Civil Engineering Reference
In-Depth Information
Thus, the load comprise a time invariant mean part (static load), a dynamic part caused
by wind turbulence (buffeting load) and a dynamic part caused by interaction between
the flow and structural motion (motion induced load), i.e.:
(
)
( )
(
)
(
)
x t
,
x
x t
,
x t
,
q
=
q
+
q
+
q
(9.39)
tot
ae
As indicated in Fig. 9.6 it is for simplicity assumed that the element length (
L
) is short
such that it may with sufficient accuracy be assumed that the flow components
(
)
(
)
(
)
Vuxt
,
vxt
and
,
wxt
are constant along half the element span.
,
+
,
The mean (static) load vector:
The static load is given by (see Eq. 5.11)
2
V
ρ
T
()
2
x
⎡
0
DC
BC
B C
0
0
⎤
q
=
⋅
−
(9.40)
⎣
D
L
M
⎦
2
Thus, the mean (static) load vector at element level is given by
⎡ ⎤
Q
1
R
=
(9.41)
⎢ ⎥
⎣ ⎦
n
Q
2
n
where
L
⎧
ρ
T
⎫
2
()
()
2
QZ
VZ
⎡
0
DC BC BC
0
0
⎤
=
⎡
⎤
⋅
⎭
(9.42)
⎨
⎬
⎣
⎦
⎣
i
i
i
D
L
M
⎦
n
2
2
⎩
n
and where
i
refers to element end 1 or 2, i.e.
i
=
1 or 2
.
The turbulence induced (buffeting) load vector:
As illustrated in Fig. 9.6, the buffeting load will depend on orientation of the element in
the flow, i.e. whether its position is horizontal or vertical, affecting the appropriate
interpretation of the flow components
(
)
(
)
(
)
uxt
,
,
vxt
and
,
wxt
. Thus, the buffeting
,
load is given by (see Eq. 5.12)
