Civil Engineering Reference
In-Depth Information
Fig. 9.7
Definition of roll angle
γ
0
0
0
⎡
⎤
⎢
⎥
(
)
(
)
2
DC I
DC
′
BC
I
DC
′
BC
I
−
−
⎢
⎥
Du
D
L
v
D
L
w
⎢
⎥
(
)
(
)
2
V
ρ
2
BC I
BC
′
+
DC
I
BC
′
+
DC
I
⎢
⎥
(
)
xt
,
Lu
L
D
v
L
D
w
ˆ
q
=
⋅
ψ v
(9.43)
⎢
⎥
00
2
2
2
2
⎢
−
2
BC I
−
BC I
′
−
BC I
′
⎥
Mu
Mv
Mw
⎢
⎥
0
0
0
⎢
⎥
⎢
⎥
0
0
0
⎣
⎦
where
I
,
I
and
I
are the turbulence intensities,
ψ
is a three by three matrix taking
w
account of the element orientation (roll angle
) in the flow (see Fig. 9.7)
γ
10 0
0sin 0
00 s
⎡
⎤
⎢
⎥
ψ
=
⎢
γ
(9.44)
0
⎥
⎢
γ
⎥
⎣
⎦
and where
v
is the reduced turbulence velocity vector
0
T
(
)
(
)
(
)
uxt
,
vxt
,
wxt
,
⎡
⎤
ˆ
v
=
(9.45)
⎢
⎥
0
σ
σ
σ
⎣
⎦
u
v
w
Thus, the turbulence induced (buffeting) load vector at element level is given by:
Q
⎡ ⎤
1
()
t
R
=
(9.46)
⎢
⎣ ⎦
n
Q
2
n
