Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

80
dESIgN CONCEPTS
Frequency
Load factors γ and resistance factors ϕ are
determined so that the strength distribution R
and the load distribution Q overlap just
slightly. In this illustration, the probability
of failure is P F = 0.001.
Frequency
distribution
of load Q
3
22
58
121
190
222
180
128
55
20
210
440
Frequency
distribution of
resistance R
272
52
20
1
5
Appropriate ϕ and γ
factors produce designs
that have only a very
slight chance of failure.
In this example, only 1
out of 1,000 properly
designed members will
fail due to the variability
inherent in Q and R.
Load effect Q
Resistance R
FIGURE 4.6 Appropriate load and resistance factors produce a satisfactory probability of failure.
Load Combinations
Loads that act on structures are inherently variable. Although the designer may make a
reasonable estimate of the service loads that are expected to act on a structure, it is likely
that the actual loads will differ from the service loads. Further, the range of variation expected
for each type of load is different. For example, live loads could be expected to vary
more widely than dead loads. To account for load variability, LRFD multiplies each type of
load by specific load factors γ i and sums the load components to obtain an ultimate load at
which failure (i.e., rupture or collapse) is considered imminent. The structure or structural
component is then proportioned so that the nominal strength φR n of the component is equal
to or greater than the ultimate load U.
For example, the ultimate load U due to a combination of dead load D and live load L
acting simultaneously on a structural steel component would be computed with the load
factors shown in the following equation
U =∑ γ Q = 1.2D + 1.6L
i ni
(4.5)
The larger load factor γ L = 1.6 associated with the live load L reflects the greater uncertainty
inherent in this type of load compared with the dead load D, which is known with much
greater certainty and, accordingly, has a smaller load factor γ D = 1.2.
Various possible load combinations must be checked, and each combination has a
unique set of load factors. For example, the ultimate load U acting on a structural steel
member through a combination of dead load D, live load L, wind load W, and snow load S
would be calculated as
U =∑ Q = 1.2D + 1.3 W + 0.5L
+ 0.5S
(4.6)
γ i ni
While load factors are generally greater than 1, lesser load factors are appropriate for some
types of loads when combinations of multiple types of load are considered. These lesser
load factors reflect the low probability that extreme events in multiple types of loads will
occur simultaneously. For example, it is not likely that the largest snow load will occur at
the same moment as the extreme wind load and the extreme live load. (It is not even likely
that the extreme wind load and the extreme live load will occur simultaneously.)