Large roofs and sports stadiums - Wind Loading of Structures - page 264

and the structural stiffness cannot be altered to accommodate design changes once the
model has been built. For important structures, a rigid pressure model test is also
advisable to obtain the distributions in pressure for the mean and background
components, as discussed earlier. The resonant response can also be computed from the
spectra and cross-spectra of the fluctuating pressures at the natural frequency or from the
time histories of the generalized forces in the contributing modes of vibration. Either
method is computationally complex and requires simultaneous pressure measurement
over the entire roof (including the underside pressure for an open stadium roof), but this
is certainly feasible and has been used for large projects at wind-tunnel laboratories in
Australia and elsewhere.
Usually the resonant response will comprise no more than 10-20% of the peak values
of critical load effects (Holmes et al., 1997), and this contribution can be calculated
separately and added to the fluctuating background response using a 'root-sum-of-squares
approach'. The effective static load distribution corresponding to each peak load effect
can then scaled up to match the recalculated peak load effect.
For very large roofs, several resonant modes can contribute, and the evaluation of
effective static loads becomes more difficult. In general, it is necessary to adopt the
approach of Section 5.3.7 in which the background response is separated from the
resonant components, as these components all have different loading distributions. The
magnitude of the contribution from each resonant mode depends on the load effect
through its influence line. Section 12.3.4 describes the application of the equivalent static
load approach to long-span bridges, when more than one resonant mode contributes. This
approach can also be applied to very large roofs; in this case, the background contribution
is treated as an additional 'mode', for which the effective load distribution is calculated
separately.
Thus, the effective static load distribution for the combined background and resonant
contributions is:
(10.1)
where the weighting factors are given by:
(10.2)
(10.3)
where σ r,B is the background component of the load effect, and the other terms are defined
in Section 12.3.4. The derivation of the background effective static load distribution,
P eff,back (x), is described in Chapter 5.