Seismic Analysis of Structures: Improvements Due to Probabilistic Concepts - Dynamic Behavior of Concrete and Seismic Engineering - page 301

which represents the square of the standard deviation of the response V X (r, W)),
which is taken, after being standardized, as an envelope: a floor (W).
Finally, we can reconstruct the oscillator spectra [S pv] floor (f, H)] using equations
[8.47] and [8.49]. An illustration of the floor spectrum calculation for which the
carrying structure behaves as a 1-dof oscillator is presented in Figure 8.10.
8.7. Creation of synthetic signals and direct numerical integration
So far we have examined seismic analysis methods that do not require any direct
time integration of the movement equations. The main interest of such methods lies
in them being more “physical”, far lighter and far more flexible to use (depending
on the problem to deal with we adjust the number of modes used), and in them being
perfectly consistent with the regulation data of the seismic source.
Nevertheless, they cannot be applied in two cases:
- when we want to carry out an experimental analysis, in the case of the shaking
table assessment of equipment, the good behavior of which has to be guaranteed
under seismic loading defined by a given ORS, for instance. The jacks of the
shaking table then need a load time law;
- when the structure has to be represented by a highly non-linear model. Then
the modal theory cannot be applied.
We could also prefer the time method for some linear but complex structures, the
modal core truncation criteria of which are not really clear or involve a very high
number of modes. As we said at the beginning of this chapter, the seismic data
associated with a site is seldom of the time kind because of the absence of
measurement data, of the “envelope” feature that we mean to give it, etc.
Therefore, the problem is as follows: from an ORS set, how can we define a
random process, the ORS of which will represent the average maxima like that
defined above?
Such a problem is not well put. Is there one solution to it? Are there several? Do
these solutions have any relationship with the physical phenomena brought into
play?
As far as we know, these questions have not been satisfactorily answered yet.