Checks a rectangular solid-timber or glulam bar under axial tension and bending about both principal axes at the ultimate limit state, to SIA 265:2021, including lateral torsional buckling. Every step shows its formula and the clause it comes from.

What it checks

Tension with biaxial bending, clause 4.2.4.1, equation (21): σ_t,0,d / f_Rd,T + σ_m,y,d / f_Rd,m,y + σ_m,z,d / f_Rd,m,z ≤ 1. The three utilisations add linearly.
Stresses: σ_t,0,d = N_d / A_net, σ_m,y,d = M_y,d / W_y and σ_m,z,d = M_z,d / W_z, with W_y = b · h² / 6 and W_z = h · b² / 6.
Net section, clause 6.1.1.8: A_net from an indicative coefficient for the fastener type, or entered directly.
Tensile resistance, clause 4.2.1.1, equation (6): f_Rd,T = f_t,0,d · η_t · η_w.
Bending resistance, clause 4.2.9.1, equation (38): f_Rd,m,y = k_m,y · f_m,d · k_h,y · k_sys · η_t · η_w. About z-z, clause 3.4.2.2 forbids applying k_h and k_sys together, so the larger of k_h,z and k_sys is taken.
Height factors k_h,y (from h) and k_h,z (from b), clause 3.4.2.3, equation (5).
Lateral torsional buckling for each axis: λ_rel,m,y and λ_rel,m,z (clause 4.2.9.3, equation (42)) and k_m,y, k_m,z (clause 4.2.9.2, equation (39)).

What you enter and what you get

You enter the member (wood type, strength class, load duration, service class, b, h), the strengths f_t,0,d and f_m,d from your copy of SIA 265 (clause 3.4.2.2, table 9), f_m,k and E_0,05 (annex B), the system factor k_sys, the design forces N_d, M_y,d and M_z,d, the method for the net section and the fastener type, and the lateral support spacings a_y and a_z.

You get the areas, section moduli, factors, resistances and stresses, and the utilisation of equation (21) with a pass or fail, each with its clause. With the Basic plan, it prints as an A4 calculation note.

Assumptions and limits

Rectangular members of solid timber (including finger-jointed and reconstituted timber) or glulam. Tension is positive.
The net area reduces the tensile stress only; W_y and W_z are taken from the full b and h. For the full connection calculation, use the tension module.
Enter a spacing of 0 where the compression edge is held continuously, which gives k_m = 1. The slenderness expression assumes a constant moment between supports.
E_0,05 is the characteristic value, not reduced by η_w. k_sys applies to structural safety verifications only.
For compression with bending, use its own module. The fire situation is its own module.

Worked example

A glulam bar GL24h, b × h = 280 × 440 mm, in service class 2 under short to permanent actions, with N_d = 33 kN, M_y,d = 103 kN·m and M_z,d = 2 kN·m, the net section from the indicative coefficient for wood–wood dowels, the compression edge held for bending about y-y and lateral supports every 5.15 m for bending about z-z. These are the module's own results for its worked example, computed when this page was built.

Inputs
Input	Value	Ref.
Wood type	Glulam
Strength class	GL24h
Load duration η_t	Short to permanent	§ 2.2.6
Service class η_w	2	§ 3.2.1.3 t.4
Section width b	280 mm
Section depth h	440 mm
Design tensile strength ∥ grain f_t,0,d	12.8 N/mm²	§ 3.4.2.2 t.9
Design bending strength f_m,d	16 N/mm²	§ 3.4.2.2 t.9
Characteristic bending strength f_m,k	24 N/mm²	§ Annexe B
Modulus of elasticity, 5% fractile E_0,05	9600 N/mm²	§ Annexe B
System factor k_sys	1.0	§ 5.7.2.2
Design tensile force N_d	33 kN
Design moment about y-y M_y,d	103 kN·m
Design moment about z-z M_z,d	2 kN·m
Section loss determined by	Indicative coefficient (pre-design)
Fastener type A_net/A	Dowel, wood–wood
Lateral support spacing, bending about y-y a_y	0 mm	§ 4.2.9.3
Lateral support spacing, bending about z-z a_z	5150 mm	§ 4.2.9.3

Calculation: Ultimate limit state
Step	Value	Ref.
Gross section areaA = b · h	A = 123,200 mm²
Net section areaA_net = 0.65 · A	A_net = 80,080 mm²	§ 6.1.1.8
Section modulus about y-yW_y = b · h² / 6	W_y = 9,034,667 mm³
Section modulus about z-zW_z = h · b² / 6	W_z = 5,749,333 mm³
Height factor, y-yk_h uses the dimension perpendicular to the axis considered, here h	k_h,y = 1.0315	§ 3.4.2.3 (5)
Height factor, z-zfor bending about z-z the relevant dimension is b	k_h,z = 1.0792	§ 3.4.2.3 (5)
Relative slenderness, y-yλ_rel,m = 1.15 · (√(a_y·h) / b) · √(f_m,k / E_0,05); 0 when the edge is held	λ_rel,m,y = 0.0000	§ 4.2.9.3 (42)
Relative slenderness, z-zλ_rel,m = 1.15 · (√(a_z·b) / h) · √(f_m,k / E_0,05)	λ_rel,m,z = 0.1569	§ 4.2.9.3 (42)
Lateral torsional buckling factor, y-y	k_m,y = 1.0000	§ 4.2.9.2 (39)
Lateral torsional buckling factor, z-z	k_m,z = 1.0000	§ 4.2.9.2 (39)
Tensile resistancef_Rd,T = f_t,0,d · η_t · η_w	f_Rd,T = 10.240 N/mm²	§ 4.2.1.1 (6)
Bending resistance, y-yf_Rd,m,y = k_m,y · f_m,d · k_h,y · k_sys · η_t · η_w	f_Rd,m,y = 13.203 N/mm²	§ 4.2.9.1 (38)
Bending resistance, z-zf_Rd,m,z = k_m,z · f_m,d · max(k_h,z ; k_sys) · η_t · η_w. For bending about z-z, §3.4.2.2 forbids applying k_h and k_sys together, so the larger of the two is taken.	f_Rd,m,z = 13.814 N/mm²	§ 3.4.2.2
Tensile stressσ_t,0,d = N_d / A_net	σ_t,0,d = 0.4121 N/mm²
Bending stress, y-yσ_m,y,d = M_y,d / W_y	σ_m,y,d = 11.4005 N/mm²
Bending stress, z-zσ_m,z,d = M_z,d / W_z	σ_m,z,d = 0.3479 N/mm²
Tension with biaxial bendingσ_t/f_t + σ_m,y/f_m,y + σ_m,z/f_m,z ≤ 1	η = 0.929 · Pass93 % of the capacity used	§ 4.2.4.1 (21)

How this module is verified

Verified clause by clause against SIA 265:2021 and against independent calculations used on real projects, before release.

Questions

Why does the net section reduce only the tensile stress?

The module takes the section moduli from the full section and applies the connection loss to the axial term only. Where the connection needs a detailed net-section calculation, the tension module provides it.

Why is the larger of k_h and k_sys taken about z-z?

Clause 3.4.2.2 forbids applying both together for bending about z-z, so the module uses the larger of the two.

Can I print the calculation?

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: 21 October 2026

Timber bar in tension and biaxial bending to SIA 265

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