Column buckling

Linear eigenvalue buckling of a column: the first three critical loads, their mode shapes, the effective length and the critical load factor — solved exactly from the end conditions, not from a table.

FREE · NO SIGN-UP v1.0.0 · verified against 5 textbook cases

INPUTUNITS: SI · kN · m

1 · End conditions bottom – top

2 · Column length m 3 · Axial load N_Ed optional — gives α_cr kN

4 · Material & section Material Section

Results update as you type. The same end conditions are used about both axes; the weaker one governs.

BUCKLING MODESpinned – pinned · z–z axis

P_CR · Z–Z AXIS1730.6 kN

LOAD FACTOR α_CR3.46

L_CR = K·L · K = 1.0004.00 m

SLENDERNESS λ̄—

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HOW IT'S CALCULATED · WITH YOUR NUMBERS

Step by step, with your numbers

01
Equilibrium████ ██ ███████ · ██████ = ██.██
02
Reactions████ ██ ███████ · ██████ = ██.██
03
Shear force████ ██ ███████ · ██████ = ██.██
04
Bending moment████ ██ ███████ · ██████ = ██.██
05
Deflection████ ██ ███████ · ██████ = ██.██
06
Stress████ ██ ███████ · ██████ = ██.██

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Reference: Timoshenko & Gere, Theory of Elastic Stability — Euler column eigenvalues.

BEYOND AN IDEAL COLUMN

Frames, shells, imperfections, non-linear buckling — we run the full stability analysis.

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