Load Combination Summary

Load Combinations are a critical aspect of design. It is important to ensure you are correctly applying the relevant design load combinations to ensure the minimum design requirements of your local design code are being met. Here, SkyCiv has released a summary of the design combinations integrated in our Structural Analysis Software for engineers to use as a reference. We have included the load combos for ASCE 7-10, AS/NZ 1170, ACI, NBCC and EN 1990.



ASCE 7-10 Load Combinations

ASCE 7 10 is a design code for the United States; focussing on the minumum requirements for structural design in the US. With this design standard, it provides the recommended load factors and load combinations to be applied to each of the load types (wind, snow, dead etc..) and is particularly useful for design codes such as AISC 360 - Structural Steel Buildings. This design standard comes with two provisions;

  • ASD - Allowable Strength Design
  • LRFD - Load and Resistance Factor Design

Below are the summarized load combination factors for ASCE 7-10 based on their provisions:

ASCE 7-10 LRFD Load Combinations

Design Code Equation Design Code Comment SkyCiv Equation SkyCiv Comment
1.4D Eq. 2.3.2.1 1.4G -
1.2D + 1.6L + 0.5(Lrr or S or R) Eq. 2.3.2.2 1.2G + 1.6QL + 0.5QS The load type "Snow" is sub-categorized into "snow", "roof live", and "rain". Selecting this load combination will automatically create 3 load combination equations due to the use of "or" in the equation specification.
1.2D + 1.6(Lrr or S or R) + (L or 0.5W) Eq. 2.3.2.3 1.2G + 1.6QS + QL
1.2G + 1.6QS + 0.5QW
Due to the presence of "or" in two places of this load combination, this generates 6 load equations. SkyCiv has separated this into two load combinations (for the L or 0.5W options) which generates 3 load equations each.
1.2D + 1.0W + L + 0.5(Lr or S or R) Eq. 2.3.2.4 1.2G + QW + QL + 0.5QS The load type "Snow" is sub-categorized into "snow", "roof live", and "rain". Selecting this load combination will automatically create 3 load combination equations due to the use of "or" in the equation specification.
1.2D + 1.0E + L + 0.2S Eq. 2.3.2.5 1.2G + QL + 0.2QS + E -
0.9D + 1.0W Eq. 2.3.2.6 0.9G + QW -
0.9D + 1.0E Eq. 2.3.2.7 0.9G + E -

ASCE 7-10 ASD Load Combinations

Design Code Equation Design Code Comment SkyCiv Equation SkyCiv Comment
D Eq. 2.4.1.1 G -
D + L Eq. 2.4.1.2 G + QL -
D + (Lr or S or R) Eq. 2.4.1.3 G + QS The load type QS "Snow" is sub-categorized into "snow", "roof live", and "rain". Selecting this load combination will automatically create 3 load combination equations due to the use of "or" in the equation specification.
D + 0.75L + 0.75(Lr or S or R) Eq. 2.4.1.4 G + 0.75QL + 0.75QS The load type QS "Snow" is sub-categorized into "snow", "roof live", and "rain". Selecting this load combination will automatically create 3 load combination equations due to the use of "or" in the equation specification.
D + (0.6W or 0.7E) Eq. 2.4.1.5 G + 0.6QW
G + 0.7E
Due to the presence of an "or" in the load combination, two load combination eqations are required to represent them. Since "wind" and "seismic" are not linked by a load type, two separate equations are given by SkyCiv, instead of auto-generating equations in the case of the QS snow load type.
D + 0.75L + 0.75(0.6W) + 0.75(Lr or S or R) Eq. 2.4.1.6a G + 0.75QL + 0.45QW + 0.75QS The load type QS "Snow" is sub-categorized into "snow", "roof live", and "rain". Selecting this load combination will automatically create 3 load combination equations due to the use of "or" in the equation specification.
D + 0.75L + 0.75(0.7E) + 0.75S Eq. 2.4.1.6b G + 0.75QL + 0.75QS + 0.525E Only one load equation is required to represent this load combination. Despite the presence of QS "Snow" load type, only one equation is generated by SkyCiv for the "snow" sub-type.
0.6D + 0.6W Eq. 2.4.1.7 0.6G + 0.6QW -
0.6D + 0.7E Eq. 2.4.1.8 0.6G + 0.7E -


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AS/NZ 1170 Load Combinations

AS/NZS 1170 is a design standard for the minimum design loads for buildings and other structures in Australia and New Zealand. The focus of this standard is to provide structural engineers with load combinations for design.

The AS 1170 load combinations can be divided into a number of criteria, depending on what is being designed for:

Stability

Design Code Equation Design Code Comment SkyCiv Equation SkyCiv Comment
Ed,stb = [0.9G] Net Destabilizing: Permanent action only (does not apply to prestressing forces) 1.35G SPC: Permanent Destabilizing
Ed,stb = [1.35G] Net Stabilizing: Permanent action only (does not apply to prestressing forces) 0.9G SPC: Permanent Stabilizing
Ed,stb = [1.2G,1.5Q] Permanent and imposed action 1.2G + 1.5QL ULS: Permanent & Imposed.
Ed,stb = [1.2G, Wu, ψc,Q] Permanent, wind and imposed action 1.2G + ψ2,1QL + QW ULS: Permanent, Wind & Imposed. The imposed action factor represented by the psi is determined by the type of QL that this equation acts against.
Ed,stb = [1.2G, Su,ψc,Q] Permanent action, actions given in Clause 4.2.3 and imposed action. 1.2G + ψ0,3QL + QS ULS: Permanent, Other, & Imposed. The imposed action factor represented by the psi is determined by the type of QL that this equation acts against.

Strength

Design Code Equation Design Code Comment SkyCiv Equation SkyCiv Comment
Ed = [1.35G] Permanent action only (does not apply to prestressing forces) 1.35G Identical to Ed,dst.
Ed = [1.2G,1.5Q] Permanent and imposed action 1.2G + 1.5QL Identical to Ed,dst.
Ed = [1.2G,1.5ψlQ] Permanent and long term imposed action 1.2G + 1.5ψ1QL ULS: Permanent & Long-term Imposed. The imposed action factor represented by the psi is determined by the type of QL that this equation acts against.
Ed = [0.9G, Wu] Permanent and wind action reversal 0.9G + Qw ULS: Permanent, Wind
Ed = [G, Eu, ψc,Q] Permanent, earthquake and imposed action G + ψ2,nQL + E SPC: Permanent, Earthquake & Imposed
Ed = [1.2G, Su,ψc,Q] Permanent action, actions given in Clause 4.2.3 and imposed action. 1.2G + ψ0,3QL + QS Identical to Ed,dst.

Serviceability Limit States

SkyCiv Equation SkyCiv Comment
G + ψ0,1QL SLS Permanent and Short-term Imposed
G + ψ1QL SLS Permanent and Long-term Imposed


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ACI 318 Load Combinations

ACI 318 is a US concrete design standard released by the American Concrete Institute specifying the minimum design loads and load factors for concrete structures. Fundamentally, all structures/structural members should possess design strengths at all sections at least equal to the required strengths calulated for the factored loads and forces in combinations.

Chapter 9 of the code details the strength and serviceability load combination requirements of structural members:

ACI 318 Load Combinations

Design Code Equation Design Code Comment SkyCiv Equation SkyCiv Comment
U = 1.4D Eq. 9-1 1.4G -
U = 1.2D + 1.6L + 0.5(Lr or S or R) Eq. 9-2 1.2G + 1.6QL + 0.5QS The load type QS "Snow" is sub-categorized into "snow", "roof live", and "rain". Selecting this load combination will automatically create 3 load combination equations due to the use of "or" in the combination.
U = 1.2D + 1.6(Lr or S or R) + (1.0L or 0.5W or 0.8W) Eq. 9-3. Referencing R9.2-Required Strength (b): Where W is based on service-level wind loads, 0.8W shall be used in place of 0.5W in Eq. 9-3. 1.2G + 1.6QS + ψ1QW
1.2G + 1.6QS + QL
This load combination involves 3 terms. As in the combination for Eq. 9-2, QS will create 3 equations to account for the "or" statement for "snow", "roof live", and "rain".

The third term is either L (live) or W (wind). SkyCiv represents this by 2 separate load combinations (each generating 3 equations). To account for service level requirements in R9.2(b), users can select load types "Wind: strength" or "Wind: service level" to apply factors 0.5 or 0.8 (respectively) to their load groups.
U = 1.2D + (1.0 or 1.6)W + 1.0L + 0.5(Lr or S or R) Eq. 9-4. Referencing R9.2-Required Strength (b): Where W is based on service-level wind loads, 1.6W shall be used in place of 1.0W in Eq. 9-4. 1.2G + γuQW + QL + 0.5QS This load combination involves 4 terms. As in the combination for Eq. 9-2, QS will create 3 equations to account for the "or" statement for "snow", "roof live", and "rain".

The second term for W (wind) has two possible factors. To account for service level requirements in R9.2(b), users can select load types "Wind: strength" or "Wind: service level" to apply factors 1.0 or 1.6 (respectively) to their load groups.
U = 1.2D + (1.0 or 1.4)E + 1.0L + 0.2S Eq. 9-5. Referencing R9.2-Required Strength (c): Where E is based on service-level forces, 1.4E shall be used in place of 1.0E in Eq. 9-5. 1.2G + γaE + QL + 0.2QS This load combination involves 4 terms. As "snow" is explicitly mentioned in the combination, QS will only generate one equation.

The second term for E (seismic) has two possible factors. To account for service level requirements in R9.2(c), users can select load types "Seis: strength" or "Seis: service level" to apply factors 1.0 or 1.4 (respectively) to their load groups.
U = 0.9D + (1.0 or 1.6)W Eq. 9-6. Referencing R9.2-Required Strength (b): Where W is based on service-level wind loads, 1.6W shall be used in place of 1.0W in Eq. 9-6. 0.9G + γuQW This load combination involves 2 terms. Only 1 equation is generated.

The second term for W (wind) has two possible factors. To account for service level requirements in R9.2(b), users can select load types "Wind: strength" or "Wind: service level" to apply factors 1.0 or 1.6 (respectively) to their load groups.
U = 0.9D + (1.0 or 1.4)E Eq. 9-7. Referencing R9.2-Required Strength (c): Where E is based on service-level forces, 1.4E shall be used in place of 1.0E in Eq. 9-7. 0.9G + γaE This load combination involves 2 terms. Only 1 equation is generated.

The second term for E (seismic) has two possible factors. To account for service level requirements in R9.2(c), users can select load types "Seis: strength" or "Seis: service level" to apply factors 1.0 or 1.4 (respectively) to their load groups.


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NBCC 2010 - Canadian Load Combinations

NBCC 2010 is the Canadian provision for the design and construction new buildings. It provides minimum technical provisions for the design and construction of new buildings. For the purposes of Canadian load combinations, Part 4 of the design code provides specifications for limit states design:

NBCC 2010 Load Combinations

Design Code Equation Design Code Comment SkyCiv Equation SkyCiv Comment
Principal Loads: 1.4D Table 4.1.3.2.A - Case 1 1.4G -
Principal Loads: (1.25D or 0.9D) + 1.5L
Companion Loads: 0.5S or 0.4W
Table 4.1.3.2.A - Case 2 γuG + 1.5QL
γuG + 1.5QL + 0.5QS
γuG + 1.5QL + 0.4QW
Since there is an "or" in the companion load, when considering no companion load as an option, a total of 3 equations are generated. SkyCiv represents this with 3 load combinations. The factor for the dead load may be either 1.25 (unfavorable) or 0.9 (favorable). SkyCiv offers you the option to assign your load groups to the "Dead: unfavorable" or "Dead: favorable" load types which will apply the factors accordingly. Each SkyCiv load combination here will only generate one equation.
Principal Loads: (1.25D or 0.9D) + 1.5S
Companion Loads: 0.5L or 0.4W
Table 4.1.3.2.A - Case 3 γuG + 1.5QS
γuG + 1.5QS + 0.5QL
γuG + 1.5QS + 0.4QW
As above.
Principal Loads: (1.25D or 0.9D) + 1.4W
Companion Loads: 0.5L or 0.5S
Table 4.1.3.2.A - Case 4 γuG + 1.4QW
γuG + 1.4QW + 0.5QL
γuG + 1.4QW + 0.5QS
As above.
Principal Loads: 1.0D + 1.0E
Companion Loads: 0.5L + 0.25S
Table 4.1.3.2.A - Case 5 G + E
G + E + 0.5QL + 0.25QS
This case generates 2 equations when considering the principal loads alone, or the principal loads and companion loads together. SkyCiv represents these by two separate equations.




EN 1990:2002 EC0, EN 1991 EC1 Eurocode Load Combinations

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 Eurocode load combinations of actions for limit states design. The ultimate limit states for loss of equilibrium (EQU), internal failure (STR), ground deformation (GEO) need to be checked together with accidental/seismic (ALS) and servicibility limit states (SLS) when appropriate.

ULS: EQU

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 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.

ULS: STR

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 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.

ULS: GEO

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 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.

ALS: Accidental and Seismic

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 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.

SLS

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 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.


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