Free Eurocode 2 Structural Design Tools – RC Beams, Slabs, Columns & Deflection
Calculate the required tension reinforcement area for a singly or doubly reinforced rectangular RC beam under a design bending moment, to Eurocode 2 (BS EN 1992-1-1). Based on the simplified rectangular stress block method.
Design shear links (stirrups) for a rectangular RC beam to Eurocode 2 using the variable strut inclination method. Calculates minimum link spacing and checks shear capacity.
Design tension reinforcement for a one-way spanning solid RC slab per unit width (1m strip) to Eurocode 2. Includes span-to-depth ratio check for deflection control.
Calculate the axial load capacity of a short rectangular or circular RC column under concentric axial load, and check minimum/maximum reinforcement requirements to Eurocode 2.
Check whether a beam or slab satisfies the simplified span-to-depth deflection limit in Eurocode 2. This method avoids a full deflection calculation for most standard cases.
Calculate design loads for ULS (Ultimate Limit State) and SLS (Serviceability Limit State) using Eurocode 0 (EN 1990) load combination expressions for buildings. Covers expression 6.10, 6.10a/b, and characteristic / quasi-permanent SLS combinations.
| Grade | fck (N/mm²) | fcm (N/mm²) | fctm (N/mm²) | Ecm (GPa) | εcu2 (‰) |
|---|---|---|---|---|---|
| C20/25 | 20 | 28 | 2.21 | 30 | 3.5 |
| C25/30 | 25 | 33 | 2.56 | 31 | 3.5 |
| C30/37 | 30 | 38 | 2.90 | 33 | 3.5 |
| C32/40 | 32 | 40 | 3.02 | 33 | 3.5 |
| C35/43 | 35 | 43 | 3.21 | 34 | 3.5 |
| C40/50 | 40 | 48 | 3.51 | 35 | 3.5 |
| C45/55 | 45 | 53 | 3.80 | 36 | 3.5 |
| C50/60 | 50 | 58 | 4.07 | 37 | 3.5 |
| Bar φ (mm) | 1 bar | 2 bars | 3 bars | 4 bars | 5 bars | 6 bars | Per metre @ 100mm | Per metre @ 150mm | Per metre @ 200mm |
|---|---|---|---|---|---|---|---|---|---|
| 8 | 50 | 101 | 151 | 201 | 251 | 302 | 503 | 335 | 251 |
| 10 | 79 | 157 | 236 | 314 | 393 | 471 | 785 | 524 | 393 |
| 12 | 113 | 226 | 339 | 452 | 565 | 679 | 1131 | 754 | 565 |
| 16 | 201 | 402 | 603 | 804 | 1005 | 1206 | 2011 | 1340 | 1005 |
| 20 | 314 | 628 | 942 | 1257 | 1571 | 1885 | 3142 | 2094 | 1571 |
| 25 | 491 | 982 | 1473 | 1963 | 2454 | 2945 | 4909 | 3272 | 2454 |
| 32 | 804 | 1608 | 2413 | 3217 | 4021 | 4825 | 8042 | 5362 | 4021 |
| 40 | 1257 | 2513 | 3770 | 5027 | 6283 | 7540 | 12566 | 8378 | 6283 |
| Exposure Class | Description | Min. Cover (mm) | Typical Application |
|---|---|---|---|
| XC1 | Dry or permanently wet | 15 | Interior slabs, buried concrete below water table |
| XC2 | Wet, rarely dry | 25 | Foundations, retaining walls |
| XC3/XC4 | Moderate/cyclic humidity | 35 | External walls, balconies |
| XD1 | Moderate chlorides | 40 | Car park decks |
| XD2 | Wet, chlorides | 40 | Swimming pools, bridges |
| XS1 | Marine, airborne salt | 40 | Coastal structures |
| XS3 | Tidal/splash zone | 55 | Seawall, jetty |
| XF1 | Freeze/thaw, moderate saturation | 35 | Exposed external concrete |
Add a construction tolerance allowance Δcdev = 10mm (UK NA) to the minimum cover cmin to obtain the nominal cover cnom: cnom = cmin + Δcdev.
| Parameter | Symbol | Persistent / Transient | Accidental |
|---|---|---|---|
| Concrete (strength) | γc | 1.50 | 1.20 |
| Reinforcing steel | γs | 1.15 | 1.00 |
| Design concrete strength | fcd | α·fck/γc = 0.567fck | 0.667fck |
| Design steel strength | fyd | fyk/γs = 0.87fyk | fyk/1.0 |
| Permanent action (unfav.) | γG | 1.35 | 1.00 |
| Variable action (unfav.) | γQ | 1.50 | 1.00 |
Key Eurocode 2 references: BSI – BS EN 1992 (Eurocode 2) | The Concrete Society | Institution of Structural Engineers | Steel Construction Info | The Concrete Centre
BS EN 1992-1-1 (Eurocode 2, Part 1-1) replaced BS 8110 as the primary UK standard for the design of concrete structures in 2010. It is used alongside the UK National Annex (NA) which modifies certain nationally determined parameters. The UK NA uses γc = 1.5 and γs = 1.15 as standard partial material factors.
The design compressive strength of concrete in EC2 is fcd = α·fck/γc where α = 0.85 (long-term effects factor) and γc = 1.5, giving fcd = 0.567·fck. For C30/37, fcd = 0.567 × 30 = 17 N/mm².
The design yield strength of reinforcement in EC2 is fyd = fyk/γs = fyk/1.15 = 0.87·fyk. For B500B/B500C steel (the standard UK rebar), fyd = 0.87 × 500 = 435 N/mm². This is slightly higher than the BS 8110 value of 0.87·fy = 400 N/mm² (for 460 N/mm² steel).
The dimensionless bending parameter K = MEd/(bd²fck) is the central check in EC2 beam bending design. If K ≤ K’ (= 0.167 for ξ ≤ 0.45d), the section can be designed as singly reinforced. If K > K’, compression steel is required or the section dimensions must be increased.
The internal lever arm z = d[0.5 + √(0.25 − K/1.134)] is limited to a maximum of 0.95d (to prevent over-estimation of lever arm in lightly loaded sections). The required tension steel area is then As = MEd/(fyd·z).
EC2 requires minimum tension reinforcement in beams and slabs of As,min = 0.26(fctm/fyk)bd ≥ 0.0013bd. For C30/37 and B500B steel: fctm = 2.9 N/mm², giving As,min ≈ 0.0015bd. This minimum applies regardless of the moment demand.
EC2 uses the variable strut inclination method for shear design, where the designer can choose the angle θ of the concrete compression strut between 21.8° (cotθ=2.5) and 45° (cotθ=1.0). A smaller angle requires less shear link steel but higher compression in the concrete strut. The strut angle is often taken as 45° for simplicity in domestic structures.
EC2 allows deflection to be checked by the simplified span/depth ratio method (Table 7.4N) rather than by detailed calculation in most cases. The basic ratios are: simply supported beam/slab L/d = 20×K; continuous end span 26×K; cantilever 8×K; flat slab 24×K (where K accounts for the structural system).
A column is classified as short if the slenderness ratio λ = L0/i ≤ λlim (typically 25–35 for most domestic columns). Short columns can be designed for axial load only without second-order effects. Slender columns require additional design moment to account for buckling effects (EC2 Clause 5.8).
The UK NA to EN 1990 permits the use of either Expression 6.10 (γG·Gk + γQ·Qk) or the less favourable of Expressions 6.10a and 6.10b. The 6.10a/6.10b approach uses γG = 0.925×1.35 = 1.25 (approx.) for the permanent-load-dominated case, saving material cost where permanent loads are small relative to imposed loads.
The nominal concrete cover cnom = cmin + Δcdev where Δcdev = 10mm (UK NA). cmin depends on exposure class and structural class. For typical internal RC slabs (XC1), cmin = 15mm → cnom = 25mm. For external elements (XC3), cmin = 25mm → cnom = 35mm.
The calculators on this page implement simplified EC2 design expressions suitable for preliminary design and checking only. A full structural design must consider second-order effects, torsion, punching shear, fatigue, fire resistance, and serviceability crack widths, among other checks. All structural elements must be designed or verified by a Chartered Structural Engineer.
Eurocode 2 (BS EN 1992-1-1) is the European standard for the design of concrete structures, adopted in the UK in 2010 to replace BS 8110. It applies to all reinforced and prestressed concrete buildings and civil engineering structures designed in the UK. It is used alongside the UK National Annex, which specifies nationally determined parameters (NDPs) including partial material factors, imposed load values, and deflection limits. Despite Brexit, the UK retains the Eurocodes as the primary suite of structural design standards, and BEIS confirmed in 2022 that BS EN Eurocodes remain the designated standards for UK structural design for the foreseeable future.
fck is the characteristic cylinder compressive strength of concrete at 28 days, used in Eurocode 2 design (European system). fcu is the characteristic cube compressive strength, used in the old BS 8110 design system. UK ready-mix concrete grades are specified to BS 8500 using cylinder strength notation (C25/30, C30/37, etc.) where the first number is fck (cylinder) and the second is fcu (cube). Approximately: fcu ≈ 1.25×fck. So C30/37 concrete has fck = 30 N/mm² and fcu = 37 N/mm².
For a simply supported beam with a uniformly distributed load (UDL), the maximum design bending moment at mid-span is: MEd = wEd·L²/8, where wEd is the design UDL (in kN/m) and L is the effective span (in metres). The design UDL is calculated from the load combination: wEd = 1.35·Gk + 1.5·Qk (using Expression 6.10). For a point load P at mid-span: MEd = PEd·L/4. For a cantilever with UDL: MEd = wEd·L²/2 at the fixed end.
For a domestic ground floor slab in a dry interior (exposure class XC1), the minimum cover to reinforcement is cmin = 15mm, giving a nominal cover of cnom = 25mm (cmin + 10mm construction tolerance). In practice, most UK structural engineers specify 25mm nominal cover for interior ground floor slabs. For external slabs or those in contact with aggressive ground (sulphate-bearing soils), the exposure class increases and covers of 35–50mm may be required. Always check the specific exposure class with your structural engineer.
A short column can be designed for concentric axial load without considering geometric second-order effects (P-delta effects). EC2 defines a column as short if its slenderness ratio λ = L0/i is less than the limiting slenderness λlim, where L0 is the effective length and i is the radius of gyration. For a typical domestic column with moderate axial load, λlim is approximately 25–35. A slender column has λ > λlim and must be designed to resist an additional design moment ΔM accounting for buckling — requiring more detailed calculation per EC2 Clause 5.8. Most domestic columns (3–4m storey height, 250–400mm section) are short columns.
Yes — in virtually all cases, any reinforced concrete structural element (beam, slab, column, or foundation) in a UK building requires design by or verification by a Chartered Structural Engineer (MIStructE, FIStructE, or CEng with structural engineering specialism). This is a requirement of Part A (Structure) of the Building Regulations, which requires that structural elements are designed to withstand all reasonable loads. Building Control will typically require structural calculations prepared and signed by a qualified engineer for any significant RC work. The calculators on this page provide useful preliminary estimates and learning tools, but are not a substitute for professional structural engineering design.