What is ultimate limit state check (ULS), and what is serviceability limit state check (SLS)? Here are the central formulas from Eurocode 5 with DK NA:2024, the k_mod table and a worked example.
Introduction
Eurocode 5 distinguishes between two control levels: Ultimate Limit State (ULS) and Serviceability Limit State (SLS). ULS checks whether the structure bears without failure; SLS checks whether the deflection is acceptable in use.
Design strength and k_mod
k_mod accounts for wood under sustained load being weaker than under short-term load. It depends on load duration and use class (AK). AK1 is heated indoor climate, AK2 unheated/ventilated, AK3 outdoor.
| Load duration | AK 1 & 2 | AK 3 |
|---|---|---|
| Permanent (> 10 years) | 0,60 | 0,50 |
| Long (6 months–10 years) | 0,70 | 0,55 |
| Medium (1 week–6 months) | 0,80 | 0,65 |
| Short (< 1 week) | 0,90 | 0,70 |
| Very short (wind/snow) | 1,10 | 0,90 |
Source: EC5 table 3.1, reproduced in strongtie.dk – Load-bearing capacities.
ULS—bending and shear
Characteristic strength parameters for two common grades (DS/EN 338 / DS/EN 14080): C24 has bending strength f_m,k = 24 MPa, shear f_v,k = 4.0 MPa, E_0,mean = 11,000 MPa. GL28h (glulam) has f_m,k = 28 MPa, f_v,k = 3.5 MPa, E_0,mean = 12,600 MPa.
SLS — deflection
Worked example
A GL28h glulam beam 115 × 315 mm, clear span 4.0 m, uniformly distributed design load q_d = 12.2 kN/m (permanent load, SC1). k_mod = 0.60, γ_M = 1.30. f_m,d = 0.60 · 28 / 1.30 ≈ 12.9 MPa. M_max = 12.2 · 4.0² / 8 = 24.4 kNm. W = (0.115 · 0.315²) / 6 ≈ 1.90 × 10⁻³ m³. σ_m,d = 24.4 / 1.90 × 10⁻³ ≈ 12.8 MPa — just within the limit. Utilisation ≈ 99 %. The example is calculated directly from the EC5 formulas (W = b·h²/6; σ_m,d = M/W ≤ f_m,d).
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