Seismic Analysis of Structures: Improvements Due to Probabilistic Concepts - Dynamic Behavior of Concrete and Seismic Engineering - page 306

Figure 8.11. Diagram of a bi-linear-strain hardening elasto-plastic oscillator
The idea involves comparing the limit intensities of the impulses bringing about
collapse that can be calculated thanks to:
- elastic analysis: we will write that the displacement remains lower than x e ;
- elasto-plastic analysis: we will write that the displacement remains lower than
Px e .
We can distinguish three frequency ranges:
(i) If ZW << 1, it is the low frequency range of the ORS. The maximum relative
displacement of the mass depends little on the stiffness law and it is given
approximately by x max = IW. A purely elastic analysis gives a limit intensity I le = x e /W.