Civil Engineering Reference
In-Depth Information
where
B
0
is
B
s
evaluated at
s
equal to 0 (the reduction due to correlation over the whole
height of the tower is important.
F
10
,
F
11
and
F
12
are additional non-dimensional
parameters;
F
12
is a non-dimensional stiffness for the tower.
It can be seen from Equations (11.6), (11.7) and (11.8) that the gust response factor
depends on the type of load effect under consideration, as well as the level on the tower at
which it is evaluated.
An alternative approach for the along-wind loading and response of slender towers
and chimneys is the equivalent (or effective) static load distribution approach discussed
in Section 5.4 (see also Holmes, 1996b). This approach allows variations in dimension
shape and mass over the height of a tower of complex shape to be easily incorporated.
Examples of effective static wind load distributions derived for a 160 m tower are given
in Figures 5.11 and 5.12.
11.5
Cross-wind response of tall slender towers
The strength of regular vortex shedding from a tower of uniform or slightly tapered cross-
section is often strong enough to produce significant dynamic forces in the cross-wind
direction. If the damping of a slender tower of a solid cross-section is low, high-
amplitude vibrations can occur if the frequency of vortex shedding coincides with a
natural frequency of the structure. The velocity at which this coincidence occurs is known
as the
critical velocity
. If the critical velocity is very high, i.e. outside the design range,
no problems should arise, as the resonant condition will not occur. Conversely, if the
critical velocity is very low, there will also not be a problem as the aerodynamic
excitation forces will be low. However, significant vibration could occur if a critical
velocity falls in the range 10-40 m/s.
Because of the higher rate of vortex shedding for a circular cross-section compared
with that for a square or rectangular section of the same cross-wind breadth, the critical
velocity is significantly lower.
Methods of calculation of cross-wind response of slender towers or chimneys fall into
two classes:
(i) those based on sinusoidal excitation; and
(ii) those based on random excitation.
In the following sections, methods developed mainly for structures of circular
crosssection are described. However, in principle they can be applied to structures of any
(constant) cross-section.
11.5.1
Sinusoidal excitation models
The assumption that the vortex-shedding phenomenon generates near-sinusoidal
crosswind forces on circular cylinders can be linked to the work of Scruton and co-
workers in the 1950s and 1960s (summarized in Scruton, 1981). In this formulation, the
excitation forces were treated solely as a form of negative aerodynamic damping, but this
is equivalent to sinusoidal excitation by applied forces. Such models are good ones for
