Civil Engineering Reference
In-Depth Information
Basu's random excitation approach (structures 1 and 2 only) and (c) the hybrid approach
of ESDU (1996).
The three methods compared in Table 11.2 clearly give significant variations in
estimated response to vortex shedding, for all three structures. In the case of structure 1,
Table 11.1
Structural properties
Property
Structure 1
Structure 2
Structure 3
Height (m)
100
250
25
Diameter (m)
4.9
20
0.55-0.20 (tapered)
Surface roughness (mm)
0.1
1
0.15
Natural frequency (Hz)
0.5
0.3
0.5
Mode shape exponent
2
1.6
2
Mass/unit height (kg/m) (top third)
1700
50,000
30
Critical damping ratio
0.005
0.01
0.005
Table 11.2
Calculated values of maximum rms tip deflection/
diameter (at or near critical velocity)
Method
Structure 1
Structure 2
Structure 3
(a)
0.080
0.032
0.016
(b)
0.214
0.0045
NA
(c)
0.308
0.0054
0.014
all methods predict large amplitudes characteristic of lock-in, although methods (b) and
(c) predict higher amplitudes. Method (a), based on sinusoidal excitation, overestimates
the response of structure 2 (a large reinforced concrete chimney), which is subject to
wide-band excitation with low amplitudes. Methods (b) and (c) predict similar maximum
response for structure 2.
Vickery and Basu's model has generally been used for high Reynolds numbers only,
and has not been applied to structure 3, which is clearly in the sub-critical regime. The
other methods predict a low response amplitude for structure 3 which has a very low
critical velocity in the first mode, although this type of low-mass pole or mast has a
history of occasional large vortex-shedding responses, sometimes in higher modes, and
often producing fatigue problems. One of the main problems in predicting their behaviour
is in predicting the structural damping ratio, which is often very amplitude dependent.
11.6
Cooling towers
The vulnerability of large hyperbolic natural draught cooling towers to wind action was
emphasized in the 1960s by the collapse of the Ferrybridge Towers in the United
Kingdom (Figure 1.11). This event provoked research work on the wind loading and
