Civil Engineering Reference
In-Depth Information
As mentioned above, many used ESA in their studies. Two examples, one
for PC and one for steel girder bridges, are illustrated in Chapter 15 as part
of the redundancy analysis. Bridge model, attack scenarios, and structural
responses were discussed in Sections 15.4 and 15.5.
17.2.5 Wind analysis
Wind induces two typical aerodynamic phenomena in long-span bridges:
fluttering and buffeting. The former is an aerodynamic instability that may
cause failure of the bridge, and the latter is an aerodynamic random vibra-
tion that may lead to fatigue damage, excessive vibration, and large dis-
placements. The wind velocities at which the bridge starts to flutter are
called flutter velocities. Aerodynamic design must ensure that the critical
flutter velocity is higher than the maximum wind velocity at the site and
that the bridge does not vibrate excessively under gusty winds. Flutter may
occur in both laminar and turbulent flows. Buffeting is a random response
of structures to turbulent flow.
Natural winds, which are turbulent in nature, cause both flutter and buf-
feting problems (Cai et al. 1999).
Aerodynamic loading is commonly separated into self-excited and buffet-
ing forces. The self-excited forces acting on a unit deck length are expressed
as a function of the so-called flutter derivatives (Scanlan 1978a), which can
be expressed as
L
D
M
se
{
F
}
U F q U F q
2
[
]{ }
2
[
]{ }
=
=
+
(17.16)
se
se
d
v
se
Similarly, the buffeting forces (Scanlan 1978b) are expressed as
L
D
M
b
{
F
}
U C
2
[
]{ }
=
=
η
(17.17)
b
b
b
b
where:
L
se
,
D
se
, and
M
se
are the self-excited lift force, drag force, and torsional
moment, respectively
[
F
d
] and [
F
v
] are the flutter derivative matrices corresponding to dis-
placement and velocity, respectively
[
C
b
] is the static coefficient matrix
{η} is the vector of turbulent wind components normalized by mean
wind velocity
U
, which is distinguished from the mean value
-
in the previous expres-
sion, will be interpreted as the mean or instantaneous wind veloc-
ity in different cases
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