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Find the Shear and Moment on the Beam

  1. Nov 24, 2012 #1
    1. The problem statement, all variables and given/known data

    Derive expressions for the shear force V and bending moment M as functions of x in the cantilever beam loaded as shown. Then answer the questions.

    At x = 2 ft,
    V =
    M =

    At x = 9.3 ft
    V =
    M =

    I have attached an image of the question

    The maximum (absolute value) shear force in the beamis 2109.19 lb
    The maximum (absolute value) bending moment in the beam is lb·ft


    2. Relevant equations

    W = -dV/dx

    dM = Vdx

    3. The attempt at a solution
    First I found the equation w = w0+kx2

    When x = 0
    120 lb/ft = w0 +k(0)2

    Hence w0 = 120 lb/ft

    When x = 11.3'
    320 lb/ft = 120 + k(11.3)2
    k = 1.566

    Hence:
    w = 120 + 1.566x2\

    To find the shear, V, I took the integral of w because:

    w = -dV/dx hence
    -∫w = V

    V = -120x - 1.566x2

    Thus when x = 2
    V = -120(2) - 1.566(2)3
    V = -244.176

    When x = 9.3
    V = -120(9.3) - 1.566(9.3)3
    V = -1535.87

    For the Moments I did the following

    dm = Vdx
    m = ∫V
    m = ∫-120x - 0.522x3
    m = -0.135x4-60x2

    When x = 2
    m = -242.

    When x = 9.3
    m = -6165.607

    Then to try and calculate the maximum shear:

    V = -120(11.3)-0.522(11.3)3
    V = -2109.19

    But it wants the absolute value, hence V = 2109.19

    For the max bending moment:

    m = -0.1325(11.3)3 - 60x2
    m = -9789.17

    But it wants the absolute value, hence V = 9789.17
    Except for the max shear all of my values are wrong and I'm at a loss for what I should do. Help would be greatly appreciated. Thank you
     

    Attached Files:

    Last edited: Nov 24, 2012
  2. jcsd
  3. Nov 24, 2012 #2

    SteamKing

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    No image attached.
     
  4. Nov 24, 2012 #3
    Sorry. I have now fixed it. Thank you for pointing that out.
     
  5. Nov 24, 2012 #4

    SteamKing

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    In order to obtain the correct shear force and bending moment diagrams for this beam, you must first find the fixed end reaction and moment which keep the beam in equilibrium. Remember, at the free end, V = M = 0.
     
  6. Nov 25, 2012 #5
    Although steamking has wise words, in this case you CAN work from the right hand end without the reactions. Let e be the distance from the RH end, positive to the left... Ehen ev is .. and Mv is ... (use the definitions). When you have finished, the reactions should appear when v=11.3'. You then have a check on any errors made.Northbysouth, when you integrated, did you forget the arbitrary constant?
     
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