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A not-so-standard buckling problem

  1. Dec 22, 2013 #1
    Hey guys, this came up in one of my past papers, and I'm not quite sure where to go with it.

    The diagram shows an idealized structure consisting of an L-shaped rigid bar structure supported b linearly elastic springs at A and C. Rotational Stiffness is denoted βR and translational stiffness is denoted β. If βR = 3βL2/2, determine the critical buckling load PCR for the structure




    PCR = C2EI/L, where C is a constant which depends on the end characteristics of the bar, E is youngs modulus, I is inertia, and L is the length of the bar.

    Given that the Bar is simply supported, that meant that Le was equal to L/2 i though, and by Le = L/sqrt(C), that gave C a value of 1/4




    My first though was to try and resolve the forces being applied, so I took moments about the point of maximum deflection, L/2, when a force of P is applied, where P<PCR. But I got lost there, because I can't figure out what the moment due to the stiffnesses would be, since they are a ratio due to the force applied/ deflection, and I dont know what deflection there would be at the point the spring is attached to
     

    Attached Files:

  2. jcsd
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