Euler Buckling Formula

Theorem

 * $F = \dfrac {\pi^2 E I} {\paren {K L}^2}$

where:
 * $F$ = maximum or critical force (vertical load on column)
 * $E$ = modulus of elasticity
 * $I$ = area moment of inertia of the cross section of the rod
 * $L$ = unsupported length of column
 * $K$ = column effective length factor, whose value depends on the conditions of end support of the column, as follows:


 * For both ends pinned (hinged, free to rotate), $K = 1.0$
 * For both ends fixed, $K = 0.50$
 * For one end fixed and the other end pinned, $K \approx 0.699$
 * For one end fixed and the other end free to move laterally, $K = 2.0$


 * $K L$ is the effective length of the column

Also known as
The Euler buckling formula is also known as the Euler column formula.