Environmental Engineering Reference
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of a structure or a large portion of it. The probability of structural col-
lapse is a surrogate for all other metrics, and limiting that probability
addresses the fundamental goal. Most first-generation probability-based
structural design codes focus on that performance objective. Other per-
formance metrics—direct economic losses from structural damage,
indirect losses due to interruption of function, forgone opportunities,
and loss of amenity—have not been addressed in current construction
regulations but may be of concern to certain stakeholder groups in cer-
tain types of infrastructure facilities.
The use of classical structural reliability principles and code calibra-
tion has historically formed the basis for the development of load com-
binations in American Society of Civil Engineers (ASCE) Standard 7-10,
Minimum Design Loads for Buildings and Other Structures (ASCE 2010);
Eurocode 1, Actions on Structures (CEN 1994); and structural strength
criteria found in most standards and specifications (e.g., AASHTO 2007;
ACI 2005; AISC 2010). Such codified procedures gloss over the issue of
consequence and context by presuming that “risk” and “probability of
collapse” are identical. However, these procedures avoid the difficulty
of selecting appropriate risk (loss) metrics and transform the analysis of
risk into a problem amenable to solution by principles of structural reli-
ability theory (Ellingwood 1994; Melchers 1999), which is an essential
step in first-generation probability-based structural design.
In modern probability-based limit states design codes, the require-
ment that the reliability equal or exceed a target reliability is transformed
into a traditional safety-checking equation:
(
) <
(
)
Required￿ strength￿
Q
design￿ strength￿
R
(()
A-1
d
d
The required strength to resist loads, shown on the left-hand side of the
equation, is determined from structural analysis by using factored loads,
while the design strength (or factored resistance) on the right-hand side
is determined by using nominal material strengths and dimensions and
partial resistance factors. The load and resistance factors are functions of
the uncertainties associated with the load and resistance variables and the
target reliability index. The target reliability index, in turn, may depend
on the failure mode (e.g., brittle or ductile) and the consequences of
a member failure (e.g., local damage, possibility of global instability).
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