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Column Buckling (Euler)

🏗️ Civil · Critical buckling load, stress, and slenderness ratio calculation

🧮 Calculate∑ Formula✅ Verification📚 Sources

Support Condition (K effective length factor)

Column Length L (m)

E (GPa)

I — weak axis (cm⁴)

Cross-Section Area A (cm²)

🧱 Fill from Material (optional)

Uncertainty mode (Monte Carlo, n=10,000)

Critical load Pcr654 kN

Critical stress σcr229.5 MPa

Slenderness λ = KL/r95.04

ValidityElastic buckling region

Pcr = π²EI / (KL)²

💡 Default values are for the weak axis of an HEA 100 profile. The Euler formula is only valid for elastic (slender, λ ≳ 90 in steel) columns.

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

Long, slender columns (compression members) can buckle sideways suddenly and unpredictably well before reaching their yield strength. Swiss mathematician Leonhard Euler’s 1744 work, the first mathematical explanation of this phenomenon, still forms the basis of elastic buckling analysis today.

The effective length factor (K) depends on the column’s end support conditions and converts the real length into “an equivalent pinned-pinned column length”:

Pinned at both ends: K = 1.0 (reference case)
Fixed at both ends: K = 0.5 (4× stronger)
Fixed-free (cantilever): K = 2.0 (4× weaker)

The slenderness ratio (λ = KL/r) determines the validity limit of the Euler formula. In steel columns, behavior above λ ≈ 90 is elastic buckling (Euler formula valid); below that, it’s inelastic buckling/yielding (different, separate formulas required — e.g. the Johnson parabola). This tool shows a warning when the slenderness comes out low.

✅ Verified

This tool's calculation logic has been checked against a hand-computed numerical verification test. Test source: src/lib/calc/burkulma.test.ts.

[2] Hibbeler, R. C.. Mechanics of Materials, 10 ed.. Pearson, 2017. ↗
[21] CEN. EN} 1993-1-1 (Eurocode 3) — Çelik Yapıların Tasarımı: Genel Kurallar. European Committee for Standardization, 2005. (2014'te A1 değişiklik eki ile güncellendi (EN 1993-1-1:2005+A1:2014)) ↗

Column Buckling (Euler) — EngineersLab calc card

Formula: Pcr = π²EI / (KL)²

Sources: [2] Mechanics of Materials; [21] EN} 1993-1-1 (Eurocode 3) — Çelik Yapıların Tasarımı: Genel Kurallar

Tool version: 1.1.0 · Date:

Source URL: https://engineerslab.com.tr/en/araclar/burkulma

Results are for educational and preliminary-sizing purposes; final engineering design decisions must reference the relevant standards and a licensed engineer's approval.