Civil Engineering Reference
In-Depth Information
concerned with
h
alone and reliability analysis examines
h
and
p
together
(e.g. the probability of moment due to an earthquake exceeding the capac-
ity of the beam). Vulnerability analysis identifi es
h
with maximum
c
so that
action can be taken to reduce
c -
this is particularly important for critical
systems. One needs to be careful about the terminology. In disaster reduc-
tion literature (see e.g. UN ISDR 2004), risk is calculated as the product of
hazard and vulnerability. A useful summary of different specialist uses of
risk, hazard and vulnerability (particularly focusing on climate change
research) was given in a report by the Tyndall Centre for Climate Change
Research (2003). The core idea of risk remains as the chance of some future
hazard and the consequences that will be caused if it comes about. When
we think of risk, we are thinking of a potentially dangerous situation which
might or might not exist in the future with consequences we want to avoid.
It is also important to realize that risk has to be understood in context. In
the context of earthquake engineering, hazard is the earthquake and vul-
nerability depends on the design, construction and maintenance of a facility.
The risk is the anticipated loss when the hazard impacts on the facility.
8.3
Identifi cation of vulnerability
A structure is robust if it can withstand arbitrary damage, whereas it is
vulnerable if small damage produces disproportionately large consequences.
The latter concept has been developed into structural vulnerability analysis
(Wu
et al.
1993; Lu
et al.
1999; Agarwal
et al.
2001a, 2003). It is a theory of
form and connectivity, and aims at identifying weak links in a structure. In
brief, it requires the following three processes:
• building a model of the form of a structure using the concept of rings
and rounds;
• representing the structure in a hierarchical form through successive
clustering; and
•
identifying various failure scenarios by a search through the hierarchical
model.
8.3.1 Rings and rounds
The function of a structure is to transmit force from one point to another
in space without losing its integrity. A consideration of form is essential to
that integrity. A structural ring or a structural round is a minimum structural
path which can withstand a set of forces in 2D and 3D, respectively. For a
pin-jointed structure, three members connected together form a just-stiff
ring (Fig. 8.1a). Introduction of a pin (or a cut) into a just-stiff ring turns it
into a mechanism (Fig. 8.1b). If a pin joint is replaced by a rigid joint an
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