Civil Engineering Reference
In-Depth Information
Thus, for a circular cross-section, the instantaneous lateral force per unit length based on
quasi-steady assumptions can be written:
(11.20)
Basu and Vickery (1983), in developing a method suitable for prediction of the combined
cross-wind response of real structures in the atmospheric boundary layer, used the
following expression for the mean square modal coordinate in the jth mode:
(11.21)
where
S
ℓ,υ
(n
j
), S
ℓ,t
(n
j
)
are respectively the spectral densities, evaluated at the natural
frequency,
n
j
,
of the cross-wind forces due to vortex shedding and lateral turbulence.
Equation (11.21) is based on the assumption that the spectral density is constant over the
resonant peak, as previously used to derive Equation (5.13).
A comparison of the peak-to-peak cross-wind deflection at the top of the 330m-high
Emley Moor television tower computed by the random vibration approach of Vickery and
Basu, and compared with measurements, is shown in Figure 11.4. Calculations were
made for the first four modes of vibration. There was some uncertainty in the appropriate
structural damping for this tower, but generally good agreement was obtained.
Comparisons were also made with full-scale response measurements from several
reinforced concrete chimneys (Vickery and Basu, 1984). The average agreement was
quite good but some scatter was shown.
11.5.3
Hybrid model
Item 96030 of the Engineering Sciences Data Unit (ESDU, 1996) covers the response of
structures of circular and polygonal cross-section to vortex shedding. A computer
program and spreadsheet is provided to implement the methods. ESDU 96030 covers
uniform, tapered and stepped cylindrical or polygonal structures, and also yawed flow
situations.
The method used in ESDU 96030 appears to be a hybrid of the two previously
described approaches. For low amplitudes of vibration, a random excitation model
similar to that of Vickery and Basu has been adopted. At high amplitudes, i.e. in lock-in
situations, a sinusoidal excitation model has been adopted with a cross-wind force
coefficient that is non-linearly dependent on the vibration amplitude. The response is
postulated to switch intermittently between a random wide-band response and a constant
amplitude sinusoidal type as lock-in occurs.
