Civil Engineering Reference
In-Depth Information
Example 6.5
For a simple beam type of bridge let us set out to calculate the vortex shedding induced dynamic
response at
0
T
[
]
x
L
2
0
=
associated with the mode shape
φ
=
φ
with corresponding
r
z
0.8
rad s
/
sin
x L
eigen-frequency
. Thus,
in this case it is only the across wind vertical direction that is of any interest. Typical variation of
some basic data is illustrated in Fig. 6.15.
ω
=
. Let us again for simplicity assume that
φ
=
π
z
z
Fig. 6.15
Top left and right: Non-dimensional cross sectional load spectrum and co-
spectrum, lower left: aerodynamic damping coefficient, lower right: maximum vortex
shedding induced dynamic response vs.
ζ
z
The top left hand side diagram shows the non-dimensional cross sectional load spectrum
associated with vortex shedding in the across wind direction (see Eq. 5.33)
()
⎡
2
⎤
ωω
S
⎛
1
⎞
1
ω
ω
−
ωω
q
z
exp
⎢
s
⎥
=
⋅
⋅
−
⎜
⎟
2
b
b
⎢
⎥
σ
π
⎝
⎠
q
z
s
z
⎣
⎦
z
