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Deflection by integration of load equation

  1. Apr 16, 2009 #1
    1. The problem statement, all variables and given/known data

    Determine the equation for the deflection curve for the cantilever supported at A with a load given by: q=q0*sin([tex]\pi[/tex]x/L).

    2. Relevant equations



    3. The attempt at a solution

    I think this is pretty straightforward, but want to be sure. I did a similar problem with a simply supported beam with the same load equation, shown in the attached diagram. Am I safe to assume that the ONLY difference in this problem with a cantilever is the boundary conditions used to solve for C1, C2, etc?

    The boundary conditions would be:
    at x=0,y=0....and at x=0,moment=0.
    right?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Apr 16, 2009 #2

    minger

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    Right, typically you say to yourself what is zero at the boundaries. For a simply supported beam, the deflections are zero; for a fixed-fixed beam, both deflections and angles are zero. In the case of a cantilevered beam, on the fixed end you have zero angle and zero deflection, but the million dollar question is what is zero at the free end?
     
  4. Apr 16, 2009 #3
    The moment, right?

    Going back to my "attempt at a solution", I believe I screwed up. For the cantilever, at x=0, y=0...and at x=0, dy/dx=0. I had put that at x=0,moment=0, which is wrong. Also, I'm going to need to use: @x=L,shear force=0...and @x=L,moment=0.
     
  5. Apr 16, 2009 #4

    minger

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    Science Advisor

    Yup, you're right on track now. Good luck
     
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