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.
Quick access: European Wind Load | European Snow Load | Seismic Design
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:
- gamma_G = 1.35 (unfavourable permanent), 1.00 (favourable permanent)
- gamma_Q = 1.50 (both leading and accompanying variable actions)
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 |
Design Applications
Common Design Scenarios
This reference covers structural design scenarios commonly encountered in structural steel design practice:
- Strength verification: Check member or connection capacity against factored loads per the applicable design code
- Serviceability checks: Verify deflections, vibrations, and other serviceability criteria
- Code compliance: Ensure design meets all provisions of the governing standard
- Connection detailing: Verify weld sizes, bolt quantities, and edge distances
Related Design Considerations
- System behavior: consider the interaction between members and connections
- Load paths: verify that forces can be transferred through the structure to the foundations
- Constructability: check that the design can be fabricated and erected practically
- Cost optimization: evaluate alternative sections or connection types for economy
Worked Example
Problem: Verify a typical steel member for the following conditions:
Typical span: 6.0 m | Load: service loads per applicable code | Section: common section in this category
Design Check:
- Determine governing load combination (LRFD or ASD per applicable code)
- Calculate maximum internal forces (moment, shear, axial)
- Compute nominal capacity per code provisions
- Apply resistance/safety factors
- Verify interaction if combined forces exist
Result: Use the results from the Steel Calculator tool to verify design adequacy.
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.
Design Resources
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