# Homework Help: A not-so-standard buckling problem

1. Dec 22, 2013

### irishmts

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 Î²R and translational stiffness is denoted Î². If Î²R = 3Î²L2/2, 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

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