Understanding SLS Load Combinations in Eurocode Design: Characteristic, Frequent and Quasi-Permanent Loads Explained Part 2 of 3
- MTS DNC ENERGY CONSULTANTS LIMITED
- 6 days ago
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📐 Understanding ψ (Psi) Combination Factors
As explained in Part 1, variable actions do not normally reach their maximum characteristic value at the same time.
For example, consider an office building:
The maximum number of occupants may occur during a large meeting.
Maximum storage loads may occur during a particular period.
Snow loading may occur during severe winter conditions.
The probability that all these actions reach their maximum values simultaneously is very low.
To account for this, EN 1990 introduces combination factors known as: ψ (Psi) Factors
These factors reduce variable actions depending on how frequently they are expected to occur.
The three main factors used in SLS design are:
Symbol | Name | Purpose |
ψ₀ | Combination factor | Used for characteristic (rare) combinations |
ψ₁ | Frequent factor | Used for frequent combinations |
ψ₂ | Quasi-permanent factor | Used for long-term effects |
🏗️ ψ₀ – Combination Factor
The ψ₀ factor represents a variable action that is present together with another leading variable action but is unlikely to reach its maximum value.
Example:
A roof is designed for:
Snow load
Roof maintenance load
It is unlikely that:
Maximum snow loading occurs
AND maintenance personnel are accessing the roof
at exactly the same time.
Therefore, the accompanying action is reduced using ψ₀.
Example:
Characteristic SLS combination:
Gk + Qk,snow + ψ₀Qk,maintenance
where:
Snow is the leading variable action
Maintenance is the accompanying variable action
🏗️ ψ₁ – Frequent Factor
The ψ₁ factor represents loads that occur regularly but are still below the maximum characteristic value.
It represents a situation that happens reasonably often during the life of the structure.
Examples:
Normal office occupancy
Regular pedestrian traffic
Normal operational loading
The frequent combination is often used when checking:
Human comfort
Vibration
Sensitive equipment operation
Example:
Gk + ψ₁Qk,office
The imposed load is reduced because maximum occupancy is not expected every day.
🏗️ ψ₂ – Quasi-Permanent Factor
The ψ₂ factor represents the long-term average effect of variable actions.
These are loads that are expected to exist for a significant proportion of the building's life.
Examples:
Average occupancy
Permanent furniture loads
Long-term storage
The quasi-permanent combination is used for:
Long-term deflection
Creep effects
Appearance
Permanent deformation
Example:
Gk + ψ₂Qk,office
📊 Typical ψ Factors for Buildings
The exact values depend on the action type and the relevant National Annex.
Typical values from EN 1990 Table A1.1 are shown below.
Action Category | ψ₀ | ψ₁ | ψ₂ |
Category A – Domestic and residential areas | 0.7 | 0.5 | 0.3 |
Category B – Office areas | 0.7 | 0.5 | 0.3 |
Category C – Congregation areas | 0.7 | 0.7 | 0.6 |
Category D – Shopping areas | 0.7 | 0.7 | 0.6 |
Category E – Storage areas | 1.0 | 0.9 | 0.8 |
Category F/G – Traffic areas | 0.7 | 0.7 | 0.6 |
Category H – Roofs | 0.0–0.6* | 0.0–0.2* | 0.0* |
Snow load ≤1000m altitude | 0.5 | 0.2 | 0.0 |
Snow load >1000m altitude | 0.7 | 0.5 | 0.2 |
Wind load | 0.6 | 0.2 | 0.0 |
*Values depend on roof category and National Annex requirements.
Important: Engineers must always verify the applicable National Annex because countries can modify recommended Eurocode values.
⚖️ SLS Combination Equations According to EN 1990
EN 1990 defines three main serviceability combinations.
🔴 1. Characteristic Combination (Rare Combination)
The characteristic combination represents the highest service load expected during the building lifetime.
General expression:
Ed = ΣGk + Qk,1 + Σψ₀,iQk,i
Where:
Gk = permanent actions
Qk,1 = leading variable action
ψ₀Qk = accompanying variable actions
The leading variable action is taken at its full characteristic value.
Other variable actions are reduced.
Example
Office floor:
Permanent load:
Gk = 5.0 kN/m²
Office imposed load:
Qk = 3.0 kN/m²
Additional movable partition load:
Qk = 1.0 kN/m²
For office areas:
ψ₀ = 0.7
Characteristic combination:
= 5.0 + 3.0 + 0.7 × 1.0
= 8.7 kN/m²
🟡 2. Frequent Combination
The frequent combination represents a load condition that occurs regularly.
General expression:
Ed = ΣGk + ψ₁,1Qk,1 + Σψ₂,iQk,i
The leading variable action is reduced using ψ₁.
Other variable actions are reduced using ψ₂.
Example
Using the same office:
Gk = 5.0 kN/m²
Qk = 3.0 kN/m²
ψ₁ = 0.5
ψ₂ = 0.3
Frequent combination:
= 5.0 + (0.5 × 3.0)
= 6.5 kN/m²
🟢 3. Quasi-Permanent Combination
The quasi-permanent combination represents long-term sustained loading.
General expression:
Ed = ΣGk + Σψ₂,iQk,i
All variable actions are reduced using ψ₂.
Example
Office loading:
Gk = 5.0 kN/m²
Qk = 3.0 kN/m²
ψ₂ = 0.3
Quasi-permanent combination:
= 5.0 + (0.3 × 3.0)
= 5.9 kN/m²
🧱 Comparing the Three Combinations
Using the office example:
Combination | Calculation | Result |
Characteristic | 5 + 3 + (0.7×1) | 8.7 kN/m² |
Frequent | 5 + (0.5×3) | 6.5 kN/m² |
Quasi-permanent | 5 + (0.3×3) | 5.9 kN/m² |
The important observation is:
Characteristic > Frequent > Quasi-permanent
This reflects the probability of occurrence.
The rarer the event, the higher the load considered.
🏢 Why This Matters in Real Buildings
A structural engineer does not design every part of a building for the same loading condition. Different checks require different assumptions. For example:
Floor beam strength
May require:
ULS combination
because the question is: "Will it fail?"
Floor vibration
May require:
Frequent combination
because the question is: "Will occupants feel uncomfortable?"
Long-term deflection
May require:
Quasi-permanent combination
because the question is: "Will the floor permanently deform over many years?"
Common Mistake: Assuming SLS Uses Maximum Loads
A common misunderstanding is:
"Why don't we always check the structure with the maximum possible load?"
The reason is that SLS is not about preventing collapse.
It is about predicting realistic building behaviour.
Using maximum loads for every serviceability check would result in:
Overly conservative designs
Increased construction costs
Excessive material use
The Eurocode approach provides a realistic balance between safety, comfort and economy.
References
EN 1990 – Eurocode: Basis of Structural and Geotechnical Design
EN 1991-1-1 – Actions on Structures: Densities, Self-weight and Imposed Loads
EN 1991-1-3 – Actions on Structures: Snow Loads
Relevant National Annex
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The content provided in this post is for informational purposes only and should not be construed as professional engineering, architectural, or surveying advice. While every effort is made to ensure the accuracy and reliability of the information presented, it is not a substitute for a thorough, site-specific inspection or the expertise of a qualified professional. For detailed guidance on foundation issues, structural integrity, or repairs, always consult with a licensed engineer, architect, or surveyor. The authors and publishers are not responsible for any damages or losses resulting from the use or reliance on this information.