UK Load Combinations — EN 1990 + UK NA Guide
Structural design in the UK follows EN 1990:2002 + UK National Annex for load combinations. The partial factor format ensures reliability across all limit states. The UK NA modifies some ψ factors and recommends specific partial factors for UK practice.
Ultimate Limit State Combinations
The UK National Annex to EN 1990 defines three sets for STR and GEO limit states:
STR/GEO Set A (geotechnical): [ 1.35 G*{k,\sup} + 1.5 Q*{k,1} + \sum 1.5 \psi*{0,i} Q*{k,i} ]
STR/GEO Set B (structural — governs for UK building design): [ 1.35 G*{k,\sup} + 1.5 Q*{k,1} + \sum 1.5 \psi*{0,i} Q*{k,i} ]
STR/GEO Set C (variable action favourable): [ 1.0 G*{k,\inf} + 1.5 Q*{k,1} + \sum 1.5 \psi*{0,i} Q*{k,i} ]
The UK NA recommends Set B for most buildings and Set A for geotechnical verifications.
ψ Factors per EN 1990 Table A1.1 for Buildings
| Load Type | ψ₀ (combination) | ψ₁ (frequent) | ψ₂ (quasi-permanent) |
|---|---|---|---|
| Imposed — domestic, office | 0.7 | 0.5 | 0.3 |
| Imposed — storage | 1.0 | 0.9 | 0.8 |
| Imposed — vehicle (≤ 30 kN) | 0.7 | 0.5 | 0.6 |
| Wind loads | 0.5 | 0.2 | 0.0 |
| Snow loads (≤ 1000 m) | 0.5 | 0.2 | 0.0 |
| Temperature (non-fire) | 0.6 | 0.5 | 0.0 |
Partial Factors for Actions per UK NA
| Action | γ_f favourable | γ_f unfavourable |
|---|---|---|
| Permanent — self-weight | 1.0 | 1.35 |
| Permanent — superimposed | 1.0 | 1.35 |
| Variable — imposed | 0 | 1.5 |
| Variable — wind | 0 | 1.5 |
| Variable — snow | 0 | 1.5 |
| Accidental | 1.0 | 1.0 |
| Seismic (E_d) | 1.0 | 1.0 |
Serviceability Limit State Combinations
Characteristic (irreversible SLS): [ Gk + Q{k,1} + \sum \psi*{0,i} Q*{k,i} ]
Frequent (reversible SLS): [ Gk + \psi{1,1} Q*{k,1} + \sum \psi*{2,i} Q_{k,i} ]
Quasi-permanent (long-term SLS): [ Gk + \sum \psi{2,i} Q_{k,i} ]
Accidental and Seismic Combinations
Accidental: G_k + A_d + ψ_1,1 Q_k,1 + Σ ψ_2,i Q_k,i
Seismic (EN 1998-1 + UK NA): G_k + E_d + Σ ψ_2,i Q_k,i
Worked Example — Office Floor Beam
Given: 533×210 UB 92, office floor. G_k = 35 kN/m (slab + self-weight + SDL), Q_k,1 = 20 kN/m (imposed), Q_k,2 = 3 kN/m (partitions).
ULS (Set B): F_Ed = 1.35 × 35 + 1.5 × 20 + 1.5 × 0.7 × 3 = 47.25 + 30.0 + 3.15 = 80.4 kN/m
SLS characteristic: F_ser = 35 + 20 + 0.7 × 3 = 57.1 kN/m
SLS quasi-permanent: F_qp = 35 + 0.3 × 20 + 0.3 × 3 = 41.9 kN/m
Design Resources
- UK Wind Load — EN 1991-1-4 + UK NA
- UK Snow Load — EN 1991-1-3 + UK NA
- UK Seismic Design — EN 1998-1 + UK NA
- UK Beam Design — Flexural design
- UK Column Design — Compression design
- All UK References
Frequently Asked Questions
What load combinations are used in UK practice?
The UK NA to EN 1990 defines three sets for STR/GEO. Set B is most common for UK buildings: 1.35G_k + 1.5Q_k,1 + Σ1.5ψ_0,iQ_k,i. For wind leading: 1.35G_k + 1.5W_k + Σ1.5ψ_0,iQ_k,i. Accidental: G_k + A_d + ψ_1,1Q_k,1 + Σψ_2,iQ_k,i.
What are ψ factors and when are they used?
ψ factors reduce the probability of simultaneous extreme loads. ψ₀ (combination) for ULS with multiple variables, ψ₁ (frequent) for SLS frequent and accidental, ψ₂ (quasi-permanent) for long-term and seismic. For office loads: ψ₀ = 0.7, ψ₁ = 0.5, ψ₂ = 0.3.
How does UK NA to EN 1990 differ from recommended values?
The UK NA adopts most EN 1990 recommended values but modifies: partial factors for Sets A, B, C, specific ψ values for UK structures, and simplified guidance for wind-imposed load combination. It also categorises buildings into consequence classes CC1, CC2, CC3.
How are serviceability deflections checked per UK NA?
Total deflection under characteristic combination is checked against span/200. Imposed load deflection uses frequent combination against span/300 (standard) or span/500 (brittle finishes). These limits per UK NA to EN 1990 ensure acceptable performance without damage to cladding and partitions.
Load Combinations
LRFD Load Combinations (ASCE 7-22)
The following basic load combinations govern strength design:
- 1.4D
- 1.2D + 1.6L + 0.5(Lr or S or R)
- 1.2D + 1.6(Lr or S or R) + (L or 0.5W)
- 1.2D + 1.0W + L + 0.5(Lr or S or R)
- 1.2D + 1.0E + L + 0.2S
- 0.9D + 1.0W
- 0.9D + 1.0E
ASD Load Combinations
- D + L
- D + (Lr or S or R)
- D + 0.75L + 0.75(Lr or S or R)
- D + 0.6W
- D + 0.75L + 0.75(0.6W) + 0.75(Lr or S or R)
- 0.6D + 0.6W
- 0.6D + 0.6E
The governing load combination is the one producing the most critical effect (largest positive moment, largest negative moment, maximum shear, etc.). For multi-span continuous members, each combination should be evaluated at multiple locations.
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Frequently Asked Questions
What is the recommended design procedure for this structural element?
The standard design procedure follows: (1) establish design criteria including applicable code, material grade, and loading; (2) determine loads and applicable load combinations; (3) analyze the structure for internal forces; (4) check member strength for all applicable limit states; (5) verify serviceability requirements; and (6) detail connections. Computer analysis is recommended for complex structures, but hand calculations should be used for verification of critical elements.
How do different design codes compare for this calculation?
AISC 360 (US), EN 1993 (Eurocode), AS 4100 (Australia), and CSA S16 (Canada) follow similar limit states design philosophy but differ in specific resistance factors, slenderness limits, and partial safety factors. Generally, EN 1993 uses partial factors on both load and resistance sides (γM0 = 1.0, γM1 = 1.0, γM2 = 1.25), while AISC 360 uses a single resistance factor (φ). Engineers should verify which code is adopted in their jurisdiction.
Reference only. Verify all values against the current edition of EN 1993-1-1:2005, UK National Annex, and BS EN 1090-2. This information does not constitute professional engineering advice.