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Boundary conditions for a 4th order beam deflection equation

  1. Dec 9, 2009 #1
    What would the boundary conditions be for a fourth order differential equation describing the deflection (elastic curve) of a propped cantilever beam with a uniform distributed load applied? i.e. a beam with a built in support on the left and a simple support on the right. I need 4 obviously but I am having a hard time coming up with the 4th.

    So far I have

    1. x = 0 v = 0 (no deflection at the built in support end)
    2. x = L v = 0 (no deflection at the simple support end)
    3. x = 0 dv/dx = 0 (slope of the deflection at the built in support is 0)

    and for the fourth I have seen

    x = L d^2v/dx^2=0

    but Im having some trouble wrapping my head around that last one. Is it correct?
  2. jcsd
  3. Dec 10, 2009 #2


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    yes, at the pinned simple support which is free to rotate, there can be no bending moment, which is what that boundary condition describes (at x = L, v" = M/EI = 0)
  4. Dec 10, 2009 #3
    thanks, I was getting confused because some sites had "common beam" equations that were different than others.. until i realized that the supports were on different sides and thus their coordinate system was changing. now it makes sense.
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