Seismic Analysis of Structures: Improvements Due to Probabilistic Concepts - Dynamic Behavior of Concrete and Seismic Engineering - page 307

An elasto-plastic analysis leads to I l = P x e /W. Therefore, taking plasticity into
account involves admitting a higher limit intensity of a factor P.
(ii) If ZW | 1, it is the medium frequency range of the ORS. We can suppose that
the maximum displacement of the mass occurs before the second impulse takes
place. The elastic analysis will give I le = x e Z.

J(t)

1/'t

'W

t

'W

W

-1/'t

Figure 8.12. 2-impulse stimulation model

When writing the preservation of energy, the elasto-plastic analysis will give:

2

2

I Ȧ x 2Ȧ x ȝ xx

[8.56]

2

e e e e

1

As a consequence, taking plasticity into account involves admitting a higher
limit intensity of a factor (2P 1) 1/2 .
(iii) If Z'W d 1, it is the high frequency range of the ORS. The maximum
displacement of the mass is conditioned by the application of the first acceleration
step. The elastic and elasto-plastic analyses will give the same results as far as the
limit intensity is concerned.