Civil Engineering Reference
In-Depth Information
measured peak pressure coefficients from wind-tunnel tests are valid for use in
calculation of design loads, for comparison with 1 m in loads in glass design charts.
9.5
Overall loading and dynamic response
In Chapter 5, the random, or spectral, approach to the along-wind response of tall
structures was discussed. This approach is widely used for the prediction of the response
of tall office buildings in simplified forms in codes and standards (see Chapter 15).
Dynamic response of a tall building in the along-wind direction is primarily produced by
the turbulent velocity fluctuations in the natural wind (Section 3.3). In the cross-wind
direction, loading and dynamic response is generated by random vortex shedding
(Section 4.6.3)—i.e. it is a result of unsteady separating flow generated by the building
itself, with a smaller contribution from cross-wind turbulence.
9.5.1
General response characteristics
In this section, some general characteristics of the dynamic response of tall buildings to
wind will be outlined.
By a dimensional analysis, or by application of the theory given in Section 5.3.1, it
can be demonstrated (Davenport, 1966, 1971) that the rms fluctuating deflection at the
top of a tall building of given geometry in a stationary (synoptic) wind is given to a good
approximation for the along-wind response by:
(9.22)
and for the cross-wind response by:
(9.23)
where
h
is the building height;
A
x
, A
y
constants for a particular building shape;
ρ
a
the
density of air;
ρ
b
an average building density; Uh the mean wind speed at the top of the
building;
b
the building breadth;
k
x
, k
y
exponents;
n
1
the first mode natural frequency; and
η
the critical damping ratio in the first mode of vibration.
Equations (9.22) and (9.23) are based on the assumption that the responses are
dominated by the resonant components. For along-wind response, the background
component is independent of the natural frequency. In the case of the cross-wind
response, there is no mean component but some background contribution due to cross-
wind turbulence. The assumption of dominance of resonance is valid for slender tall
buildings with first mode natural frequencies less than about 0.5 Hz and damping ratios
less than about 0.02.
The equations illustrate that the fluctuating building deflection can be reduced by
increasing either the building density or the damping. The damping term,
η,
includes
