# Load Combinations of Concrete Design

**Courses > Reinforced Concrete Design > General Topics of Concrete Material and Design > Load Combinations of Concrete Design**

### Introduction

A load combination results when more than one load type acts on the structure. Building codes usually specify a variety of load combinations together with load factors (weightings) for each load type in order to ensure the safety of the structure under different maximum expected loading scenarios. For example, in designing a staircase, a dead load factor may be 1.2 times the weight of the structure, and a live load factor may be 1.6 times the maximum expected live load. These two "factored loads" are combined (added) to determine the "required strength" of the staircase.

### Concepts and Formulas

#### ASCE 7 Load combinations:

L**oad combinations from ASCE 7-10:**

__Load combination or strength design__ (ASCE 7-10, sec, 2.3.2)

1. 1.4D

2. 1.2D+1.6L+0.5(Lr or S or R)

3. 1.2D+1.6(L_{r} or S or R)+(L or 0.5W)

4. 1.2D+1.0W+L+0.5(L_{r} or S or R)

5. 1.2D+1.0E+L+0.2S

6. 0.9D+1.0W

7. 0.9D+1.0E

__Load combination for allowable stress design__ (ASCE 7-10, Sec. 2.4)

1. D

2. D+L

3. D+(Lr or S or R)

4. D+0.75L+0.75(Lror S or R)

5. D+ (0.6W or 0.7E)

6a. D+0.75L+0.75(0.6W)+0.75(Lr or S or R)

6b. D+0.75L+0.75(0.6E)+0.75S

7. 0.6D+0.6W

5. 0.6D+0.7E

Where D is dead load; L is live load; Lr is roof live load; W is strength design wind load; E is strength design seismic load; R is rain load; and S is snow load.

L**oad combinations from ASCE 7-05**

__Load combination or strength design__ (ASCE 7-05, sec, 2.3.2)

1. 1.4(D+H)

2. 1.2(D+F+T)+1.6(L+H)+0.5(Lr or S or R)

3. 1.2D+1.6(L_{r} or S or R)+(0.5L or 0.8W)

4. 1.2D+1.6W+0.5L+0.5(L_{r} or S or R)

5. 1.2D+1.0E+0.5L+0.5(L_{r} or S or R)

6. 0.9D+1.6W+1.6H

7. 0.9D+1.0E+1.6H

__Load combination for allowable stress design__ (ASCE 7-05, Sec. 2.4.1)

1. D

2. D+L+F+H+T+(Lr or S or R)

3. D+(W or 0.7E)+L+(Lr or S or R)

4. 0.6D+W+H

5. 0.6D+0.7E+H

Where W is serviced design wind load, E is strength desogm earthquake load, F is fluid pressure, R is rain load, S is snow load, T is temperature force.

#### ACI 318 load combinations:

L**oad combinations from ACI 318-05, ACI 318-08**

__Load combination or strength design__ (Sec 9-2)

1. 1.4(D+F) (9-1)

2. 1.2(D+F+T)+1.6(L+H)+0.5(L_{r }or S or R) (9-2)

3. 1.2D+1.6(L_{r} or S or R)+(1.0L^{*} or 0.8W) (9-3)

4. 1.2D+1.6W^{**}+1.0L^{*}+0.5(L_{r} or S or R) (9-4)

5. 1.2D+1.0E^{***}+1.0L^{*}+0.2S (9-5)

6. 0.9D+1.6W^{**}+1.6H (9-6)

7. 0.9D+1.0E^{***}+1.6H (9-7)

*1.0L can be reduced to 0.5L except for garages, public assembly, and area that has 100 lb/ft^{2} of live load.

**1.6W can be reduced to 1.3W when wind load W is not reduced by directional factor (See ASCE 7-02 wind calculation)

*** Where seismic load, E is calculated based on service load, 1.4E shall be used instead of 1.0E.

**Strength reduction factor, f, ACI 318-05, ACI 318-08**

1. Tension-controlled sections, 0.9 (Sec. 9.3.2.1)

2. Compression-controlled sections (Sec. 9.3.2.2)

- Column with spiral reinforcement, 0.7
- Tie columns, 0.65.

3. f is permitted to vary from 0.65 to 0.9 when the net tensile strain in extreme tension steel at nominal strength varies from compressive control strain to 0.005.

4. Shear and torsion, 0.75 (Sec. 9.3.2.3)

5. Bearing on concrete, 0.65 (Sec. 9.3.2.4)

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