Eurocode 4 Composite Beam Design Calculator (EN 1994-1-1)
Quickly check plastic bending resistance and shear connection for a simply supported steel–concrete composite beam according to Eurocode 4.
Composite Beam Input
1. Geometry & Materials
2. Design Actions
3. Shear Connection
Assumes symmetric arrangement of shear connectors; total studs on the beam = 2 × this value.
Results
Enter your data and click “Run Eurocode 4 Checks” to see utilisation ratios and shear connection degree.
Eurocode 4 composite beam design – overview
Eurocode 4 (EN 1994-1-1) covers the design of composite steel–concrete structures. For typical building floors, composite beams consist of a rolled or welded steel section connected to a reinforced concrete slab by shear connectors (usually headed studs).
Compared with a bare steel beam, a composite beam has higher bending resistance and stiffness in sagging regions, because the concrete slab carries compression while the steel section carries most of the tension.
Key design checks for composite beams
- Ultimate limit state (ULS) bending resistance of the composite section in sagging.
- Shear connection – degree of shear connection between steel and concrete.
- Shear resistance of the steel web and connectors.
- Serviceability limit state (SLS) – deflections and crack control (not fully covered in this quick tool).
Formulas used (simplified EN 1994-1-1 approach)
1. Effective concrete flange in compression
For a simply supported composite beam in sagging, the concrete slab above the steel beam is in compression. The calculator uses the effective width \( b_\text{eff} \) you provide.
Concrete area in compression:
\( A_c = b_\text{eff} \cdot h_c \)
Design compressive force in concrete:
\( C_{c,Rd} = 0.85 \cdot \dfrac{f_{ck}}{\gamma_C} \cdot A_c \)
2. Steel section in tension
For a typical I-section in sagging, the bottom flange and part of the web are in tension. For a quick check, this tool assumes the whole steel section can reach yield in tension:
Steel area (approximate):
\( A_a \approx 2 b_f t_f + (h_a - 2 t_f) t_w \)
Design tensile force in steel:
\( T_{a,Rd} = \dfrac{f_{yk}}{\gamma_{M0}} \cdot A_a \)
3. Plastic bending resistance of composite section
The plastic neutral axis is assumed to lie within the concrete slab (typical for well-connected beams in buildings). The design plastic bending resistance is then:
\( M_{pl,Rd} = C_{c,Rd} \cdot z \)
where \( z \) is the lever arm between the concrete compressive force and the steel tensile force.
In this simplified tool, the lever arm is approximated as the distance between the centroid of the concrete flange and the centroid of the steel section, limited by the overall depth.
4. Shear connection and degree of shear connection
The total design resistance of shear connectors in one half-span is:
\( \sum P_{Rd} = N_\text{stud} \cdot P_{Rd} \)
where:
- \( N_\text{stud} \) = number of studs per half-span
- \( P_{Rd} \) = design resistance of one stud
The required longitudinal shear force for full interaction is approximated as the smaller of the concrete and steel axial capacities:
\( F_{c,Rd} = \min(C_{c,Rd}, T_{a,Rd}) \)
Degree of shear connection:
\( \eta = \dfrac{\sum P_{Rd}}{F_{c,Rd}} \)
Eurocode 4 specifies minimum degrees of shear connection depending on span, loading and ductility requirements. This tool highlights whether the provided studs are sufficient for full interaction (\( \eta \ge 1.0 \)) and reports the actual degree.
5. Utilisation ratios
Bending utilisation:
\( \mu_M = \dfrac{M_{Ed}}{M_{pl,Rd}} \)
Shear connector utilisation:
\( \mu_\eta = \dfrac{1}{\eta} \) (for full interaction target)
Values ≤ 1.0 indicate that the design satisfies the simplified checks. For detailed design, you must also verify shear, deflection, fatigue (where relevant), and detailing rules directly from EN 1994-1-1 and related Eurocodes.
Limitations and engineering judgement
- Assumes a simply supported beam in sagging bending only.
- Assumes the plastic neutral axis lies in the slab (no check for deep neutral axis in the web).
- Does not check web shear buckling, local buckling, or lateral–torsional buckling.
- Does not include construction stage checks (bare steel beam before composite action).
Always cross-check results with hand calculations or specialist software (e.g. Tekla Structural Designer, MasterSeries) for final design and documentation.
FAQ
Can I use this for precast slabs?
The principles are similar, but Eurocode 4 has specific rules for composite beams with precast units and in-situ topping. This quick tool assumes a solid or composite slab behaving as an effective flange; for precast systems, consult EN 1994-1-1 and the relevant National Annex.
How should I choose the effective slab width?
EN 1994-1-1 refers to EN 1992-1-1 for effective flange widths. For internal beams, a common approximation is the lesser of L/8 on each side of the web and the actual half-spacing to adjacent beams. For edge beams, the effective width is usually smaller on the outer side.