RC Beam Designer
EN 1992-1-1 (Eurocode 2) · simply supported beam, UDL + point load
All checks pass — 6 m span, 300×500 mm, C30, fyk 500, EN recommended values
Reinforcement
Bottom: 5Ø16 (1005 mm²)
Top: 2Ø12 (226 mm²)
Links: Ø8 2-leg @ 300 mm
MEd = 181.4 kNm · VEd = 102.6 kN · d = 454 mm
3D view
Checks
- OKFlexural capacity As,prov 1005 ≥ As,req 999 mm²
- OKMinimum reinforcement 1005 ≥ 205 mm²
- OKMaximum reinforcement 1232 ≤ 6000 mm²
- OKCover: durability (links) cnom 30 ≥ 20 mm (cmin,dur 10 for XC1, class S3; Δcdev 10)
- OKCover: bond (main bars) cnom + φlink 38 ≥ φ 16 + 10 mm
- OKBar spacing clear spacing 36 mm ≥ 25 mm
- OKWeb crushing (VRd,max) VEd 102.6 ≤ VRd,max 446.4 kN
- OKShear links Ø8 2-leg @ 300 mm (Asw/s = 0.335 ≥ 0.263)
- OKDeflection (l/d) actual 13.2 ≤ allowable 17.3
- OKCrack control (Table 7.3N) Ø16 ≤ 22 mm, spacing 52 ≤ 259 mm
Calculation
ActionsEN 1990 6.4.3.2
| Self-weight | 25 × b × h | 3.75 kN/m |
| Design UDL wEd | Exp. 6.10 | 40.31 kN/m |
| Design moment MEd | wEd L² / 8 | 181.4 kNm |
| Support reaction | wEd L / 2 | 120.9 kN |
| Design shear VEd at d from support | V − wEd d (point load not reduced) | 102.6 kN |
MaterialsEN 1992-1-1 3.1, 3.2
| fcd | αcc fck / γc | 20.00 MPa |
| fyd | fyk / γs | 434.78 MPa |
| fctm | 0.30 fck^(2/3) | 2.90 MPa |
| Ecm | 22 (fcm/10)^0.3 | 32.8 GPa |
| Effective depth d | h − c − φlink − φ/2 | 454 mm |
Flexure (ULS)EN 1992-1-1 3.1.7, 6.1
| K | MEd / (b d² fck) | 0.0978 |
| K′ (x/d = 0.45) | 0.2952 fcd / fck | 0.1968 |
| Lever arm z | d [0.5 + √(0.25 − K/(1.134 αcc/γc))] | 418 mm |
| As,req (tension) | MEd / (fyd z) | 999 mm² |
| As,min | max(0.26 fctm/fyk b d, 0.0013 b d) [9.2.1.1] | 205 mm² |
| As,max | 0.04 Ac [9.2.1.1(3)] | 6000 mm² |
Shear (ULS)EN 1992-1-1 6.2.2, 6.2.3
| k | min(1 + √(200/d), 2) | 1.664 |
| ρl | As / (bw d) ≤ 0.02 | 0.00738 |
| VRd,c | [CRd,c k (100 ρl fck)^(1/3)] bw d ≥ vmin bw d | 76.4 kN |
| Links required? | VEd > VRd,c | Yes |
| ν1 | 0.6 (1 − fck/250) | 0.528 |
| Strut angle | cot θ in [1, 2.5] | cot θ = 2.50 (θ = 21.8°) |
| VRd,max | αcw bw z ν1 fcd / (cot θ + tan θ) | 446.4 kN |
| Asw/s required | VEd / (z fywd cot θ) | 0.231 mm²/mm |
| Asw/s,min | 0.08 √fck / fyk · bw [9.2.2(5)] | 0.263 mm²/mm |
| s,max | 0.75 d [9.2.2(6)] | 341 mm |
| Additional tension force ΔFtd | 0.5 VEd cot θ | 128.3 kN |
Deflection (span/depth)EN 1992-1-1 7.4.2
| ρ0 | √fck / 1000 | 0.00548 |
| ρ | As,req / (b d) | 0.00733 |
| Basic l/d | K = 1.0 (simply supported), Exp. 7.16 | 17.1 |
| Steel factor | 500/fyk · As,prov/As,req [7.17] | 1.007 |
| Span factor | 7/L for L > 7 m | 1.000 |
| Allowable l/d | 17.3 | |
| Actual l/d | L / d | 13.2 |
Crack controlEN 1992-1-1 7.3.3
| Crack width limit wmax | exposure XC1 [Table 7.1N] | 0.4 mm |
| Steel stress σs | fyd (As,req/As,prov)(MQP/MEd) | 233 MPa |
| Max bar Ø / spacing | Table 7.3N | 22 mm / 259 mm |
| Provided Ø / spacing | 16 mm / 52 mm |
Scope: simply supported single span, uniformly distributed load plus one optional point load, rectangular or flanged (sagging) section, one or two layers of tension steel, fck ≤ 50 MPa, vertical links, no axial force, no moment redistribution. Results are an aid only and must be verified by a qualified, licensed engineer before use. Not a substitute for the full code and the relevant National Annex.