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

4.5 Load and Resistance Factor Design
LOAd ANd RESISTANCE
FACTOR dESIgN
A second common design philosophy is termed load and resistance factor design
(LRFD). This approach is most widely used in the design of reinforced concrete, steel,
and wood structures.
To illustrate the differences between the ASD and LRFD philosophies, consider the
following example: Suppose that an engineer using ASD calculates that a certain member
of a steel bridge truss will be subjected to a load of 100 kN. Using an appropriate factor of
safety for this type of member—say, 1.6—the engineer properly designs the truss member
so that it can support a load of 160 kN. Since the member strength is greater than the load
acting on it, the truss member performs its intended function. However, we know that the
load on the truss member will change throughout the lifetime of the structure. There will be
many times when no vehicles are crossing the bridge, and consequently, the member load
will be much less than 100 kN. There may also be instances in which the bridge is completely
filled with vehicles and the member load will be greater than 100 kN. The engineer
has properly designed the truss member to support a load of 160 kN, but suppose that the
steel material was not quite as strong as expected or that stresses were created in the member
during the construction process. Then the actual strength of the member could be, say,
150 kN, rather than the expected strength of 160 kN. If the actual load on our hypothetical
truss member exceeds 150 kN, the member will fail. Thus, the question is, “How likely is
it that this situation will occur?” The ASD approach cannot answer that question in any
quantitative manner.
Design provisions in LRFD are based on probability concepts. Strength design procedures
in LRFD recognize that the actual loads acting on structures and the true strength of
structural components (termed resistance in LRFD) are in fact random variables that cannot
be known with complete certainty. With the use of statistics to characterize both the load and
resistance variables, design procedures are developed so that properly designed components
have an acceptably small, but quantifiable, probability of failure, and this probability of
failure is consistent among structural elements (e.g., beams, columns, connections, etc.) of
different materials (e.g., steel vs. wood vs. concrete) used for similar purposes.
probability Concepts
To illustrate the concepts inherent in LRFD (without delving too deeply into probability
theory), consider the aforementioned truss member example. Suppose that 1,000 truss
bridges were investigated and that, in each of those bridges, a typical tension member was
singled out. For that tension member, two load magnitudes were recorded. First, the service
load effect used in the design calculations (i.e., the design tension force in this case) for a
truss member was noted. For purposes of illustration, this service load effect will be denoted
Q*. Second, the maximum tension load effect that acted on the truss member at any
time throughout the entire lifetime of the structure was identified. For each case, the maximum
tension load effect is compared with the service load effect Q* and the results are
displayed on a histogram showing the frequency of occurrence of differing load levels
(Figure 4.2). For example, in 128 out of 1,000 cases, the maximum tension load in the truss
member was 20 percent larger than the tension used in the design calculations.
For the same tension members, suppose that two strength magnitudes were recorded.
First, the calculated strength of the member was noted. For purposes of illustration, this
design strength will be denoted as resistance R*. Second, the maximum tension strength
actually available in the member was determined. This value represents the tension load
that would cause the member to fail if it were tested to destruction. The maximum tension
strength can be compared with the design resistance R*, and the results can be displayed on
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