**A guide to Eurocode Load Combinations: EN 1990:2002**

The Eurocodes are a set of standards for how structural design should be conducted within the European Union. EN 1990:2002 (ECO) sets out the basis of structural design whereas EN 1991 (EC1) specifies the actions on structures. In conjunction, these two documents provide a methodology for the combination of actions (load combinations) for limit states design. In general terms, limit states are the conditions that result in the building ceasing to meet its function that it was designed for.

Limit states are categorized as being an ultimate limit state (ULS) or serviceability limit state (SLS). ULS is concerned with the safety of people and/or safety of structure (e.g. capacity, overturning, sliding, fracture). SLS is concerned with inhibited intended use, the comfort of people, and appearance of construction works (e.g. cracking, deformation).

The following Ultimate Limit States need to be verified:

- EQU – Loss of equilibrium.
- STR – Internal failure of the structure.
- GEO – Failure or excessive deformation of the ground.

This article will focus on how SkyCiv’s auto-generated load combinations feature meets the load combination equations as specified in EN 1990:2002.

**Table A1.2(A) – Design values of actions (EQU)(Set A)**

The following assumptions are made:

- There is low variability in G
_{k}and therefore that G_{k,sup,}and G_{k,inf}need not be used. - The single-source principle for permanent loads does not apply to EQU. This means load combinations allow some permanent actions to be favorable, and others to be unfavorable.
- Variable actions include imposed loads, snow loads, wind loads, and temperature (non-fire) loads.

Permanent Actions (Unfavourable) | Permanent Actions (Favourable) | Leading Variable Action | Accompanying Variable Actions |
---|---|---|---|

1.10G_{k,j} |
0.90G_{k,j} |
1.5Q_{k,1} (0 when favorable) |
1.5ψ_{0,i}Q_{k,1} (0 when favourable) |

SkyCiv’s Implementation

SkyCiv’s Equation | SkyCiv’s Comment |
---|---|

0.9G | ULS: EQU (Favourable). All dead (G) load types will be given a 0.9 factor as this load combination is specifically for “favorable” conditions. |

γ_{Gj}G + 1.5Q_{L} + 1.5ψ_{0,1}Q_{S} + 0.75Q_{W} + 0.9Q_{T} |
ULS: EQU (Favourable/Unfavourable). Leading variable: Imposed loads Q_{L}. You may assign your permanent load groups as “Dead: Unfavourable” (with factor 1.10) or “Dead: Favourable” (with factor 0.9) load types. |

γ_{Gj}G + 1.5Q_{S} + 1.5ψ_{0,1}Q_{L} + 0.75Q_{W} + 0.9Q_{T} |
ULS: EQU (Favourable/Unfavourable). Leading variable: Snow loads Q_{S}. You may assign your permanent load groups as “Dead: Unfavourable” (with factor 1.10) or “Dead: Favourable” (with factor 0.9) load types. |

γ_{Gj}G + 1.5Q_{W} + 1.5ψ_{0,1}Q_{L} + 1.5ψ_{0,1}Q_{S} + 0.9Q_{T} |
ULS: EQU (Favourable/Unfavourable). Leading variable: Wind loads Q_{W}. You may assign your permanent load groups as “Dead: Unfavourable” (with factor 1.10) or “Dead: Favourable” (with factor 0.9) load types. |

γ_{Gj}G + 1.5Q_{T} + 1.5ψ_{0,1}Q_{L} + 1.5ψ_{0,1}Q_{S} + 0.75Q_{W} |
ULS: EQU (Favourable/Unfavourable). Leading variable: Temperature loads Q_{T}. You may assign your permanent load groups as “Dead: Unfavourable” (with factor 1.10) or “Dead: Favourable” (with factor 0.9) load types. |

**Table A1.2(B) – Design values of actions (STR/GEO)(Set B)**

The following assumptions are made:

- There is low variability in G
_{k}and therefore that G_{k,sup}and G_{k,inf}need not be used. - The single source principle for permanent loads applies in this case. This means load combinations with permanent actions will all be multiplied by the same factor (unfavorable or favorable).
- Foundations are not considered.
- Variable actions include imposed loads, snow loads, wind loads, and temperature (non-fire) loads.

Permanent Actions (Unfavourable) | Permanent Actions (Favourable) | Leading Variable Action | Accompanying Variable Actions |
---|---|---|---|

1.35G_{k,j} |
1.00G_{k,j} |
1.5Q_{k,1} (0 when favorable) |
1.5ψ_{0,i}Q_{k,1} (0 when favourable) |

SkyCiv’s Implementation

SkyCiv’s Equation | SkyCiv’s Comment |
---|---|

G | ULS: STR (Favourable). All dead (G) load types will be given a 1.0 factor as this load combination is specifically for “favorable” conditions. |

1.35G + 1.5Q_{L} + 1.5ψ_{0,1}Q_{S} + 0.75Q_{W} + 0.9Q_{T} |
ULS: STR (Unfavourable). Leading variable: Imposed loads Q_{L}. All load groups which have been assigned as a “Dead” load type will be assigned the “unfavorable” value (1.35) regardless of the subtype due to the single-source principle. |

1.35G + 1.5Q_{S} + 1.5ψ_{0,1}Q_{L} + 0.75Q_{W} + 0.9Q_{T} |
ULS: STR (Unfavourable). Leading variable: Snow loads Q_{S}. All load groups which have been assigned as a “Dead” load type will be assigned the “unfavorable” value (1.35) regardless of the subtype due to the single-source principle. |

1.35G + 1.5Q_{W} + 1.5ψ_{0,1}Q_{L} + 1.5ψ_{0,1}Q_{S} + 0.9Q_{T} |
ULS: STR (Unfavourable). Leading variable: Wind loads Q_{W}. All load groups which have been assigned as a “Dead” load type will be assigned the “unfavorable” value (1.35) regardless of the subtype due to the single-source principle. |

1.35G + 1.5Q_{T} + 1.5ψ_{0,1}Q_{L} + 1.5ψ_{0,1}Q_{S} + 0.75Q_{W} |
ULS: STR (Unfavourable). Leading variable: Temperature loads Q_{T}. All load groups which have been assigned as a “Dead” load type will be assigned the “unfavorable” value (1.35) regardless of the subtype due to the single-source principle. |

**Table A1.2(C) – Design values of actions (STR/GEO)(Set C)**

The following assumptions are made:

- There is low variability in G
_{k}and therefore that G_{k,sup}and G_{k,inf}need not be used. - Variable actions include imposed loads, snow loads, wind loads, and temperature (non-fire) loads.

Permanent Actions (Unfavourable) | Permanent Actions (Favourable) | Leading Variable Action | Accompanying Variable Actions |
---|---|---|---|

1.00G_{k,j} |
1.00G_{k,j} |
1.3Q_{k,1} (0 when favorable) |
1.3ψ_{0,i}Q_{k,1} (0 when favourable) |

SkyCiv’s Implementation

SkyCiv’s Equation | SkyCiv’s Comment |
---|---|

G | ULS: GEO (Favourable). All dead (G) load types will be given a 1.0 factor as this load combination is specifically for “favorable” conditions. |

G + 1.3Q_{L} + 1.3ψ_{0,1}Q_{S} + 0.65Q_{W} + 0.78Q_{T} |
ULS: GEO (Unfavourable). Leading variable: Imposed loads Q_{L}. |

G + 1.3Q_{S} + 1.3ψ_{0,1}Q_{L} + 0.65Q_{W} + 0.78Q_{T} |
ULS: GEO (Unfavourable). Leading variable: Snow loads Q_{S}. |

G + 1.3Q_{W} + 1.3ψ_{0,1}Q_{L} + 1.3ψ_{0,1}Q_{S} + 0.78Q_{T} |
ULS: GEO (Unfavourable). Leading variable: Wind loads Q_{W}. |

G + 1.3Q_{T} + 1.3ψ_{0,1}Q_{L} + 1.3ψ_{0,1}Q_{S} + 0.65Q_{W} |
ULS: GEO (Unfavourable). Leading variable: Temperature loads Q_{T}. |

**Table A1.3 – Design values of actions for use in accidental and seismic combinations of actions**

The following assumptions are made:

- There is low variability in G
_{k}and therefore that G_{k,sup}and G_{k,inf}need not be used. - Variable actions include imposed loads, snow loads, wind loads, and temperature (non-fire) loads.

Design Situation | Permanent Actions (Unfavourable) | Permanent Actions (Favourable) | Leading Accidental or Seismic Action | Accompanying Variable Action (Main) | Accompanying Variable Action (Others) |
---|---|---|---|---|---|

Accidental (Eq. 6.11a/b) | 1.00G_{k,j} |
1.00G_{k,j} |
A_{d} |
ψ_{1,1} or ψ_{2,1}Q_{k,1} |
ψ_{2,i}Q_{k,i} |

Seismic (Eq. 6.12a/b) | 1.00G_{k,j} |
1.00G_{k,j} |
γ_{I}A_{Ek} or A_{Ed} |
– | ψ_{2,i}Q_{k,i} |

SkyCiv’s Implementation

SkyCiv’s Equation | SkyCiv’s Comment |
---|---|

G + A + ψ_{1}Q_{L} + ψ_{2,1}Q_{S} |
ALS: ACC-a. Main accompanying variable action: Imposed loads Q_{L} |

G + A + ψ_{1}Q_{S} + ψ_{2,1}Q_{L} |
ALS: ACC-a. Main accompanying variable action: Snow loads Q_{S} |

G + A + 0.2Q_{W} + ψ_{2,1}Q_{L} + ψ_{2,1}Q_{S} |
ALS: ACC-a. Main accompanying variable action: Wind loads Q_{W} |

G + A + 0.5Q_{T} + ψ_{2,1}Q_{L} + ψ_{2,1}Q_{S} |
ALS: ACC-a. Main accompanying variable action: Temperature loads Q_{T} |

G + A + ψ_{2,1}Q_{L} + ψ_{2,1}Q_{S} |
ALS: ACC-b. Main and other accompanying variable actions equivalent |

G + E + ψ_{2,1}Q_{L} + ψ_{2,1}Q_{S} |
ALS: SEI. |

**Table A1.4.1 – Serviceability Limit States – Partial Factors for Actions**

The following assumptions are made:

- There is low variability in G
_{k}and therefore that G_{k,sup}and G_{k,inf}need not be used. - Variable actions include imposed loads, snow loads, wind loads, and temperature (non-fire) loads.
- The serviceability criteria should be specified for each project and agreed upon with the client.
- The serviceability criteria for deformations and vibrations shall be defined depending on the intended use, in relation to the serviceability requirements, and independently of the materials used for the supporting structural member.

Combination | Permanent Actions | Leading Variable Action | Accompanying Variable Actions |
---|---|---|---|

Characteristic | G_{k,j} |
Q_{k,1} |
ψ_{0,i}Q_{k,1} |

Frequent | G_{k,j} |
ψ_{1,1}Q_{k,1} |
ψ_{2,i}Q_{k,1} |

Quasi-permanent | G_{k,j} |
ψ_{2,1}Q_{k,1} |
ψ_{2,i}Q_{k,i} |

SkyCiv’s Implementation

SkyCiv’s Equation | SkyCiv’s Comment |
---|---|

G + Q_{L} + ψ_{0,1}Q_{S} + 0.5Q_{W} + 0.6Q_{T} |
SLS: Characteristic. Leading variable action: Imposed loads Q_{L} |

G + Q_{S} + ψ_{0,1}Q_{L} + 0.5Q_{W} + 0.6Q_{T} |
SLS: Characteristic. Leading variable action: Snow loads Q_{S} |

G + Q_{W} + ψ_{0,1}Q_{L} + ψ_{0,1}Q_{S} + 0.6Q_{T} |
SLS: Characteristic. Leading variable action: Wind loads Q_{W} |

G + Q_{T} + ψ_{0,1}Q_{L} + ψ_{0,1}Q_{S} + 0.5Q_{W} |
SLS: Characteristic. Leading variable action: Temperature loads Q_{T} |

G + ψ_{1}Q_{L} + ψ_{2,1}Q_{S} |
SLS: Frequent. Leading variable action: Imposed loads Q_{L} |

G + ψ_{1}Q_{S} + ψ_{2,1}Q_{L} |
SLS: Frequent. Leading variable action: Snow loads Q_{S} |

G + 0.2Q_{W} + ψ_{2,1}Q_{L} + ψ_{2,1}Q_{S} |
SLS: Frequent. Leading variable action: Wind loads Q_{W} |

G + 0.5Q_{T} + ψ_{2,1}Q_{L} + ψ_{2,1}Q_{S} |
SLS: Frequent. Leading variable action: Temperature loads Q_{T} |

G + ψ_{2,1}Q_{L} + ψ_{2,1}Q_{S} |
SLS: Quasi-permanent. |