Seismic Analysis of Structures: Improvements Due to Probabilistic Concepts - Dynamic Behavior of Concrete and Seismic Engineering - page 302

In practice, various methods allow us to make random processes, the average
characteristics of which are adjusted on an ORS family within an eigenfrequency
and damping range, and thus to produce time creations that can be used for both
calculation and experimentation.

These methods even include the correction of the most obvious non-physical
characteristics (for instance, time averages not equal to zero for acceleration
signals).

The nature of the generated signals can be quite different from one method to the
next. It would not be that important for a linear behavior structure because in this
case the ORS represent relevant values as far as the response maximum prediction is
concerned. Besides, that is the reason why the adjustment of a separable process
involves satisfying results for the direct calculation of the linear floor spectra.

In the case of a marked non-linear behavior (modeled or real structure), such
relevance is not at all obvious. Thus, from response average maxima, we can obtain
quite different results according to the method used (with adjustment on the same
ORS).

As an illustration we will hereafter give the principles of the quite commonly
used “random phase harmonic sinusoid” method.

Generally, the adjustment is carried out on a given S (f, H) ORS (H being given).
The probabilistic model used is the separable type;

* t at Ft

[8.52]

The stationary process F(t) results from a sum of sinusoids with deterministic A i
amplitudes and M i random phases that are independent and equiprobable within the
[S, S] interval:

N

¦ Ft Asin2ʌ ft+ij

[8.53]

i i i

i1

The f i values are a set of discrete frequencies that describe the studied range. We
often take: