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How to derive equation of deflecting curve for a simple beam

  1. Apr 5, 2013 #1
    1. The problem statement, all variables and given/known data

    Obtain deflection curve in terms of q, L, and EI
    fu8i06.jpg

    2. Relevant equations

    Use the second order differential equation of the deflection curve to solve.
    Meaning that the M(x) is the second derivative and you integrate twice to get V1 and V2

    3. The attempt at a solution
    From the bending moment diagram i've found that:
    (0 ≤ X ≤ 36) → M1(x) = 1800*X which is [(L/8)q](x)
    (36 ≤ X ≤ 72) → M2(x) = -100(x-72)2 - 5400(x-72) which is
    (-q/2)(x-L)2-(3L/8)q(x-L)

    From the back of the book, I can see that the answer is going to be the same as the table values (just for the opposite side). I Have tried, but cant get the right answer. Can anyone help me?
    Table values: 33m98ae.jpg
     
    Last edited: Apr 5, 2013
  2. jcsd
  3. Apr 5, 2013 #2

    SteamKing

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    You have shown the back of the book answer, not your own calculations. How can we see what is wrong with your calculations if we don't have them?
     
  4. Apr 5, 2013 #3
    yes that is what we're supposed to get, but I'm not getting close to it. Pretty much all I have to do is get the moment of the beam as a function of x for the first half of the beam and the second half. From there, we take the integral twice.

    Anyway, I think my first question is, are the moment functions right? Then we can go from there. Thanks.
     
  5. Apr 5, 2013 #4
  6. Apr 5, 2013 #5

    SteamKing

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    If you evaluate your moment expressions, you should get the same values on your bending moment diagram. Your equations don't match the curve.
     
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