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Euler buckling load

A slender column in compression can fail by suddenly bowing out sideways (buckling), long before the stress reaches the yield point. Euler's formula gives the critical load that triggers buckling, and it drops off quickly with increasing length.

P_{cr} = \dfrac{\pi^2EI}{(KL)^2}

Euler buckling load

Symbols

$P_{cr}$	critical buckling load	N
$I$	smallest second moment of area	m⁴
$K$	effective length factor
$L$	column length	m

Example

A steel column pinned at both ends ( $K=1$ ), $L = 2$ m, $I = 5\cdot10^5$ mm⁴:

$P_{cr} = \pi^2\cdot 210\,000\cdot 5\cdot10^5/2000^2 \approx 259$ kN.

Doubling the length quarters the buckling load – use the smallest

I

of the section.

Practise stress transformation and buckling for free →

← Von Mises stress · Effective length →

Part of Strength of Materials: Stress transformation and buckling.