Load factors are numbers, almost always larger than 1.0, that are used to increase the estimated loads applied to structures. They are used for loads applied to all types of members, not just beams and slabs. The loads are increased to attempt to account for the uncertainties involved in estimating their magnitudes. How close can you estimate the largest wind or seismic loads that will ever be applied to the building that you are now occupying? How much uncertainty is present in your answer?
You should note that the load factors for dead loads are much smaller than the ones used for live and environmental loads. Obviously, the reason is that we can estimate the magnitudes of dead loads much more accurately than we can the magnitudes of those other loads. In this regard, you will notice that the magnitudes of loads that remain in place for long periods of time are much less variable than are those loads applied for brief periods, such as wind and snow.
Section 9.2 of the code presents the load factors and combinations that are to be used for reinforced concrete design. The required strength, U, or the load-carrying ability of a particular reinforced concrete member, must at least equal the largest value obtained by substituting into ACI Equations 9-1 to 9-7. The following equations conform to the requirements of the International Building Code (IBC)1 as well as to the values required by ASCE/SEI 7-10.2
U = 1.4D (ACI Equation 9-1)
U = 1.2D + 1.6L + 0.5(Lr or S or R) (ACI Equation 9-2) U = 1.2D + 1.6(Lr or S or R) + (L or 0.5W ) (ACI Equation 9-3) U = 1.2D + 1.0W + L + 0.5(Lr or S or R) (ACI Equation 9-4)
U = 1.2D + 1.0E + L + 0.2S (ACI Equation 9-5)
U = 0.9D + 1.0W (ACI Equation 9-6)
U = 0.9D + 1.0E (ACI Equation 9-7)
In the preceding expressions, the following values are used:
U = the design or ultimate load the structure needs to be able to resist D = dead load
L = live load
1International Code Council, 2012, International Building Code, Falls Church, Virginia 22041-3401.
2American Society of Civil Engineers, Minimum Design Loads for Buildings and Other Structures, ASCE 7-10 (Reston, VA:
American Society of Civil Engineers), p. 7.
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4.1 Load Factors 83
Lr= roof live load S = snow load R = rain load W = wind load
E = seismic or earthquake load effects
When impact effects need to be considered, they should be included with the live loads as per ACI Section 9.2.2. Such situations occur when those loads are quickly applied, as they are for parking garages, elevators, loading docks, cranes, and others.
The load combinations presented in ACI Equations 9-6 and 9-7 contain a 0.9D value.
This 0.9 factor accounts for cases where larger dead loads tend to reduce the effects of other loads. One obvious example of such a situation may occur in tall buildings that are subject to lateral wind and seismic forces where overturning may be a possibility. As a result, the dead loads are reduced by 10% to take into account situations where they may have been overestimated.
The reader must realize that the sizes of the load factors do not vary in relation to the seriousness of failure. You may think that larger load factors should be used for hospitals or high-rise buildings than for cattle barns, but such is not the case. The load factors were developed on the assumption that designers would consider the seriousness of possible failure in specifying the magnitude of their service loads. Furthermore, the ACI load factors are minimum values, and designers are perfectly free to use larger factors as they desire. The magnitude of wind loads and seismic loads, however, reflects the importance of the structure. For example, in ASCE-7,3 a hospital must be designed for an earthquake load 50% larger than a comparable building with less serious consequences of failure.
For some special situations, ACI Section 9.2 permits reductions in the specified load factors. These situations are as follows:
(a) In ACI Equations 9-3 to 9-5, the factor used for live loads may be reduced to 0.5 except for garages, areas used for public assembly, and all areas where the live loads exceed 100 psf.
(b) If the load W is based on service-level wind loads, replace 1.0W in ACI Equations 9-4 and 9-6 with 1.6W. Also, replace 0.5W with 0.8W in ACI Equation 9-3.
(c) Frequently, building codes and design load references convert seismic loads to strength-level values (i.e., in effect they have already been multiplied by a load factor). This is the situation assumed in ACI Equations 9-5 and 9-7. If, however, service-load seismic forces are specified, it will be necessary to replace 1.0E with 1.4E in these two equations.
(d) Self-restraining effects, T, in reinforced concrete structures include the effects of tem-perature, creep, shrinkage, and differential settlement. In some cases, the effects can be additive. For example, creep, shrinkage, and reduction in temperature all cause a reduc-tion of concrete volume. Often such effects can be reduced or eliminated by proper use of control joints.
(e) Fluid loads, F, resulting from the weight and pressure of fluids shall be included with the same load factor as D in ACI Equations 9-5 through 9-7.
3American Society of Civil Engineers, Minimum Design Loads for Buildings and Other Structures. ASCE 7-10 (Reston, VA:
American Society of Civil Engineers), p. 5.
(f) Where soil loads, H, are present, they must be added to the load combinations in accor-dance with one of the following:
• where H acts alone or adds to the effects of other loads, it shall be included with a load factor of 1.6;
• where the effect of H is permanent and counteracts the effects of other loads, it shall be included with a load factor of 0.9;
• where the effect of H is not permanent but, when present, counteracts the effects of other loads, H shall not be included.
Example 4.1 presents the calculation of factored loads for a reinforced concrete column using the ACI load combinations. The largest value obtained is referred to as the critical or governing load combination and is the value to be used in design. Notice that the values of the wind and seismic loads can be different depending on the direction of those forces, and it may be possible for the sign of those loads to be different (i.e., compression or tension). This is the situation assumed to exist in the column of this example. These rather tedious calculations can be easily handled with the Excel spreadsheet entitled Load Combinations on this book’s website: www.wiley.com/college/mccormac.
Example 4.1
The compression gravity axial loads for a building column have been estimated with the following results: D= 150 k; live load from roof, Lr = 60 k; and live loads from floors, L = 300 k.
Compression wind, W= 112 k; tensile wind, W = 96 k; seismic compression load = 50 k; and tensile seismic load= 40 k. Determine the critical design load using the ACI load combinations.
S O L U T I O N
(9-1) U= 1.4D = (1.4) (150 k) = 210 k
(9-2) U= 1.2D + 1.6L + 0.5(Lror S or R)= (1.2) (150 k) + (1.6) (300 k) + (0.5) (60 k) = 690 k (9-3)(a) U= 1.2D + 1.6(Lror S or R)+ (L or 0.5W) = (1.2) (150 k) + (1.6) (60 k) + (300 k) = 576 k
(b) U= 1.2D + 1.6(Lror S or R)+ (L or 0.5W) = (1.2) (150 k) + (1.6) (60 k) + (0.5) (70 k) = 311 k (c) U= 1.2D + 1.6(Lror S or R)+ (L or 0.5W) = (1.2) (150 k) + (1.6) (60 k) + (0.5) (−60 k) = 246 k (9-4)(a) U= 1.2D + 1.0W + L + 0.5(Lror S or R)= (1.2) (150 k) + (1.0) (70 k) + (300 k) + 0.5(60 k) = 580 k
(b) U= 1.2D + 1.0W + L + 0.5(Lror S or R)= (1.2) (150 k) + (1.0) (−60 k) + (300 k) + 0.5(60 k) = 450 k (9-5)(a) U= 1.2D + 1.0E + L + 0.2S = (1.2) (150 k) + (1.0) (50 k) + (300 k) + (0.2) (0 k) = 530 k
(b) U= 1.2D + 1.0E + L + 0.2S = (1.2) (150 k) + (1.0) (−40 k) + (300 k) + (0.2) (0 k) = 440 k (9-6)(a) U= 0.9D + 1.0W = (0.9) (150 k) + (1.0) (70 k) = 205 k
(b) U= 0.9D + 1.0W = (0.9) (150 k) + (1.0) (−60 k) = 75 k (9-7)(a) U= 0.9D + 1.0E = (0.9) (150) + (1.0) (50 k) = 185 k
(b) U= 0.9D + 1.0E = (0.9) (150) + (1.0) (−40 k) = 95 k Answer: Largest value= 690 k from load case 9.2.
For most of the example problems presented in this textbook, in the interest of reducing the number of computations, only dead and live loads are specified. As a result, the only load factor combination usually applied herein is the one presented by ACI Equation 9-2.
Occasionally, when the dead load is quite large compared to the live load, it is also necessary to consider Equation 9-1.
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