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
Karakteristiske styrkeparametre for to hyppige kvaliteter (DS/EN 338 / DS/EN 14080): C24 har bøjningsstyrke f_m,k = 24 MPa, forskydning f_v,k = 4,0 MPa, E_0,mean = 11.000 MPa. GL28h (limtræ) har f_m,k = 28 MPa, f_v,k = 3,5 MPa, E_0,mean = 12.600 MPa.
SLS — deflection
Worked example
En GL28h limtræsbjælke 115 × 315 mm, lys vidde 4,0 m, jævnt fordelt designlast q_d = 12,2 kN/m (permanent last, AK1). 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 — knap inden for grænsen. Udnyttelsesgrad ≈ 99 %. Eksemplet er regnet direkte efter EC5-formlerne (W = b·h²/6; σ_m,d = M/W ≤ f_m,d).
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