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Irregular Cantilever question

  1. Aug 23, 2011 #1
    Hello,

    I am trying to figure out how to calculate displacement for an irregular cantilever beam, i.e. one that is not the normal straight-beam that you would see in a textbook.

    Please see the attached image. If the left end is fixed, and I want to calculate the displacement of point A due to an applied force at that point, how would I go about it?

    Are you still able to use M_x = EI * d^2y/dx^2 and solve for displacement by integrating? I am not exactly sure how the geometry of the weird bended shape comes into play. Thanks.

    - T
     

    Attached Files:

  2. jcsd
  3. Aug 24, 2011 #2
    The cantilever beam has three segments:
    1) Horizontal segment with moment inertia I_1
    2) Diagonal segment at middle with moment inertia I_2
    3) Diagonal segment at end with moment inertia I_3

    Note: I_2 is determined relative to global Y axis (not local Y axis). Thus, I_2>I_1 as illustrated. I_3 is not required for calculations; only its horizontal length is needed.

    The beam has four points
    A) At support
    B) Right of segment 1
    C) Right of segment 2
    D) Right of segment 3

    Procedure:
    a) Calculate flexure and deflection over segment 2
    b) Calculate flexure and deflection over segment 1
    c) Add deflection 1 and 2 to give total deflection at point C
    d) Determine curvature at point C
    e) Determine tangent of segment 3, and thus deflection of segment 4
    f) Add deflection of point step (c) to setup (e) to yield total deflection at (4)
     
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