Seismic Analysis of Structures: Improvements Due to Probabilistic Concepts - Dynamic Behavior of Concrete and Seismic Engineering - page 300

after the beginning of the stimulation, in which the expression of the H transfer
function is slightly modified to take the envelope of the source process into account:

2

X S ,IJ,f

H r,IJ,f S f

[8.50]

with:

W

³

Hr,IJ,f G r,u a IJ u exp 2iʌfu du

[8.51]

0

Figure 8.10. Floor spectra: comparison between the proposed method (synthetic spectra) and
direct time integration calculation (10 realizations)

The last step involves passing from S X (r, W, f) (r being the position of the floor
or the anchoring considered) to the associated ORS that will be the “floor spectra”
sought. To obtain this, we also go through a separable process representation.

On the one hand, we consider the average according to W of S X (r, W, f) that we
take as PSD: S floor (f), and on the other hand the integral according to f of S x (r, W, f),