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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:

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:

Permanent Actions (Unfavourable) Permanent Actions (Favourable) Leading Variable Action Accompanying Variable Actions
1.10Gk,j 0.90Gk,j 1.5Qk,1 (0 when favourable) 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 "favourable" conditions.
γGjG + 1.5QL + 1.5ψ0,1QS + 0.75QW + 0.9QT ULS: EQU (Favourable/Unfavourable). Leading variable: Imposed loads QL. You may assign your permanent load groups as "Dead: Unfavourable" (with factor 1.10) or "Dead: Favourable" (with factor 0.9) load types.
γGjG + 1.5QS + 1.5ψ0,1QL + 0.75QW + 0.9QT ULS: EQU (Favourable/Unfavourable). Leading variable: Snow loads QS. You may assign your permanent load groups as "Dead: Unfavourable" (with factor 1.10) or "Dead: Favourable" (with factor 0.9) load types.
γGjG + 1.5QW + 1.5ψ0,1QL + 1.5ψ0,1QS + 0.9QT ULS: EQU (Favourable/Unfavourable). Leading variable: Wind loads QW. You may assign your permanent load groups as "Dead: Unfavourable" (with factor 1.10) or "Dead: Favourable" (with factor 0.9) load types.
γGjG + 1.5QT + 1.5ψ0,1QL + 1.5ψ0,1QS + 0.75QW ULS: EQU (Favourable/Unfavourable). Leading variable: Temperature loads QT. 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:

Permanent Actions (Unfavourable) Permanent Actions (Favourable) Leading Variable Action Accompanying Variable Actions
1.35Gk,j 1.00Gk,j 1.5Qk,1 (0 when favourable) 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 "favourable" conditions.
1.35G + 1.5QL + 1.5ψ0,1QS + 0.75QW + 0.9QT ULS: STR (Unfavourable). Leading variable: Imposed loads QL. 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 + 1.5QS + 1.5ψ0,1QL + 0.75QW + 0.9QT ULS: STR (Unfavourable). Leading variable: Snow loads QS. 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 + 1.5QW + 1.5ψ0,1QL + 1.5ψ0,1QS + 0.9QT ULS: STR (Unfavourable). Leading variable: Wind loads QW. 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 + 1.5QT + 1.5ψ0,1QL + 1.5ψ0,1QS + 0.75QW ULS: STR (Unfavourable). Leading variable: Temperature loads QT. 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:

Permanent Actions (Unfavourable) Permanent Actions (Favourable) Leading Variable Action Accompanying Variable Actions
1.00Gk,j 1.00Gk,j 1.3Qk,1 (0 when favourable) 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 "favourable" 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

The following assumptions are made:

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

The following assumptions are made:

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.