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Distributed Loads Forces

  1. Dec 19, 2011 #1
    hi there,


    I'm getting very very confused about distributed loads.

    I am trying to figure out the resultant force of a distributed load on a beam. The function I've been given for q(x) is a polynomial (below x=0).

    I have figured out the resultant for my function q(x)=x2-2x-4. I beleive it is 9.1877 (positive being in the vertical direction). Length = 43/10

    To find the distance of the resultant from point A on the beam, I have worked it out to be (1/2*(43/10).

    I don't feel that the distance I have worked out it right and I'm not 100 percent sure about the resultant force either. Could someone please set me off in the right direction?

    Thanks in advance.
     
  2. jcsd
  3. Dec 19, 2011 #2
    Hi,

    The force of 9.1877 is correctly calculated. It is the integral of the load.

    Now to find the position of the resultant, we first calculate the moment around the point x = 0.
    M = int (x * q(x)) dx between x = 0 and x = 4.3
    = int (x^3 - 2x^2 - 4x) dx between x = 0 and x = 4.3
    = - 4.1546
    (negative because load works vertically)
    This has to be equal to the moment caused by the resultant:
    M = Fd
    with d the distance from the point x = 0.
    Hence
    d = M/F = 2.0350

    This is close to your (1/2*(43/10), but not exactly the same. How did you get there?
     
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