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Math Help - Deflection Curves

  1. #1
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    Deflection Curves

    A deflection curve is:

    EIy''''=w

    E, w, and I are constants.

    The downward direction is considered positive.

    I have these initial conditions (the beam is fixed at 0 and L):

    y(0) = 0
    y(L) = 0
    y''(0) = 0
    y''(L) = 0

    I have to find a solution for these conditions and also find the max deflection in the y direction.

    I believe I found the solution for y, but I have some constants that I am unable to define, so I am not sure how (or if) I can find the maximum deflection.

    I came up with y = (wx^4)/24EI + Ax^3/6 + Bx (A and B are yet to be defined constants)

    To find the maximum deflection, I assume I should set y' equal to zero to find the maximum, which gave:

    0 = (wx^3)/6EI + (Ax^2)/2 + B

    Is there something more I can do to find the maximum deflection?

    Thanks
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  2. #2
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    Quote Originally Posted by machi4velli View Post
    A deflection curve is:

    EIy''''=w

    E, w, and I are constants.

    The downward direction is considered positive.

    I have these initial conditions (the beam is fixed at 0 and L):

    y(0) = 0
    y(L) = 0
    y''(0) = 0
    y''(L) = 0
    Okay,
    y''''=W/EI

    Thus, integrating 4 times,
    y=W/EIx^4+Ax^3+Bx^2+Cx+D
    Where, A,B,C,D are to be determined.

    Solve the initial value problem,

    D=0,
    C=L
    B=0
    A=L/3

    Thus,
    y=W/EIx^4+L/3x^3+Lx

    To minimize this you need,
    y'=0 on 0<=x<=L
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  3. #3
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    Could you possibly explain that further? I am not sure what I may be doing incorrectly, but I got (-1/2)(w/EI)L for A and (-1/12)(w/EI)L^3 for C
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