Civil Engineering Reference
In-Depth Information
26.4
Example of fragility estimates for an offshore
wind turbine support structure
We now use the developed demand models to investigate the fragility of
an example offshore wind turbine support structure. For this purpose we
consider the confi guration of a typical 5 MW offshore wind turbine sup-
ported by a mono-pile installed in a 20 m water depth. The structure of
interest is the NREL offshore 5-MW baseline wind turbine and its specifi ca-
tions is documented by Jonkman
et al.
(2009). Important properties of
considered wind turbine are presented in Table 26.7.
Fragility is defi ned as the conditional probability of failure for a given
value of the vector
w
, which includes the mean wind speed, signifi cant wave
height, and spectral acceleration. Following Gardoni
et al.
(2002), a predic-
tive estimate of the fragility can be formulated as:
⎡
⎢
⎤
⎥
∪
()
=
{
(
)
≤
}
F
w
P
g
sk
x w
,,
Q
0
w
[26.12]
k
k
where
g
sk
(
x
,
w
,
Θ
k
) is the
k
th limit state function defi ned as
(
)
=
()
−
(
)
g
xw
,,
Q
C
w
D
xw
,,
Q
[26.13]
sk
k
sk
k
k
in which
C
sk
(
x
) represent the capacity corresponding to
D
k
(
x
,
w
,
Θ
k
) and
s
=
y
or
u
stand for yield and ultimate limit states, respectively.
In this study, we consider two modes of failure: shear and bending. Table
26.8 illustrates the proposed damage states and the corresponding limit
states for a wind turbine subject to day-to-day wind, wave and current loads
and seismic loading. Shear capacity is defi ned as
V
s
=
f
s
A
(3/4)(
R
2
+
r
2
)/(
R
2
r
2
), in which
A
,
R
and
r
stand for area, outer and inner diameter of
the cross-section, respectively and
f
s
+
Rr
+
f
y
or
f
u
, for yield and ultimate stresses.
The yield and ultimate stresses,
f
y
and
f
u
, are considered to be lognormal
=
Table 26.7
Properties of the NREL offshore 5 MW baseline wind turbine
Property
Value
Unit
Rotor diameter
126
m
Hub height
90
m
Cut-in, rated, cut-out wind speed
3, 11.4, 25
m/s
Rotor mass
110 000
kg
Nacelle mass
240 000
kg
Tower mass
347 460
kg
Tower top diameter and wall thickness
3.87, 0.019
m
Tower base diameter and wall thickness
6.00, 0.027
m
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