The nature of wind storms and windinduced damage - Wind Loading of Structures - page 26

1.6.2 Vulnerability curves
Insurance loss predictions are quite sensitive to the assumed variations of relative
building and contents damage as a function of the local wind speed. Such graphs are
known as 'vulnerability curves'. Vulnerability curves can be derived in a number of
ways. Leicester (1981) proposed the simplified form, with straight-line segments, for
Australian houses, shown in Figure 1.15. The ordinate is a 'damage index' defined as
follows for the building:
Damage index (D) =(repair cost)/(initial cost of building)
For insurance purposes it may be more appropriate to replace the denominator with the
insured value of the building. A similar definition can be applied to the building contents,
with 'replacement cost' in the numerator.
Separate lines are given for building and contents. Two parameters only need be
specified—a threshold gust speed for the onset of minor damage and a speed for the onset
of major building damage (damage index>0.2).
Walker (1995) proposed the following relationships for housing in Queensland,
Australia.
For pre-1980 buildings:
(1.21)
For post-1980 buildings:
(1.22)
Clearly in both cases D is limited to the range 0-1.0.
The relationship of Equation (1.21) was also found to agree well with the recorded
damage and wind speed estimates of Hurricane 'Andrew' (see Table 1.1).
A simple form of a vulnerability curve for a fully engineered structure consisting of a
large number of members or components with strengths of known probability distribution
can be derived. The failure of each component is assumed to be independent of all the
others, and they are all designed to resist the same wind load, or speed. Thus, the
expected fractional damage to the complete structure, for a given wind speed, is the
proportion of failed components expected at that wind speed. If all the components have
the same probability distribution of strength, which would be true if they were all
designed to the same codes, then the vulnerability curve can simply be derived from the
cumulative distribution of strength of any element.
A curve derived in this way (Holmes, 1996) is shown in Figure 1.16, for a structure
comprising components with a lognormal distribution of strength, with a mean/nominal
strength of 1.20 and a coefficient of variation of 0.13, values which are appropriate for
steel components. The nominal design gust wind speed is taken as 65 m/s. This curve can