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gal, 2005), that there would be instances when
the classical viscous damping assumption would
underestimate the peak deflection and fail to
capture the occurrence of nonlinearity in the par-
ent frame. So this aspect poses a risk of the parent
frame becoming nonlinear and the damping
model used in the analysis might fail to capture
that effect, meaning that the resulting optimal
distribution might no longer be optimal.
In this section we have only qualitatively em-
phasized the significance of the contribution of
the in-structure damping in the overall structural
response. From the studies carried out in this
section we can state that in-structure damping
models affect the optimal distribution of dampers;
but at this point of time we are unable to define
the extent of its effect. Further research is needed
in this area.
tion focuses mainly on the realism of the linearity
assumption rather than delving into the details of
stability issues associated with development of the
nonlinearity. Readers interested in the techniques
of circumventing of the stability issues associated
with inelasticity in the parent frame should refer
to Lavan et al. (2008), and Cimellaro et al. (2009).
At first the effect of adding dampers into a
parent structure is illustrated schematically. Fig-
ures 14a and 14b illustrate the effect of adding
dampers into a building frame and the effect is
expressed in terms of reduction in seismic input
energy dissipated by the frame. E1 represents the
total input energy and E2 represents the energy
dissipated by the parent frame fitted with dampers.
Evidently it could be seen that once a damper is
added into the frame there is a reduction in the
seismic energy that needs to be dissipated by the
parent frame (E2<E1 in Figure 14b). But a closer
look at Figure 14b epitomizes the fact that there
is still a specific amount of energy that needs to
be dissipated by the parent frame. This specific
amount of dissipated energy would determine
whether the parent frame remains elastic or not.
So as demanded by the algorithms used in the
literature, if the parent frame needs to remain in
the elastic state (with no ductility mobilized) the
input energy should be reduced to that level so as
to cause only elastic stresses in the parent frame.
In other words, this means that dampers would
need to dissipate all the excess energy that might
cause inelastic excursions in the parent frame.
Now what could this requirement mean in
realistic terms? To answer this question, we use
the results obtained from the Chi-Chi earthquake
ground motion. The study mainly attempts to
qualitatively illustrate the amount of damping
required for a reduction of the input energy to a
desired level so that the frame remains elastic. In
order to satisfy this objective, the amount of
damping required to reduce the original elastic
spectra to an equivalent spectra is calculated, such
that the newly derived equivalent elastic spectra
has force amplitudes similar to a spectra of the
DISCUSSIONS ON REALISM OF
LINEARITY ASSUMPTION
In this section we intend to review the implica-
tions of the linearity assumption from a real world
implementation point of view. Most of the research
summarized in Section 3 investigated novel
techniques for arriving at an optimal distribution
of dampers and presented very useful methods;
but one common fact that could be observed in
majority of these methods is that most of the
techniques require the parent frame to be linearly
elastic during the seismic excitation. Also majority
of the techniques are formulated in the frequency
or state space domain where eigenvalues and ei-
genvectors determine the dynamic performance.
This implies that in order for the above recorded
techniques to be valid in a major seismic event,
the frame has to remain linearly elastic. The
other concern is that if in case the parent frame
becomes inelastic, there would be stability issues
(Cimellaro et al. 2009). This would make most of
the optimal positioning techniques presented in
literature invalid. The remaining part of this sec-
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