What is Euler buckling?

Euler buckling is the sudden lateral deflection of a slender column under axial compression. The critical load Pcr = π²EI/(KL)² is the maximum axial load before buckling occurs. Below Pcr, the column remains straight; at Pcr, it becomes unstable.

What is the effective length factor K?

K accounts for end conditions: K=0.5 (both ends fixed), K=0.7 (one fixed, one pinned), K=1.0 (both pinned), K=2.0 (one fixed, one free/cantilever). Lower K means higher critical load.

What is the slenderness ratio?

Slenderness ratio λ = KL/r, where r is the radius of gyration. High λ (>100-120) means the column is slender and Euler's formula applies. For short columns (low λ), inelastic buckling or crushing governs.

When does Euler's formula not apply?

Euler's formula assumes elastic behavior and applies only when the critical stress σcr = Pcr/A is below the yield strength. For short/intermediate columns where σcr > σy, use Johnson's parabola or other inelastic buckling criteria.

How do I increase a column's buckling capacity?

Increase I (use a shape with more material far from the centroid), increase E (use stiffer material), reduce L (add intermediate bracing), or improve end fixity (lower K). The most effective approach depends on practical constraints.

Herramienta de ingeniería gratuita

Calculadora de pandeo de Euler

Calcule la carga crítica de pandeo, la tensión crítica y la relación de esbeltez para columnas usando la fórmula de Euler P_cr = π²EI/(KL)².

Pcr = π²EI/(KL)²K = 0.5–2.0#168

Módulo elástico E (GPa)

Momento de inercia I (cm⁴)

Área de la sección transversal A (cm²)

Longitud de la columna L (m)

Condición de extremo (factor K)

Preajustes rápidos

Resultados

Carga crítica de pandeo Pcr

—

Tensión crítica σcr

—

Relación de esbeltez λ

—

Longitud efectiva KL

—

Radio de giro r

—

Visualización del pandeo de la columna

Fórmula de pandeo de Euler

Factores de longitud efectiva

Condición de extremo	K	KL (efectiva)
Ambos extremos fijos	0.5	0.5L
Fijo–Articulado	0.7	0.7L
Ambos extremos articulados	1.0	L
Fijo–Libre (voladizo)	2.0	2L

⚠️ Nota: La fórmula de Euler se aplica solo para pandeo elástico (σ_cr < σ_y). Para columnas intermedias, use la parábola de Johnson o las curvas de columnas del Eurocódigo/AISC.