In Eurocode design, we don't just "check if it's strong enough." We verify the structure against specific Ultimate Limit States (ULS). The most common point of confusion for engineers is deciding which partial safety factors apply to a specific check. Are we checking for sliding, or are we checking if the beam snaps?
1. Defining the Limit States
EN 1990 categorizes ULS into several types depending on the nature of the potential failure:
- EQU (Equilibrium): Loss of static equilibrium of the structure as a rigid body. Think of a retaining wall overturning or a light canopy blowing away. Here, the strength of the materials is usually irrelevant; it’s all about weight vs. uplift/overturning.
- STR (Internal Resistance): Internal failure or excessive deformation of the structure or its members. This is your "bread and butter"—checking if a steel beam yields or a concrete column crushes.
- GEO (Geotechnical): Failure or excessive deformation of the ground. This covers bearing capacity, settlement, and slope stability.
2. Partial Safety Factors for Loads
To account for uncertainty, we multiply characteristic loads by partial factors ($\gamma$). Under standard persistent and transient design situations, the factors for the UK and most of Europe are:
Crucial Distinction: In an **EQU** check, the "unfavorable" permanent load factor increases to **1.1** (or 1.05) and the "favorable" factor (the weight holding it down) drops to **0.9**. This is a much tighter margin than STR design!
3. Combination Equations: 6.10 vs. 6.10a & 6.10b
When calculating the design effect ($E_d$), engineers have two choices for STR/GEO checks. The goal is to find the "worst-case" scenario.
Option 1: Equation 6.10
This is the "standard" approach used for simplicity. It applies the full factors to both Permanent and Variable loads simultaneously.
Option 2: Equations 6.10a and 6.10b
Most National Annexes allow you to use the lesser of these two. This often yields a more economical design, especially when the dead load is significantly higher than the live load.
- 6.10a: Focuses on permanent loads (usually $\gamma_G = 1.35$).
- 6.10b: Reduces the permanent load factor (often using a $\xi$ factor of 0.92, making $\gamma_G \approx 1.25$) but keeps the full variable load.
4. Accidental and Seismic Limit States
Beyond standard gravity and wind loads, structures must be verified for extreme events. In these cases, we accept higher levels of damage to prevent total collapse, so safety factors are significantly reduced.
- Accidental Situations (A): Fire, explosions, or vehicle impacts. Here, $\gamma_G$ and $\gamma_A$ (the accidental load) are typically taken as **1.0**. We use "frequent" or "quasi-permanent" values for other variable loads.
- Seismic Situations (AE): Earthquakes. Similar to accidental design, we use a $\gamma$ of **1.0**. The focus shifts from strength to ductility—ensuring the structure can dissipate energy through controlled deformation.
Key Takeaways
- EQU is for stability: If your check involves "overturning" or "sliding," your permanent load factors change to 1.1/0.9.
- STR is for strength: Use 1.35/1.0.
- Use 6.10b for economy: In heavy structures (like concrete slabs), 6.10b will almost always result in a lighter reinforcement requirement.
Manually tracking which $\psi$ and $\gamma$ factors apply to which limit state is a recipe for errors. Our StrucTalogue Load Combinations Tool automatically generates Equilibrium, Strength, Geotechnical, Accidental, and Seismic combinations for ULS and SLS based on your specific Eurocode National Annex.