# Eurocode Structural Design ## Table of Contents - [[#Overview]] - [[#Limit State Design Philosophy]] - [[#Ultimate Limit States ULS]] - [[#Serviceability Limit States SLS]] - [[#Actions and Their Classification]] - [[#Partial Safety Factors]] - [[#Partial Factors for Actions]] - [[#Partial Factors for Materials]] - [[#Action Combination Expressions]] - [[#ULS Persistent and Transient Design Situations]] - [[#ULS Accidental Design Situations]] - [[#ULS Seismic Design Situations]] - [[#SLS Combinations]] - [[#Characteristic vs Design Values]] - [[#Combination Factors Psi]] - [[#Reliability Classes and Consequence Classes]] - [[#Design Working Life]] - [[#Worked Example Action Combination]] - [[#Practical Notes for Architects]] - [[#References and Standards]] --- ## Overview Eurocode structural design follows the semi-probabilistic partial factor method established in EN 1990 (Eurocode 0: Basis of Structural Design). This framework ensures adequate structural reliability by applying partial safety factors to both actions (loads) and material resistances, then verifying that no limit state is exceeded. This article details the action combination rules, partial factors, and reliability framework that underpin all material-specific Eurocodes (EN 1992–EN 1999). See [[Eurocodes Overview]] for the full Eurocode suite and material-specific provisions. --- ## Limit State Design Philosophy The Eurocodes verify structural adequacy at defined limit states — conditions beyond which the structure no longer fulfils the design requirements. ### Ultimate Limit States ULS ULS relates to structural safety and protection of people. The following ULS categories are defined: | ULS Type | Description | |----------|----------------------------------------------------------| | EQU | Loss of static equilibrium of the structure as a rigid body | | STR | Internal failure or excessive deformation of the structure or structural members | | GEO | Failure or excessive deformation of the ground in which soil/rock strength is significant | | FAT | Fatigue failure of the structure or structural members | | UPL | Loss of equilibrium due to uplift by water pressure | | HYD | Hydraulic heave, piping, or erosion caused by hydraulic gradients | The most commonly used ULS verification in building design is **STR** (structural member design) and **EQU** (stability checks such as overturning). ### Serviceability Limit States SLS SLS relates to the functioning of the structure under normal use, occupant comfort, and appearance: - **Deflection**: Limiting vertical and horizontal deflections to prevent damage to finishes, cladding, and partitions. - **Cracking**: Limiting crack widths in concrete to protect reinforcement and maintain appearance. - **Vibration**: Limiting dynamic response to prevent occupant discomfort (particularly in lightweight floors and footbridges). - **Settlement**: Limiting differential settlement of foundations. SLS criteria are typically specified in the material-specific Eurocodes and the National Annexes. --- ## Actions and Their Classification Actions (loads) are classified by their variation in time: | Classification | Symbol | Description | Examples | |---------------|--------|------------------------------------------|-----------------------------------------| | Permanent | G | Actions that are constant or vary negligibly over the design working life | Self-weight, fixed equipment, earth pressure, prestress | | Variable | Q | Actions that vary significantly over time | Imposed loads, wind, snow, temperature | | Accidental | A | Actions of short duration and low probability | Explosions, vehicle impact, fire | | Seismic | AEd | Actions due to earthquakes | Seismic inertial forces | Each action is further characterised by spatial variation (fixed or free) and its effect (favourable or unfavourable). --- ## Partial Safety Factors ### Partial Factors for Actions Partial factors for actions (γ) account for: - Possible unfavourable deviation of action values from characteristic values. - Modelling inaccuracies. - Uncertainty in the assessment of effects of actions. **Recommended values for persistent and transient design situations (STR/GEO)**: | Factor | Applied to | Unfavourable | Favourable | |--------|----------------------|--------------|------------| | γG | Permanent actions | 1.35 | 1.00 | | γQ | Variable actions | 1.50 | 0.00 | | γA | Accidental actions | 1.00 | — | | γP | Prestressing actions | Per material Eurocode | Per material Eurocode | **For EQU verification** (equilibrium): | Factor | Applied to | Destabilising | Stabilising | |--------|----------------------|---------------|-------------| | γG | Permanent actions | 1.10 | 0.90 | | γQ | Variable actions | 1.50 | 0.00 | These are recommended values per EN 1990 Annex A1. National Annexes may modify them. ### Partial Factors for Materials Material partial factors (γM) account for: - Unfavourable deviation of material properties from characteristic values. - Inaccuracies in conversion factors and resistance models. - Geometric deviations. | Material | Symbol | Recommended ULS Value | |----------------------------|--------|----------------------| | Concrete | γc | 1.50 | | Reinforcing steel | γs | 1.15 | | Structural steel | γM0 | 1.00 | | Structural steel (buckling) | γM1 | 1.00 | | Structural steel (net section)| γM2 | 1.25 | | Timber (fundamental) | γM | 1.30 | | Masonry | γM | 2.0–3.0 (NA dependent)| | Connections (steel bolts) | γM2 | 1.25 | For SLS verifications, material partial factors are typically taken as 1.0. --- ## Action Combination Expressions ### ULS Persistent and Transient Design Situations EN 1990 provides two approaches for combining actions at ULS: **Expression 6.10 (single expression)**: ``` Ed = Σ γG,j · Gk,j + γQ,1 · Qk,1 + Σ γQ,i · ψ0,i · Qk,i ``` Where: - Gk,j = characteristic value of permanent action j - Qk,1 = characteristic value of the leading variable action - Qk,i = characteristic value of accompanying variable actions - ψ0,i = combination factor for the accompanying variable action **Expressions 6.10a and 6.10b (alternative, less conservative approach permitted by some National Annexes)**: ``` 6.10a: Ed = Σ γG,j · Gk,j + γQ,1 · ψ0,1 · Qk,1 + Σ γQ,i · ψ0,i · Qk,i 6.10b: Ed = Σ ξ · γG,j · Gk,j + γQ,1 · Qk,1 + Σ γQ,i · ψ0,i · Qk,i ``` Where ξ = reduction factor for permanent actions (recommended ξ = 0.925 per UK NA, giving ξ × 1.35 = 1.25). The design value Ed is taken as the most unfavourable of 6.10a and 6.10b. The choice between 6.10 and 6.10a/b is a Nationally Determined Parameter. ### ULS Accidental Design Situations ``` Ed = Σ Gk,j + Ad + ψ1,1 · Qk,1 + Σ ψ2,i · Qk,i ``` Where Ad = design value of the accidental action. All partial factors on permanent and variable actions are 1.0. The leading variable action uses ψ1 (frequent value) and accompanying actions use ψ2 (quasi-permanent value). ### ULS Seismic Design Situations ``` Ed = Σ Gk,j + AEd + Σ ψ2,i · Qk,i ``` Where AEd = design value of seismic action. Variable actions use the quasi-permanent combination factor ψ2. ### SLS Combinations Three SLS combinations address different duration scenarios: **Characteristic (rare) combination**: ``` Ed = Σ Gk,j + Qk,1 + Σ ψ0,i · Qk,i ``` **Frequent combination**: ``` Ed = Σ Gk,j + ψ1,1 · Qk,1 + Σ ψ2,i · Qk,i ``` **Quasi-permanent combination**: ``` Ed = Σ Gk,j + Σ ψ2,i · Qk,i ``` --- ## Characteristic vs Design Values | Term | Symbol | Definition | |----------------------|--------|-----------------------------------------------------------| | Characteristic value | Xk | Value of an action or material property with a prescribed probability of not being exceeded | | Design value | Xd | Value obtained by dividing (material) or multiplying (action) the characteristic value by the appropriate partial factor | | Representative value | Xrep | Characteristic value modified by a combination (ψ) factor | | Nominal value | Xnom | Value used where statistical data is insufficient | **For actions**: Design value = γ × Characteristic value (× ψ where applicable). **For materials**: Design value = Characteristic value / γM. Characteristic material strengths are defined as the 5th percentile of the statistical distribution (e.g., fck for concrete, fy for steel). --- ## Combination Factors Psi ψ factors reduce variable actions when they act in combination, recognising that it is improbable for all variable actions to reach their maximum values simultaneously: | Variable Action | ψ0 | ψ1 | ψ2 | |--------------------------|-------|-------|-------| | Imposed loads — Category A (domestic) | 0.7 | 0.5 | 0.3 | | Imposed loads — Category B (office) | 0.7 | 0.5 | 0.3 | | Imposed loads — Category C (assembly) | 0.7 | 0.7 | 0.6 | | Imposed loads — Category D (shopping) | 0.7 | 0.7 | 0.6 | | Imposed loads — Category E (storage) | 1.0 | 0.9 | 0.8 | | Snow loads (altitude ≤ 1000 m) | 0.5 | 0.2 | 0.0 | | Wind loads | 0.5 | 0.2 | 0.0 | | Temperature actions | 0.6 | 0.5 | 0.0 | Values shown are recommended per EN 1990 Annex A1. National Annexes may specify different values. --- ## Reliability Classes and Consequence Classes EN 1990 links the required structural reliability to the consequences of failure: | Consequence Class | Description | Reliability Class | β (50 years) | Example | |------------------|------------------------------------------|-------------------|--------------|-----------------------------------| | CC1 | Low consequence for loss of human life | RC1 | 3.3 | Agricultural buildings, greenhouses| | CC2 | Medium consequence | RC2 | 3.8 | Residential, offices, public buildings | | CC3 | High consequence | RC3 | 4.3 | Grandstands, concert halls, high-rise| β is the target reliability index. Higher reliability classes may require: - Increased partial factors (KFI factor applied to γG and γQ). - Enhanced quality management and inspection. - Third-party design checking. Most buildings fall within CC2 / RC2. --- ## Design Working Life The design working life is the assumed period during which the structure is used for its intended purpose with anticipated maintenance: | Category | Design Working Life (years) | Examples | |----------|----------------------------|-----------------------------------------| | 1 | 10 | Temporary structures | | 2 | 10–25 | Replaceable structural parts | | 3 | 15–30 | Agricultural and similar structures | | 4 | 50 | Building structures and common structures| | 5 | 100 | Monumental buildings, bridges, civil engineering | Design working life affects the characteristic values of climatic actions (wind, snow) through return period adjustments, and influences durability requirements (concrete cover, corrosion protection). --- ## Worked Example Action Combination **Scenario**: Office building floor (Category B), subjected to: - Permanent action: Gk = 5.0 kN/m² (self-weight + finishes) - Imposed load: Qk,1 = 2.5 kN/m² (leading variable action) - Partition allowance: Qk,2 = 0.8 kN/m² (accompanying variable, ψ0 = 0.7) **Using Expression 6.10**: ``` Ed = 1.35 × 5.0 + 1.50 × 2.5 + 1.50 × 0.7 × 0.8 Ed = 6.75 + 3.75 + 0.84 Ed = 11.34 kN/m² ``` **Using Expressions 6.10a / 6.10b (UK NA, ξ = 0.925)**: ``` 6.10a: Ed = 1.35 × 5.0 + 1.50 × 0.7 × 2.5 + 1.50 × 0.7 × 0.8 Ed = 6.75 + 2.625 + 0.84 = 10.22 kN/m² 6.10b: Ed = 0.925 × 1.35 × 5.0 + 1.50 × 2.5 + 1.50 × 0.7 × 0.8 Ed = 6.244 + 3.75 + 0.84 = 10.83 kN/m² ``` Design value = max(6.10a, 6.10b) = **10.83 kN/m²** (6.10b governs, as is typical when permanent actions are significant). --- ## Practical Notes for Architects - Architects are not expected to perform structural calculations, but understanding the partial factor framework enables effective coordination with structural engineers and informed decision-making about structural implications of architectural choices. - When briefing structural engineers, clearly define the intended building use (Category A–E) as this determines the imposed load and combination factor values. - Consequence class affects design rigour and cost: CC3 requires third-party checking and may increase structural member sizes. Discuss early with the structural engineer. - Design working life influences maintenance strategy: specify 50-year components for standard buildings, 100-year for significant civic and cultural buildings. - The choice of 6.10 vs 6.10a/b varies by country. Confirm with the structural engineer which National Annex applies and which expressions are permitted. - Material partial factors directly affect member sizes: concrete (γc = 1.5) requires a larger safety margin than structural steel (γM0 = 1.0), which is one reason steel structures can be more slender. - Fire design uses modified partial factors (typically γGA = 1.0 for permanent actions, ψ1 or ψ2 for variable actions) reflecting the reduced probability of combined extreme events. --- ## References and Standards - EN 1990:2002+A1: Eurocode 0 — Basis of Structural Design - EN 1990 Annex A1: Application for Buildings - EN 1991-1-1: Eurocode 1 — Actions on Structures — General Actions — Densities, Self-weight, Imposed Loads - National Annexes to EN 1990 (country-specific) - [[Eurocodes Overview]] - [[Fire Safety Building Regulations]] - [[International Building Code IBC]] --- #codes #structural #eurocodes #partialfactors #limitstates #ULS #SLS