UK Partial Factors — EN 1990 UK NA Table NA.A1.2(B)

For persistent and transient design situations (ULS):

For accidental design situations: gamma_G = 1.00, gamma_Q = 1.00, Ad = nominal accidental action.

For SLS (characteristic): gamma_G = 1.00, gamma_Q = 1.00 (all partial factors = 1.0).

ULS Combination Expressions

Eq. 6.10 — General Expression (EN 1990 Clause 6.4.3.2)

Sum over j >= 1: gamma_G,j x Gk,j + gamma_Q,1 x Qk,1 + Sum over i > 1: gamma_Q,i x psi_0,i x Qk,i

The UK NA does NOT adopt Eq. 6.10 as the standard method. Instead, the UK NA adopts either Eq. 6.10a or Eq. 6.10b, with Eq. 6.10b being the standard for UK building structures.

Eq. 6.10a — Alternative for Strength (GEO/STR)

Max of:

• (a) Sum: gamma_G,j x Gk,j + gamma_Q,1 x psi_0,1 x Qk,1 + Sum i>1: gamma_Q,i x psi_0,i x Qk,i
• (b) Sum: xi x gamma_G,j x Gk,j + gamma_Q,1 x Qk,1 + Sum i>1: gamma_Q,i x psi_0,i x Qk,i

Where xi = 0.925 for buildings (UK NA reduction factor for permanent actions).

Eq. 6.10a is generally more conservative than 6.10b. It is sometimes used for geotechnical design or where the permanent action proportion is very high.

Eq. 6.10b — UK NA Standard for Buildings

The standard ULS combination expression adopted by the UK NA for building structures:

Sum: xi x gamma_G,j x Gk,j + gamma_Q,1 x Qk,1 + Sum i>1: gamma_Q,i x psi_0,i x Qk,i

Where xi = 0.925 (UK NA to BS EN 1990, Table NA.A1.2(B)).

Simplified for common UK steel building with dead + imposed + wind:

Max of:

• 1.35 x 0.925 x Gk + 1.5 x Qk (imposed leading) = 1.25Gk + 1.5Qk
• 1.35 x 0.925 x Gk + 1.5 x Wk (wind leading) + 1.5 x 0.7 x Qk = 1.25Gk + 1.5Wk + 1.05Qk

Note: 1.35 x 0.925 = 1.249 (approximately 1.25). This is the UK NA's practical simplification.

UK NA Psi Factors — Combination Coefficients

psi_0 (combination value) — for combining with leading variable action:

psi_1 (frequent value) — for SLS and fire:

psi_2 (quasi-permanent value) — for long-term effects and creep:

Worked Example — Multi-Storey UK Steel Frame

Building: 6-storey steel frame, braced core, office use (Category B). Roof accessible for maintenance only (Category H). Wind to BS EN 1991-1-4. Snow per BS EN 1991-1-3 (London, H = 30 m).

Actions per floor (typical internal beam):

• Gk = 45 kN/m (dead: slab + finishes + services + partitions)
• Qk = 30 kN/m (imposed: office occupancy, 3.0 m tributary width)

ULS Combinations (Eq. 6.10b, UK NA standard):

LC1 — Imposed leading: FEd = 1.25 x 45 + 1.5 x 30 = 56.25 + 45.0 = 101.25 kN/m

LC2 — Wind leading (beam subject to wind via cladding): FEd = 1.25 x 45 + 1.5 x Wk + 1.5 x 0.7 x 30 = 56.25 + 1.5Wk + 31.5 kN/m

SLS Characteristic (deflection check): FEd,SLS = 45 + 30 = 75 kN/m (all partial factors = 1.0)

Accidental Combinations — EN 1990 Clause 6.4.3.3

For accidental design situations (e.g., blast, vehicle impact):

Sum: Gk,j + Ad + psi_1,1 x Qk,1 + Sum i>1: psi_2,i x Qk,i

Where Ad is the design accidental action, psi_1 is the frequent value for the leading variable action with the accident, and psi_2 is the quasi-permanent value for accompanying actions.

UK NA adoption: The UK NA adopts the EN 1990 recommended expression without modification. For most UK building structures, accidental combinations are not governing (robustness is addressed through tying requirements per Approved Document A).

Fire Limit State — EN 1990 Clause 6.4.3.3 + EN 1991-1-2

Combination for fire design:

Sum: Gk,j + psi_1,1 x Qk,1 + Sum i>1: psi_2,i x Qk,i

UK NA fire combination for typical office building:

• Permanent: 1.00 x Gk
• Imposed (leading, office): psi_1 x Qk = 0.5 x Qk
• Wind (accompanying): psi_2 x Wk = 0 x Wk (wind not combined with fire in UK practice)

Simplified: FEd,fire = Gk + 0.5Qk for office buildings.

The reduced load reflects the lower probability of full imposed load coinciding with a fire event. Member capacity in fire is also reduced (Clause 4.2.3 of EN 1993-1-2).

UK NA vs Other National Annexes — Key Differences

The UK NA is slightly more economical than the German NA (xi = 0.925 versus 0.85) for buildings where permanent actions dominate the total load. For wind-governed designs, the UK NA psi_0 = 0.5 (versus 0.6 recommended) is less punitive when wind is the accompanying action.

Practical UK Design Notes

When to use Eq. 6.10a instead of 6.10b:

Eq. 6.10a may be more appropriate when: (1) the geotechnical design governs (retaining walls, foundations) — the UK NA to EN 1997 may reference 6.10a; (2) the permanent action is significantly larger than the variable action (heavy concrete floors on steel beams); (3) the designer specifically wants to separate permanent-dominated and variable-dominated combinations for clarity.

Imposed load reduction (EN 1991-1-1 Clause 6.3.1.2):

The UK NA adopts the recommended reduction factor alpha_A for multi-storey buildings (more than 2 storeys). For columns: the total imposed load may be reduced by alpha_n = (2 + (n-2) x psi_0) / n for n storeys above. For a 6-storey column: alpha_n = (2 + 4 x 0.7) / 6 = 0.80 — a 20 % reduction in total column imposed load.

Wind + snow combination:

The UK NA psi_0 = 0.5 for both wind and snow (H <= 100 m). When wind and snow accompany each other, the combination coefficient 0.5 applies to whichever is the accompanying action. In practice, wind rarely governs with full snow load simultaneously in UK conditions, so the wind-leading + snow-accompanying and snow-leading + wind-accompanying combinations are checked separately, and the worst case governs.

Frequently Asked Questions

Why does the UK NA use Eq. 6.10b instead of Eq. 6.10?

The UK NA adopted Eq. 6.10b because UK research (BRE Digest 517 and SCI RT 1233) demonstrated that the EN 1990 Eq. 6.10 produces combinations that are 5-15 % more conservative than BS 5950 for typical UK building structures. The UK NA Eq. 6.10b with xi = 0.925 produces results that are approximately equivalent to the BS 5950 partial factors (gamma_f = 1.4 dead + 1.6 imposed), maintaining historical UK reliability levels while conforming to the Eurocode framework.

What is the xi factor and why is it 0.925 in the UK NA?

The xi factor is a reduction applied to unfavourable permanent actions to account for the lower variability of permanent loads compared to variable loads. EN 1990 recommends xi = 0.85, but the UK NA increases this to xi = 0.925. UK research demonstrated that the recommended 0.85 value was overly conservative for UK construction, where higher-quality control on concrete slabs and finishes results in lower dead load variability. The UK NA xi = 0.925 corresponds approximately to the BS 5950 gamma_f = 1.4 on dead load when combined with gamma_G = 1.35 (1.35 x 0.925 = 1.25 approximately equivalent to 1.4 x 0.9).

How are crane loads combined in UK steel design?

Crane loads (EN 1991-3) are treated as a single variable action. The UK NA to EN 1991-3 specifies psi factors for crane actions: psi_0 = 1.0 (crane is always the leading variable action when present), psi_1 = 0.9 (frequent), psi_2 = 0.0 (quasi-permanent — cranes are either present or absent). For UK portal frame buildings with overhead cranes, the crane ULS combination is typically: 1.25Gk + 1.5Qk,crane + 1.5 x 0.5 x Qk,snow (crane leading, snow accompanying with psi_0 = 0.5).

Related Pages

• UK Load Combinations Reference — EN 1990 overview for steel design
• UK Wind Load Reference — EN 1991-1-4 UK NA wind loads
• UK Snow Load Reference — EN 1991-1-3 UK snow loads
• UK Seismic Design — EN 1998-1 UK NA
• UK Steel Properties — Material data
• UK Fire Rating Guide — EN 1993-1-2 fire engineering
• European Load Combinations — Compare EU NAs

Educational reference only. All partial factors and combination expressions are per BS EN 1990:2002 + A1:2005 with UK National Annex, BS EN 1991-1-1 with UK NA, and BS EN 1991-1-3/4 with UK NAs. Verify all values against the current editions of the standards and the applicable National Annex for your project jurisdiction. Designs must be independently verified by a Chartered Structural Engineer registered with the Institution of Structural Engineers (IStructE) or the Institution of Civil Engineers (ICE). Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent professional verification.