1. Project information
Calculation report
| Date | 31/10/2026 |
|---|
2. Overview of the structure
The structure with the numbers of the nodes (n), members (m) and supports (S), and the length of each member (mm).
| Sections and materials | Members |
|---|---|
| RECT 50x100 · C24 | 1 |
2 nodes, 1 members · consequence class CC1, new build · design code Eurocode · Z is the vertical axis · units: kN, kNm, mm.
3. Summary of the results
| Quantity | Max. value | Combination | Where |
|---|---|---|---|
| Moment My (strong axis) | 0.5 kNm | ULS 6.10b (CC1 new) | member b, x = 750 mm |
| Normal force N (− compression) | 0.0 kN | ULS 6.10a (CC1 new) | – |
| Shear force Vz (strong axis) | 1.3 kN | ULS 6.10b (CC1 new) | member b, x = 0 mm |
| Vertical reaction | 1.3 kN | ULS 6.10b (CC1 new) | node A |
| Displacement (max., incl. between nodes) | 1.99 mm | SLS char. | member b, x = 750 mm |
| Deflection of a member (relative to chord) | 2.68 mm (L/559) | SLS char. | member b |
Moments, forces and reactions: the governing ULS combination. Displacement: the governing SLS combination (the ULS combinations if there is no SLS combination).
Highest unity check: UC 0.45 in member b (RECT 50x100): deflection (SLS).
4. Nodes, members and supports
Nodes
| Node | x (mm) | y (mm) | z (mm) | Support |
|---|---|---|---|---|
| A | 0 | 0 | 0 | S1 |
| B | 1500 | 0 | 0 | S2 |
Members
| Member | Nodes | L (mm) | Section | Material | Remarks |
|---|---|---|---|---|---|
| b | A – B | 1500 | RECT 50x100 | C24 | sideways supports at 1000 |
Supports
| Support | Node | Restraint | Springs |
|---|---|---|---|
| S1 | A | pinned (translations fixed) | |
| S2 | B | pinned (translations fixed) |
5. Loads
Loads: Permanent (G)
| Type | On | Value |
|---|---|---|
| Line load | member b | X 0.00, Y 0.00, Z -0.54 kN/m |
Loads: Variable (Q)
| Type | On | Value |
|---|---|---|
| Line load | member b | X 0.00, Y 0.00, Z -0.82 kN/m |
The self weight of members, walls and slabs is automatic (case SW) and is not drawn. Loads are shown as in the model; combination factors are in the table at the end.
6. Load combinations
Consequence class CC1, new build.
| Combination | Kind | SW | G | Q |
|---|---|---|---|---|
| ULS 6.10a (CC1 new) | ULS | 1.22 | 1.22 | 0.54 |
| ULS 6.10b (CC1 new) | ULS | 1.08 | 1.08 | 1.35 |
| SLS char. | SLS | 1 | 1 | 1 |
| ULS 0.9·G favourable (CC1 new) | ULS | 0.9 | 0.9 | 0 |
| ULS 0.9·G + Variable (Q) (CC1 new) | ULS | 0.9 | 0.9 | 1.35 |
| ULS γG·G permanent only (CC1 new) | ULS | 1.22 | 1.22 | 0 |
| ULS 0.9·G + ψ0 variable (CC1 new) | ULS | 0.9 | 0.9 | 0.54 |
| SLS permanent (G) | SLS | 1 | 1 | 0 |
| SLS quasi-permanent (G + ψ2·Q) | SLS | 1 | 1 | 0.3 |
| SLS frequent (G + ψ1·Q) | SLS | 1 | 1 | 0.5 |
SW = Self weight; G = Permanent (G); Q = Variable (Q). SW = self weight.
7. Moments, normal forces and shear forces
Bending moment
Maximum 0.5 kNm in member b, x = 750 mm. (ULS 6.10b (CC1 new))
Normal force
Maximum 0.0 kN (− compression) in member , x = 0 mm. (ULS 6.10a (CC1 new))
Shear force
Maximum 1.3 kN in member b, x = 0 mm. (ULS 6.10b (CC1 new))
Largest section forces per member — ULS 6.10b (CC1 new)
| Member | L (mm) | |M| max (kNm) | N at max |N| (kN) | |V| max (kN) |
|---|---|---|---|---|
| b | 1500 | 0.5 | 0.0 | 1.3 |
The 12 members with the largest moment. All members are in the calculation; open a member for the full values.
Support reactions
Largest vertical reaction 1.3 kN at node A. Total vertical reaction 2.6 kN. (ULS 6.10b (CC1 new))
Support reactions (envelope of the ULS combinations)
| Support | Node | x, y, z (mm) | FX (kN) | FY (kN) | FZ (kN) |
|---|---|---|---|---|---|
| S1 | A | 0, 0, 0 | 0.0 | 0.0 | 1.3 |
| S2 | B | 1500, 0, 0 | 0.0 | 0.0 | 1.3 |
For every component the value of the largest magnitude over all ULS combinations (sign as in the global axes, Z up), so the horizontal reactions are included. The largest vertical reaction (total 2.6 kN) occurs in ULS 6.10b (CC1 new). Forces in kN; there are no horizontal reactions or support moments.
Vertical support reactions: envelope of the ULS combinations (min / max)
| Support | Node | Min (kN) | Max (kN) |
|---|---|---|---|
| S1 | A | 0.38 | 1.28 |
| S2 | B | 0.38 | 1.28 |
Deformation
Maximum displacement 1.99 mm at node b. (SLS char.)
Deflection and sway check (SLS)
| Member | L (mm) | δ (mm) | Limit | Limit (mm) | δ / limit | |
|---|---|---|---|---|---|---|
| b | 1500 | 2.68 | L/250 | 6.00 | 0.45 | within the limit |
δ is the largest deflection relative to the chord between the member ends (columns: the horizontal sway of the top relative to the bottom, h = height; the bending of the column itself is not part of this check) in SLS char.. Standard limit L/250; set a stricter limit (e.g. L/500 with masonry or a brittle finish) per member. The values are project requirements: check the National Annex.
Results per combination
| Combination | M min (kNm) | M max (kNm) | V min (kN) | V max (kN) | N min (kN) | N max (kN) | Vertical reaction (kN): S1 / S2 | Max. displacement (mm) |
|---|---|---|---|---|---|---|---|---|
| ULS 6.10a (CC1 new) | 0.00 | 0.32 | -0.85 | 0.85 | 0.00 | 0.00 | 0.85 / 0.85 | 1.62 |
| ULS 6.10b (CC1 new) | 0.00 | 0.48 | -1.28 | 1.28 | 0.00 | 0.00 | 1.28 / 1.28 | 2.46 |
| SLS char. | 0.00 | 0.39 | -1.04 | 1.04 | 0.00 | 0.00 | 1.04 / 1.04 | 1.99 |
| ULS 0.9·G favourable (CC1 new) | 0.00 | 0.14 | -0.38 | 0.38 | 0.00 | 0.00 | 0.38 / 0.38 | 0.73 |
| ULS 0.9·G + Variable (Q) (CC1 new) | 0.00 | 0.45 | -1.21 | 1.21 | 0.00 | 0.00 | 1.21 / 1.21 | 2.32 |
| ULS γG·G permanent only (CC1 new) | 0.00 | 0.19 | -0.51 | 0.51 | 0.00 | 0.00 | 0.51 / 0.51 | 0.98 |
| ULS 0.9·G + ψ0 variable (CC1 new) | 0.00 | 0.27 | -0.71 | 0.71 | 0.00 | 0.00 | 0.71 / 0.71 | 1.36 |
| SLS permanent (G) | 0.00 | 0.16 | -0.42 | 0.42 | 0.00 | 0.00 | 0.42 / 0.42 | 0.81 |
| SLS quasi-permanent (G + ψ2·Q) | 0.00 | 0.23 | -0.61 | 0.61 | 0.00 | 0.00 | 0.61 / 0.61 | 1.16 |
| SLS frequent (G + ψ1·Q) | 0.00 | 0.27 | -0.73 | 0.73 | 0.00 | 0.00 | 0.73 / 0.73 | 1.40 |
Moment and shear force about the strong axis, section forces at 21 points per member; N − = compression. Displacement: the largest, including between the nodes.
8. Unity checks and calculations
Members coloured by their governing unity check: green up to UC 1.00, red above. The deflection check counts too.
| Member | Section | UC | Governing check |
|---|---|---|---|
| b | RECT 50x100 | 0.45 | deflection (SLS) |
Member calculations
Detailed calculations of the members with a check (concrete EN 1992-1-1, steel EN 1993-1-1 / AISC 360).
Timber member b — RECT 50x100, C24
NEN-EN 1995-1-1 (Eurocode 5), ultimate limit state. Characteristic strengths from EN 338.
1. Input
| Section | b × h | 50 × 100 mm |
| Strength class | fm,k, ft,0,k, fc,0,k, fv,k | C24: 24, 14.5, 21, 4 N/mm² |
| Stiffness | E0,05, E0,mean | 7400, 11000 N/mm² |
| Service class | kmod permanent / medium / short | 1: 0.6 / 0.8 / 0.9 (kdef = 0.6) |
| Length | 1500 mm | |
| Lateral restraint points | unrestrained lengths | 1000 mm, 500 mm |
| Load position, ky, kz | top, 1, 1 |
1a. Design values, governing combination (medium-term)
| kmod, γM | table 3.1, NB | 0.8, 1.3 |
| kh | bending y, bending z, tension | 1.084, 1.246, 1.084 |
| fm,y,d, fm,z,d | kmod kh fm,k / γM | 16.02, 18.40 N/mm² |
| ft,0,d, ft,90,d | 9.68, 0.25 N/mm² | |
| fc,0,d, fc,90,d | 12.92, 1.54 N/mm² | |
| fv,d | 2.46 N/mm² |
1b. Stability
Stability parameters member
NEN-EN 1995-1-1 6.3.2
| System length and buckling lengths | l_sys = L, l_cr = k·L = l_sys = 1500 mm, l_cr,y = 1500 mm, l_cr,z = 1500 mm | 1500 mm |
| Slenderness λ_y, λ_z [NEN-EN 1995-1-1 (6.21)] | l_cr / i, i_y = h/√12, i_z = b/√12 = λ_y = 52, λ_z = 103.9 | 51.962 |
| Relative slenderness λ_rel,y, λ_rel,z [NEN-EN 1995-1-1 (6.21, 6.22)] | λ/π · √(f_c,0,k / E_0,05) = λ_rel,y = 0.881, λ_rel,z = 1.762 | 0.8811 |
| Straightness factor β_c [NEN-EN 1995-1-1 (6.29)] | solid timber = β_c = 0.2 | 0.2 |
| k_y, k_z [NEN-EN 1995-1-1 (6.27, 6.28)] | 0.5 (1 + β_c (λ_rel − 0.3) + λ_rel²) = k_y = 0.946, k_z = 2.199 | 0.94628 |
| k_c,y, k_c,z [NEN-EN 1995-1-1 (6.25, 6.26)] | 1 / (k + √(k² − λ_rel²)) = k_c,y = 0.774, k_c,z = 0.285 given for every member; the buckling check itself applies under compression | 0.77436 |
2. Results per combination
| ULS 6.10a (CC1 new) (medium-term) | Bending, x = 750 mm | 0.24 |
| ULS 6.10b (CC1 new) (medium-term) | Bending, x = 750 mm | 0.36 |
| ULS 0.9·G favourable (CC1 new) (permanent) | Bending, x = 750 mm | 0.14 |
| ULS 0.9·G + Variable (Q) (CC1 new) (medium-term) | Bending, x = 750 mm | 0.34 |
| ULS γG·G permanent only (CC1 new) (permanent) | Bending, x = 750 mm | 0.19 |
| ULS 0.9·G + ψ0 variable (CC1 new) (medium-term) | Bending, x = 750 mm | 0.20 |
3. Calculation of every combination
ULS 6.10a (CC1 new) 0.24
0.24 Bending x = 750 mm
NEN-EN 1995-1-1 6.1.6 (6.11, 6.12)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, medium-term = k_mod = 0.8 | 0.8 |
| Partial factor γ_M [NB table NA.2] | solid timber = γ_M = 1.3 | 1.3 |
| Size factor k_h [NEN-EN 1995-1-1 3.2(3)] | min(1.3; (150/h)^0.2) = h = 100 mm: k_h,m,y = 1.084, tension k_h,t = 1.084 | 1.0845 |
| Design bending strength f_m,y,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · k_h · f_m,k / γ_M = 0.8 · 1.084 · 24 / 1.3 = 16.02 | 16.017 N/mm² |
| Bending stress σ_m,y,d | M_y / W_y = 0.317 kNm / 83.3 cm³ = 3.8 | 3.8044 N/mm² |
| Check (6.11) | σ_m,y/f_m,y + k_m σ_m,z/f_m,z ≤ 1 = 0 + 0.238 + 0 = 0.238 | 0.23752 |
| Check (6.12) [k_m = 0.7 (rectangular section)] | k_m σ_m,y/f_m,y + σ_m,z/f_m,z ≤ 1 = 0 + 0.166 + 0 = 0.166 | 0.16627 |
0.24 Lateral torsional buckling x = 750 mm
NEN-EN 1995-1-1 6.3.3 (6.33)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, medium-term = k_mod = 0.8 | 0.8 |
| Partial factor γ_M [NB table NA.2] | solid timber = γ_M = 1.3 | 1.3 |
| Size factor k_h [NEN-EN 1995-1-1 3.2(3)] | min(1.3; (150/h)^0.2) = h = 100 mm: k_h,m,y = 1.084, tension k_h,t = 1.084 | 1.0845 |
| Design bending strength f_m,y,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · k_h · f_m,k / γ_M = 0.8 · 1.084 · 24 / 1.3 = 16.02 | 16.017 N/mm² |
| Bending stress σ_m,y,d | M_y / W_y = 0.317 kNm / 83.3 cm³ = 3.8 | 3.8044 N/mm² |
| Effective length l_ef [NEN-EN 1995-1-1 table 6.1 (simply supported, uniform load)] | 0.9·l + 2h = l = 1000 mm: l_ef = 1100 mm | 1100 mm |
| Critical bending stress σ_m,crit [NEN-EN 1995-1-1 6.3.3 (6.32)] | 0.78 b² E_0,05 / (h · l_ef) = 0.78 · 50² · 7400 / (100 · 1100) = 131.18 | 131.18 N/mm² |
| Relative slenderness λ_rel,m [NEN-EN 1995-1-1 (6.30)] | √(f_m,k / σ_m,crit) = √(24 / 131.18) = 0.428 | 0.42773 |
| Lateral buckling factor k_crit [NEN-EN 1995-1-1 (6.34)] | 1 (≤ 0.75); 1.56 − 0.75λ (≤ 1.4); 1/λ² = k_crit = 1 | 1 |
| Check (6.33) | σ_m,d / (k_crit f_m,d) ≤ 1 = 0.238 = 0.238 | 0.23752 |
0.15 Shear x = 0 mm
NEN-EN 1995-1-1 6.1.7 (6.13)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, medium-term = k_mod = 0.8 | 0.8 |
| Design shear strength f_v,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · f_v,k / γ_M = 0.8 · 4 / 1.3 = 2.46 | 2.4615 N/mm² |
| Shear stress τ_d [NEN-EN 1995-1-1 (6.13, 6.13a)] | 1.5 V / (k_cr b h), k_cr = 0.67 = 1.5 · 0.845 kN / (0.67 · 50 · 100) = 0.379 | 0.37854 N/mm² |
| Check (6.13) | τ_d / f_v,d ≤ 1 = 0.379 / 2.46 = 0.154 | 0.15378 |
ULS 6.10b (CC1 new) 0.36
0.36 Bending x = 750 mm
NEN-EN 1995-1-1 6.1.6 (6.11, 6.12)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, medium-term = k_mod = 0.8 | 0.8 |
| Partial factor γ_M [NB table NA.2] | solid timber = γ_M = 1.3 | 1.3 |
| Size factor k_h [NEN-EN 1995-1-1 3.2(3)] | min(1.3; (150/h)^0.2) = h = 100 mm: k_h,m,y = 1.084, tension k_h,t = 1.084 | 1.0845 |
| Design bending strength f_m,y,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · k_h · f_m,k / γ_M = 0.8 · 1.084 · 24 / 1.3 = 16.02 | 16.017 N/mm² |
| Bending stress σ_m,y,d | M_y / W_y = 0.482 kNm / 83.3 cm³ = 5.78 | 5.781 N/mm² |
| Check (6.11) | σ_m,y/f_m,y + k_m σ_m,z/f_m,z ≤ 1 = 0 + 0.361 + 0 = 0.361 | 0.36093 |
| Check (6.12) [k_m = 0.7 (rectangular section)] | k_m σ_m,y/f_m,y + σ_m,z/f_m,z ≤ 1 = 0 + 0.253 + 0 = 0.253 | 0.25265 |
0.36 Lateral torsional buckling x = 750 mm
NEN-EN 1995-1-1 6.3.3 (6.33)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, medium-term = k_mod = 0.8 | 0.8 |
| Partial factor γ_M [NB table NA.2] | solid timber = γ_M = 1.3 | 1.3 |
| Size factor k_h [NEN-EN 1995-1-1 3.2(3)] | min(1.3; (150/h)^0.2) = h = 100 mm: k_h,m,y = 1.084, tension k_h,t = 1.084 | 1.0845 |
| Design bending strength f_m,y,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · k_h · f_m,k / γ_M = 0.8 · 1.084 · 24 / 1.3 = 16.02 | 16.017 N/mm² |
| Bending stress σ_m,y,d | M_y / W_y = 0.482 kNm / 83.3 cm³ = 5.78 | 5.781 N/mm² |
| Effective length l_ef [NEN-EN 1995-1-1 table 6.1 (simply supported, uniform load)] | 0.9·l + 2h = l = 1000 mm: l_ef = 1100 mm | 1100 mm |
| Critical bending stress σ_m,crit [NEN-EN 1995-1-1 6.3.3 (6.32)] | 0.78 b² E_0,05 / (h · l_ef) = 0.78 · 50² · 7400 / (100 · 1100) = 131.18 | 131.18 N/mm² |
| Relative slenderness λ_rel,m [NEN-EN 1995-1-1 (6.30)] | √(f_m,k / σ_m,crit) = √(24 / 131.18) = 0.428 | 0.42773 |
| Lateral buckling factor k_crit [NEN-EN 1995-1-1 (6.34)] | 1 (≤ 0.75); 1.56 − 0.75λ (≤ 1.4); 1/λ² = k_crit = 1 | 1 |
| Check (6.33) | σ_m,d / (k_crit f_m,d) ≤ 1 = 0.361 = 0.361 | 0.36093 |
0.23 Shear x = 0 mm
NEN-EN 1995-1-1 6.1.7 (6.13)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, medium-term = k_mod = 0.8 | 0.8 |
| Design shear strength f_v,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · f_v,k / γ_M = 0.8 · 4 / 1.3 = 2.46 | 2.4615 N/mm² |
| Shear stress τ_d [NEN-EN 1995-1-1 (6.13, 6.13a)] | 1.5 V / (k_cr b h), k_cr = 0.67 = 1.5 · 1.285 kN / (0.67 · 50 · 100) = 0.575 | 0.57522 N/mm² |
| Check (6.13) | τ_d / f_v,d ≤ 1 = 0.575 / 2.46 = 0.234 | 0.23368 |
ULS 0.9·G favourable (CC1 new) 0.14
0.14 Bending x = 750 mm
NEN-EN 1995-1-1 6.1.6 (6.11, 6.12)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, permanent = k_mod = 0.6 | 0.6 |
| Partial factor γ_M [NB table NA.2] | solid timber = γ_M = 1.3 | 1.3 |
| Size factor k_h [NEN-EN 1995-1-1 3.2(3)] | min(1.3; (150/h)^0.2) = h = 100 mm: k_h,m,y = 1.084, tension k_h,t = 1.084 | 1.0845 |
| Design bending strength f_m,y,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · k_h · f_m,k / γ_M = 0.6 · 1.084 · 24 / 1.3 = 12.01 | 12.013 N/mm² |
| Bending stress σ_m,y,d | M_y / W_y = 0.142 kNm / 83.3 cm³ = 1.7 | 1.704 N/mm² |
| Check (6.11) | σ_m,y/f_m,y + k_m σ_m,z/f_m,z ≤ 1 = 0 + 0.142 + 0 = 0.142 | 0.14185 |
| Check (6.12) [k_m = 0.7 (rectangular section)] | k_m σ_m,y/f_m,y + σ_m,z/f_m,z ≤ 1 = 0 + 0.099 + 0 = 0.099 | 0.099298 |
0.14 Lateral torsional buckling x = 750 mm
NEN-EN 1995-1-1 6.3.3 (6.33)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, permanent = k_mod = 0.6 | 0.6 |
| Partial factor γ_M [NB table NA.2] | solid timber = γ_M = 1.3 | 1.3 |
| Size factor k_h [NEN-EN 1995-1-1 3.2(3)] | min(1.3; (150/h)^0.2) = h = 100 mm: k_h,m,y = 1.084, tension k_h,t = 1.084 | 1.0845 |
| Design bending strength f_m,y,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · k_h · f_m,k / γ_M = 0.6 · 1.084 · 24 / 1.3 = 12.01 | 12.013 N/mm² |
| Bending stress σ_m,y,d | M_y / W_y = 0.142 kNm / 83.3 cm³ = 1.7 | 1.704 N/mm² |
| Effective length l_ef [NEN-EN 1995-1-1 table 6.1 (simply supported, uniform load)] | 0.9·l + 2h = l = 1000 mm: l_ef = 1100 mm | 1100 mm |
| Critical bending stress σ_m,crit [NEN-EN 1995-1-1 6.3.3 (6.32)] | 0.78 b² E_0,05 / (h · l_ef) = 0.78 · 50² · 7400 / (100 · 1100) = 131.18 | 131.18 N/mm² |
| Relative slenderness λ_rel,m [NEN-EN 1995-1-1 (6.30)] | √(f_m,k / σ_m,crit) = √(24 / 131.18) = 0.428 | 0.42773 |
| Lateral buckling factor k_crit [NEN-EN 1995-1-1 (6.34)] | 1 (≤ 0.75); 1.56 − 0.75λ (≤ 1.4); 1/λ² = k_crit = 1 | 1 |
| Check (6.33) | σ_m,d / (k_crit f_m,d) ≤ 1 = 0.142 = 0.142 | 0.14185 |
0.09 Shear x = 0 mm
NEN-EN 1995-1-1 6.1.7 (6.13)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, permanent = k_mod = 0.6 | 0.6 |
| Design shear strength f_v,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · f_v,k / γ_M = 0.6 · 4 / 1.3 = 1.85 | 1.8462 N/mm² |
| Shear stress τ_d [NEN-EN 1995-1-1 (6.13, 6.13a)] | 1.5 V / (k_cr b h), k_cr = 0.67 = 1.5 · 0.379 kN / (0.67 · 50 · 100) = 0.17 | 0.16956 N/mm² |
| Check (6.13) | τ_d / f_v,d ≤ 1 = 0.17 / 1.85 = 0.092 | 0.091843 |
ULS 0.9·G + Variable (Q) (CC1 new) 0.34
0.34 Bending x = 750 mm
NEN-EN 1995-1-1 6.1.6 (6.11, 6.12)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, medium-term = k_mod = 0.8 | 0.8 |
| Partial factor γ_M [NB table NA.2] | solid timber = γ_M = 1.3 | 1.3 |
| Size factor k_h [NEN-EN 1995-1-1 3.2(3)] | min(1.3; (150/h)^0.2) = h = 100 mm: k_h,m,y = 1.084, tension k_h,t = 1.084 | 1.0845 |
| Design bending strength f_m,y,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · k_h · f_m,k / γ_M = 0.8 · 1.084 · 24 / 1.3 = 16.02 | 16.017 N/mm² |
| Bending stress σ_m,y,d | M_y / W_y = 0.453 kNm / 83.3 cm³ = 5.44 | 5.4402 N/mm² |
| Check (6.11) | σ_m,y/f_m,y + k_m σ_m,z/f_m,z ≤ 1 = 0 + 0.34 + 0 = 0.34 | 0.33965 |
| Check (6.12) [k_m = 0.7 (rectangular section)] | k_m σ_m,y/f_m,y + σ_m,z/f_m,z ≤ 1 = 0 + 0.238 + 0 = 0.238 | 0.23776 |
0.34 Lateral torsional buckling x = 750 mm
NEN-EN 1995-1-1 6.3.3 (6.33)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, medium-term = k_mod = 0.8 | 0.8 |
| Partial factor γ_M [NB table NA.2] | solid timber = γ_M = 1.3 | 1.3 |
| Size factor k_h [NEN-EN 1995-1-1 3.2(3)] | min(1.3; (150/h)^0.2) = h = 100 mm: k_h,m,y = 1.084, tension k_h,t = 1.084 | 1.0845 |
| Design bending strength f_m,y,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · k_h · f_m,k / γ_M = 0.8 · 1.084 · 24 / 1.3 = 16.02 | 16.017 N/mm² |
| Bending stress σ_m,y,d | M_y / W_y = 0.453 kNm / 83.3 cm³ = 5.44 | 5.4402 N/mm² |
| Effective length l_ef [NEN-EN 1995-1-1 table 6.1 (simply supported, uniform load)] | 0.9·l + 2h = l = 1000 mm: l_ef = 1100 mm | 1100 mm |
| Critical bending stress σ_m,crit [NEN-EN 1995-1-1 6.3.3 (6.32)] | 0.78 b² E_0,05 / (h · l_ef) = 0.78 · 50² · 7400 / (100 · 1100) = 131.18 | 131.18 N/mm² |
| Relative slenderness λ_rel,m [NEN-EN 1995-1-1 (6.30)] | √(f_m,k / σ_m,crit) = √(24 / 131.18) = 0.428 | 0.42773 |
| Lateral buckling factor k_crit [NEN-EN 1995-1-1 (6.34)] | 1 (≤ 0.75); 1.56 − 0.75λ (≤ 1.4); 1/λ² = k_crit = 1 | 1 |
| Check (6.33) | σ_m,d / (k_crit f_m,d) ≤ 1 = 0.34 = 0.34 | 0.33965 |
0.22 Shear x = 0 mm
NEN-EN 1995-1-1 6.1.7 (6.13)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, medium-term = k_mod = 0.8 | 0.8 |
| Design shear strength f_v,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · f_v,k / γ_M = 0.8 · 4 / 1.3 = 2.46 | 2.4615 N/mm² |
| Shear stress τ_d [NEN-EN 1995-1-1 (6.13, 6.13a)] | 1.5 V / (k_cr b h), k_cr = 0.67 = 1.5 · 1.209 kN / (0.67 · 50 · 100) = 0.541 | 0.54131 N/mm² |
| Check (6.13) | τ_d / f_v,d ≤ 1 = 0.541 / 2.46 = 0.22 | 0.21991 |
ULS γG·G permanent only (CC1 new) 0.19
0.19 Bending x = 750 mm
NEN-EN 1995-1-1 6.1.6 (6.11, 6.12)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, permanent = k_mod = 0.6 | 0.6 |
| Partial factor γ_M [NB table NA.2] | solid timber = γ_M = 1.3 | 1.3 |
| Size factor k_h [NEN-EN 1995-1-1 3.2(3)] | min(1.3; (150/h)^0.2) = h = 100 mm: k_h,m,y = 1.084, tension k_h,t = 1.084 | 1.0845 |
| Design bending strength f_m,y,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · k_h · f_m,k / γ_M = 0.6 · 1.084 · 24 / 1.3 = 12.01 | 12.013 N/mm² |
| Bending stress σ_m,y,d | M_y / W_y = 0.192 kNm / 83.3 cm³ = 2.31 | 2.3099 N/mm² |
| Check (6.11) | σ_m,y/f_m,y + k_m σ_m,z/f_m,z ≤ 1 = 0 + 0.192 + 0 = 0.192 | 0.19229 |
| Check (6.12) [k_m = 0.7 (rectangular section)] | k_m σ_m,y/f_m,y + σ_m,z/f_m,z ≤ 1 = 0 + 0.135 + 0 = 0.135 | 0.1346 |
0.19 Lateral torsional buckling x = 750 mm
NEN-EN 1995-1-1 6.3.3 (6.33)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, permanent = k_mod = 0.6 | 0.6 |
| Partial factor γ_M [NB table NA.2] | solid timber = γ_M = 1.3 | 1.3 |
| Size factor k_h [NEN-EN 1995-1-1 3.2(3)] | min(1.3; (150/h)^0.2) = h = 100 mm: k_h,m,y = 1.084, tension k_h,t = 1.084 | 1.0845 |
| Design bending strength f_m,y,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · k_h · f_m,k / γ_M = 0.6 · 1.084 · 24 / 1.3 = 12.01 | 12.013 N/mm² |
| Bending stress σ_m,y,d | M_y / W_y = 0.192 kNm / 83.3 cm³ = 2.31 | 2.3099 N/mm² |
| Effective length l_ef [NEN-EN 1995-1-1 table 6.1 (simply supported, uniform load)] | 0.9·l + 2h = l = 1000 mm: l_ef = 1100 mm | 1100 mm |
| Critical bending stress σ_m,crit [NEN-EN 1995-1-1 6.3.3 (6.32)] | 0.78 b² E_0,05 / (h · l_ef) = 0.78 · 50² · 7400 / (100 · 1100) = 131.18 | 131.18 N/mm² |
| Relative slenderness λ_rel,m [NEN-EN 1995-1-1 (6.30)] | √(f_m,k / σ_m,crit) = √(24 / 131.18) = 0.428 | 0.42773 |
| Lateral buckling factor k_crit [NEN-EN 1995-1-1 (6.34)] | 1 (≤ 0.75); 1.56 − 0.75λ (≤ 1.4); 1/λ² = k_crit = 1 | 1 |
| Check (6.33) | σ_m,d / (k_crit f_m,d) ≤ 1 = 0.192 = 0.192 | 0.19229 |
0.12 Shear x = 0 mm
NEN-EN 1995-1-1 6.1.7 (6.13)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, permanent = k_mod = 0.6 | 0.6 |
| Design shear strength f_v,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · f_v,k / γ_M = 0.6 · 4 / 1.3 = 1.85 | 1.8462 N/mm² |
| Shear stress τ_d [NEN-EN 1995-1-1 (6.13, 6.13a)] | 1.5 V / (k_cr b h), k_cr = 0.67 = 1.5 · 0.513 kN / (0.67 · 50 · 100) = 0.23 | 0.22984 N/mm² |
| Check (6.13) | τ_d / f_v,d ≤ 1 = 0.23 / 1.85 = 0.124 | 0.1245 |
ULS 0.9·G + ψ0 variable (CC1 new) 0.20
0.20 Bending x = 750 mm
NEN-EN 1995-1-1 6.1.6 (6.11, 6.12)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, medium-term = k_mod = 0.8 | 0.8 |
| Partial factor γ_M [NB table NA.2] | solid timber = γ_M = 1.3 | 1.3 |
| Size factor k_h [NEN-EN 1995-1-1 3.2(3)] | min(1.3; (150/h)^0.2) = h = 100 mm: k_h,m,y = 1.084, tension k_h,t = 1.084 | 1.0845 |
| Design bending strength f_m,y,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · k_h · f_m,k / γ_M = 0.8 · 1.084 · 24 / 1.3 = 16.02 | 16.017 N/mm² |
| Bending stress σ_m,y,d | M_y / W_y = 0.267 kNm / 83.3 cm³ = 3.2 | 3.1985 N/mm² |
| Check (6.11) | σ_m,y/f_m,y + k_m σ_m,z/f_m,z ≤ 1 = 0 + 0.2 + 0 = 0.2 | 0.1997 |
| Check (6.12) [k_m = 0.7 (rectangular section)] | k_m σ_m,y/f_m,y + σ_m,z/f_m,z ≤ 1 = 0 + 0.14 + 0 = 0.14 | 0.13979 |
0.20 Lateral torsional buckling x = 750 mm
NEN-EN 1995-1-1 6.3.3 (6.33)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, medium-term = k_mod = 0.8 | 0.8 |
| Partial factor γ_M [NB table NA.2] | solid timber = γ_M = 1.3 | 1.3 |
| Size factor k_h [NEN-EN 1995-1-1 3.2(3)] | min(1.3; (150/h)^0.2) = h = 100 mm: k_h,m,y = 1.084, tension k_h,t = 1.084 | 1.0845 |
| Design bending strength f_m,y,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · k_h · f_m,k / γ_M = 0.8 · 1.084 · 24 / 1.3 = 16.02 | 16.017 N/mm² |
| Bending stress σ_m,y,d | M_y / W_y = 0.267 kNm / 83.3 cm³ = 3.2 | 3.1985 N/mm² |
| Effective length l_ef [NEN-EN 1995-1-1 table 6.1 (simply supported, uniform load)] | 0.9·l + 2h = l = 1000 mm: l_ef = 1100 mm | 1100 mm |
| Critical bending stress σ_m,crit [NEN-EN 1995-1-1 6.3.3 (6.32)] | 0.78 b² E_0,05 / (h · l_ef) = 0.78 · 50² · 7400 / (100 · 1100) = 131.18 | 131.18 N/mm² |
| Relative slenderness λ_rel,m [NEN-EN 1995-1-1 (6.30)] | √(f_m,k / σ_m,crit) = √(24 / 131.18) = 0.428 | 0.42773 |
| Lateral buckling factor k_crit [NEN-EN 1995-1-1 (6.34)] | 1 (≤ 0.75); 1.56 − 0.75λ (≤ 1.4); 1/λ² = k_crit = 1 | 1 |
| Check (6.33) | σ_m,d / (k_crit f_m,d) ≤ 1 = 0.2 = 0.2 | 0.1997 |
0.13 Shear x = 0 mm
NEN-EN 1995-1-1 6.1.7 (6.13)
| Modification factor k_mod [NEN-EN 1995-1-1 3.1.3] | table 3.1, service class 1, medium-term = k_mod = 0.8 | 0.8 |
| Design shear strength f_v,d [NEN-EN 1995-1-1 2.4.1(1)] | k_mod · f_v,k / γ_M = 0.8 · 4 / 1.3 = 2.46 | 2.4615 N/mm² |
| Shear stress τ_d [NEN-EN 1995-1-1 (6.13, 6.13a)] | 1.5 V / (k_cr b h), k_cr = 0.67 = 1.5 · 0.711 kN / (0.67 · 50 · 100) = 0.318 | 0.31826 N/mm² |
| Check (6.13) | τ_d / f_v,d ≤ 1 = 0.318 / 2.46 = 0.129 | 0.12929 |
Serviceability results
Deflection of the member relative to the chord between its ends, per serviceability combination. Final deflection with creep: quasi-permanent and permanent combinations all × (1 + k), characteristic combination G × (1 + k) + Q × (1 + ψ2·k).
| Combination | Deflection (mm) | Final incl. creep (mm) | Reaction at the start (kN) |
|---|---|---|---|
| SLS char. | 1.99 | 2.68 | 1.04 |
| SLS permanent (G) | 0.81 | 1.29 | 0.42 |
| SLS quasi-permanent (G + ψ2·Q) | 1.16 | 1.86 | 0.61 |
| SLS frequent (G + ψ1·Q) | 1.40 | – | 0.73 |
Deflection checks (NEN-EN 1995-1-1 NB)
| Check | Value (mm) | Limit (mm) | Ratio |
|---|---|---|---|
| w1 permanent load, instantaneous | 0.81 | ||
| w2 creep (final − instantaneous) | 0.70 | ||
| winst instantaneous, G + Q | 1.99 | 6.00 (L/250) | 0.33 |
| wbij = wfin − w1 | 1.88 | 4.50 (L/333) | 0.42 |
| wnet,fin final, incl. creep | 2.68 | 6.00 (L/250) | 0.45 |
Conclusion
Maximum unity check = 0.36 — ULS 6.10b (CC1 new): Bending, x = 750 mm.
Connections and fire are not checked. Bearing stress and notches are only checked where you enter a bearing length or a notch; the support reaction is the shear force at the end of the member, or the sum of both sides where another member continues over the support. Load-duration classes follow the load case type (G permanent, Q medium-term, wind short-term).
Calculation steps are in SI units (mm, N, kN, kNm, N/mm²).
For training, testing and educational use; not for the design of real structures.
For training, testing and educational use only. Not for design of real structures. Results are unverified. THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND. Not a substitute for review by a licensed Professional Engineer (PE/SE) or equivalent.