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Calculating the maximum bending moment on a bridge

  1. Mar 13, 2013 #1
    1. The problem statement, all variables and given/known data

    Calculate the maximum bending moment on the bridge section using the values given.

    (REFER TO DIAGRAM ATTACHED)

    mass of bridge = 9250 kg
    mass of car = 2250 kg
    length of bridge section = 26 m

    2. Relevant equations

    I worked out previously that:
    Reaction at A = reaction at B = 56407.5 N , which I got right

    ƩFx = 0;
    ƩFy = 0;
    ƩM = 0;

    3. The attempt at a solution

    I know the maximum Bending Moment is at x = 13m (because shear force = 0 ant x = 13m)


    weight of bridge = 6250 x 9.81 = 90742.5 N
    weight of car = 22072.5 N

    I tried three ways, I know the 1st is wrong.

    1st method:

    Bending Moment max:
    = 90742.5N x 13m + 22072.5N x 13m
    = 1466595 N.m

    2nd method:

    Bending Moment max:
    make a cut at 0≤x<13m , (shear force) v = 56407.5 N
    so integrate this to get BM at x = 13m:
    BM = 56407.5x
    so at x = 13m:
    Bending Moment max = 56407.5 x 13 = 733297.5 N.m

    3rd method:

    Bending Moment max
    = wL/4 (for point load car) + wL^2/8 (uniformly distributed load of bridge)
    = 22072.5 x 26/4 + 90742.5 x (26 x 26)/8
    = 7811212.5 N.m

    So, I'm quite stuck on the method.

    Thank you so much for any help!!
     

    Attached Files:

    Last edited: Mar 13, 2013
  2. jcsd
  3. Mar 13, 2013 #2

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    In the third bending moment calculation, you have used the entire weight of the bridge rather than the weight per meter for w.
     
  4. Mar 16, 2013 #3
    Thanks!
    I did what you said and got it right :D
     
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