Euler Buckling Formula

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Theorem

$F = \dfrac {\pi^2 E I} {\left({K L}\right)^2}$

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


Proof


Also known as

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


Source of Name

This entry was named for Leonhard Paul Euler.


Sources