Civil Engineering Reference
In-Depth Information
where
is the corresponding angle
of flow incidence. Transformation into structural axis is given by
V
is the instantaneous relative wind velocity and
α
rel
q
⎡⎤
cos
sin
0
q
β
−
β
⎡
⎤⎡ ⎤
y
D
⎢⎥
⎢
⎥⎢ ⎥
(
)
xt
,
q
sin
cos
0
q
q
=
=
β
β
⋅
(5.2)
⎢⎥
⎢
tot
z
⎥⎢ ⎥
L
⎢⎥
⎢
q
0
0
1
⎥⎢ ⎥
q
⎣
⎦⎣ ⎦
⎣⎦
θ
M
tot
where:
⎛
⎞
wr
Vur
−
z
β
=
arctan
(5.3)
⎜
⎟
⎜
⎟
+−
⎝
⎠
y
The first linearization involves the assumption that the fluctuating flow components
(
)
(
)
wxt
are small as compared to
V
, and that structural displacements (as
well as cross sectional rotation) are also small. Then
cos
uxt
and
,
,
1
β ≈
and
(
)
(
)
(
)
sin
tan
wr
/
V ur
wr V
/
β
≈
β
≈≈−
β
+− ≈−
, and thus
z
y
z
(
)
2
⎫
2
2
(
)
2
VVur
=+− +− ≈ + −
⎪
⎬
⎪
wr
V
22
u
r
rel
y
z
y
(5.4)
r
w
z
rr
rr
VV
α
=++≈++−
β
θθ
θθ
⎭
The second linearization involves the flow incidence dependent load coefficients. As
illustrated in Fig. 5.2, the nonlinear variation of the load coefficient curves is replaced by
the following linear approximation
()
()
()
()
()
()
()
()
()
C
C
C
′
⎡
α
⎤ ⎡
α
⎤
⎡
α
⎤
D
D
D
⎢
⎥ ⎢
⎥
⎢
⎥
C
C
C
′
α
=
α
+
α
⋅
α
(5.5)
⎢
⎥ ⎢
⎥
⎢
⎥
L
L
f
L
⎢
⎥ ⎢
⎥
⎢
⎥
C
C
C
′
α
α
α
⎣
⎦ ⎣
⎦
⎣
⎦
M
M
M
where
α
and
are the mean value and the fluctuating part of the angle of incidence,
α
f
and where
C
′
,
C
′
and
C
′
are the slopes of the load coefficient curves at
α
.
D
M
