EN 1990 Load Combinations — Partial Factor Combinations per Eurocode

Complete reference for load combinations per EN 1990:2002 Eurocode — Basis of Structural Design. STR/GEO limit state combinations (Equations 6.10, 6.10a/6.10b), partial factors gamma_G and gamma_Q, psi reduction factors for imposed, wind, snow, and temperature actions. Serviceability limit state combinations (characteristic, frequent, quasi-permanent). Worked 3-storey steel office frame load take-down example.

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EN 1990 Limit States

Limit State Symbol Combination Checks
Ultimate (STR) ULS 6.10 or 6.10a/6.10b Strength, stability
Ultimate (GEO) ULS 6.10 or 6.10a/6.10b Geotechnical failure
SLS (characteristic) SLS 6.14b Irreversible damage
SLS (frequent) SLS 6.15b Reversible damage
SLS (quasi-permanent) SLS 6.16b Long-term effects
Accidental ULS 6.11a/6.11b Fire, impact, explosion
Seismic ULS EN 1998-1 Earthquake

ULS Combinations — STR Limit State

Equation 6.10 (Primary)

Sum(gamma_G,j x G_k,j) + gamma_Q,1 x Q_k,1 + Sum(gamma_Q,i x psi_0,i x Q_k,i)

Where:

Alternative: Equations 6.10a and 6.10b

Some National Annexes (e.g., UK NA) permit using the less onerous of:

Combination Permanent (unfavourable) Leading Variable Accompanying Variable
6.10a 1.35 x G_k 1.50 x psi_0 x Q_k,1 1.50 x psi_0 x Q_k,i
6.10b xi x 1.35 x G_k 1.50 x Q_k,1 1.50 x psi_0 x Q_k,i

Where xi = 0.85 (UK NA) or 0.89 (recommended).

PSI Factors for Buildings (EN 1990 Table A1.1)

Action psi_0 psi_1 psi_2
Imposed — residential 0.7 0.5 0.3
Imposed — offices 0.7 0.5 0.3
Imposed — storage 1.0 0.9 0.8
Imposed — retail 0.7 0.7 0.6
Wind 0.6 0.2 0.0
Snow (H <= 1000 m) 0.5 0.2 0.0
Snow (H > 1000 m) 0.7 0.5 0.2
Temperature (non-fire) 0.6 0.5 0.0

Worked Example — 3-Storey Steel Office Frame

Location: Manchester, UK. 3 storeys, 6.0 m bay spacing.

Load Case Roof (kN/m2) Floor (kN/m2)
Self-weight (G_k) 3.5 4.5
Imposed (Q_k) 0.75 3.5
Wind (Q_k) 0.75 kN/m2 on facade -
Snow (Q_k) 0.6 -

ULS Combination (6.10) — Wind Leading

Roof: 1.35 x 3.5 + 1.50 x 0.75 + 1.50 x 0.7 x 0.75 = 6.65 kN/m2 Floor: 1.35 x 4.5 + 1.50 x 0.7 x 3.5 = 9.76 kN/m2

ULS Combination (6.10) — Imposed Leading

Roof: 1.35 x 3.5 + 1.50 x 0.75 + 1.50 x 0.5 x 0.6 = 6.31 kN/m2 Floor: 1.35 x 4.5 + 1.50 x 3.5 = 11.33 kN/m2

Location Governing Load (kN/m2) Leading Action
Roof 6.65 Wind
Floor 11.33 Imposed

National Annex Variations

Country Set gamma_G (unfav) gamma_Q xi
UK 6.10a/6.10b 1.35/1.15 1.50 0.85
Germany 6.10 1.35 1.50 -
France 6.10 1.35 1.50 -
Netherlands 6.10 1.35 1.50 -
Italy 6.10 1.35 1.50 0.85

Frequently Asked Questions

What is the difference between the 6.10 and 6.10a/6.10b approaches?

Equation 6.10 uses gamma_G = 1.35 for all permanent actions. The 6.10a/6.10b split approach (UK NA, Italian NA) uses two checks: 6.10a with gamma_G = 1.35 and reduced variable action (psi_0 factor on the leading action), and 6.10b with reduced permanent factor (xi x 1.35) and full variable action. The less onerous governs. This can be more economical when permanent actions dominate.

When should wind be the leading variable action vs imposed load?

The leading variable action is whichever produces the most onerous effect. For roof members, wind or snow typically governs. For floor beams, imposed load governs. For global frame stability, wind should be checked as leading. Each ULS combination must be checked with each variable action considered as the leading action.

Related Pages

Educational reference only. Load combinations per EN 1990:2002 Annex A1. Verify psi factors and partial factors against the applicable National Annex. Results are PRELIMINARY - NOT FOR CONSTRUCTION without independent verification.

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