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Continuous beam deflection (structural)

  1. Apr 14, 2015 #1
    1. The problem statement, all variables and given/known data

    Using continuous beam theory, constructing BM diagram from points b to c, to calculate the max deflection. I only found a have a single solution, though the BM digram show two points of zero bending. I can provide the solution.

    [edit: Rb = 685 N]

    2. Relevant equations

    d2v/dx2=-M(x)/ (IE)

    3. The attempt at a solution
    please find attached

    [edit: please find revised attachment]
     

    Attached Files:

    Last edited: Apr 14, 2015
  2. jcsd
  3. Apr 14, 2015 #2

    SteamKing

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    The point of max. deflection within a span will not occur where the BM is zero, it will occur close to where the BM is a maximum.

    If you had a single beam which was fixed at both ends with an evenly distributed load applied, there would be two points where the BM = 0, but obviously, the maximum deflection would occur in the center of the beam. :wink:

    If you were to make a rough sketch the deflected shape of this beam with its loading, you would see that there should be only one point in each span where the deflection will be a maximum or minimum. :smile:
     
  4. Apr 14, 2015 #3
    Thank-you for your post.

    Obviously, max deflection can not occur at BM = 0. In this case the fixed moments are not equal, therefore it won't occur at centre of beam.

    Given, I've used 'three moment equation(s)' to arrive at the given moments at b and c, and reaction at b (reaction b is under the support b).

    My question is, given the manner in which I've formulated the M(x) equation. Is it correct- given I have fixed unequal (in this case) BM's at points b and c, with a free moment due to dist load?

    Your thoughts.

    [edit] Please let me know if you need more information [edit]
     
    Last edited: Apr 14, 2015
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