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

Design or check a singly reinforced rectangular concrete beam to Eurocode 2. Enter span, loads, section size, material strengths and cover – the tool computes design moment, required tension steel area and flexural capacity.

Beam Inputs

Design mode:

Geometry & materials

Loads & safety factors

Design mode: required tension steel As,req will be calculated from design moment MEd.

Results

Enter inputs and click “Calculate” to see design results.

How the Eurocode 2 beam design calculator works

This tool implements a simplified flexural design of a singly reinforced rectangular beam according to Eurocode 2 (EN 1992‑1‑1). It is ideal for preliminary sizing, quick checks and teaching.

1. Load model and design moment

For a simply supported beam with uniform load, the maximum bending moment at midspan is:

Self‑weight:

\( w_{sw} = 25 \,\text{kN/m}^3 \cdot b \cdot h \) (with b, h in m)

Total characteristic load:

\( w_k = w_{sw} + g_k + q_k \)

Design load (fundamental combination):

\( w_d = \gamma_G (w_{sw} + g_k) + \gamma_Q q_k \)

Design moment:

\( M_{Ed} = \dfrac{w_d L^2}{8} \)

2. Material design strengths

Concrete and steel design strengths follow EN 1992‑1‑1:

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

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

with typical values \( \alpha_{cc} = 0.85 \), \( \gamma_c = 1.5 \), \( \gamma_s = 1.15 \).

3. Effective depth and lever arm

The effective depth is:

\( d = h - c_{nom} \)

For preliminary design, the internal lever arm is approximated as:

\( z \approx 0.9 d \)

This is accurate for under‑reinforced sections where the neutral axis is relatively shallow.

4. Required tension steel area As,req

Equilibrium of internal forces gives:

\( M_{Ed} = T z = A_s f_{yd} z \)

so

\( A_{s,req} = \dfrac{M_{Ed}}{f_{yd} z} \)

5. Minimum and maximum reinforcement

Eurocode 2 specifies minimum and maximum reinforcement ratios to control cracking and ensure ductile behaviour. This tool uses typical simplified expressions:

Minimum tension steel (approx.):

\( A_{s,min} \approx 0.26 \dfrac{f_{ctm}}{f_{yk}} b d \)

Maximum tension steel (approx.):

\( A_{s,max} \approx 0.04 \, b \, h \)

If the required area is below As,min, the minimum is recommended. If it exceeds As,max, a doubly reinforced or T‑beam design is usually required.

6. Moment resistance MRd and utilization

Given a chosen As, the design moment resistance is:

\( M_{Rd} = A_s f_{yd} z \)

The utilization ratio is:

\( \eta = \dfrac{M_{Ed}}{M_{Rd}} \)

Values η ≤ 1.0 indicate that the section is adequate in bending (ignoring shear and other checks).

7. Steel strain and ductility check (simplified)

To ensure a ductile, under‑reinforced section, the steel strain at ultimate should exceed the yield strain:

\( \varepsilon_{yd} = \dfrac{f_{yd}}{E_s} \)

with \( E_s \approx 200\,000 \,\text{MPa} \).

This calculator estimates the steel strain using a simplified rectangular stress block and reports whether εs > εyd.

Limitations and engineering judgement

  • Only singly reinforced rectangular sections are covered (no compression steel, no flanges).
  • Shear design, anchorage, bar spacing, cover, crack width and deflection checks are not included.
  • National Annex parameters may differ from the default values used here.
  • Always have final designs checked and signed off by a qualified structural engineer.

Frequently asked questions

Can I use this for continuous beams?

The calculator assumes a simply supported span with a uniform load. For continuous beams, you can still use it by inputting the design moments obtained from a frame analysis, but you must override the automatic MEd and use a more advanced workflow. For now, treat this as a single‑span tool.

How do I choose fck and fyk?

Use the concrete strength class specified by your project (e.g. C25/30 → fck = 25 MPa) and the reinforcing steel grade (e.g. B500B → fyk = 500 MPa). If in doubt, consult the project specifications or your local National Annex.

Does the calculator include self‑weight?

Yes, if “Self‑weight included?” is set to “Yes”. The beam self‑weight is computed from the section dimensions and a density of 25 kN/m³. If you already accounted for self‑weight in gk, set this option to “No”.

How should I round the bar arrangement?

After obtaining As,req, select a practical bar arrangement (e.g. 3Ø20, 4Ø16) with As,prov ≥ As,req. Then use the “Check capacity” mode to verify MRd and utilization. Always check detailing rules for spacing, cover and anchorage.