From classic elastic column buckling theory, the Euler buckling load is the compressive axial force necessary to cause lateral instability of a vertical, weightless column. The formula for the Euler buckling load is:

\lambda = \sqrt{\frac{\sigma_F}{\sigma_{ET}}}

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\sigma_{ET} = \frac{\pi^2 El_f}{A_e\left(KL\right)^2}