Civil Engineering Reference
In-Depth Information
Fig. 5.1
Instantaneous flow and displacement quantities
As can be seen, the usual assumption that any fluctuating quantity can be split into a
time invariant mean part and a zero mean fluctuating part is adopted (as previously
mentioned in chapter 1.3). Thus, t
he
cross
s
ection at a
n
arbitrary position along the span
is first given the displacements
()
()
()
y
rx
,
z
rx
and
rx
θ
. In this position the wind
(
)
(
)
velocity vector is
wxt
in the
vertical across wind direction. It is about this position that the structure oscillates. The
cross section is then given the additional dynamic displacements
Vuxt
,
in the along wind horizontal direction and
,
+
(
)
(
)
y
rxt
,
,
z
rxt
and
,
(
)
. In this position the instantaneous cross sectional drag, lift and moment forces in
flow axes are by definition given by
rxt
θ
,
(
)
⎡
()
()
()
⎤
⎡
qxt
,
⎤
DC
⋅
α
D
D
⎢
⎥
1
⎢
⎥
(
)
2
qxt
,
V
BC
=
ρ
⋅
⋅
α
α
(5.1)
⎢
⎥
⎢
⎥
L
rel
L
2
⎢
⎥
(
)
⎢
⎥
qxt
,
2
BC
⋅
⎣
⎦
⎢
⎥
M
⎣
⎦
M
