Environmental Engineering Reference
In-Depth Information
the conventional GRF approach, in the proposed methodology [43], there are two
contributions for the resonant component. The square of the non-
dimensionalized form of background component of the gust factor
2
G
can be
expressed as
2
2
2
∞
2
2
2
∞
Φ
F
Ψ
Φ
F
Ψ
CS,1
−
TT
C
S,1
CS,2
−
TT
C
S,
2
CS,2
2
B
∫
∫
G
=
S
()d
f
f
+
S
()d
f
f
( 14 )
MF1MF1
MF2MF2
44
2
2
44
2
2
16
π
f
Mx
16
π
f
M x
CS,1
CS,1
CS,2
CS,2
0
0
The integral in eqn (14) may be evaluated numerically, or by assuming the
integrand to be a white noise, or from a known value of turbulence intensity.
The resonant component of the gust factor comprises of two non-dimensionalized
terms representing contributions of the fi rst and second modes of vibration,
2
R,1
G
and
, respectively. These terms are given by the expressions:
2
R,2
G
2
2
2
ΦΦ
S
(
f
)
Ψ
CS, -TT
j
CS,
j
MF MF
j
j
CS,
j
j
2
R,
G
=
,
j
= 1, 2
(15 )
j
33
2
2
64p f
M
x
x
CS, j
CS, j
CS, j
where
Ψ
j
is the peak factor associated with mode '
j
'. Thus, the closed form solution
for the displacement GRF,
G
DISP-CF
, is obtained as
2
2
2
G
=+
1
G
+
G
+
G
(16 )
DISP
−
CF
B
R,1
R,2
where
G
B
and
G
R,
j
represent the background and resonant components of the
displacement GRF, respectively.
3.3 Bending moment GRF
A GRF also has been derived based on the bending moment GRF [41] at the tower
base,
G
BM
by [43] which is presented for comparison. Similar to the displacement
GRF,
G
BM
will contain contributions from two modes of vibration and is obtained
as the ratio of the expected maximu
m
base bending mom
e
nt,
Y
MAX
(
t
) (=
Ψ
s
BM
),
H
2
to the mean base bending moment,
y
(
∫
0.5
r
C
() () () d).
z B z v z
z z
The RMS of
0
D
the base bending moment,
s
BM
, is obtained from the equation:
1/2
⎛
∞
⎞
2
2
∑
2
∫
(17 )
s
=Γ
S
()
f
H
() d
f
f
⎜
⎟
BM
j
MF MF
j
j
D,
j
⎝
⎠
j
=
1
0
where
Γ
is given by
j
H
2
∫
Γ= π
(2
f
)
m z
( )
Φ
( ) d
z z z
(18 )
j
CS,
j
CS,
j
0
The base bending moment GRF,
G
BM
may be obtained as
s
=+Ψ
B
M
G
1
(19 )
BM
y
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