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·
The
solution for the buckling load for various end conditions was first solved
by Euler, and the buckling behavior
is known as "Euler Instability"
· The
shape of the rod in compression can be described by the equation:
(d2y/
dx2 ) - K2 y = 0
where:
K2 = {FC/EI}, E = Young's Modulus, I = Second moment
of area = (A2/4π)
for a circular rod
· The
boundary conditions are: y = 0 at x = 0, L.
· The
solutions for this eigen value problem have the form:
y
= A cos(Kx) + B sin(Kx).
· Application
of the boundary conditions gives: A = 0. For the non-trivial case, B is
non-zero, i.e sin(KL) = 0, or (KL) = nπ
so that:
y(x)
= B sin(nπx/L). |
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