Euler Buckling Calculator

Estimate ideal elastic critical load for a slender column with a stated support condition.

Euler buckling uses an ideal straight, prismatic column with centric load and linear-elastic behavior. Use the weak-axis second moment of area.

End condition
Euler critical load (Pcr)4,112.171 kN924,452.743 lbf
Effective buckling length (KL)2 mK = 1

Important: the result is not an allowable load or design resistance. Real columns have imperfections, eccentricity, residual stress and connection flexibility; yielding or inelastic buckling may govern before Euler buckling.

Method

Euler's ideal critical load is Pcr = π2EI/(KL)2. The effective-length factor K is determined by the selected ideal end condition.

Worked example

A 2 m pin-ended steel column with E = 200 GPa and I = 8.333 × 106 mm4 has an ideal Euler critical load of about 4,112 kN.

Important limits

This is an ideal elastic buckling result, not an allowable or factored design capacity. It is appropriate only as a slender-column screening calculation; use the governing structural standard for inelastic behavior, imperfections, load eccentricity and safety factors.

References

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