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Finding maximum bending moment when shear force equation is known

  1. Mar 17, 2013 #1
    1. The problem statement, all variables and given/known data

    Calculate the Maximum Bending Moment of the bridge section using the values given.
    Ra = 61837.91667 N
    Rb = 78304.5833 N
    (please refer to attached diagram)

    2. Relevant equations

    shear force is = 0 when x = 13.755998 m
    (I worked this distance and the shear force equation out and found it to be correct)

    Shear force equation is: v = (950/13)x2 + 3490.096154x - 61837.91667

    3. The attempt at a solution

    3. The attempt at a solution

    Integrate shear force equation:
    ∫(950/13)x2 + 3490.096154x - 61837.91667

    = (950/39)x3 + (3490.096154/2)x2 - 61837.91667x + C

    when x = 0, c = 0

    Maximum bending moment = (950/39)x3 + (3490.096154/2)x2 - 61837.91667x when x = 13.755998 m

    ∴ Maximum bending moment = -457024.4582 Nm

    BUT, I know that the max bending moment is definitely not the answer I calculated.

    Any help you can offer me will be greatly appreciated!
    Thanks
     

    Attached Files:

  2. jcsd
  3. Mar 17, 2013 #2
    First, restrict your calculations to four significant figures, to reduce errors (ironically). Then check with standard formula WL/6 where W is the total load. That is for the triangular load. Add WL/8 for the UDL. Since first writing this I have found an error in your work The coefficient 950/13 for the x^2 term needs checking. In general you would do better to work in kN units.
     
    Last edited: Mar 17, 2013
  4. Mar 17, 2013 #3

    SteamKing

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    Your shear force equation is wrong. To check, substitute x = 0 and x = 26, and get the corresponding shear values. Check these with the reactions to see if the bridge is in equilibrium.
     
  5. Mar 17, 2013 #4

    nvn

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    Kasthuri: Your shear force equation appears correct. Your maximum bending moment in post 1 appears correct. Nice work. I currently do not know why you, and others, currently seem to think it is wrong. Why do you think your answer is wrong?
     
  6. Mar 17, 2013 #5

    SteamKing

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    I reiterate, your shear force equation is incorrect.
    Where does the factor 950/13 come from? The load diagram clearly states that q at the right end of the bridge is 3800 N/m.
    Why do you take Ra as negative in the shear force equation?
    Clearly, if you evaluate the shear force equation at x = 0, you should obtain a shear force equal to the reaction at A.
    Your bending moment calculation won't be correct until you get the correct shear force equation.
     
  7. Mar 18, 2013 #6
    This is the shear force equation: (I missed the '2' initially, I'm sorry for that!)

    v = (9250/13)x2 + 3490.096154x - 61837.9166

    So through integrating from x = 0 to x = 13.756m I get that bending moment:
    MAX BM = 885754.75 Nm
     
  8. Mar 18, 2013 #7
    I just now realised that it isn't in equilibrium, thanks.
    Ignore my earlier comment. I looked back on my working and found the 950/13 comes from the weight of the triangular loading:
    W = 1/2(base)(height)
    = 1/2(x)(3800/26)(x)
    = 950/13(x^2)
     
  9. Mar 18, 2013 #8
    I have fixed my shear force equation and integrated it:
    ∫ - (950/13)x2 - 3490.096154x + 61837.91667 from x = 0 to x = 13.756 metres:

    BM = 61837.91667x - (3490.096154x2)/2 - [(950/13)]x3/3

    so integrating from x=0 to x=13.756m:

    BM max = 457024.483 Nm
     
  10. Mar 18, 2013 #9

    SteamKing

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    Sorry, but 1/2(x)*(3800/26)*x is NOT equal to (950/13)*x^2
     
  11. Mar 18, 2013 #10

    SteamKing

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    Cancel last post. Sorry.
     
  12. Mar 19, 2013 #11
    Thank you so much for your help SteamKing! :D
    I got it right :)
     
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