration of problem: http://goo.gl/gk68Fl [Broken]

    2. Relevant equations
    [itex]Deflection = \Delta = \int \frac{Mx*mx}{EI}[/itex]
    Elastic curve equation of the simply supported beam for this case:
    [itex]\delta = \frac{Qx}{960LEI}(5L^2-4x^2)^2[/itex]

    3. The attempt at a solution
    I found Mx and mx, and I integrate from [itex]\frac{L}{2}[/itex] to [itex]L[/itex]. My answer is: [itex]\frac{QL^4}{120EI}[/itex].
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Oct 4, 2013 #2

    nvn

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    raymanmusic: After you integrated from 0.5*L to L, did you multiply by 2? You must multiply by 2, which I think you did, because your current answer in post 1 is correct.
     
    Last edited: Oct 4, 2013
  4. Oct 5, 2013 #3
    Actually I did not multiply by 2, but I still got the correct answer. What did I do wrong?

    Attempt at a solution: http://goo.gl/qFYMoG [Broken]
     
    Last edited by a moderator: May 6, 2017
  5. Oct 5, 2013 #4

    nvn

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    raymanmusic: First, your expression for qx currently looks wrong.

    Secondly, your domain (0.5*L, L) for mx looks different from your domain for Mx. But then you combine these two incompatible domains in your integral. Or are you seeing a novel approach I did not envision yet?
     
    Last edited: Oct 5, 2013
  6. Oct 5, 2013 #5
    Thanks! I've made some corrections to my calculations. I think it's easier to understand now.

    Attempt at solution: http://goo.gl/qFYMoG [Broken]
     
    Last edited by a moderator: May 6, 2017
  7. Oct 5, 2013 #6

    nvn

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    Excellent work, raymanmusic. Your answer is correct.
     
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