Steel beam calculator — EN 1993-1-1 with the Dutch National Annex
Check a rolled steel beam (IPE, HEA, HEB, HEM or your own I-section) over one to five spans. Enter the spans, the supports and the characteristic permanent (G) and imposed (Q) loads; the calculator combines them to EN 1990 with the Dutch factors, finds the moment and shear envelopes and checks the beam.
Lateral-torsional buckling follows the method of the Dutch National Annex (Annex NB.NB) per segment between lateral restraints. Deflections are checked against the limits of the Dutch NB to EN 1990.
Open this example in the calculator →
What it checks
- Cross-section class (EN 1993-1-1 §5.5)
- Bending and shear resistance, bending–shear interaction (§6.2)
- Lateral-torsional buckling per segment, M_cr by the Dutch NB method (§6.3.2, Annex NB.NB)
- Deflection, appearance and additional deflection (EN 1990 A1.4.3 with NB limits)
Scope
- Continuous beam, 1–5 spans, cantilevers allowed; up to 10 loads (uniform, partial, point).
- Doubly symmetric rolled I/H sections, class 1 to 3.
- Load combinations EN 1990 6.10a/6.10b with the Dutch consequence-class factors.
Not covered (the calculator says NOT COVERED instead of approximating)
- Class 4 sections, axial force, torsion.
- Load arrangements whose LTB moment shape the Dutch NB gives only in graphs.
- Hollow sections, channels and angles until the remaining NEN readings are in.
Worked example
A single span of 6.0 m on two pinned supports, carrying 5.0 kN/m permanent and 6.0 kN/m imposed load (category A, floors) plus the beam's self-weight. Section 300 × 150 mm (user-defined, IPE 300 dimensions), steel S235, top flange continuously restrained.
Inputs
| Input | Value |
|---|---|
| Profile (or user-defined) | user-defined |
| h (user-defined) | 300 mm |
| b (user-defined) | 150 mm |
| t_w (user-defined) | 7.1 mm |
| t_f (user-defined) | 10.7 mm |
| root radius r (user-defined) | 15 mm |
| Steel grade | S235 |
| Consequence class | CC2 |
| Imposed-load category (for ψ) | A |
| Lateral restraint of the beam | continuous |
| Element type (deflection limits) | floor |
Main steps
| Step | Clause | Working | |
|---|---|---|---|
| Max sagging moment span 1 | EN 1993-1-1 §5.4.2; EN 1991-1-1 6.2.1(1) | M_Ed,1 = envelope max (6.10b, Q on all spans) = x = 3 m = 69.74 kNm | |
| Shear force at support 1 (axis) | EN 1993-1-1 §5.4.2 | V_Ed,s1 = envelope max |V| at the support axis = x = 0 m = 46.49 kN | |
| Shear force at support 2 (axis) | EN 1993-1-1 §5.4.2 | V_Ed,s2 = envelope max |V| at the support axis = x = 6 m = 46.49 kN | |
| Yield strength | EN 1993-1-1 §3.2.1, Table 3.1 (NB) | f_y = S235, t ≤ 40 mm = S235, t = 10.7 mm = 235 MPa | ⚠ |
| Cross-section class | EN 1993-1-1 §5.5.2, Table 5.2 | class = max(flange: 9ε / 10ε / 14ε ; web: 72ε / 83ε / 124ε) = flange 1, web 1 = 1 | |
| Bending resistance of the cross-section | EN 1993-1-1 §6.2.5(2), Eq. (6.13) (NB) | M_c,Rd = W_pl,y · f_y / γ_M0 = 6.284e+05 · 235 / 1 = 147.7 kNm | ⚠ |
| Plastic shear resistance | EN 1993-1-1 §6.2.6(2), Eq. (6.18) | V_pl,Rd = A_v · (f_y / √3) / γ_M0 = 2568 · (235 / √3) / 1 = 348.4 kN | |
| Bending span 1 | EN 1990 §6.4.2(3), Eq. (6.8) | M_Ed / M_c,Rd = M_Ed / M_c,Rd ≤ 1.0 = 69.74 / 147.7 = 0.4723 | PASS ⚠ |
| Shear support 1 | EN 1990 §6.4.2(3), Eq. (6.8) | V_Ed / V_pl,Rd = V_Ed / V_pl,Rd ≤ 1.0 = 46.49 / 348.4 = 0.1334 | PASS ⚠ |
| Shear support 2 | EN 1990 §6.4.2(3), Eq. (6.8) | V_Ed / V_pl,Rd = V_Ed / V_pl,Rd ≤ 1.0 = 46.49 / 348.4 = 0.1334 | PASS ⚠ |
| Deflection span 1 (appearance) | EN 1990 §A1.4.3 (NB) | w_qp / w_lim = w_qp / (0.004 · l) ≤ 1.0 = 6.938 / (0.004 · 6000) = 0.2891 | PASS ⚠ |
| Deflection span 1 (additional, frequent) | EN 1990 §A1.4.3 (NB) | w_add,freq / w_lim = w_add,freq / (0.003 · l) ≤ 1.0 = 2.885 / (0.003 · 6000) = 0.1603 | PASS ⚠ |
Outcome
PASS — all checks satisfied ⚠
- 1 span (6 m) on pinned – pinned supports; user-defined (300 × 150 mm), S235, class 1.
- 3 characteristic loads, combined with EN 1990 6.10a/6.10b (CC2, use category A) in 4 load cases.
- Governing: Bending span 1 — 69.7 kNm demand against 147.7 kNm capacity, unity check 0.47 (OK).
- All 5 checks pass.
| Result | Value |
|---|---|
| UC Bending span 1 | 0.4723 |
| UC Shear support 1 | 0.1334 |
| UC Shear support 2 | 0.1334 |
| UC Deflection span 1 (appearance) | 0.2891 |
| UC Deflection span 1 (additional, frequent) | 0.1603 |
| Governing UC | 0.4723 (Bending span 1) |
| M_c,Rd | 147.7 kNm |
| V_pl,Rd | 348.4 kN |
| class | 1 |
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 ⚠ |
| f_y source | product standard or Table 3.1 | EN 1993-1-1 3.2.1(1) (NB) | transcribed ⚠ |
| f_y | 235 N/mm2 | EN 1993-1-1 Table 3.1 (NB) | transcribed ⚠ |
| γ_M0 | 1 | EN 1993-1-1 6.1(1) (NB) | transcribed ⚠ |
| η | 1.2 for steel grades ≤ S460; 1.0 for grades > S460 | EN 1993-1-5 5.1(2) (NB) | transcribed ⚠ |
| ψ1 | 0.5 | EN 1990 Table NB.2 – A1.1 (NB) | transcribed ⚠ |
| ψ2 | 0.3 | EN 1990 Table NB.2 – A1.1 (NB) | transcribed ⚠ |
| w_max/l | 0.004 fraction of l_rep | EN 1990 A1.4.3(4) (NB) | transcribed ⚠ |
| w_add/l | 0.003 fraction of l_rep | EN 1990 A1.4.3(3) (NB) | transcribed ⚠ |
| l_rep | l_rep = 2 × cantilever length | EN 1990 A1.4.3(3) (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 1990 §6.5.3(2)a, Eq. (6.14b) (NB), EN 1990 §6.5.3(2)b, Eq. (6.15b), EN 1990 §6.5.3(2)c, Eq. (6.16b), EN 1990 §A1.4.3 (NB), EN 1990 §A1.4; EN 1993-1-1 §7.2, EN 1991-1-1 §characteristic value (input), EN 1991-1-1 §§5 (profile mass), EN 1993-1-1 §3.2.1, Table 3.1 (NB), EN 1993-1-1 §5.4.2, EN 1993-1-1 §5.4.2; EN 1991-1-1 6.2.1(1), EN 1993-1-1 §5.5.2, Table 5.2, EN 1993-1-1 §6.2.5(2), Eq. (6.13) (NB), EN 1993-1-1 §6.2.6(2), Eq. (6.18), EN 1993-1-1 §6.2.6(3)a, EN 1993-1-1 §6.2.6(3)a (NB), EN 1993-1-1 §6.2.6(6), EN 1993-1-1 §6.3.2.1
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