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## 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.

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

• There is low variability in Gk and therefore that Gk,sup, and Gk,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.
Permanent Actions (Unfavourable) Permanent Actions (Favourable) Leading Variable Action Accompanying Variable Actions
1.10Gk,j 0.90Gk,j 1.5Qk,1 (0 when favorable) 1.5ψ0,iQk,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.

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

• There is low variability in Gk and therefore that Gk,sup and Gk,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.
Permanent Actions (Unfavourable) Permanent Actions (Favourable) Leading Variable Action Accompanying Variable Actions
1.35Gk,j 1.00Gk,j 1.5Qk,1 (0 when favorable) 1.5ψ0,iQk,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 + 1.5QL + 1.5ψ0,1QS + 0.75QW + 0.9QT ULS: STR (Unfavourable). Leading variable: Imposed loads QL. 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 + 1.5QS + 1.5ψ0,1QL + 0.75QW + 0.9QT ULS: STR (Unfavourable). Leading variable: Snow loads QS. 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 + 1.5QW + 1.5ψ0,1QL + 1.5ψ0,1QS + 0.9QT ULS: STR (Unfavourable). Leading variable: Wind loads QW. 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 + 1.5QT + 1.5ψ0,1QL + 1.5ψ0,1QS + 0.75QW ULS: STR (Unfavourable). Leading variable: Temperature loads QT. 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)

• There is low variability in Gk and therefore that Gk,sup and Gk,inf need not be used.
Permanent Actions (Unfavourable) Permanent Actions (Favourable) Leading Variable Action Accompanying Variable Actions
1.00Gk,j 1.00Gk,j 1.3Qk,1 (0 when favorable) 1.3ψ0,iQk,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 + 1.3QL + 1.3ψ0,1QS + 0.65QW + 0.78QT ULS: GEO (Unfavourable). Leading variable: Imposed loads QL.
G + 1.3QS + 1.3ψ0,1QL + 0.65QW + 0.78QT ULS: GEO (Unfavourable). Leading variable: Snow loads QS.
G + 1.3QW + 1.3ψ0,1QL + 1.3ψ0,1QS + 0.78QT ULS: GEO (Unfavourable). Leading variable: Wind loads QW.
G + 1.3QT + 1.3ψ0,1QL + 1.3ψ0,1QS + 0.65QW ULS: GEO (Unfavourable). Leading variable: Temperature loads QT.

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

• There is low variability in Gk and therefore that Gk,sup and Gk,inf need not be used.
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) 1.00Gk,j 1.00Gk,j Ad ψ1,1 or ψ2,1Qk,1 ψ2,iQk,i
Seismic (Eq. 6.12a/b) 1.00Gk,j 1.00Gk,j γIAEk or AEd ψ2,iQk,i

SkyCiv’s Implementation

SkyCiv’s Equation SkyCiv’s Comment
G + A + ψ1QL + ψ2,1QS ALS: ACC-a. Main accompanying variable action: Imposed loads QL
G + A + ψ1QS + ψ2,1QL ALS: ACC-a. Main accompanying variable action: Snow loads QS
G + A + 0.2QW + ψ2,1QL + ψ2,1QS ALS: ACC-a. Main accompanying variable action: Wind loads QW
G + A + 0.5QT + ψ2,1QL + ψ2,1QS ALS: ACC-a. Main accompanying variable action: Temperature loads QT
G + A + ψ2,1QL + ψ2,1QS ALS: ACC-b. Main and other accompanying variable actions equivalent
G + E + ψ2,1QL + ψ2,1QS ALS: SEI.

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

• There is low variability in Gk and therefore that Gk,sup and Gk,inf need not be used.
• 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 Gk,j Qk,1 ψ0,iQk,1
Frequent Gk,j ψ1,1Qk,1 ψ2,iQk,1
Quasi-permanent Gk,j ψ2,1Qk,1 ψ2,iQk,i

SkyCiv’s Implementation

SkyCiv’s Equation SkyCiv’s Comment
G + QL + ψ0,1QS + 0.5QW + 0.6QT SLS: Characteristic. Leading variable action: Imposed loads QL
G + QS + ψ0,1QL + 0.5QW + 0.6QT SLS: Characteristic. Leading variable action: Snow loads QS
G + QW + ψ0,1QL + ψ0,1QS + 0.6QT SLS: Characteristic. Leading variable action: Wind loads QW
G + QT + ψ0,1QL + ψ0,1QS + 0.5QW SLS: Characteristic. Leading variable action: Temperature loads QT
G + ψ1QL + ψ2,1QS SLS: Frequent. Leading variable action: Imposed loads QL
G + ψ1QS + ψ2,1QL SLS: Frequent. Leading variable action: Snow loads QS
G + 0.2QW + ψ2,1QL + ψ2,1QS SLS: Frequent. Leading variable action: Wind loads QW
G + 0.5QT + ψ2,1QL + ψ2,1QS SLS: Frequent. Leading variable action: Temperature loads QT
G + ψ2,1QL + ψ2,1QS SLS: Quasi-permanent.