Timber beam calculator — EN 1995-1-1 with the Dutch National Annex
Check a rectangular solid timber or glulam beam over one to five spans. Choose the strength class (C… or GL…), the service class and the load-duration class of the imposed load; the calculator applies k_mod for each combination and lets the worse case govern each check.
Deflections include creep (k_def) and are checked against the Dutch NB limits, the same rules as for steel beams.
Open this example in the calculator →
What it checks
- Bending with size factor k_h and lateral-torsional buckling k_crit (EN 1995-1-1 §6.1.6, §6.3.3)
- Shear with k_cr (§6.1.7)
- Compression perpendicular to the grain at the supports (§6.1.5)
- Deflection with creep (§2.2.3, §7.2 and EN 1990 A1.4.3 with NB limits)
Scope
- Continuous beam, 1–5 spans, cantilevers allowed; up to 10 loads.
- Rectangular solid softwood or glulam sections.
- Load duration per combination: k_mod for permanent loads and for the imposed load's class.
Not covered (the calculator says NOT COVERED instead of approximating)
- Floor vibration and fire design — not yet included.
- Shear deformation in the deflection (bending deflection only).
Worked example
A single span of 4.5 m on two pinned supports with 100 mm bearing, carrying 1.5 kN/m permanent and 2.0 kN/m imposed load (category A, medium-term) plus self-weight. Glulam GL24h, 90 × 270 mm, service class 1, compression edge continuously restrained.
Inputs
| Input | Value |
|---|---|
| Width b | 90 mm |
| Height h | 270 mm |
| Strength class (C… solid, GL… glulam) | GL24h |
| Service class (moisture) | 1 |
| Load-duration class of the variable load Q | medium |
| Consequence class | CC2 |
| Imposed-load category (for ψ) | A |
| Bearing length at the supports | 100 mm |
| Lateral restraint of the beam | continuous |
| Element type (deflection limits) | floor |
Main steps
| Step | Clause | Working | |
|---|---|---|---|
| Max sagging moment span 1 — permanent loads only | EN 1995-1-1 §5.1; EN 1991-1-1 6.2.1(1) | M_Ed,1 = envelope max (6.10a, no Q) = x = 2.25 m = 5.468 kNm | |
| Shear force at support 1 (axis) — permanent loads only | EN 1995-1-1 §5.1 | V_Ed,s1 = envelope max |V| at the support axis = x = 0 m = 4.86 kN | |
| Shear force at support 2 (axis) — permanent loads only | EN 1995-1-1 §5.1 | V_Ed,s2 = envelope max |V| at the support axis = x = 4.5 m = 4.86 kN | |
| Max sagging moment span 1 — with variable load | EN 1995-1-1 §5.1; EN 1991-1-1 6.2.1(1) | M_Ed,1 = envelope max (6.10b, Q on all spans) = x = 2.25 m = 12.45 kNm | |
| Shear force at support 1 (axis) — with variable load | EN 1995-1-1 §5.1 | V_Ed,s1 = envelope max |V| at the support axis = x = 0 m = 11.07 kN | |
| Shear force at support 2 (axis) — with variable load | EN 1995-1-1 §5.1 | V_Ed,s2 = envelope max |V| at the support axis = x = 4.5 m = 11.07 kN | |
| Modification factor k_mod (permanent-term) | EN 1995-1-1 §3.1.3, Table 3.1 (NB) | k_mod = glulam, service class 1, permanent-term = SC1, permanent = 0.6 | ⚠ |
| Modification factor k_mod (medium-term) | EN 1995-1-1 §3.1.3, Table 3.1 (NB) | k_mod = glulam, service class 1, medium-term = SC1, medium = 0.8 | ⚠ |
| Design bending strength (permanent) | EN 1995-1-1 §2.4.1, Eq. (2.14) | f_m,d = k_mod · f_m,k / γ_M = 0.6 · 24 / 1.25 = 11.52 MPa | |
| Design bending strength (medium) | EN 1995-1-1 §2.4.1, Eq. (2.14) | f_m,d = k_mod · f_m,k / γ_M = 0.8 · 24 / 1.25 = 15.36 MPa | |
| Lateral restraint | EN 1995-1-1 §6.3.3(5) | k_crit = 1.0 (compression edge continuously restrained) = input = 1 | |
| Bending stress — bending span 1 (medium) | EN 1995-1-1 §6.1.6 | σ_m,d = M_d / W = 1.245e+07 / 1.094e+06 = 11.39 MPa | |
| Bending span 1 | EN 1995-1-1 §6.1.6(1), 6.3.3(3), Eq. (6.33) | σ_m,d / (k_crit · k_h · f_m,d) = σ_m,d / (k_crit · k_h · f_m,d) ≤ 1.0 = 11.39 / 16.64 = 0.6846 | PASS ⚠ |
| Shear stress at support 1 (medium) | EN 1995-1-1 §6.1.7(1)–(2), Eq. (6.60) | τ_d = 1.5 · V_d / (k_cr · b · h) = 1.5 · 1.107e+04 / (1 · 90 · 270) = 0.6834 MPa | |
| Shear support 1 | EN 1995-1-1 §6.1.7(1), Eq. (6.13) | τ_d / f_v,d = τ_d / f_v,d ≤ 1.0 = 0.6834 / 2.24 = 0.3051 | PASS ⚠ |
| Bearing support 1 | EN 1995-1-1 §6.1.5(1), Eq. (6.3) | σ_c,90,d / f_c,90,d = σ_c,90,d / f_c,90,d ≤ 1.0 = 0.9462 / 1.6 = 0.5914 | PASS ⚠ |
| Shear stress at support 2 (medium) | EN 1995-1-1 §6.1.7(1)–(2), Eq. (6.60) | τ_d = 1.5 · V_d / (k_cr · b · h) = 1.5 · 1.107e+04 / (1 · 90 · 270) = 0.6834 MPa | |
| Shear support 2 | EN 1995-1-1 §6.1.7(1), Eq. (6.13) | τ_d / f_v,d = τ_d / f_v,d ≤ 1.0 = 0.6834 / 2.24 = 0.3051 | PASS ⚠ |
| Bearing support 2 | EN 1995-1-1 §6.1.5(1), Eq. (6.3) | σ_c,90,d / f_c,90,d = σ_c,90,d / f_c,90,d ≤ 1.0 = 0.9462 / 1.6 = 0.5914 | PASS ⚠ |
| Deflection span 1 (characteristic, incl. creep) | EN 1995-1-1 §2.2.3, 7.2 | w_tot,1 = elastic line, worst Q arrangement + creep = x = 2.25 m = 15.47 mm | |
| Deflection span 1 (appearance) | EN 1990 §A1.4.3 (NB); EN 1995-1-1 7.2 (NB) | w_qp / w_lim = w_qp / (0.004 · l) ≤ 1.0 = 11.07 / (0.004 · 4500) = 0.6151 | PASS ⚠ |
| Deflection span 1 (additional, frequent) | EN 1990 §A1.4.3 (NB); EN 1995-1-1 7.2 (NB) | w_add,freq / w_lim = w_add,freq / (0.003 · l) ≤ 1.0 = 7.297 / (0.003 · 4500) = 0.5405 | PASS ⚠ |
Outcome
PASS — all checks satisfied ⚠
- 1 span (4.5 m) on pinned – pinned supports; 90 × 270 mm GL24h, service 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 — 11.4 MPa demand against 16.6 MPa capacity, unity check 0.68 (OK).
- All 7 checks pass.
| Result | Value |
|---|---|
| UC Bending span 1 | 0.6846 |
| UC Shear support 1 | 0.3051 |
| UC Bearing support 1 | 0.5914 |
| UC Shear support 2 | 0.3051 |
| UC Bearing support 2 | 0.5914 |
| UC Deflection span 1 (appearance) | 0.6151 |
| UC Deflection span 1 (additional, frequent) | 0.5405 |
| Governing UC | 0.6846 (Bending span 1) |
| k_mod (permanent) | 0.6 |
| k_mod (medium) | 0.8 |
| k_def | 0.6 |
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 ⚠ |
| γ_M | 1.25 | EN 1995-1-1 2.4.1(1), Table 2.3 (NB) | transcribed ⚠ |
| k_mod | 0.6 | EN 1995-1-1 3.1.3, Table 3.1 (NB) | transcribed ⚠ |
| k_mod | 0.8 | EN 1995-1-1 3.1.3, Table 3.1 (NB) | transcribed ⚠ |
| k_cr | Prismatic section: 1.0. I/T section with solid-timber or glulam web: 1.0 when web thickness ≥ flange width; 0.8 when web thickness < half flange width; linear treatment for intermediate thicknesses. Other I/T sections: 1.0. Box sections: use summed web thickness, with the same 1.0/0.8 conditions. | EN 1995-1-1 6.1.7(2) (NB) | transcribed ⚠ |
| k_def | 0.6 | EN 1995-1-1 3.1.4, Table 3.2 (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 §6.4.3.2, 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 1995-1-1 7.2 (NB), EN 1991-1-1 §characteristic value (input), EN 1991-1-1 §§4 (mean density of the strength class), EN 1995-1-1 §2.2.3, 7.2, EN 1995-1-1 §2.4.1, Eq. (2.14), EN 1995-1-1 §2.4.1, Table 2.3 (NB), EN 1995-1-1 §3.1.3, Table 3.1 (NB), EN 1995-1-1 §3.1.4, Table 3.2 (NB), EN 1995-1-1 §3.3(3), Eq. (3.2), EN 1995-1-1 §5.1, EN 1995-1-1 §5.1; EN 1991-1-1 6.2.1(1), EN 1995-1-1 §6.1.5(1), Eq. (6.3), EN 1995-1-1 §6.1.6, EN 1995-1-1 §6.1.6(1), 6.3.3(3), Eq. (6.33), EN 1995-1-1 §6.1.6; 6.3.3(3), EN 1995-1-1 §6.1.7(1), Eq. (6.13), EN 1995-1-1 §6.1.7(1)–(2), Eq. (6.60), EN 1995-1-1 §6.1.7(2) (NB), EN 1995-1-1 §6.3.3(5), EN 338 / EN 14080 §GL24h: EN 14080:2013 Table 5 as reproduced by structuralbasics.com
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