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Calculate reaction in hyper static beam

  1. Feb 24, 2012 #1
    1. The problem statement, all variables and given/known data
    Calculate the reaction MA

    http://alkaspace.com/is.php?i=134123&img=E-3.1.jpg


    2. Relevant equations



    3. The attempt at a solution
    First I have put the reaction By as an hyper static force. Then I found the deflection in B with the force By as a variable.

    vb= [itex]\frac{w}{24EI}[/itex](3L4-4a3L+a4) - [itex]\frac{B_{y}L^{3}}{3EI}[/itex]

    Then I know that vb=0 because it is on a reaction. With that I find that
    By= [itex]\frac{w}{8L^{3}}[/itex][3L4-4a3L+a4]

    Now I just have to calculate the moment with
    Mb=(a+b/2)bw-LBy

    My final answer is [itex]\frac{wb^{2}}{8L^{2}}[2L^{2}+6L^{4}-b^{2}][/itex]

    In the book, the final answer is [itex]\frac{wb^{2}}{8L^{2}}[2L^{2}-b^{2}][/itex].

    I only have a 6L4 that isn't supposed to be here. Please help.


    PytLov
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 24, 2012 #2
    If the answer in the book is "In the book, the final answer is wb28L2[2L2−b2].", what is the question, exactly?
     
  4. Feb 24, 2012 #3
    Sorry, I should have added: If you put b=L, in the book answer, you get the wrong answer wL^2/8
     
  5. Feb 24, 2012 #4
    The question is "what are the reactions" and I gave you the answer of the moment at point A. Maybe the book answer is wrong, it's a book from 1992. But I still don't know if I have the good answer, and I think that hyper static structure is really hard. If someone knows the good answer that would be really nice !


    PytLov
     
  6. Feb 24, 2012 #5
    Sorry again. If you put b=L then the book is correct. If you could show all your working or references to formulas, then maybe someone would see an algebraic error.
     
  7. Feb 24, 2012 #6
    Well, I was writing my solution, and now I get the good answer... no idea what was my mistake. But thank you anyway.

    PytLov
     
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