Wood Element Bending Capacity

1 Applied Design Loads (ULS)

M_y,Ed = kN·m design bending moment y-y

M_z,Ed = kN·m design bending moment z-z

Design values at Ultimate Limit State (ULS). Include load combination factors γ_F·ψ per EN 1990 before entry.

2 Element Dimensions — Rectangular Cross-section

Dimensions

h = mm depth (strong axis)

b = mm width (weak axis)

Section Properties

A= b · h = 30000mm²

I_y= b·h³/12 = 100.00×10⁶ mm⁴

I_z= b³·h/12 = 56.25×10⁶ mm⁴

Figure 1 — Rectangular cross-section with axes (interactive)

3 Material Properties — C14

Timber Strength Class (EN 338)

Class:

f_m,k = N/mm² char. bending strength

ρ_wood = 350 kg/m³ mean density (EN 338)

Modification Factors

γ_M = EN 1995-1-1 Table 2.3

k_mod = EN 1995-1-1 Table 3.1

k_h = 1.000 EN 1995-1-1 §3.2(3)

k_h = min((150/h)^0.2, 1.3) when h < 150 mm and ρ < 700 kg/m³; else k_h = 1.0

EN 338 Class Properties (N/mm²)

Class	f_m,k	f_t,0,k	f_c,0,k	f_v,k	E_0,mean kN/mm²	ρ_mean kg/m³

4 Design Bending Strength

Per EN 1995-1-1 §2.4.1, Eq. (2.14): f_m,d = k_mod · k_h · f_m,k / γ_M

f_m,y,d = f_m,z,d = k_mod · k_h · f_m,k / γ_M = 8.62 N/mm² (same value for both axes — rectangular section)

5 Design Bending Stresses

σ_m,y,d = M_y,Ed · (h/2) / I_y = 4.00 N/mm²

Design bending stress about the principal y-y axis (EN 1995-1-1 §6.1.6)

σ_m,z,d = M_z,Ed · (b/2) / I_z = 0.67 N/mm²

Design bending stress about the principal z-z axis (EN 1995-1-1 §6.1.6)

k_m = 0.7 for rectangular sections EN 1995-1-1 §6.1.6(2)

6 Biaxial Bending Verification — EN 1995-1-1 §6.1.6

Check 1 — Strong axis (y-y) governs — Eq. (6.11)

(σ_m,y,d/f_m,y,d) + k_m·(σ_m,z,d/f_m,z,d) = 0.518 ≤ 1.00 OK Eq. (6.11)

Check 2 — Weak axis (z-z) governs — Eq. (6.12)

k_m·(σ_m,y,d/f_m,y,d) + (σ_m,z,d/f_m,z,d) = 0.402 ≤ 1.00 OK Eq. (6.12)

Governing utilization ratio

0.518

Utilization

51.8 %

Element status

✓ ADEQUATE

References: EN 1995-1-1:2004 — Eurocode 5: Design of timber structures — Part 1-1: Common rules and rules for buildings | EN 338:2003 — Structural timber; Strength classes

Wood Element — Bending Moment Capacity