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Uniformly distributed load - Max bending moment help

  1. Mar 20, 2015 #1
    1. The problem statement, all variables and given/known data
    I have to work out the reactions at A & D. Sketch the shear force diagram for the beam and sketch the bending moment diagram.

    i have worked out the reactions at A=56kN and D=34kN. I have done the SFD. I am just struggling doing the bending moment diagram and dont know how to work out the maximum bending moment.

    2. Relevant equations


    3. The attempt at a solution
    RA + RD = 90kN

    5RD = (20X1) + (60X2) + (10X3)
    5RD = 170kN
    RD = 34kN

    RA=56kN.

    I have done the SFD.

    Bending moment diagram i have to state the three significant values.

    I have left side as (56x1) = 56kN M
    right hand side is (34x2) = 68kN M
    i just dont know how to work out the maximum bending moment would appreciate any help
     

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  2. jcsd
  3. Mar 20, 2015 #2

    SteamKing

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    If you have the shear force diagram, this should tell you at which locations to look for the maximum bending moment.

    After all, dM / dx = V, where V is the shear force and M is the bending moment.

    What can you say about dM / dx where the bending moment is a maximum?
     
  4. Mar 20, 2015 #3
    How would i go about doing my bending moment diagram from this sfd. how do i put data into that equation. i worked out x as 1.2m
     

    Attached Files:

  5. Mar 20, 2015 #4

    SteamKing

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    The equation was not put there so that you could calculate M, but to illustrate how to use the shear force diagram to find the locations along the beam where M is a maximum.

    If you want to find where a given function has a maximum, in this case the function is M(x), or bending moment as a function of position x along the beam, the point(s) at which the first derivative is zero coincide with the locations where the function has a maximum or minimum.

    In other words, if you want to find x where M(x) has a max. or min. value, then dM(x) / dx = 0. Since also dM(x) / dx = V(x), then the points x1, x2, ..., at which the shear force V(x) = 0 are also the points at which the bending moment has a maximum or minimum value.

    This is a basic application of the derivative and should have been covered in your calculus course.
     
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