Eurocode 3 Steel Column Design Calculator (Compression & Buckling)

Design steel columns in axial compression according to EN 1993-1-1:2005 (Eurocode 3). Compute plastic resistance, buckling resistance, non‑dimensional slenderness and utilization in seconds.

Column Input Data

Assumptions

  • Axially loaded prismatic steel column (no bending).
  • Design according to EN 1993‑1‑1, Annex A / Table 6.2.
  • Single buckling axis at a time (major or minor).
m
mm²
mm⁴
mm⁴
kN

Design Results

Enter data and click “Calculate” to see Eurocode 3 column checks.

How the Eurocode 3 Column Design Calculator Works

This tool follows EN 1993‑1‑1:2005 (Eurocode 3) for axially compressed steel members. It computes the plastic resistance of the cross‑section, the non‑dimensional slenderness, the reduction factor for buckling, and the design buckling resistance.

1. Plastic axial resistance of the cross‑section

The plastic resistance to compression of the cross‑section is:

\( N_{pl,Rd} = \dfrac{A \cdot f_y}{\gamma_{M0}} \)
  • \(A\) – cross‑section area [mm²]
  • \(f_y\) – yield strength [MPa = N/mm²]
  • \(\gamma_{M0}\) – partial factor for resistance of cross‑sections (typically 1.0)

The calculator converts the result to kN.

2. Effective length and Euler critical load

The effective length is:

\( L_{cr} = k \cdot L \)

where \(L\) is the system length and \(k\) is the effective length factor depending on end restraints.

The Euler critical load for the chosen buckling axis is:

\( N_{cr} = \dfrac{\pi^2 \cdot E \cdot I}{L_{cr}^2} \)
  • \(E\) – Young’s modulus (taken as 210 000 MPa)
  • \(I\) – second moment of area about the relevant axis [mm⁴]

3. Non‑dimensional slenderness

Eurocode 3 defines the non‑dimensional slenderness as:

\( \lambda = \sqrt{\dfrac{A \cdot f_y}{N_{cr}}} \)

4. Buckling curve and imperfection factor α

Depending on the section type and buckling axis, Eurocode 3 assigns a buckling curve (a0, a, b, c, d) with an imperfection factor α. Typical values are:

  • Curve a0: α = 0.13
  • Curve a: α = 0.21
  • Curve b: α = 0.34
  • Curve c: α = 0.49
  • Curve d: α = 0.76

5. Reduction factor for buckling χ

The reduction factor χ is obtained from:

\( \phi = 0.5 \left[ 1 + \alpha \left( \lambda - 0.2 \right) + \lambda^2 \right] \)
\( \chi = \dfrac{1}{\phi + \sqrt{\phi^2 - \lambda^2}} \)

and limited to χ ≤ 1.0.

6. Design buckling resistance

The design buckling resistance of the column is:

\( N_{b,Rd} = \dfrac{\chi \cdot A \cdot f_y}{\gamma_{M1}} \)

where \(\gamma_{M1}\) is the partial factor for member buckling (often 1.0).

7. Utilization ratio

The utilization of the column in pure compression is:

\( \eta = \dfrac{N_{Ed}}{N_{b,Rd}} \)

If η ≤ 1.0, the column satisfies the Eurocode 3 buckling check for the given design load NEd. The calculator highlights the result as “OK” or “Not OK” for quick assessment.

Design Tips and Typical Choices

  • Use the major axis (y‑y) for strong‑axis buckling and the minor axis (z‑z) for weak‑axis checks.
  • Choose the buckling curve according to EN 1993‑1‑1 Table 6.2 for your section type (rolled I‑section, welded, hollow section, etc.).
  • For braced frames with pinned ends, k ≈ 1.0 is usually appropriate; for cantilevers, k ≈ 2.0.
  • Always verify section class and interaction with bending and shear when applicable.

Disclaimer

This calculator is intended as a quick design aid and educational tool. It does not replace a full Eurocode 3 design, detailed checks for combined bending and compression, local buckling, or connection design. Always verify results and apply professional engineering judgment before using them in practice.