Seismic Analysis of Structures: Improvements Due to Probabilistic Concepts - Dynamic Behavior of Concrete and Seismic Engineering - page 293

characterization is used, although in some cases it is not the best suited, as we will
show later.
Therefore, the problem involves specifying the meaning of ORS in probabilistic
terms. As we recalled at the beginning, the ORS represents the maximum reached
during the seismic stimulation by the response of a harmonic oscillator. The notion
was analyzed in probabilistic terms in the previous section.
One ORS point represents a random variable. Calculating the response to a given
seismic signal represents a carrying out of that random variable. Figure 8.8 shows
such calculation results. We can observe quite fluctuating curves that reflect the
straggling. Actually, the regulation curves used by engineers are much smoother.
Though they result from various averages not necessarily consistent with a well-
defined random process, they should be considered as a statistic average associated
with a random process.
Figure 8.8. OSR associated with a seismic signal (the higher the damping,
the lower the statistical fluctuation)
The first goal of probabilistic seismic analysis is therefore to adjust a random
process to the regulation ORS data considered as the statistic average of the
“maximum reached” random variable. In fact, the problem has several solutions that
may involve quite different results in the case of very non-linear structure behaviors.
Let us return to the criticisms of the modal method listed above. The first
concerned the simple quadratic combination hypothesis. As a matter of fact, there
are actually two distinct causes of non-verification of this hypothesis.