Engineering Eurocode 3 (EN 1993) Steel Design Helper
Quickly classify steel sections and estimate bending and axial resistance according to Eurocode 3 (EN 1993‑1‑1). Ideal for preliminary design and teaching.
Disclaimer: This tool is for educational and preliminary design only. Always verify results against the full Eurocode 3 provisions and your National Annex, and have final designs checked by a qualified structural engineer.
1. Cross‑Section Classification (EN 1993‑1‑1, Cl. 5.5)
Determine the Eurocode 3 class (1–4) of an I‑section flange and web in bending about the major axis. This uses simplified limits for internal compression parts.
Material & stress
Section geometry (mm)
How this Eurocode 3 steel design helper works
This page is a compact companion to EN 1993‑1‑1 (Eurocode 3: Design of steel structures – General rules and rules for buildings). It does not replace the code, but it helps you perform the most common hand‑checks faster and with fewer mistakes.
1. Cross‑section classification (Classes 1–4)
Eurocode 3 classifies steel cross‑sections based on their susceptibility to local buckling of plates in compression. The class determines whether you may use plastic, elastic or effective section properties.
Plate slenderness for an internal compression part:
\[ \lambda_p = \frac{c}{t} \]
where \( c \) is the plate width (or outstand) and \( t \) is the plate thickness.
Eurocode 3 gives limit values \( \lambda_{p,1}, \lambda_{p,2}, \lambda_{p,3} \) that depend on the stress level and steel grade.
In this tool we use simplified expressions of the form \[ \lambda_{p,\text{limit}} = k \cdot \varepsilon, \quad \varepsilon = \sqrt{\frac{235}{f_y}} \] with different factors \( k \) for Class 1, 2 and 3, calibrated to typical values in EN 1993‑1‑1 Tables 5.2 and 5.3.
2. Bending resistance \( M_{Rd} \)
For a laterally restrained beam in pure bending about the major axis, Eurocode 3 defines:
Plastic bending resistance (Class 1 or 2):
\[ M_{pl,Rd} = \frac{W_{pl,y} \, f_y}{\gamma_{M0}} \]
Elastic bending resistance (Class 3):
\[ M_{el,Rd} = \frac{W_{el,y} \, f_y}{\gamma_{M0}} \]
The calculator automatically selects the appropriate expression based on the cross‑section class you choose and compares the design moment \( M_{Ed} \) with the design resistance \( M_{Rd} \) to give a utilization ratio.
3. Axial compression and buckling
For a member in axial compression, Eurocode 3 reduces the plastic resistance by a buckling reduction factor \( \chi \) that depends on the non‑dimensional slenderness \( \bar{\lambda} \) and the chosen buckling curve.
Plastic axial resistance:
\[ N_{pl,Rd} = \frac{A \, f_y}{\gamma_{M1}} \]
Non‑dimensional slenderness:
\[ \bar{\lambda} = \frac{L_{cr}}{i} \sqrt{\frac{f_y}{\pi^2 E}} \]
Buckling reduction factor (EN 1993‑1‑1, Eq. 6.3):
\[ \phi = 0.5 \left[1 + \alpha \left(\bar{\lambda} - 0.2\right) + \bar{\lambda}^2 \right] \]
\[ \chi = \frac{1}{\phi + \sqrt{\phi^2 - \bar{\lambda}^2}} \]
Design buckling resistance:
\[ N_{b,Rd} = \chi \, N_{pl,Rd} \]
The imperfection factor \( \alpha \) is chosen via the buckling curve (a0, a, b, c, d) according to EN 1993‑1‑1 Table 6.2. The tool lets you pick \( \alpha \) directly so you can quickly explore the effect of different curves.
Limitations and good practice
- The tool assumes uniform bending or compression and does not handle interaction formulas for combined \( N \) and \( M \).
- Lateral‑torsional buckling of beams is not checked; you must verify it separately.
- Class 4 sections are not supported; use effective section properties from EN 1993‑1‑5.
- Always apply the National Annex values for partial factors and buckling curves in real projects.