Page 99 - Forensic Structural Engineering Handbook

DESIGN CODES AND STANDARDS 2.5

P
F

0 [In(R/Q)] In(R/Q)
βσ m
In(R/Q)

FIGURE 2.2 Definition of reliability index (from AISC).

ASD versus LRFD and USD
The allowable stress design (ASD) method can be represented by the inequality

∑ Q ≤ R n
i
FS
where ΣQ = the required strength, which is the summation of the load effects Q (i.e., forces
i i
or moments), and R /FS = the design strength, which is the nominal strength or resistance
n
R , divided by a factor of safety. When divided by the appropriate section property (i.e.,
n
area or section modulus), the two sides of the inequality become the actual stress and allow-
able stress, respectively.
The greatest attribute of allowable stress design has been its simplicity, since the vari-
able risks and the probability of failure need not be considered in the design process. In
most design situations, this method can be used to produce reasonably safe and usable
structures. However, the allowable stress design method assumes that the ultimate limit
states will automatically be satisfied by the use of allowable stresses. Depending on the
variability of the materials and loads, this assumption may not always be valid.
Commonly cited shortcomings of allowable stress design include the inability to prop-
erly account for the variability of the resistances and loads, lack of knowledge of the level
of safety, and the inability to deal with groups of loads where one load increases at a dif-
ferent rate than the others. The latter condition is especially serious when a relatively con-
stant load such as dead load counteracts the effects of a highly variable load such as wind.
The load and resistance factor design (LRFD) and ultimate strength design (USD)
methods may be summarized by
Σg Q ≤ jR n
i
i
where Σg Q = the required strength corresponding to the summation of the various load effects
i i
Q , multiplied by their respective load factors g , and fR = the design strength corresponding
i i n