Reinforced concrete beam calculator — EN 1992-1-1 with the Dutch National Annex
Design check of a rectangular reinforced concrete beam over one to five spans. Enter the spans, supports, characteristic loads, section, concrete class, bars and stirrups; the calculator builds the load combinations with the Dutch factors, applies the load arrangements of EN 1992-1-1 §5.1.3, and checks bending at every span and support and shear at every support.
Cover follows the Dutch NB from the exposure class and design life, and the detailing rules (minimum and maximum reinforcement, bar and stirrup spacing) are checked with the Dutch NB values.
Open this example in the calculator →
What it checks
- Nominal cover and effective depth (EN 1992-1-1 §4.4.1)
- Bending resistance, sagging and hogging (§6.1)
- Shear resistance with stirrups (§6.2.3)
- Detailing: minimum/maximum reinforcement, minimum shear reinforcement, spacing (§8.2, §9.2)
Scope
- Continuous beam, 1–5 spans, cantilevers allowed; up to 10 loads.
- Constant rectangular section, one reinforcement layout for the whole beam.
- Compression reinforcement ignored in bending and shear taken at the support axis (both conservative).
Not covered (the calculator says NOT COVERED instead of approximating)
- Serviceability checks (crack width, deflection) — not yet included.
- Axial force and torsion.
Worked example
A single span of 6.0 m on two pinned supports, carrying 15 kN/m permanent and 10 kN/m imposed load (category A) plus self-weight. Section 300 × 500 mm, C30/37, B500B, exposure class XC1; 3Ø20 bottom, 2Ø12 top, stirrups Ø8 at 200 mm.
Inputs
| Input | Value |
|---|---|
| Section width | 300 mm |
| Section height | 500 mm |
| Concrete strength class | C30/37 |
| Reinforcement grade | B500B |
| Exposure class (governing) | XC1 |
| Design working life | 50 yr |
| Consequence class | CC2 |
| Imposed-load category (for ψ) | A |
| Bottom bars: number | 3 |
| Bottom bars: diameter | 20 mm |
| Top bars: number (blank = none) | 2 |
| Top bars: diameter | 12 mm |
| Stirrups: diameter (blank = none) | 8 mm |
| Stirrups: number of legs | 2 |
| Stirrups: spacing | 200 mm |
Main steps
| Step | Clause | Working | |
|---|---|---|---|
| Max sagging moment span 1 | EN 1992-1-1 §5.4; 5.1.3 (NB) | M_Ed,1 = envelope max (6.10b, Q on all spans) = x = 3 m = 168.8 kNm | |
| Shear force at support 1 (axis) | EN 1992-1-1 §5.4; 6.2.1(8) | V_Ed,s1 = envelope max |V| at the support axis = x = 0 m = 112.5 kN | |
| Shear force at support 2 (axis) | EN 1992-1-1 §5.4; 6.2.1(8) | V_Ed,s2 = envelope max |V| at the support axis = x = 6 m = 112.5 kN | |
| Design compressive strength concrete | EN 1992-1-1 §3.1.6(1)P (NB) | f_cd = α_cc · f_ck / γ_C = 1 · 30 / 1.5 = 20 MPa | ⚠ |
| Design yield strength reinforcement | EN 1992-1-1 §3.2.7(2) (NB) | f_yd = f_yk / γ_S = 500 / 1.15 = 434.8 MPa | ⚠ |
| Nominal cover | EN 1992-1-1 §4.4.1.1(2), Eq. (4.1); 4.4.1.3(1)P (NB) | c_nom = c_min + Δc_dev = 10 + 5 = 15 mm | ⚠ |
| Nominal cover to stirrups, governed by the main bars | EN 1992-1-1 §4.4.1.2(3), Eqs. (4.1)–(4.2) (NB) | c_nom = max(c_nom,stirrup ; max(Ø_main ; c_min,dur ; 10) + Δc_dev − Ø_stirrup) = max(15 ; max(20 ; 10 ; 10) + 5 − 8) = 17 mm | ⚠ |
| Effective depth, bottom bars | EN 1992-1-1 §4.4.1.1(1) (geometry) | d_bottom = h − c_nom − Ø_stirrup − Ø_bottom/2 = 500 − 17 − 8 − 20/2 = 465 mm | |
| Effective depth, top bars | EN 1992-1-1 §4.4.1.1(1) (geometry) | d_top = h − c_nom − Ø_stirrup − Ø_top/2 = 500 − 17 − 8 − 12/2 = 469 mm | |
| Reinforcement yields | EN 1992-1-1 §3.2.7, Fig. 3.8 | ε_s ≥ ε_yd = ε_s / ε_yd ≥ 1 = 0.01556 / 0.002174 = 7.16 | PASS ⚠ |
| Design bending resistance | EN 1992-1-1 §6.1 | M_Rd = A_s · f_yd · z = 942.5 · 434.8 · 430.9 = 176.6 kNm | |
| Shear resistance with stirrups | EN 1992-1-1 §6.2.3(3) | V_Rd = min(V_Rd,s ; V_Rd,max) = min(228.7 ; 457.2) = 228.7 kN | |
| Bending span 1 (sagging) | EN 1990 §6.4.2(3), Eq. (6.8) | M_Ed / M_Rd = M_Ed / M_Rd ≤ 1.0 = 168.8 / 176.6 = 0.9558 | PASS ⚠ |
| Shear support 1 | EN 1990 §6.4.2(3), Eq. (6.8) | V_Ed / V_Rd = V_Ed / V_Rd ≤ 1.0 = 112.5 / 228.7 = 0.492 | PASS ⚠ |
| Shear support 2 | EN 1990 §6.4.2(3), Eq. (6.8) | V_Ed / V_Rd = V_Ed / V_Rd ≤ 1.0 = 112.5 / 228.7 = 0.492 | PASS ⚠ |
| Minimum reinforcement, bottom bars | EN 1992-1-1 §9.2 (NB) — detailing | A_s,min / A_s = A_s,min / A_s ≤ 1.0 = 181.7 / 942.5 = 0.1927 | PASS ⚠ |
| Maximum reinforcement, bottom bars | EN 1992-1-1 §9.2 (NB) — detailing | A_s / A_s,max = A_s / A_s,max ≤ 1.0 = 942.5 / 6000 = 0.1571 | PASS ⚠ |
| Maximum reinforcement, top bars | EN 1992-1-1 §9.2 (NB) — detailing | A_s / A_s,max = A_s / A_s,max ≤ 1.0 = 226.2 / 6000 = 0.0377 | PASS ⚠ |
| Minimum shear reinforcement | EN 1992-1-1 §9.2.2(5) (NB) | ρ_w,min / ρ_w = ρ_w,min / ρ_w ≤ 1.0 = 0.0008764 / 0.001676 = 0.523 | PASS ⚠ |
| Stirrup spacing along the beam | EN 1992-1-1 §9.2.2(6) (NB) | s / s_l,max = s / s_l,max ≤ 1.0 = 200 / 300 = 0.6667 | PASS ⚠ |
| Transverse spacing of stirrup legs | EN 1992-1-1 §9.2.2(8) (NB) | s_t / s_t,max = s_t / s_t,max ≤ 1.0 = 258 / 500 = 0.516 | PASS ⚠ |
| Clear bar spacing, bottom bars | EN 1992-1-1 §8.2(2) (NB) | s_min / s_clear = s_min / s_clear ≤ 1.0 = 21 / 95 = 0.2211 | PASS ⚠ |
| Clear bar spacing, top bars | EN 1992-1-1 §8.2(2) (NB) | s_min / s_clear = s_min / s_clear ≤ 1.0 = 21 / 226 = 0.09292 | PASS ⚠ |
Outcome
PASS — all checks satisfied ⚠
- 1 span (6 m) on pinned – pinned supports; section 300 × 500 mm, C30/37, B500B.
- 3 characteristic loads, combined with EN 1990 6.10a/6.10b (CC2, use category A) in 4 load cases.
- Governing: Bending span 1 — 168.8 kNm demand against 176.6 kNm capacity, unity check 0.96 (OK).
- All 11 checks pass.
| Result | Value |
|---|---|
| UC Bending span 1 | 0.9558 |
| UC Shear support 1 | 0.492 |
| UC Shear support 2 | 0.492 |
| UC Minimum reinforcement, bottom bars | 0.1927 |
| UC Maximum reinforcement, bottom bars | 0.1571 |
| UC Maximum reinforcement, top bars | 0.0377 |
| UC Minimum shear reinforcement | 0.523 |
| UC Stirrup spacing along the beam | 0.6667 |
| UC Transverse spacing of stirrup legs | 0.516 |
| UC Clear bar spacing, bottom bars | 0.2211 |
| UC Clear bar spacing, top bars | 0.09292 |
| Governing UC | 0.9558 (Bending span 1) |
| M_Rd bottom | 176.6 kNm |
| c_nom | 17 mm |
Dutch National Annex values used
| Symbol | Value | Clause | Status |
|---|---|---|---|
| ψ0 | 0.4 | EN 1990 Table NB.2 – A1.1 (NB) | transcribed ⚠ |
| γ_G,sup | 1.35 | EN 1990 Table NB.4 – A1.2(B) (NB) | transcribed ⚠ |
| γ_Q,1 | 1.5 | EN 1990 Table NB.4 – A1.2(B) (NB) | transcribed ⚠ |
| γ_G,sup | 1.2 | EN 1990 Table NB.4 – A1.2(B) (NB) | transcribed ⚠ |
| γ_Q,1 | 1.5 | EN 1990 Table NB.4 – A1.2(B) (NB) | transcribed ⚠ |
| C_max | C90/105 | EN 1992-1-1 3.1.2(2)P (NB) | transcribed ⚠ |
| f_yk,max | 600 MPa | EN 1992-1-1 3.2.2(3)P (NB) | transcribed ⚠ |
| α_cc | 1 | EN 1992-1-1 3.1.6(1)P (NB) | transcribed ⚠ |
| γ_C | 1.5 | EN 1992-1-1 2.4.2.4(1), Table 2.1N (NB) | transcribed ⚠ |
| γ_S | 1.15 | EN 1992-1-1 2.4.2.4(1), Table 2.1N (NB) | transcribed ⚠ |
| S_rec | S4 | EN 1992-1-1 4.4.1.2(5) (NB) | transcribed ⚠ |
| C_min,ΔS(XC1) | C30/37 | EN 1992-1-1 4.4.1.2(5), Table 4.3N (NB) | transcribed ⚠ |
| S_min | S1 | EN 1992-1-1 4.4.1.2(5) (NB) | transcribed ⚠ |
| c_min,dur(S3,XC1) | 10 mm | EN 1992-1-1 4.4.1.2(5), Table 4.4N (NB) | transcribed ⚠ |
| Δc_dur,γ | 0 mm | EN 1992-1-1 4.4.1.2(6) (NB) | transcribed ⚠ |
| Δc_dur,st | 0 mm | EN 1992-1-1 4.4.1.2(7) (NB) | transcribed ⚠ |
| Δc_dur,add | 0 mm | EN 1992-1-1 4.4.1.2(8) (NB) | transcribed ⚠ |
| Δc_dev | 5 mm | EN 1992-1-1 4.4.1.3(1)P (NB) | transcribed ⚠ |
| ν | 0.6*(1 - fck/250) | EN 1992-1-1 6.2.2(6) (NB) | transcribed ⚠ |
| ν1 | nu | EN 1992-1-1 6.2.3(3) (NB) | transcribed ⚠ |
| α_cw | 1 (non-prestressed); 1 + sigma_cp/fcd for 0 < sigma_cp <= 0.25 fcd; 1.25 for 0.25 fcd < sigma_cp <= 0.5 fcd; 2.5*(1 - sigma_cp/fcd) for 0.5 fcd < sigma_cp < 1.0 fcd | EN 1992-1-1 6.2.3(3) (NB) | transcribed ⚠ |
| cot θ_min | 1 | EN 1992-1-1 6.2.3(2) (NB) | transcribed ⚠ |
| cot θ_max | 2.5 | EN 1992-1-1 6.2.3(2) (NB) | transcribed ⚠ |
| A_s,min | As,min = min(As,min1 ; As,min2); As,min1 = area per 6.1 to resist ME,min with NE,min; ME,min = fctm·W·η/(η−1) [NE,min compression] | fctm·W·η/(η+1) [NE,min tension] | fctm·W [pure bending]; η = e·Ac/W; (second pair, labelled ME,min in NB) = fctm·Ac·η/(η−1) [compression] | fctm·Ac·η/(η+1) [tension]; As,min2 = 1.25 × area required at ULS mm² | EN 1992-1-1 9.2.1.1(1) (NB) | transcribed ⚠ |
| A_s,max | As,max = 0.04·Ac mm² | EN 1992-1-1 9.2.1.1(3) (NB) | transcribed ⚠ |
| ρ_w,min | ρw,min = (0.08·√fck)/fyk | EN 1992-1-1 9.2.2(5) (NB) | transcribed ⚠ |
| s_l,max | no shear reinforcement required: 300 mm; shear reinforcement required: min(0.75·d·(1 + cot α) ; 300 mm) mm | EN 1992-1-1 9.2.2(6) (NB) | transcribed ⚠ |
| s_t,max | VEd ≤ 0.5·VRd,max: 500 mm; VEd > 0.5·VRd,max: 0.75·d ≤ 500 mm mm | EN 1992-1-1 9.2.2(8) (NB) | transcribed ⚠ |
| k1 | 1 | EN 1992-1-1 8.2(2) (NB) | transcribed ⚠ |
| k2 | 5 mm | EN 1992-1-1 8.2(2) (NB) | transcribed ⚠ |
Clauses used in the worked example
EN 1990 §6.4.2(3), Eq. (6.8), EN 1990 §6.4.3.2, Eq. (6.10a), Table A1.2(B) (NB), EN 1990 §6.4.3.2, Eq. (6.10b), Table A1.2(B) (NB), EN 1991-1-1 §Table A.1 (reinforced concrete 25 kN/m³), EN 1991-1-1 §characteristic value (input), EN 1992-1-1 §3.1.2, Table 3.1, EN 1992-1-1 §3.1.2, Table 3.1 (NB), EN 1992-1-1 §3.1.6(1)P (NB), EN 1992-1-1 §3.1.7(3), Eq. (3.19), EN 1992-1-1 §3.1.7(3), Eq. (3.21), EN 1992-1-1 §3.1.7, Table 3.1, EN 1992-1-1 §3.2.2, Annex C (NB), EN 1992-1-1 §3.2.7(2) (NB), EN 1992-1-1 §3.2.7(4), EN 1992-1-1 §3.2.7, Fig. 3.8, EN 1992-1-1 §4.4.1.1(1) (geometry), EN 1992-1-1 §4.4.1.1(2), Eq. (4.1); 4.4.1.3(1)P (NB), EN 1992-1-1 §4.4.1.2(2), Eq. (4.2) (NB), EN 1992-1-1 §4.4.1.2(3), Eqs. (4.1)–(4.2) (NB), EN 1992-1-1 §4.4.1.2(3), Table 4.2, EN 1992-1-1 §4.4.1.2(5) (NB), EN 1992-1-1 §4.4.1.2(5), Table 4.3N (NB), EN 1992-1-1 §4.4.1.2(5), Table 4.4N (NB), EN 1992-1-1 §5.4; 5.1.3 (NB), EN 1992-1-1 §5.4; 6.2.1(8), EN 1992-1-1 §6.1, EN 1992-1-1 §6.1(2), Fig. 3.5, EN 1992-1-1 §6.1(2), Fig. 3.8, EN 1992-1-1 §6.1(2), Fig. 6.1, EN 1992-1-1 §6.1, Fig. 3.5, EN 1992-1-1 §6.2.2(6), Eq. (6.6N) (NB), EN 1992-1-1 §6.2.3(1), EN 1992-1-1 §6.2.3(2) (NB limits) (NB), EN 1992-1-1 §6.2.3(3), EN 1992-1-1 §6.2.3(3) (NB), EN 1992-1-1 §6.2.3(3), Eq. (6.8), EN 1992-1-1 §6.2.3(3), Eq. (6.9), EN 1992-1-1 §8.2 (geometry), EN 1992-1-1 §8.2(2) (NB), EN 1992-1-1 §9.2 (NB) — detailing, EN 1992-1-1 §9.2.1.1(1) (NB), EN 1992-1-1 §9.2.1.1(1) (NB); 6.1, EN 1992-1-1 §9.2.1.1(3) (NB), EN 1992-1-1 §9.2.2(5) (NB), EN 1992-1-1 §9.2.2(5), Eq. (9.4), EN 1992-1-1 §9.2.2(6) (NB), EN 1992-1-1 §9.2.2(8), EN 1992-1-1 §9.2.2(8) (NB), EN 1992-1-1 §geometry
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