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:
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(L_{r} or S or R) | Eq. 2.3.2.2 | 1.2G + 1.6Q_{L} + 0.5Q_{S} | 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(L_{r} or S or R) + (L or 0.5W) | Eq. 2.3.2.3 | 1.2G + 1.6Q_{S} + Q_{L} 1.2G + 1.6Q_{S} + 0.5Q_{W} |
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(L_{r} or S or R) | Eq. 2.3.2.4 | 1.2G + Q_{W} + Q_{L} + 0.5Q_{S} | 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 + Q_{L} + 0.2Q_{S} + E | - |
0.9D + 1.0W | Eq. 2.3.2.6 | 0.9G + Q_{W} | - |
0.9D + 1.0E | Eq. 2.3.2.7 | 0.9G + E | - |
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 + Q_{L} | - |
D + (L_{r} or S or R) | Eq. 2.4.1.3 | G + Q_{S} | The load type Q_{S} "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(L_{r} or S or R) | Eq. 2.4.1.4 | G + 0.75Q_{L} + 0.75Q_{S} | The load type Q_{S} "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 + 0.6Q_{W} 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 Q_{S} snow load type. |
D + 0.75L + 0.75(0.6W) + 0.75(L_{r} or S or R) | Eq. 2.4.1.6a | G + 0.75Q_{L} + 0.45Q_{W} + 0.75Q_{S} | The load type Q_{S} "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 + 0.75Q_{L} + 0.75Q_{S} + 0.525E | Only one load equation is required to represent this load combination. Despite the presence of Q_{S} "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 + 0.6Q_{W} | - |
0.6D + 0.7E | Eq. 2.4.1.8 | 0.6G + 0.7E | - |
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:
Design Code Equation | Design Code Comment | SkyCiv Equation | SkyCiv Comment |
---|---|---|---|
E_{d,stb} = [0.9G] | Net Destabilizing: Permanent action only (does not apply to prestressing forces) | 1.35G | SPC: Permanent Destabilizing |
E_{d,stb} = [1.35G] | Net Stabilizing: Permanent action only (does not apply to prestressing forces) | 0.9G | SPC: Permanent Stabilizing |
E_{d,stb} = [1.2G,1.5Q] | Permanent and imposed action | 1.2G + 1.5Q_{L} | ULS: Permanent & Imposed. |
E_{d,stb} = [1.2G, Wu, ψ_{c,Q}] | Permanent, wind and imposed action | 1.2G + ψ_{2,1}Q_{L} + Q_{W} | ULS: Permanent, Wind & Imposed. The imposed action factor represented by the psi is determined by the type of Q_{L} that this equation acts against. |
E_{d,stb} = [1.2G, Su,ψ_{c,Q}] | Permanent action, actions given in Clause 4.2.3 and imposed action. | 1.2G + ψ_{0,3}Q_{L} + Q_{S} | ULS: Permanent, Other, & Imposed. The imposed action factor represented by the psi is determined by the type of Q_{L} that this equation acts against. |
Design Code Equation | Design Code Comment | SkyCiv Equation | SkyCiv Comment |
---|---|---|---|
E_{d} = [1.35G] | Permanent action only (does not apply to prestressing forces) | 1.35G | Identical to E_{d,dst}. |
E_{d} = [1.2G,1.5Q] | Permanent and imposed action | 1.2G + 1.5Q_{L} | Identical to E_{d,dst}. |
E_{d} = [1.2G,1.5ψ_{l}Q] | Permanent and long term imposed action | 1.2G + 1.5ψ_{1}Q_{L} | ULS: Permanent & Long-term Imposed. The imposed action factor represented by the psi is determined by the type of Q_{L} that this equation acts against. |
E_{d} = [0.9G, W_{u}] | Permanent and wind action reversal | 0.9G + Q_{w} | ULS: Permanent, Wind |
E_{d} = [G, E_{u}, ψ_{c,Q}] | Permanent, earthquake and imposed action | G + ψ_{2,n}Q_{L} + E | SPC: Permanent, Earthquake & Imposed |
E_{d} = [1.2G, Su,ψ_{c,Q}] | Permanent action, actions given in Clause 4.2.3 and imposed action. | 1.2G + ψ_{0,3}Q_{L} + Q_{S} | Identical to Ed,dst. |
SkyCiv Equation | SkyCiv Comment |
---|---|
G + ψ_{0,1}Q_{L} | SLS Permanent and Short-term Imposed |
G + ψ_{1}Q_{L} | SLS Permanent and Long-term Imposed |
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:
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(L_{r} or S or R) | Eq. 9-2 | 1.2G + 1.6Q_{L} + 0.5Q_{S} | The load type Q_{S} "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(L_{r} 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 + 1.6Q_{S} + ψ_{1}Q_{W}
1.2G + 1.6Q_{S} + Q_{L} |
This load combination involves 3 terms. As in the combination for Eq. 9-2, Q_{S} 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(L_{r} 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 + γ_{u}Q_{W} + Q_{L} + 0.5Q_{S} |
This load combination involves 4 terms. As in the combination for Eq. 9-2, Q_{S} 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 + γ_{a}E + Q_{L} + 0.2Q_{S} |
This load combination involves 4 terms. As "snow" is explicitly mentioned in the combination, Q_{S} 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 + γ_{u}Q_{W} |
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 + γ_{a}E |
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. |
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:
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 |
γ_{u}G + 1.5Q_{L} γ_{u}G + 1.5Q_{L} + 0.5Q_{S} γ_{u}G + 1.5Q_{L} + 0.4Q_{W} |
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 |
γ_{u}G + 1.5Q_{S} γ_{u}G + 1.5Q_{S} + 0.5Q_{L} γ_{u}G + 1.5Q_{S} + 0.4Q_{W} |
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 |
γ_{u}G + 1.4Q_{W} γ_{u}G + 1.4Q_{W} + 0.5Q_{L} γ_{u}G + 1.4Q_{W} + 0.5Q_{S} |
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 + 0.5Q_{L} + 0.25Q_{S} |
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.
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 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. |
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 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. |
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 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}. |
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 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. |
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 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. |