Seismic risk analysis of wind turbine support structures - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 729

Table 26.8 Proposed damage states

Damage state Description Performance level

No signifi cant
damage (ND)

No structural damage

Tower base shear or moment
exceeds yield limits

Permanently
out-of-
service (PO)

Support structure yields
Permanent excessive
deformations will make
the turbine out-of-service

Tower base shear or moment
exceeds ultimate limits

Complete (C) Support structure is unable

to carry additional loads

random variables with a mean of 300 and 410 MPa (for a structural steel
of grade S235 according to EN 10 025 standard; CEN, 2004), respectively
and a coeffi cient of variation of 10%. In addition, M y = f y S is used to calcu-

late the yield bending moment capacity in which S elastic section modulus.

Finally, we calculate the ultimate bending moment capacity using a moment-
curvature diagram constructed for the tubular cross-section of tower, based
on the stress-strain curve for structural steel of grade S235. Therefore, for
the structure of interest, ultimate bending moment is the maximum moment
in the moment-curvature diagram with a mean of 390.6 MN m and a stan-
dard deviation of 39.57 MN m. Monte Carlo simulations are used to esti-
mate the fragility for each failure mode and to assess the system fragility
of the wind turbine support structure, where all the model parameters and
error terms in the developed demand models are considered as random
variables.
Figure 26.6 shows the predictive fragility estimates for the example off-
shore wind turbine plotted as a function of the spectral acceleration, S a , in
units of g , at the natural period of the support structure ( T n

=

2.5 s) within
its linear elastic range, for both yield and ultimate limit states. The dotted,
solid and dashed lines in the fi gure show the fragility due to the ultimate
bending failure mode for cut-in, rated and cut-out wind speeds, respectively.
Cut-in and cut-out wind speeds are the limits of the range of wind speeds
in which a turbine is operating and producing power. The rated wind speed
is the wind speed at which a control system is activated to limit the aero-
dynamic forces on the blades of the wind turbine and keep the power
generated constant by changing the blade pitch angle. As shown in the
fi gure, the fragility at the rated wind speed is higher than the fragilities at
the other two wind speeds due to the higher wind speed than the cut-in

=