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minimize the seismic isolated building top story
displacement and that of the base isolation system
using a multi-objective optimization solution.
Therefore, the far and near fault effects are implic-
itly considered in the earthquake acceleration time
history records selected for dynamic analysis of
the building. So, explicitly not much attention is
given to this behavior of the base isolated building,
which is needed in real design practice. Generally,
many different systems of isolators are proposed
and patented each year. In this investigation,
elastomeric-base isolation systems are studied for
which some brief descriptions are provided in the
following (Pourzeynali & Zarif, 2008).
respect to the ground. The stiffness and damping
of LRB systems are selected to provide the spe-
cific values of the two parameters namely the
isolation time-period (
T
b
) and damping ratio
ξ
( )
defined as (Matsagar & Jangid, 2003):
m
k
T
=2
π
s
(3)
b
b
c
m
ξ
=
2
b
(4)
b
ω
s
b
where
m
s
is the total mass of the building and
base slab, defined in Equation (9); and
ω
Laminated Rubber Bearings
=
2 /
π
T
b
is the isolator frequency.
The laminated rubber bearing (LRB) systems (or
low-damping bearings) are composed of the rubber
plates and steel shims built in a single unit. The
internal steel plates reduce the lateral bulging of
the bearings and increase the vertical stiffness
(Naeim & Kelly, 1999). Low-damping bearings
with low horizontal stiffness shift the fundamental
time period of the structure to avoid resonance
with the excitations. The damping constant of the
system varies considerably with the strain of the
bearings. Based on test results of Tarics (1984)
the damping ratio depends on the strain level of
the bearing. LRB isolators have been extensively
tested at the University of California and found
suitable for many applications (Kelly 1986). The
main feature of the LRB systems is the parallel
action of linear spring and damping (Matsagar &
Jangid, 2003). The restoring force developed in
the bearing,
F
b
, is given by (Matsagar & Jangid,
2003):
Lead-Rubber Bearings
The lead-rubber bearings were invented in New
Zealand in 1975 and have been used extensively
in New Zealand, Japan, and the United States
(Naeim & Kelly, 1999). These systems are gener-
ally referred as N-Z systems. N-Z bearings are
similar to the LRB systems, but in order to provide
an additional means of energy dissipation and
initial rigidity against minor earthquakes and
winds, a central lead-core system is used (Skinner
et al., 1975; Robinson, 1982). This system es-
sentially behaves as hysteretic damping device
(Kelly et al. 1972, 1977, and 1986; Skinner et al.
1975; Datta 1996). The force-deformation be-
havior of the N-Z bearings is generally repre-
sented by non-linear characteristics (see Figure
1). In the present study, the bilinear hysteretic
model of these isolators is used (Matsagar &
Jangid, 2004). The bilinear hysteretic loop, as
shown in Figure 1, is characterized by three pa-
rameters namely: (1) yield strength
F
y
, (2) elastic
and plastic stiffness values
k
b1
and
k
b2
, respec-
tively, and (3) yield displacement
ν
y
(Matsagar &
Jangid, 2004). The restoring force developed in
F
=
c v
+
k v
(2)
b
b b
b b
where
c
b
and
k
b
are damping and stiffness of LRB
systems, respectively;
υ
and
are the relative
displacement and velocity of the base slab with
υ
b
b
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