Civil Engineering Reference
In-Depth Information
As mentioned above, the relevant time window is of limited length such that the
component in the main flow direction may be split into a time invariant mean value and
a fluctuating part. Thus, the instantaneous wind velocity vector is defined by
(
)
(
)
(
)
⎫
Uxyzt Vxyz
,
,
,
,
,
uxyzt
,
,
,
=
+
f
f
f
f
f
f
f
f
f
⎪
⎪
⎬
⎪
⎪
⎭
(
)
vx y z t
,
,
,
(1.2)
f
f
f
(
)
wx y z t
,
,
,
f
f
f
where
V
is the mean value in the main flow direction, and
u
,
v
and
w
are the turbulence
components whose time domain mean values are zero. Since the main flow direction is
assumed perpendicular to the span of the structure, the velocity vector may be greatly
simplified depending on structural orientation. Thus, Eq. 1.2 may be reduced to
(
)
(
)
⎫
Uy t
,
=+
V uy t
,
⎪
⎬
⎪
⎭
f
f
(1.3)
(
)
wy t
,
f
for a line
−like horizontal structure (e.g. a bridge), and into
(
)
(
)
(
)
Uz t
,
Vz
uz t
,
⎫
=
+
⎪
⎬
⎪
⎭
f
f
f
(1.4)
(
)
vz t
,
f
for a vertical structure (e.g. a tower). As shown in Fig. 1.3 the structure is described in a
Cartesian coordinate system
[
]
x yz
, with origo at the shear centre of the cross section,
x
is in the span direction and with
y
and
z
parallel to the main neutral structural axis
(i.e. the neutral axis with respect to cross sectional bending). Correspondingly, the wind
load drag, lift and pitching moment components (per unit length along the span) are all
referred to the shear centre and split into a mean and a fluctuating part, i.e.
,,
()
()
()
(
)
qx
qxt
,
,
,
⎡
⎤⎡ ⎤
y
y
⎢
⎥⎢ ⎥
(
)
qx
qxt
qq
+=
+
(1.5)
⎢
⎥⎢ ⎥
z
z
⎢
⎥⎢ ⎥
(
)
qx
qxt
⎣
⎦⎣ ⎦
θ
θ
Similarly, the response displacements
()
()
()
(
)
rx
rxt
,
,
,
⎡ ⎤⎡ ⎤
⎢
⎥⎢ ⎥
+=
y
y
(
)
rx
rxt
rr
+
(1.6)
⎢ ⎥⎢ ⎥
⎢ ⎥⎢ ⎥
⎣ ⎦⎣ ⎦
z
z
(
)
rx
rxt
θ
θ
