Seismic Analysis of Structures: Improvements Due to Probabilistic Concepts - Dynamic Behavior of Concrete and Seismic Engineering - page 308

These results are extrapolated to the case of an average seismic stimulation:
Constituting the “inelastic spectrum” involves applying the reduction factors
defined above within the three frequency ranges to the original ORS. Then we will
use the new spectrum to apply the modal method the way we would do with a linear
behavior structure.
In the para-seismic Eurocode, we use a more continuous reduction factor
depending on the frequency but based on the same principles (Figure 8.13).
Figure 8.13. Inelastic reduction coefficient for a 4-ductility factor
dispersion effect between successive signals
Applying the technique raises some problems:
- the most serious one lies in the application of a system that cannot be reduced
to 1 dof. Actually it is difficult to define “basic solutions” (the equivalent of linear
natural modes); moreover, the result we are trying to achieve generally cannot be
represented in the shape of a sum of the contributions of these basic solutions.
Applying the modal method starting from those hypotheses can bring about very
serious errors;