Civil Engineering Reference
In-Depth Information
12.3
The nature of dynamic response of long-span bridges
There are several mechanisms, in various wind speed ranges, which can excite resonant
dynamic response in the decks of long-span bridges, as follows:
• Vortex-shedding excitation (Section 4.6.3) which usually occurs in low wind speeds
and low turbulence conditions (e.g. Frandsen, 2001).
• Flutter instabilities (Section 5.5.3) of several types, which occur at very high wind
speeds for
aerodynamically stable
decks, as a result of the dominance of self-excited
aerodynamic forces (Sabzevari and Scanlan, 1968). These always involve torsional
(rotational) motions and may also involve vertical bending motions.
• Buffeting excitation (Section 4.6.1) caused by the fluctuating forces induced by
turbulence (Davenport, 1962; Scanlan and Gade, 1977). This occurs over a wide range
of wind speeds and normally increases monotonically with increasing wind speed.
The nature of these mechanisms is discussed in the following sections.
Table 12.1
Some recorded cases of vortex-shedding induced
vibrations of bridges
Name
Natural
frequency (Hz)
Critical
velocity (m/s)
Max.
amplitude
(mm)
Reference
Long's Creek
Bridge
0.6
12
100-170
Wardlaw (1971)
Wye Bridge
0.46
7.5
35
Smith (1980)
Waal River
0.44
9-12
50
van Nunen and Persoon
(1982)
Great Belt
East
0.13-0.21
4.5-9
320
Larsen
et al.
(1999),
Frandsen (2001)
12.3.1
Vortex-shedding excitation
Under certain conditions, vortex-shedding excitation can induce significant, but limited,
amplitudes of vibration. The conditions required for this to occur are most, or all, of the
following:
• wind direction normal to the longitudinal axis of the bridge;
• low turbulence conditions (typically
I
u
less than 0.05);
• a wind speed in a narrow critical range (5-12 m/s); and
• low damping (1% of critical or less).
The above conditions can be satisfied for both short-to-medium span cable-stayed bridges
crossing water and longer span suspension bridges. With Strouhal numbers in the range
of 0.1-0.2 (based on the depth of the deck cross section) and natural frequencies in the
