Material and cross-section, shared by every verification. Change the verification above and these stay as they are.
Checks a rectangular solid-timber or glulam member under axial compression and bending about both axes, to SIA 265:2021: the cross-section where the member is held against buckling, and buckling with bending where it is not. Every step shows its formula and the clause it comes from.
You enter the member, the strengths fc,0,d, fc,0,k, fm,d, fm,k and E0,05 from your copy of SIA 265, the system factor, the lateral support spacings, the actions at the stabilised section and at the unstabilised section (Nd, My,d, Mz,d for each, since they usually differ), any loss of section, the role of the member and the buckling lengths.
You get the three checks with their utilisations and every intermediate value with its clause, and figures. With the Basic plan, it prints as an A4 calculation note.
A glulam member GL24h, b × h = 680 × 280 mm, in service class 2, with N_d = 199 kN, M_y,d = 93 kN·m and M_z,d = 1 kN·m at both sections, and buckling lengths and lateral support spacings of 6.82 m. These are the module's own results for its worked example, computed when this page was built.
| Input | Value | Ref. |
|---|---|---|
| Wood type | Glulam | |
| Strength class | GL24h | |
| Load duration ηt | Short to permanent | § 2.2.6 |
| Service class ηw | 2 | § 3.2.1.3 t.4 |
| Section width b | 680 mm | |
| Section depth h | 280 mm | |
| Design compressive strength ∥ grain fc,0,d | 16 N/mm² | § 3.4.2.2 t.9 |
| Characteristic compressive strength ∥ grain fc,0,k | 24 N/mm² | § Annexe B |
| Design bending strength fm,d | 16 N/mm² | § 3.4.2.2 t.9 |
| Characteristic bending strength fm,k | 24 N/mm² | § Annexe B |
| Modulus of elasticity, 5% fractile E0,05 | 9600 N/mm² | § Annexe B |
| System factor ksys | 1.0 | § 5.7.2.2 |
| Lateral support spacing, bending about y-y ay | 6820 mm | § 4.2.9.3 |
| Lateral support spacing, bending about z-z az | 6820 mm | § 4.2.9.3 |
| Design compressive force Nd | 199 kN | |
| Design moment about y-y My,d | 93 kN·m | |
| Design moment about z-z Mz,d | 1 kN·m | |
| Section loss determined by | None — gross section | |
| Design compressive force Nd | 199 kN | |
| Design moment about y-y My,d | 93 kN·m | |
| Design moment about z-z Mz,d | 1 kN·m | |
| Section loss determined by | None — gross section | |
| Role of the member λlim | Main load-bearing element | § 4.2.8.4 |
| Buckling length given by | Entered directly | |
| Buckling length about y-y lk,y | 6820 mm | |
| Buckling length about z-z lk,z | 6820 mm |
| Step | Value | Ref. |
|---|---|---|
| Gross section areaA = b · h | A = 190,400 mm² | |
| Net section areagross section | Anet = 190,400 mm² | |
| Section modulus about y-yWy = b · h² / 6 | Wy = 8,885,333 mm³ | |
| Section modulus about z-zWz = h · b² / 6 | Wz = 21,578,667 mm³ | |
| Height factor, y-yuses the dimension perpendicular to the axis, here h | kh,y = 1.0792 | § 3.4.2.3 (5) |
| Height factor, z-zfor bending about z-z the relevant dimension is b | kh,z = 1.0000 | § 3.4.2.3 (5) |
| Relative slenderness, y-yλrel,m = 1.15 · (√(ay·h) / b) · √(fm,k / E0,05) | λrel,m,y = 0.1169 | § 4.2.9.3 (42) |
| Relative slenderness, z-zλrel,m = 1.15 · (√(az·b) / h) · √(fm,k / E0,05) | λrel,m,z = 0.4422 | § 4.2.9.3 (42) |
| Lateral torsional buckling factor, y-y | km,y = 1.0000 | § 4.2.9.2 (39) |
| Lateral torsional buckling factor, z-z | km,z = 1.0000 | § 4.2.9.2 (39) |
| Compressive resistancefRd,C = fc,0,d · ηt · ηw | fRd,C = 12.800 N/mm² | § 4.2.2.1 (10) |
| Bending resistance, y-yfRd,m,y = km,y · fm,d · kh,y · ksys · ηt · ηw | fRd,m,y = 13.814 N/mm² | § 4.2.9.1 (38) |
| Bending resistance, z-zfRd,m,z = km,z · fm,d · max(kh,z ; ksys) · ηt · ηw. §3.4.2.2 forbids applying kh and ksys together for bending about z-z. | fRd,m,z = 12.800 N/mm² | § 3.4.2.2 |
| Compressive stressσc,0,d = Nd / Anet | σc,0,d = 1.0452 N/mm² | |
| Bending stress, y-yσm,y,d = My,d / Wy | σm,y,d = 10.4667 N/mm² | |
| Bending stress, z-zσm,z,d = Mz,d / Wz | σm,z,d = 0.0463 N/mm² | |
| Compression with biaxial bending, cross-section(σc/fc)² + σm,y/fm,y + σm,z/fm,z ≤ 1 | η = 0.768 · Pass77 % of the capacity used | § 4.2.4.2 (22) |
| Step | Value | Ref. |
|---|---|---|
| Net section areagross section | Anet = 190,400 mm² | |
| Straightness factor | βc = 0.10 | § 4.2.8.3 |
| Compressive stressσc,0,d = Nd / Anet at this section | σc,0,d = 1.0452 N/mm² | |
| Independent axesThe verification may be carried out independently for the two principal axes, which is why the two checks below are not combined into one. | §4.2.8.5 | § 4.2.8.5 |
| Step | Value | Ref. |
|---|---|---|
| Radius of gyration about y-yiy = 0.289 · h | iy = 80.92 mm | |
| Buckling length about y-y | lk,y = 6,820 mm | |
| Slenderness about y-yλy = lk,y / iy | λy = 84.281 | § 4.2.8.4 |
| Relative slenderness, y-yλrel = (λ/π)·√(fc,0,k / E0,05), not less than 0.30 | λrel,y = 1.3414 | § 4.2.8.4 (34) |
| Auxiliary factor, y-yk = 0.5 · [1 + βc·(λrel − 0.3) + λrel²] | ky = 1.4517 | § 4.2.8.2 (31) |
| Buckling coefficient, y-ykc = 1 / (k + √(k² − λrel²)), with k from equation (31) above | kc,y = 0.4983 | § 4.2.8.2 (30) |
| Compressive resistance, y-yfRd,C,y = kc,y · fc,0,d · ηt · ηw | fRd,C,y = 6.378 N/mm² | |
| Bending stress, y-y | σm,y,d = 10.4667 N/mm² | |
| Buckling about y-y with bending about y-yσc/(kc,y·fc) + σm,y/(km,y·fm) ≤ 1 | η = 0.922 · Pass92 % of the capacity used | § 4.2.8.5 (37) |
| Step | Value | Ref. |
|---|---|---|
| Radius of gyration about z-ziz = 0.289 · b | iz = 196.52 mm | |
| Buckling length about z-z | lk,z = 6,820 mm | |
| Slenderness about z-zλz = lk,z / iz | λz = 34.704 | § 4.2.8.4 |
| Relative slenderness, z-zλrel = (λ/π)·√(fc,0,k / E0,05), not less than 0.30 | λrel,z = 0.5523 | § 4.2.8.4 (34) |
| Auxiliary factor, z-zk = 0.5 · [1 + βc·(λrel − 0.3) + λrel²] | kz = 0.6652 | § 4.2.8.2 (31) |
| Buckling coefficient, z-zkc = 1 / (k + √(k² − λrel²)), with k from equation (31) above | kc,z = 0.9655 | § 4.2.8.2 (30) |
| Compressive resistance, z-zfRd,C,z = kc,z · fc,0,d · ηt · ηw | fRd,C,z = 12.358 N/mm² | |
| Bending stress, z-z | σm,z,d = 0.0463 N/mm² | |
| Buckling about z-z with bending about z-zσc/(kc,z·fc) + σm,z/(km,z·fm) ≤ 1 | η = 0.088 · Pass9 % of the capacity used | § 4.2.8.5 (37) |
Verified clause by clause against SIA 265:2021 and against independent calculations used on real projects, before release.
The section held against buckling and the section where buckling can occur usually carry different actions, and they are verified with different equations: (22) for the cross-section, (37) for buckling with bending.
That is the form of SIA 265 equation (22) for compression with bending on the cross-section; the buckling check, equation (37), is linear in each term.
The full calculation is shown on screen, free and without an account. A print-ready A4 calculation note is part of the Basic plan.
Norm: SIA 265:2021 · Page updated: 20 October 2026