Seismic Analysis of Structures: Improvements Due to Probabilistic Concepts - Dynamic Behavior of Concrete and Seismic Engineering - page 276

Thus, this results in data that are unlikely to represent a real motion but,
considering the way to characterize the frequency content and the modal method
using the data, which constitutes a consistent set.

Let us examine the situation more accurately. The frequency content of the
seismic signal is characterized by the oscillator response spectra (ORS), the

definition of which is determined by the following:

- given a high degree of freedom oscillator (mass, spring, damper system) with
imposed movement at anchoring points (Figure 8.3): x soil (t). The oscillator is
characterized by its resonance frequency f and damping ratio H;

- given x(t) the relative motion of the oscillator mass (x(t) = x struct (t) - x soil (t)),
the maximum value reached by the absolute value of x(t) will be called S (f,H).

Figure 8.3. Diagram of the seismically excited harmonic oscillator

By varying f and H, we obtain a curve network that is the ORS characterizing the
x soil (t) signal.

The ORS are typically represented in the form of:

- pseudo-velocities S pv (f,H) = 2Sf S (f,H);
- pseudo-accelerations S pa (f,H) = (2Sf) 2 S (f,H).
The ORS include 3 frequency bands (Figure 8.4):

- the very low frequency band ( 0.1 Hz) for which we can observe an
asymptotic behavior in S (f,H) = (x soil ) max ;
- the frequency band where the seismic energy is located and where we can
observe an amplification effect all the wider the smaller H is;

- the high frequency band (! 20 to 30 Hz) where we can observe a behavior in S
(f,H) = J smax /(2Sf) 2 .