## 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 safety of people and/or safety of structure (e.g. capacity, overtuning, sliding, fracture). SLS is concerned with inhibited intended use, comfort of people, and appearance of construction works (e.g. cracking, deformation).

The following Ultimate Limit States need to be verifed:

- 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 principal for permanent loads does not apply for EQU. This means load combinations allow some permanent actions to be favourable, and others to be unfavourable.
- 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 favourable) |
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 “favourable” 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 principal for permanent loads applies in this case. This means load combinations with permanent actions will all be multiplied by the same factor (unfavourable or favourable).
- 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 favourable) |
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 “favourable” 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 group which have been assigned as a “Dead” load type will be assigned the “unfavourable” value (1.35) regardless of the subtype due to the single source principal. |

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 group which have been assigned as a “Dead” load type will be assigned the “unfavourable” value (1.35) regardless of the subtype due to the single source principal. |

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 group which have been assigned as a “Dead” load type will be assigned the “unfavourable” value (1.35) regardless of the subtype due to the single source principal. |

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 group which have been assigned as a “Dead” load type will be assigned the “unfavourable” value (1.35) regardless of the subtype due to the single source principal. |

## 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 favourable) |
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 “favourable” 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 with the client.
- The serviceability criteria for deformations and vibrations shall be defined depending on the intended use, in relation to the servicability 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. |