Eurocode 2 Column Design Calculator (EN 1992-1-1)

Preliminary design and check of rectangular reinforced concrete columns to Eurocode 2, including axial capacity, slenderness and second-order effects.

1. Input Data

Note: This tool is for educational and preliminary design only. Always verify with full Eurocode 2 calculations and your National Annex.

Assumptions: Rectangular prismatic column, constant section, symmetric reinforcement, predominantly axial compression with limited uniaxial bending.

Geometry

Effective height in the critical direction (after end fixity factors).

To reinforcement centreline: cnom + 0.5·ϕbar (assumed).

Materials

Design Actions (ULS)

Uniaxial bending about the strong axis (depth h).

Used for second-order amplification (5.8.8).

Longitudinal Reinforcement

Assumed symmetrically arranged.

Typical 1–4% for columns.

2. Results & Checks

Eurocode 2 Column Design – Methodology

This calculator follows the main steps of Eurocode 2 (EN 1992-1-1) for the design of axially loaded reinforced concrete columns with uniaxial bending:

  1. Determine material design strengths fcd and fyd.
  2. Compute gross section properties and slenderness λ.
  3. Check whether second-order effects must be considered.
  4. Amplify first-order moment if required (braced / unbraced frames).
  5. Estimate axial resistance NRd and utilisation.
  6. Check minimum and provided longitudinal reinforcement ratio.

1. Material design strengths

For normal-weight concrete, Eurocode 2 defines the design compressive strength:

\( f_{cd} = \dfrac{\alpha_{cc} \, f_{ck}}{\gamma_c} \)

where typically αcc = 0.85 (may vary by National Annex), fck is the characteristic cylinder strength (MPa) and γc is the partial factor for concrete.

For reinforcing steel:

\( f_{yd} = \dfrac{f_{yk}}{\gamma_s} \)

2. Slenderness and effective length

The non-dimensional slenderness λ in the critical direction is:

\( \lambda = \dfrac{l_0}{i} \)

where l0 is the effective height and i is the radius of gyration of the section in the bending plane.

For a rectangular section of width b and depth h, bending about the strong axis (depth h):

\( A_c = b \, h \)    \( I = \dfrac{b h^3}{12} \)    \( i = \sqrt{\dfrac{I}{A_c}} \)

3. Slenderness limit λlim

Eurocode 2 clause 5.8.3.1 provides a simplified slenderness limit λlim above which second-order effects must be considered. A common approximation for braced columns is:

\( \lambda_{lim} \approx 20 \, \phi \, \sqrt{\dfrac{A_c}{A_s}} \)

where φ is an imperfection factor (often ≈ 1.0 for typical columns). This tool uses a conservative simplified expression calibrated for typical building columns.

If λ ≤ λlim, second-order effects may be neglected. Otherwise, they must be included.

4. Second-order effects (moment magnification)

For slender columns in braced frames, Eurocode 2 allows a moment magnification approach:

\( M_{Ed,2} = k \, M_{0Ed} \)

\( k = \dfrac{1}{1 - \dfrac{N_{Ed}}{N_{cr}}} \)

The critical buckling load Ncr for a pinned-pinned column is:

\( N_{cr} = \dfrac{\pi^2 E_{cm} I}{l_0^2} \)

where Ecm is the secant modulus of concrete (Eurocode 2 Table 3.1).

5. Axial resistance NRd

For a short column under predominant compression, a conservative estimate of the design axial resistance is:

\( N_{Rd} \approx \nu \, f_{cd} \, A_c + A_s \, f_{yd} \)

where ν is a reduction factor for concrete strength in compression (often ≈ 0.6–0.7 for columns, depending on slenderness and confinement).

The utilisation ratio is then:

\( \eta_N = \dfrac{N_{Ed}}{N_{Rd}} \)

6. Minimum longitudinal reinforcement

Eurocode 2 clause 9.5.2 specifies minimum longitudinal reinforcement for columns:

\( \rho_{l,min} = \max\left(0.10 \dfrac{N_{Ed}}{A_c f_{cd}}, \; 0.002\right) \)

and the maximum reinforcement ratio is typically 4% (ρl,max = 0.04).

The provided reinforcement ratio is:

\( \rho_{l,prov} = \dfrac{A_{s,prov}}{A_c} \)

Worked Example

Consider the default input values:

  • b = 300 mm, h = 500 mm, L0 = 3.0 m
  • Concrete C25/30 (fck = 25 MPa), steel fyk = 500 MPa
  • NEd = 1500 kN, MEd = 60 kNm, M0Ed = 50 kNm
  • 8Ø16 longitudinal bars

After clicking “Calculate”, the tool will report the slenderness λ, whether second-order effects are required, the amplified design moment MEd,2, the estimated axial resistance NRd, and whether the provided reinforcement satisfies minimum and strength requirements.

Limitations & Good Practice

  • The calculator assumes symmetric reinforcement and uniaxial bending only.
  • Shear, confinement, detailing (lap lengths, anchorage, ties) are not checked.
  • Interaction between axial load and bending is treated approximately; for heavily loaded or slender columns, use full interaction diagrams or specialised software.
  • Always apply the National Annex to Eurocode 2 for your country (values of γ, αcc, Ecm, etc.).

FAQ

Can I design circular columns with this tool?

The current version is tailored to rectangular sections. For circular columns, the same principles apply but section properties and reinforcement layout differ. A dedicated circular-column module is recommended.

How accurate is the moment magnification method?

For typical building columns with moderate slenderness, the Eurocode 2 moment magnification approach gives results close to more advanced second-order analysis. For very slender columns or irregular frames, a full 2nd-order frame analysis is preferable.

Which safety factors should I use?

Default values γc = 1.5 and γs = 1.15 are common, but your National Annex may specify different values. Always check your local code requirements.