Load Factors in the Strength Design of Concrete

Background

We talked earlier about Load Combinations (here). Our discussion focused on how we combine Dead, Live, and Snow loads in the determination of an appropriate width of footing for our `Concrete House'. In designing the footing we need (needed) to look at the conditions of Dead load only (generally won't control), Dead plus Snow, Dead plus Live, and Dead plus some percentage of the Snow and Live acting simultaneously. In other words, the design Snow load is probably some `fifty-year event', and the design Live load is probably some rare, but not outlandishly rare, event, but both events occurring simultaneously might indeed be outlandishly rare. Or, while both occurring simultaneously wouldn't be impossible, it might not be reasonable, or economical, to design for such. Not that we couldn't, and in fact the `Code' does not disallow us from doing so ... but neither does it make us design for what might occur way too rarely.

Strength Design

... That was Allowable Stress Design (ASD). And, in ASD the factors of safety in design are in the allowable stresses (not the loads); and so we didn't even deal with factors of safety in our conversation about Load Combinations. But in the Strength Design (SD) approach (or Load and Resistance Factor Design, LRFD, for steel and wood), the loads also have factors of safety `attached' to them. Thus, things get more complicated, but also more interesting.

The factors of safety attached to the loads, or Load Factors, account for legitimate uncertainty in the design loads. Some kinds of loads have more `uncertainty' than others. For example, the International Building Code (IBC, what I refer to as the `Code' above) assigns, for example, 1.4 to Dead loads, and 1.6 to, for example, Snow loads (factored up 40 and 60 percent, respectively). Dead loads are the weights of building/construction materials; Snow load is the weight of some `big future amount of snow'. In our construction documents, we can be (and often are) quite specific about building materials, but the design snow load is just our best prediction. We can go down to the local building supply store and actually handle (and weigh) construction materials, but that 50-year snow storm hasn't happened yet, and may not, for many years. We generally base our prediction of future events, on the past ... how certain is that? ... (and especially in this `environment' of `climate change'). Or, the brick, or wood, or steel, or (whatever) ... that we specify tomorrow, gets delivered to the project next month, and installed shortly after that, will probably maintain pretty much the same weight through the service life of the building. But the occupants (people) are going to come and go, and who knows what the average person will weigh 50 years from now.

So, in the Strength Design Approach we see (and deal with) the uncertainty assigned to each load. And we will also see, as with ASD, that while the factored load represents some upper limit value, these upper limit values are not all considered to be occurring simultaneously. Such case(s) might not be impossible, but are acknowledged (or anticipated) to be so rare, ... that it would not be reasonable, necessary, or economical (or both), to design for such.

Strength Design Load Factors

Here are some of them ...

(2003 IBC, Chapter 16 ... gravity loads ... adapted to Residential Construction / Residential Occupancy Live load ... and around here where the governing `roof' condition is snow)

... 1.4 D

... 1.2 D + 1.6 L + 0.5 S

... 1.2 D + 1.6 S + 0.5 L ...

(of which we choose the greater effect ... or so-called `worst case')

where,

D = for Dead load,

L = Occupancy Live load, and

S = Snow load.

So, while it is recognized that the reasonable upper limit for Dead is 1.4 D, and the reasonable upper limit for Occupancy Live is 1.6 L, and for Snow is 1.6 S, it is also recognized that only a portion of each `upper limit' is expected to occur simultaneously with another `upper limit'.

Example

So, let's take the previous example (in the discussion of Load Combinations, here), and calculate the factored line load on the supporting soil.

From before,

D = 2649 plf ... (28 x 11 footing)

L = 320 plf

S = 760 plf

FACTORED ...

1.4 D = 1.4 (2649 plf) = 3709 plf

1.2 D + 1.6 L + 0.5 S = 1.2 (2649) + 1.6 (320) + 0.5 (760) = 3179 + 512 + 380 = 4071 plf

1.2 D + 0.5 L + 1.6 S = 1.2 (2649) + 0.5 (320) + 1.6 (760) = 3179 + 160 + 1216 = 4555 plf

The `controlling' value from the above is ... 4555 plf.

The controlling design condition is ... Dead load increased 20%, Snow load increased 60%, simultaneous with 50% of the Occupancy Live load.

Conclusion

So, now we see how loads `combine' when using the Strength Design approach (or LRFD in steel, and coming on in wood). By `loads' we mean the design loads, also known as Service loads, and when we combine them we attach factors to them, which reflect the uncertainty in the load, and, more particularly, the amount (or fraction) of the uncertainty when the loads act simultaneously with one another.

References

Load Combinations in Allowable Stress Design, Jeff Filler, Associated Content.

International Building Code, International Code Council, 4051 West Flossmoor Road, Country Club Hills, IL 60478.