Need some help with overhanging beam deflection!

  1. Hey all, first post!

    Looking to find a deflection equation for a simply supported overhanging beam with two supports and a point- load at the end of the canteliever. I can determine reactions at the supports but i am having trouble finding deflection between the supports.

    Any help is appreciated!

    the beam in question looks like (a) in the following picture but if we call L/2 a, instead.

    [​IMG]
     
  2. jcsd
  3. SteamKing

    SteamKing 9,599
    Staff Emeritus
    Science Advisor
    Homework Helper

    This is a tricky problem. A simply supported beam with an overhanging load and no other appreciable loading is statically unstable. You have not provided any details about your calculations, so I am unable to comment on their validity. The so-called 'conjugate beam' you show reflects different end conditions from the original beam. The slope and deflection at C for the 'conjugate beam' must both vanish, whereas neither vanish at C for the given beam.
     
  4. Sorry my mistake; the beam is restrained at A, vertically so I guess the triangle needs to be pointing the other way. The beam is no longer statically unstable now, right?

    Ive done a number of calcs intergrating something like: P*a*x/LEI, with a number of variations to find slope then deflection, But I always seem to be ending up with an answer that would be mm^2 instead of mm. I was hoping someone might be able to go through finding the answer for me so I can find the deflection at many points along the A-B section.

    Oh and the second example shouldn't be there at all. I just had to find a picture that was something like the problem I have as I couldn't upload my own pic.
     
  5. jhae2.718

    jhae2.718 1,160
    Gold Member

    I'd solve the beam equation to find the displacement as a function of x or get an approximate solution using virtual work or finite elements.
     
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