Civil Engineering Reference
In-Depth Information
REMARK.- Peak factor corrections are based on stationary process considerations.
As a first approximation, it is possible to take the transient feature into account by
replacing the damping H with the equivalent damping given by [8.40].
8.6. Direct calculation of the floor spectra
The seismic calculation of a complex structure is performed in several steps:
- the first step involves the calculation of buildings, including the soil-
foundation interaction effects and simplified modeling of large equipment;
- the second step involves detailed calculation of large equipment;
- in some cases a third step is necessary to study the secondary equipment, i.e.
the pipework connecting the main equipment.
If we want to avoid time calculations and therefore continue to apply the modal
method concept, then at the start of the second and third steps we will need the ORS
associated with the motions of the floors on which the large equipment rests or to
which the secondary equipment is anchored. However, the modal method such as it
has been described so far does not allow us to obtain such information when it is
applied to the first step.
The objective of the so-called “floor spectrum direct calculation” method is to
answer that question. As in the previous section, it implies resorting to an accurate
probabilistic definition of seismic loading. On this occasion we will be driven to
study the transient feature of the loading and of the response of the structure, which
has only been touched on so far.
8.6.1.
Representation of non-stationary processes
If staying at a second order characterization, a general (non-stationary) process
fulfills a correlation function depending on two time variables:
ȡ t,t
or ȡ t, IJ with: t = t
t
/ 2 and
W
t
t
12
1
2
2
1
A PSD can be defined either by carrying a double Fourier transform of the
correlation function or by performing a simple Fourier transform (with regard to W).
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