Civil Engineering Reference
In-Depth Information
Equation (4.15) is a quasi-steady relationship between mean-square pressure fluctuations
and mean-square longitudinal velocity fluctuations.
To predict peak pressures by the quasi-steady assumption,
(4.16)
Thus, according to the quasi-steady assumption, we can predict peak pressures (maxima
and minima) by using mean pressure coefficients with a peak gust wind speed. This is the
basis of many codes and standards that use a peak gust as a basic wind speed (see
Chapter 15). Its main disadvantage is that building-induced pressure fluctuations (the
second source described in Section 4.6.1) are ignored. Also when applied to wind
pressures over large areas, it is conservative because full correlation of the pressure peaks
is implied. These effects and the way they are treated in codes and standards are
discussed in Chapter 15.
4.6.3
Body-induced pressure fluctuations and vortex-shedding forces
The phenomena of separating shear layers and vortex shedding have already been
introduced in Sections 4.1, 4.3.1, 4.4.1 and 4.5 in descriptions of the flow around some
basic bluff-body shapes. These phenomena occur whether the flow upstream is turbulent
or not, and the resulting surface pressure fluctuations on a bluff body can be
distinguished from those generated by the flow fluctuations in the approaching flow.
The regular vortex shedding into the wake of a long bluff body results from the
rolling-up of the separating shear layers alternately on one side, then the other, and occurs
on bluff bodies of all cross-sections. A regular pattern of decaying vortices, known as the
von Karman vortex 'street', appears in the wake. Turbulence in the approaching flow
tends to make the shedding less regular, but the strengths of the vortices are maintained,
or even enhanced. Vibration of the body may also enhance the vortex strength, and the
vortex-shedding frequency may change to the frequency of vibration, in a phenomenon
known as
lock-in
.
As each vortex is shed from a bluff body, a strong cross-wind force is induced towards
the side of the shed vortex. In this way, the alternate shedding of vortices induces a nearly
harmonic (sinusoidal) cross-wind force variation on the structure.
For a given cross-sectional shape, the frequency of vortex shedding,
n
s
,
is proportional
to the approaching flow speed and inversely proportional to the width of the body. It may
be expressed in a non-dimensional form, known as the
Strouhal number, St:
(4.17)
where
b
is the cross-wind body width and
U
the mean flow speed.
The Strouhal number varies with the shape of the cross-section, and for circular and
other cross-sections with curved surfaces varies with the Reynolds number. Some
