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Buckling shape

  1. Jun 19, 2011 #1
    1. The problem statement, all variables and given/known data
    A uniform beam with stiffness EI, cross section A and length L is subjected to a force P. The beam is an ideal column. When the force P reaches a critical value and moves distance a downwards, the first buckling mode has the shape:

    [tex]
    v(x) = C \sin \left( \frac{ \pi x}{L} \right) [/tex] for [tex] 0 \leq x \leq L [/tex]

    Determine the constant C.


    http://img710.imageshack.us/img710/6766/81286000.png [Broken]




    2. Relevant equations
    Use the assumption of small deflections and small rotations.


    3. The attempt at a solution
    I assume (as a first approximation) that the beam can't be shortened (e.g. no PL/(EA)). I can setup an integral from 0 to L-a equalling L relating the distance a to C but this integral cannot be expressed in elementary functions, am I doing something wrong?
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
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