Which units does the calculator use?

Material stresses are in MPa (N/mm²), geometry in mm and mm⁴, length in m (converted to mm internally), and forces are reported in kN. This keeps formulas dimensionally consistent with Eurocode practice.

How is the non-dimensional slenderness λ̄ computed?

λ̄ = sqrt(A·fy / Ncr) where Ncr = π²·E·I / Le². The effective length Le depends on end restraints via the factor k.

Which buckling curve should I select?

Eurocode 3 Table 6.1 assigns curves based on section type, axis, and fabrication. As a rule: curve a0 or a for favorable shapes, b/c for typical hot-rolled I-sections, and d for less favorable members. Always confirm with the relevant product standard/NA.

Which partial factors are used?

By default γM0 = 1.0 and γM1 = 1.0 (recommended values). Your National Annex may prescribe different values. You can override them in the calculator.

Does the tool check local buckling or class?

This tool focuses on member buckling resistance in compression per EN 1993-1-1 Clause 6.3. It assumes an adequate cross-section class for the plastic resistance provided. Check local buckling/class separately where required.

Can I rely on this calculator for final design?

Use it for preliminary and verification calculations. Always apply engineering judgment and consult the full Eurocode text and your National Annex before issuing design documents.

Eurocode 3 Steel Column Compression & Buckling Calculator

This professional-grade tool computes the axial compression buckling resistance of steel columns according to Eurocode 3 (EN 1993-1-1). It is designed for structural engineers and advanced students to verify design capacity, slenderness and utilization rapidly and accurately.

Calculator

Governing buckling axis *

About y-axis (use Iy)

About z-axis (use Iz)

Cross-sectional area A *

mm²

Second moment of area Iy

mm⁴

Second moment of area Iz

mm⁴

Steel yield strength fy *

MPa

Modulus of elasticity E *

MPa

Member length L *

End restraints (effective length) *

Buckling curve (imperfection factor α) *

Partial factor γM0

–

Partial factor γM1

–

Applied design axial load NEd

Results

Effective length Le – mm (– m)

Euler critical load Ncr –

Non-dimensional slenderness λ̄ –

Imperfection α / φ / χ –

Section plastic resistance Npl,Rd –

Buckling resistance Nb,Rd –

Utilization η = NEd / Nb,Rd –

Status Awaiting input

Data Source and Methodology

Authoritative source: EN 1993-1-1:2005 + A1:2014 Eurocode 3 — Design of steel structures — Part 1-1: General rules and rules for buildings, Clause 6.3 (Member buckling in compression). Official overview: European Commission – JRC Eurocodes. Additional context: Eurocode Applied.

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formula Explained

$$ N_{b,Rd} = \chi \cdot \frac{A\, f_y}{\gamma_{M1}} $$ $$ \chi = \frac{1}{\varphi + \sqrt{\varphi^2 - \bar{\lambda}^2}} \quad \text{with} \quad \varphi = \tfrac{1}{2}\left[1 + \alpha\left(\bar{\lambda} - 0.2\right) + \bar{\lambda}^2 \right] $$ $$ \bar{\lambda} = \sqrt{\frac{A f_y}{N_{cr}}}, \qquad N_{cr} = \frac{\pi^2 E I}{L_e^2}, \qquad L_e = k \cdot L $$ $$ N_{pl,Rd} = \frac{A\, f_y}{\gamma_{M0}} $$ where: A [mm²], E [MPa], fy [MPa], I [mm⁴], L [mm], k [–], α per buckling curve.

Glossary of Variables

Definitions of inputs and outputs
Symbol	Name	Unit	Description
A	Area	mm²	Gross cross-sectional area of the member.
Iy, Iz	Second moment of area	mm⁴	About y or z axis. Choose the governing axis.
fy	Yield strength	MPa	Characteristic yield stress of steel.
E	Elastic modulus	MPa	Modulus of elasticity of steel (≈210000 MPa).
L	Member length	m	Clear length between effective restraints.
k	Effective length factor	–	Depends on end restraints; Le = k·L.
Le	Effective length	mm	Used in Euler buckling check.
Ncr	Euler critical load	kN	Ideal elastic buckling load.
λ̄	Non-dimensional slenderness	–	EC3 slenderness parameter, function of Ncr.
α	Imperfection factor	–	Set by the chosen buckling curve.
φ	Auxiliary factor	–	Used to compute reduction factor χ.
χ	Reduction factor	–	Reduces plastic strength for buckling.
Npl,Rd	Plastic section resistance	kN	A·fy/γM0.
Nb,Rd	Buckling resistance	kN	χ·A·fy/γM1.
NEd	Design axial load	kN	Applied factored compression action.
η	Utilization	–	NEd / Nb,Rd.

How It Works: A Step-by-Step Example

Given: A = 6500 mm², Iy = 8.5e8 mm⁴, Iz = 2.4e8 mm⁴, fy = 355 MPa, E = 210000 MPa, L = 3.0 m, end condition pinned–pinned (k = 1.0), buckling about y-axis, curve b (α = 0.34), γM0 = γM1 = 1.0.

Effective length: Le = k·L = 1.0 × 3.0 m = 3000 mm.
Euler load about y: Ncr = π² E Iy / Le².
Slenderness: λ̄ = sqrt(A·fy / Ncr).
φ = 0.5 [1 + α(λ̄ − 0.2) + λ̄²] and χ = 1 / (φ + sqrt(φ² − λ̄²)).
Npl,Rd = A·fy/γM0 and Nb,Rd = χ·A·fy/γM1. If NEd = 850 kN, utilization η = 850 / Nb,Rd.

The calculator performs these steps instantly and displays intermediate values so you can audit the calculation.

Frequently Asked Questions (FAQ)

What differentiates curves a0, a, b, c, d?

They represent different sensitivity to imperfections and residual stresses. Less favorable curves (higher α) produce lower χ at a given slenderness. Use the Eurocode’s Table 6.1 and your NA to select the correct curve.

Can I enter radius of gyration instead of I?

Yes indirectly: I = A·i². If you know i, compute I and enter it. Future versions will add a dedicated toggle.

Does the tool include shear or bending interaction?

No. This module covers pure axial compression buckling. For combined bending and axial force, use EC3 interaction checks per Clause 6.3.3.

Why do I see χ = 1.0 for very stocky members?

At very low slenderness, buckling is not governing and χ approaches 1.0 (limited slightly below 1.0 per EC3 expression).

What accuracy/rounding is used?

Internally the tool uses full precision JS floating-point and reports values rounded to sensible engineering units (e.g., kN with two decimals).

Tool developed by Ugo Candido. Content verified by CalcDomain Engineering Editorial.
Last reviewed for accuracy on: September 14, 2025.