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Load Combinations: ACI 318-11

In the United States, ACI 318-11 covers the materials, design, and construction of structural concrete used in buildings and applicable nonbuilding structures. It also covers the evaluation of strength for concrete structures that already exist.

Chapter 9 of the code details the strength and serviceability requirements of structural members. 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.

Required strength (U) shall be at least equal to the effects of factored loads in equations 9-1 through 9-7.

This article will focus on how SkyCiv’s auto generated load combinations feature meets the load combination equations as specified in ACI 318-11.

9.2.1 Required Strength

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 + ψ₁Q_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_uQ_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_aE + 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_uQ_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_aE	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.

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 + ψ₁Q_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_uQ_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_aE + 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_uQ_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_aE

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.

Load Combinations: ACI 318-11

9.2.1 Required Strength

Example: All Load Types Assigned