Civil Engineering Reference
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Figure 8.4 also shows the clustering hierarchy. There are six possible rings
formed by members [1,2,5], [3,4,5], [5,6,8'], [5,7,9], [6,7,10], and [8,9,10]. The
best ring (in terms of well-formedness defi ned earlier) amongst these six
rings should form a seed cluster. There are three pairs of rings which have
identical attributes. Rings formed by members [6,7,10] or [8,9,10] have the
highest well-formedness. Hence clustering can start with these and one of
them is chosen at random to form cluster C1. This cluster grows to form a
higher level cluster C2 by including neighbouring node 4 and members 5
and 9. Next member 8 is added in to form a new cluster C3 with an increase
the well-formedness. Then clusters C4 and C5 are formed by including the
neighbouring nodes and members. The choice to include node 1 fi rst is
arbitrary, because the members connecting to both nodes 1 and 2 are identi-
cal and produce the same attributes when added in to cluster C4. Lastly,
the ground is added in to form cluster C6 which is the whole structure.
The clustering hierarchy is used to fi nd failure scenarios. Members 2 and
3 have the minimum damage demand because they are the longest (cross-
sectional areas being the same). The minimum failure scenario is to damage
member 3 or 4 because they join the growing cluster last. The maximum
failure scenario is to pin members 2 and 3 because they produce the
maximum consequence with minimum damage demand. The total failure
scenario is identical to the maximum failure scenario in this example. Other
total failure scenarios are to pin members 3 and 4, or members 1 and 2, but
they have less vulnerability index. These are rather obvious results but the
example helps to illustrate the analysis procedure.
8.4
Analysis of risk
In vulnerability theory, actions causing damage are not specifi ed and damage
may result from one or more possible actions. These may include degrada-
tion of material (e.g. corrosion of steel), extreme natural hazards, vehicle
impact, intentional damage (e.g. terrorist bombing), fi re, and many more.
Some actions have the potential to cause damage to many structural
members simultaneously. It is possible, at least qualitatively, to assess the
likelihood of certain actions.
Each failure scenario with the potential to cause large consequences, as
obtained from vulnerability analysis, is considered in turn and an assess-
ment is made about the likelihood. This requires the consideration of all
possible actions that may lead to this particular failure scenario. Hence
there is a need to gather evidence for each deterioration event in this failure
scenario due to each action as illustrated in Fig. 8.5. For ease of explanation,
let us focus on the fi rst deterioration event. It may be caused due to any
action such as higher live load, strong earthquake load, corrosion, sabotage,
etc. Thus evidence needs to be collected about the dependability of each
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