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Liner buckling

  1. Jan 2, 2015 #1
    1. The problem statement, all variables and given/known data
    A beam (e.g. a steel liner) of a length L is bent between two supports, as shown in fig (a).
    According to the Euler column, the shape is a half period of a sine.
    Now, a force P is applied at the axis of symmetry - fig (b).
    What is the shape of the liner? y=f(x)
    Instead of the general case, let's choose P so weak that the liner remains always convex (h1=0.9*h or so ...).

    3. The attempt at a solution
    I followed the "Strength of Materials and Structures" of Case-Chilver-Ross (ISBN:0340719206)
    and tried to modify the 18.9 - "Strut with uniformly distributed lateral loading"
    to a "... with concentrated lateral load" .
    How to apply the boundary conditions so that the length of the liner (arc length) L remains constant?
  2. jcsd
  3. Jan 2, 2015 #2


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    Gold Member

    What value is the ratio h/d for your problem? If the ratio is very large, your sinusoidal shape is not correct.
  4. Jan 3, 2015 #3
    Agreed. But this way the drawing is more clear.
    Is there a solution when h/d is:
    a) so low that sine shape stands?
    b) so large that it is not a sine any more?
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