Bending resistance of a reinforced concrete section — EN 1992-1-1 with the Dutch NB
Find the design bending resistance M_Rd of a singly reinforced rectangular section and compare it with your design moment M_Ed. The calculator finds the neutral axis from horizontal equilibrium with the rectangular stress block, checks that the reinforcement yields and gives the lever arm and the unity check.
Open this example in the calculator →
What it checks
- Design strengths f_cd and f_yd with the Dutch NB partial factors (EN 1992-1-1 §3.1.6, §3.2.7)
- Neutral axis, steel strain and lever arm (§6.1, rectangular stress block)
- Unity check M_Ed / M_Rd (EN 1990 §6.4.2)
Scope
- Rectangular section, tension reinforcement only, pure bending.
- Concrete classes C12/15 to C90/105 (λ and η reduced above C50/60).
Not covered (the calculator says NOT COVERED instead of approximating)
- Compression reinforcement, axial force, negative moments.
Worked example
Section b × h = 300 × 500 mm with effective depth d = 450 mm, 3Ø20 (A_s = 942.5 mm²), C30/37 and B500B, design moment M_Ed = 150 kNm.
Inputs
| Input | Value |
|---|---|
| Section width | 300 mm |
| Section height | 500 mm |
| Effective depth | 450 mm |
| Tension reinforcement area | 942.5 mm² |
| Concrete strength class | C30/37 |
| Reinforcement grade | B500B |
| Design bending moment | 150 kNm |
Main steps
| Step | Clause | Working | |
|---|---|---|---|
| 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 | ⚠ |
| Neutral axis depth (horizontal equilibrium) | EN 1992-1-1 §6.1(2), Fig. 3.5 | x = A_s · f_yd / (η · f_cd · λ · b) = 942.5 · 434.8 / (1 · 20 · 0.8 · 300) = 85.37 mm | |
| Reinforcement yields | EN 1992-1-1 §3.2.7, Fig. 3.8 | ε_s ≥ ε_yd = ε_s / ε_yd ≥ 1 = 0.01495 / 0.002174 = 6.876 | PASS ⚠ |
| Lever arm | EN 1992-1-1 §6.1, Fig. 3.5 | z = d − λ · x / 2 = 450 − 0.8 · 85.37 / 2 = 415.9 mm | |
| Design bending resistance | EN 1992-1-1 §6.1 | M_Rd = A_s · f_yd · z = 942.5 · 434.8 · 415.9 = 170.4 kNm | |
| Unity check bending | EN 1990 §6.4.2(3), Eq. (6.8) | M_Ed / M_Rd = M_Ed / M_Rd ≤ 1.0 = 150 / 170.4 = 0.8802 | PASS ⚠ |
Outcome
PASS — all checks satisfied ⚠
| Result | Value |
|---|---|
| M_Rd | 170.4 kNm |
| x | 85.37 mm |
| z | 415.9 mm |
| utilization | 0.8802 |
Dutch National Annex values used
| Symbol | Value | Clause | Status |
|---|---|---|---|
| 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 ⚠ |
Clauses used in the worked example
EN 1990 §6.4.2(3), Eq. (6.8), 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 §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
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