Which Eurocode clauses does this tool follow?

Ultimate flexural design per EN 1992-1-1:2004, notably Sections 3.1 for material properties and stress block parameters, 2.4.2.4 for partial safety factors, and 6.1 for bending. η–λ rectangular stress block is applied with ductility limits on x/d.

Does the calculator enforce minimum tensile reinforcement?

Yes. It reports As,min per EN 1992-1-1 using As,min = max(0.26 f_ctm/f_yk × b × d, 0.0013 × b × d) with f_ctm from Table 3.1 for normal weight concrete.

Are shear and serviceability checks included?

No. This tool focuses on ULS flexural design. Verify shear, punching, deflection, crack width and anchorage separately according to EN 1992-1-1.

Inputs are in SI: lengths in mm, moments in kNm, strengths in MPa. Internally, moments are converted to Nmm for consistency.

Can I override safety factors?

Defaults are γ_c = 1.5 and γ_s = 1.15. You may adjust them to match your National Annex, but do so with care.

How are η and λ chosen?

For f_ck ≤ 50 MPa, η = 1.0 and λ = 0.8. For higher strengths, EN 1992-1-1 recommends η = 1 − (f_ck − 50)/200 and λ = 0.8 − (f_ck − 50)/400.

Eurocode 2 Concrete Beam Flexural Design Calculator

This professional-grade tool sizes tensile and compression reinforcement for rectangular reinforced concrete beams under bending per EN 1992-1-1 (Eurocode 2). It is designed for structural engineers and advanced students who need fast, transparent and standards-compliant design outputs.

Beam Inputs

Auto: add compression steel if required Force singly reinforced (warn if insufficient)

Design bending moment M_Ed *

kNm

Beam width b *

Overall depth h *

Nominal cover c_nom *

Stirrup diameter

Assumed tension bar diameter

Assumed compression bar diameter

Materials

Concrete cylinder strength f_ck *

MPa

Steel yield strength f_yk *

MPa

Partial factor γ_c

Partial factor γ_s

Results

Effective depths d = — mm, d′ = — mm

Material design strengths f_cd = — MPa, f_yd = — MPa

Neutral axis and lever arm x = — mm, z = — mm

Required tensile steel As — mm²

Compression steel As′ (if needed) — mm²

Minimum tensile steel As,min — mm²

Singly reinforced limit M_Rd,lim — kNm

Bar suggestion (tension) —

Status Awaiting input…

Data Source and Methodology

Authoritative source: EN 1992-1-1:2004 (Eurocode 2) — Design of concrete structures — Part 1-1: General rules and rules for buildings. Official PDF: EN 1992-1-1:2004. Sections referenced include 2.4.2.4 (material safety factors), 3.1 (material properties and stress block parameters), and 6.1 (bending).

All calculations strictly follow the formulas and data provided by this source.

The Formula Explained

Design strengths:

f_cd = α_cc · f_ck / γ_c, f_yd = f_yk / γ_s

Rectangular stress block (for normal-weight concrete):

η = 1.0, λ = 0.8 for f_ck ≤ 50 MPa; otherwise η = 1 − (f_ck − 50)/200, λ = 0.8 − (f_ck − 50)/400

Effective depths:

d = h − c_nom − ϕ_link − 0.5·ϕ_tension, d′ = c_nom + ϕ_link + 0.5·ϕ_compression

Ductility limit on neutral axis depth:

x_lim = ξ_lim · d, where ξ_lim = 0.45 for f_ck ≤ 50 MPa (use 0.35 otherwise)

Nominal internal forces and moment:

C_c = b · η · f_cd · λ · x

z = d − 0.5·λ·x

Singly reinforced resistance:

M_Rd = C_c · z

Required tensile steel when M_Ed ≤ M_Rd,lim:

A_s = C_c / f_yd = b · η · f_cd · λ · x / f_yd

With doubly reinforcement when M_Ed > M_Rd,lim:

M_Rd,lim at x = x_lim; A_s,lim = b · η · f_cd · λ · x_lim / f_yd

M_2 = M_Ed − M_Rd,lim; A_s′ = A_s2 = M_2 / (f_yd · (d − d′)); A_s,total = A_s,lim + A_s2

Minimum tensile steel (EN 1992-1-1):

A_s,min = max(0.26·f_ctm/f_yk · b·d, 0.0013 · b·d)

Mean tensile strength (normal-weight): f_ctm ≈ 0.30·f_ck^(2/3)

Glossary of Variables

M_Ed: Design bending moment (kNm)
b, h: Beam width and overall depth (mm)
c_nom: Nominal cover (mm)
ϕ_link, ϕ_tension, ϕ_compression: Stirrup, tension bar and compression bar diameters (mm)
d, d′: Effective depths to tension and compression reinforcement (mm)
f_ck, f_yk: Concrete and steel characteristic strengths (MPa)
γ_c, γ_s: Partial safety factors for concrete and steel (–)
f_cd, f_yd: Design strengths (MPa)
η, λ: Stress-block factors (–)
x: Neutral axis depth (mm); x_lim: code ductility limit (mm)
z: Lever arm (mm)
A_s: Required tensile steel area (mm²); A_s′: compression steel area (mm²)
A_s,min: Minimum tensile steel per code (mm²)

Worked Example — Step by Step

How It Works: A Step-by-Step Example

Given: b = 300 mm, h = 550 mm, c_nom = 30 mm, ϕ_link = 8 mm, ϕ_tension = 20 mm, ϕ_compression = 16 mm, M_Ed = 200 kNm, f_ck = 30 MPa, f_yk = 500 MPa, γ_c = 1.5, γ_s = 1.15.

Effective depths: d = 550 − 30 − 8 − 0.5×20 = 512 mm; d′ = 30 + 8 + 0.5×16 = 46 mm.
Design strengths: f_cd = 1.0×30/1.5 = 20 MPa; f_yd = 500/1.15 ≈ 434.8 MPa. Stress-block: η = 1.0, λ = 0.8.
Ductility limit: ξ_lim = 0.45 → x_lim = 0.45×512 ≈ 230.4 mm. Then M_Rd,lim = b·η·f_cd·λ·x_lim·(d − 0.5·λ·x_lim) ≈ 300×1×20×0.8×230.4×(512 − 0.4×230.4) Nmm ≈ 2.14×10^8 Nmm = 214 kNm.
Since M_Ed = 200 kNm ≤ 214 kNm, singly reinforced. Solve M_Ed = C_c·z to find x, then A_s = C_c/f_yd. The calculator does this automatically and returns A_s and bar suggestions.

Finally, verify A_s ≥ A_s,min per EN 1992-1-1. If not, increase A_s to meet the minimum.

Note: Always carry out separate checks for shear, serviceability and detailing per Eurocode 2.

Frequently Asked Questions (FAQ)

Is this calculator suitable for T-beams or flanged sections?

The current version assumes a rectangular section at ULS. For T- and L-sections, determine the effective flange in compression (EN 1992-1-1 5.3) and use an equivalent rectangular web if applicable.

What if my National Annex specifies different γ factors?

You can override γ_c and γ_s. Ensure you apply the correct values mandated by your jurisdiction.

Does the tool consider bar spacing and cover checks?

It provides bar count suggestions only. You must verify spacing, cover, anchorage and lap lengths per EN 1992-1-1 Section 8.

How accurate is the rectangular stress block approach?

It is the normative method in EN 1992-1-1 for ULS flexure and yields conservative, code-compliant results when parameters (η, λ) are applied correctly.

Can I input a negative moment for hogging regions?

Yes, but interpret the tension zone accordingly. The tool focuses on magnitudes; placement of tension reinforcement depends on moment sign.

What strength class mapping should I use?

For example, C25/30 → f_ck = 25 MPa; C30/37 → f_ck = 30 MPa. Use cylinder strengths for f_ck.

Tool developed by Ugo Candido. Content verified by CalcDomain Engineering Editors.
Last reviewed for accuracy on: September 14, 2025.