Eurocode 4 Composite Column Design Calculator (EN 1994-1-1)
Quickly estimate the design axial resistance of steel–concrete composite columns according to Eurocode 4 (EN 1994‑1‑1), combining steel, concrete and reinforcement contributions.
Composite Column Axial Resistance (Npl,Rd)
Scope & assumptions
- Based on EN 1994‑1‑1 plastic resistance of composite compression members (Class 1–3).
- Axial compression only (no bending, no buckling check).
- Uniform cross-section, full shear connection, normal-weight concrete.
Eurocode 4 composite column design – method overview
Eurocode 4 (EN 1994‑1‑1) provides rules for the design of composite steel–concrete columns. For Class 1–3 cross-sections in pure compression, the design axial resistance can be obtained from the plastic resistance of the composite section, combining the contributions of:
- the structural steel profile (I‑section, hollow section, etc.),
- the concrete encasement or infill, and
- any longitudinal reinforcing bars.
Plastic axial resistance of composite cross-section
For a short composite column in uniform compression (no buckling), EN 1994‑1‑1 allows the design resistance to be taken as:
\( N_{pl,Rd} = \dfrac{A_s f_{y,a}}{\gamma_{M}} + \dfrac{A_c \alpha_{cc} f_{ck}}{\gamma_{C}} + \dfrac{A_{sl} f_{y,d}}{\gamma_{M}} \)
where:
- \(A_s\) = area of structural steel section (mm² or cm²)
- \(f_{y,a}\) = yield strength of structural steel (MPa)
- \(A_c\) = effective concrete area in compression
- \(\alpha_{cc}\) = coefficient for long‑term effects and type of loading (≈ 0.85)
- \(f_{ck}\) = characteristic cylinder strength of concrete (MPa)
- \(A_{sl}\) = area of longitudinal reinforcement
- \(f_{y,d}\) = yield strength of reinforcement (MPa)
- \(\gamma_M, \gamma_C\) = material partial factors (National Annex)
The calculator implements this expression in a unit‑consistent way, converting areas given in cm² and stresses in MPa into kN. It then compares the resulting \( N_{pl,Rd} \) with the design axial load \( N_{Ed} \) to obtain a utilization ratio.
Step‑by‑step calculation procedure
- Input geometry and materials. Determine the steel area \(A_s\), concrete area \(A_c\) and reinforcement area \(A_{sl}\) from your chosen section (e.g. encased I‑section, CFST).
- Choose material strengths. Use characteristic values \(f_{y,a}\), \(f_{ck}\), \(f_{y,d}\) according to EN 1993‑1‑1 and EN 1992‑1‑1.
- Apply partial factors. Select \(\gamma_M\) and \(\gamma_C\) according to your National Annex (default values are provided for quick checks).
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Compute each contribution.
- Steel: \( N_{a,Rd} = A_s f_{y,a} / \gamma_M \)
- Concrete: \( N_{c,Rd} = A_c \alpha_{cc} f_{ck} / \gamma_C \)
- Rebar: \( N_{s,Rd} = A_{sl} f_{y,d} / \gamma_M \)
- Sum to get total resistance. \( N_{pl,Rd} = N_{a,Rd} + N_{c,Rd} + N_{s,Rd} \).
- Check utilization. Compute \( \eta = N_{Ed} / N_{pl,Rd} \). For the cross‑section check, Eurocode requires \( \eta \le 1.0 \).
Worked example (encased I‑section)
Consider a composite column with:
- Steel I‑section: \(A_s = 80\ \text{cm}^2\), \(f_{y,a} = 355\ \text{MPa}\)
- Concrete encasement: \(A_c = 900\ \text{cm}^2\), \(f_{ck} = 30\ \text{MPa}\)
- Longitudinal reinforcement: \(A_{sl} = 8\ \text{cm}^2\), \(f_{y,d} = 500\ \text{MPa}\)
- \(\alpha_{cc} = 0.85\), \(\gamma_M = 1.0\), \(\gamma_C = 1.5\)
Using the calculator (areas in cm², stresses in MPa):
- Steel: \( N_{a,Rd} \approx 2\,840\ \text{kN} \)
- Concrete: \( N_{c,Rd} \approx 15\,300\ \text{kN} \)
- Rebar: \( N_{s,Rd} \approx 400\ \text{kN} \)
- Total: \( N_{pl,Rd} \approx 18\,540\ \text{kN} \)
If the design axial load is \( N_{Ed} = 4\,000\ \text{kN} \), the utilization is \( \eta \approx 0.22 \), so the cross‑section axial resistance is adequate. A full design would then check buckling, interaction with bending, and detailing.
Limitations and engineering judgement
- The tool does not perform member buckling checks or interaction with bending moments.
- Local buckling, shear connection, fire resistance and detailing are outside its scope.
- It assumes normal‑weight concrete and full composite action along the member length.
- Always verify results against hand calculations and the full Eurocode 4 provisions.
This calculator is intended as an educational and preliminary design aid. It must not be used as the sole basis for final design decisions without review by a qualified structural engineer.
Frequently asked questions
Can I use this for slender composite columns?
You can use the calculator to obtain the cross‑section resistance \( N_{pl,Rd} \), which is also needed for slender column design. However, for slender members you must additionally determine the elastic critical load \( N_{cr} \), the reduction factor \( \chi \) and apply the appropriate interaction formulae from EN 1994‑1‑1 and EN 1993‑1‑1. Those steps are not covered here.
How should I determine the effective concrete area Ac?
For encased sections, \(A_c\) is usually the gross concrete area minus the steel section area and any large voids, subject to the limitations and reductions given in Eurocode 4 (e.g. for cover, openings, local buckling). For concrete‑filled tubes, \(A_c\) is the internal area of the tube. In all cases, follow the detailing and confinement rules in EN 1994‑1‑1.
Which partial factors should I use?
The default values in the calculator (γM = 1.0, γC = 1.5, αcc = 0.85) are typical but may differ in your National Annex. Always check the applicable National Annex and project specifications and adjust the factors accordingly.
Does the calculator check fire resistance?
No. Fire design of composite columns is covered in EN 1994‑1‑2 and requires additional reduction factors for material strengths, temperature distributions, and sometimes simplified or advanced calculation models. This tool is limited to ambient temperature ultimate limit state checks.