EN 1990 Limit State Design Philosophy

EN 1990 (Eurocode: Basis of Structural Design) is the foundation document for all structural Eurocodes. It establishes the limit state design philosophy and defines the load combination framework used by EN 1991 (Actions), EN 1993 (Steel), EN 1992 (Concrete), and EN 1994 (Composite). The fundamental requirement is:

A structure shall be designed and executed in such a way that it will, during its intended life with appropriate degrees of reliability and in an economical way, sustain all actions and influences likely to occur during execution and use, and remain fit for the use for which it is required. (EN 1990, Cl. 2.1(1)P)

Design verification at both ULS and SLS is mandatory. The partial factor method converts characteristic action values into design values, which are then compared against factored resistances from the material Eurocode (e.g., EN 1993-1-1 for steel).

Ultimate Limit State (ULS) — Four Verification Types

EN 1990 distinguishes four ULS verification types:

For structural steel building frames, STR is the governing ULS type for member design (beam, column, connection checks). GEO governs foundation and base plate design. EQU applies to the overall stability check (e.g., overturning of a lightweight steel canopy in wind uplift).

ULS Load Combinations — Full Equation 6.10 (Fundamental)

EN 1990 Cl. 6.4.3.2 provides the fundamental ULS combination (Expression 6.10):

∑ γG,j Gk,j  "+"  γP P  "+"  γQ,1 Qk,1  "+"  ∑ γQ,i ψ0,i Qk,i
  j≥1                                  i>1

Where:

• Gk,j = characteristic permanent action j (dead load, superimposed dead load)
• P = prestressing action (rarely relevant in structural steel design)
• Qk,1 = characteristic value of the leading variable action (e.g., imposed floor load, or wind, or snow)
• Qk,i = characteristic value of accompanying variable action i (i > 1)
• γG,j = partial factor for permanent action j
• γQ,1 = partial factor for leading variable action
• γQ,i = partial factor for accompanying variable action
• ψ0,i = combination factor for accompanying variable action i (reduces the accompanying action to its "combination value")

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

Note: The UK National Annex may modify these values. Always consult the site-specific NA. Common refinements include reducing γG,sup to 1.20 when permanent actions are well-characterised (e.g., known steel section self-weight).

Simplified ULS — Equations 6.10a and 6.10b

For buildings, EN 1990 permits the use of two simplified expressions (6.10a and 6.10b) in place of the full 6.10. The governing combination is the more onerous of 6.10a and 6.10b:

Equation 6.10a (permanent action dominates):

∑ γG,j Gk,j  "+"  γQ,1 ψ0,1 Qk,1  "+"  ∑ γQ,i ψ0,i Qk,i
  j≥1                                 i>1

Equation 6.10b (variable action dominates):

∑ ξj γG,j Gk,j  "+"  γQ,1 Qk,1  "+"  ∑ γQ,i ψ0,i Qk,i
  j≥1                                  i>1

Where ξj = 0.85 is a reduction factor for permanent actions in Equation 6.10b (the reduced permanent load effect recognises that all permanent actions are unlikely to simultaneously reach their maximum). The effective permanent factor becomes 0.85 × 1.35 = 1.15 in 6.10b.

Decision Rule

Compare NEd from 6.10a and 6.10b and take the larger value:

For most steel building frames (Gk ≈ 25-35% of total factored load), Equation 6.10b governs.

ψ Factor Tables — EN 1990 Table A1.1 (Buildings)

ψ factors reduce variable actions to account for the reduced probability of simultaneous occurrence. Three types are defined:

• ψ0 — Combination value (for accompanying actions in ULS and irreversible SLS)
• ψ1 — Frequent value (for frequent SLS combination)
• ψ2 — Quasi-permanent value (for long-term effects, creep, and seismic mass)

Wind and Snow ψ Factors

Note: In the UK, wind ψ0 = 0.5 (per UK NA to EN 1990). Always check the relevant National Annex.

Serviceability Limit State (SLS) Combinations

EN 1990 Cl. 6.5.3 defines three SLS combinations:

Characteristic Combination (Irreversible Limit States)

For irreversible SLS (e.g., cracking of brittle finishes, permanent deformation):

∑ Gk,j  "+"  P  "+"  Qk,1  "+"  ∑ ψ0,i Qk,i
j≥1                           i>1

Frequent Combination (Reversible Limit States)

For frequent SLS (e.g., deflection causing discomfort, vibration):

∑ Gk,j  "+"  P  "+"  ψ1,1 Qk,1  "+"  ∑ ψ2,i Qk,i
j≥1                                     i>1

Quasi-Permanent Combination (Long-Term Effects)

For long-term appearance, creep effects, and horizontal deflection of tall buildings:

∑ Gk,j  "+"  P  "+"  ∑ ψ2,i Qk,i
j≥1                   i≥1

SLS Deflection Limits (EN 1993-1-1 NA.2.23 — UK NA)

Accidental Design Situation

For accidental actions (explosion, impact, fire, localised failure), EN 1990 Expression 6.11b:

∑ Gk,j  "+"  Ad  "+"  (ψ1,1 or ψ2,1) Qk,1  "+"  ∑ ψ2,i Qk,i
j≥1                                                i>1

Where Ad is the design accidental action. For fire design, ψ1,1 is used for the leading variable action (giving a realistic fire-compartment load). For EN 1991-1-2 fire design of steel frames, the quasi-permanent load level typically controls.

Seismic Design Situation

For seismic actions per EN 1998 (Expression 6.12b):

∑ Gk,j  "+"  AEd  "+"  ∑ ψ2,i Qk,i
j≥1                    i≥1

Where AEd is the design seismic action (AEd = γI × AEk, where γI = importance factor from EN 1998-1 Cl. 4.2.5). ψ2 factors for seismic mass calculation are:

The seismic mass comes from Gk + Σ ψE,i × Qk,i per EN 1998-1 Cl. 3.2.4, where ψE,i = φ × ψ2,i and φ = 1.0 for roof, 0.5 for independently occupied storeys (correlation factor).

Worked Example — 4-Storey Steel Office Frame

Design the interior column between ground and first floor of a 4-storey steel-framed office building. Determine the maximum ULS axial force using EN 1990 combinations.

Given Data

Column tributary accumulates 3 floors above this level plus roof (total 4 levels).

Step 1 — Characteristic Values at Column Base

Cumulative Gk = 4 × (180 + 45) = 900 kN Cumulative Qk = 3 × 120 + 30 = 390 kN Roof snow Qk,snow = 45 kN

Step 2 — Identify Leading and Accompanying Actions

Three checks required (leading action varied):

• Check 1: Imposed floor load leading, snow accompanying
• Check 2: Snow leading, imposed accompanying
• Check 3: Wind leading (typically not column-governing unless wind dominates — omitted here for brevity)

Step 3 — Equation 6.10b (Use simplified building expression)

ψ0 for snow = 0.5 (UK H ≤ 1000 m). ψ0 for imposed (Cat B) = 0.7. γG = 1.35, γQ = 1.5, ξ = 0.85.

Check 1 — Imposed Leading:

NEd,1 = 0.85 × 1.35 × 900 + 1.5 × 390 + 1.5 × 0.5 × 45
     = 1.1475 × 900 + 585 + 33.75
     = 1032.75 + 585 + 33.75
     = 1651.5 kN

Check 2 — Snow Leading:

NEd,2 = 0.85 × 1.35 × 900 + 1.5 × 45 + 1.5 × 0.7 × 390
     = 1032.75 + 67.5 + 409.5
     = 1509.75 kN

Governing ULS axial force: NEd = 1652 kN (Check 1, imposed floor load is the leading action).

Step 4 — SLS Characteristic (for column shortening)

NSLS,char = 900 + 390 + 0.5 × 45 = 1312.5 kN

This is used for assessing column axial shortening and for foundation settlement calculations.

Combination Quick-Reference Card

Frequently Asked Questions

What is the difference between EN 1990 Equation 6.10 and the simplified 6.10a/6.10b?

Equation 6.10 is the full (generic) expression that requires checking each variable action in turn as the leading action and applying the same γQ (1.5) to the leading variable. Equations 6.10a and 6.10b are a simplified two-equation alternative for buildings only. 6.10a applies a reduced ψ0 factor to the leading variable (capturing the case where permanent loads are dominant), while 6.10b applies a reduction factor ξ = 0.85 to permanent loads (capturing the case where the variable action dominates). The designer checks both and takes the larger result. For typical steel frames, 6.10b governs, but 6.10a can govern in heavily-loaded transfer structures.

When should I use the frequent SLS combination instead of the characteristic combination?

Use the frequent combination (ψ1 on leading variable) for reversible limit states — the structure returns to acceptable performance once the load is removed. Examples include: floor vibrations that cause discomfort, temporary excessive deflections under infrequent peak loads, and crack-width checks where the crack closes on load removal. Use characteristic (full variable action, no reduction) for irreversible limit states where damage is permanent: cracking of partition walls, permanent set in steel members, damage to brittle finishes.

How do I combine imposed load and wind for a steel portal frame?

For a single-storey steel portal frame, wind load is often the leading variable action (check both cases). When wind is leading (6.10b): design wind × 1.5 + imposed × ψ0 × 1.5 where ψ0 = 0.7 for Category H roof imposed load (but ψ0(H) = 0.0, meaning imposed roof load vanishes when wind is leading). When imposed is leading: imposed × 1.5 + wind × 0.5 × 1.5. In practice, the wind-leading case often governs the frame design (rafter and column bending moments) for low-rise buildings in exposed locations.

What psi factor do I use for storage areas in a steel-framed warehouse?

Storage areas are Category E under EN 1991-1-1 Table 6.1. The relevant ψ factors are: ψ0 = 1.0, ψ1 = 0.9, ψ2 = 0.8. The ψ0 = 1.0 means that when storage load is accompanying (not leading), it is taken at full value — there is no reduction for the probability of simultaneous occurrence. This reflects the fact that warehouses are likely to be fully loaded at any time. This is a critical provision: storage loads drive heavy steel sections and can govern the column and foundation design.

How does the UK National Annex modify the EN 1990 combination factors?

The UK NA makes several important changes to the recommended values: (1) It allows the use of Equations 6.10a and 6.10b for buildings with the standard recommended factors. (2) Wind ψ0 is reduced from 0.6 to 0.5 (BS EN 1990 UK NA, Table NA.A1.2). (3) For buildings designed to BS EN 1993-1-1, the UK NA permits a pragmatic approach where ULS combinations can use only Eq. 6.10b (with ξ = 0.925 for steel self-weight only, 0.85 for all permanent). (4) Snow ψ0 for altitudes below 1000 m is 0.5. Always check the current UK NA before finalising design combinations; the above reflects the 2008 + A1:2014 version.

Related Pages

• EN 1993 Steel Design Overview →
• European Wind Load per EN 1991-1-4 →
• European Snow Load per EN 1991-1-3 →
• EN 1998 Seismic Design →
• EN 1993 Column Buckling →
• European Steel Fire Protection per EN 1993-1-2 →
• AS 4100 Load Combinations (Australia) →
• AISC 360 Load Combinations (USA) →

Educational reference only. Verify all partial factors and ψ values against the current National Annex for the building jurisdiction. Design combinations must be independently verified by a qualified structural engineer. Results are PRELIMINARY — NOT FOR CONSTRUCTION without professional structural engineering review.

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