Eurocode 4 Composite Steel–Concrete Design Calculator (EN 1994)
Quick helper for preliminary design of composite steel–concrete beams and columns according to Eurocode 4 (EN 1994‑1‑1). Not a substitute for full code checks.
Composite Beam Design (Eurocode 4) EN 1994‑1‑1, mainly §§6.2–6.6
This module estimates the plastic bending resistance of a simply supported composite beam in the sagging region and the required shear connectors for a given design moment. It assumes:
- Full interaction along the span (unless limited by studs).
- Uniform slab over the steel beam, no openings.
- Concrete in compression only, steel in tension/compression.
Steel section (I‑beam)
Use major‑axis plastic modulus of bare steel section.
Approximate lever arm for steel tension.
Concrete slab (effective width)
Shear connectors & design moment
From EN 1994‑1‑1 §6.6.3.1 for headed studs.
How this Eurocode 4 composite design helper works
Eurocode 4 (EN 1994‑1‑1 and EN 1994‑1‑2) covers composite steel–concrete structures such as beams, slabs and columns. The official code and commentaries are extensive; this tool focuses on a few key design quantities that are useful in early sizing and quick checks:
- Plastic bending resistance of a composite beam in sagging bending.
- Required and provided shear connection (headed studs) and degree of shear connection η.
- Simplified axial resistance of a short composite column.
The calculations follow the general philosophy of Eurocode 4 but use simplified assumptions and do not replace a full code‑compliant design. Always verify final designs with the full EN 1994 text and relevant National Annex.
1. Composite beam design – key formulas
For a composite beam in sagging bending, the concrete slab is in compression and the steel section mainly in tension. The plastic resistance is governed by the smaller of the compressive capacity of the slab and the tensile capacity of the steel section, provided that enough shear connectors are installed to develop full interaction.
1.1 Concrete compression force
Effective concrete area:
\[ A_{c,eff} = b_{eff} \cdot h_c \]
Design compressive strength of concrete:
\[ f_{cd} = \frac{0.85 \, f_{ck}}{\gamma_c} \]
Concrete compression force (limited by concrete):
\[ N_{c,Rd} = A_{c,eff} \, f_{cd} \]
1.2 Steel tension force
Design yield strength of steel:
\[ f_{yd} = \frac{f_y}{\gamma_M} \]
Steel tension force:
\[ N_{a,Rd} = A_a \, f_{yd} \]
The governing axial force in the composite section is the smaller of the two:
\[ N_{pl,Rd} = \min(N_{c,Rd},\, N_{a,Rd}) \]
1.3 Plastic bending resistance
The plastic bending resistance is approximated by multiplying the governing force by an internal lever arm between the concrete compression resultants and the steel tension resultants. In this simplified helper we use an approximate lever arm based on the distance between the plastic neutral axis and the steel centroid:
\[ M_{pl,Rd} \approx N_{pl,Rd} \cdot z_a \]
where \(z_a\) is entered directly as an approximate lever arm (in metres in the internal calculation).
1.4 Shear connection and degree of shear connection η
Headed studs (or other shear connectors) must be provided to transfer longitudinal shear between steel and concrete. The total design shear resistance of all studs in the span is:
\[ \sum P_{Rd} = n \cdot P_{Rd} \]
For full shear connection, the required longitudinal shear is approximately equal to the concrete compression force \(N_{c,Rd}\). The degree of shear connection is then:
\[ \eta = \frac{\sum P_{Rd}}{N_{c,Rd}} \]
Eurocode 4 sets minimum values for η depending on span, loading and whether the beam is in a building or bridge. As a rough guide, values above 0.8–1.0 are typically required for full or near‑full interaction.
2. Composite column design – simplified axial resistance
For a short composite column with full interaction and no significant bending, the design axial resistance can be approximated as the sum of the design resistances of the steel and concrete components:
Steel contribution:
\[ N_{a,Rd} = \frac{A_a \, f_y}{\gamma_a} \]
Concrete contribution (with reduction factor ηc):
\[ N_{c,Rd} = \eta_c \, \frac{A_c \, f_{ck}}{\gamma_c} \]
Total axial resistance:
\[ N_{Rd} = N_{a,Rd} + N_{c,Rd} \]
The utilisation ratio shown by the calculator is:
\[ \text{Utilisation} = \frac{N_{Ed}}{N_{Rd}} \]
In a full Eurocode 4 design, additional checks are required for buckling, second‑order effects, imperfections, interaction with bending moments, and detailing rules for reinforcement and shear connection.
3. Typical workflow with this tool
- Select Composite beam or Composite column mode.
- Enter material strengths, section properties and partial factors according to your National Annex.
- For beams, input the number and resistance of studs and the design bending moment.
- Click Calculate to see capacities and utilisation ratios.
- Adjust section sizes, slab width/thickness or number of studs until utilisation is within your target range (e.g. 0.6–0.9).
- Use the results as a starting point and perform full Eurocode 4 checks in your detailed design software or hand calculations.
4. Limitations and engineering judgement
This calculator is intended for conceptual and educational use. It does not:
- Apply all reduction factors, interaction curves or buckling checks from EN 1994‑1‑1.
- Account for fire design (EN 1994‑1‑2), local buckling, partial shear connection rules, or construction stage effects.
- Replace the need for a qualified structural engineer and a full code‑compliant design.
Always cross‑check results against the official Eurocode 4 text, National Annexes, and your organisation’s design procedures before issuing drawings or specifications.
FAQ
Is this calculator fully Eurocode 4 compliant?
No. It follows the general design philosophy and main equations for composite beams and columns, but it omits many detailed checks (buckling, interaction, serviceability, fatigue, construction stages, etc.). Use it only for quick estimates and preliminary sizing.
Where do I get accurate section properties and stud resistances?
Use manufacturer data sheets or section tables for steel beams to obtain plastic modulus and area. Stud resistances should be taken from EN 1994‑1‑1 §6.6.3 and any product approvals, considering concrete strength, stud diameter and welding details.
What utilisation ratio should I aim for?
For preliminary design, many engineers target a utilisation between 0.6 and 0.9 for ultimate limit state checks. Lower utilisation may be appropriate where stiffness or deflection controls, or where future load increases are expected.
Can I use this for composite bridges?
The underlying principles are similar, but bridge design under Eurocode 4 involves additional requirements (fatigue, dynamic effects, traffic loading, etc.). This tool is primarily oriented toward building‑type composite members.