Geology Reference
In-Depth Information
Figure 1. Bilinear hysteretic model of the lead rubber bearings used in this study
Structural Model of the
Base-Isolated Building
these isolation bearings can also be represented
by Equation (1) by replacing the
k
b
by appropriate
k
b1
and
k
b2
in elastic and plastic phases, respec-
tively. In this study, the values of
ν
y
and
γ
=
k
As shown in Figure 2, to study the performance
of base isolation systems, the mathematical model
of an
N
-story base-isolated building structure is
idealized as a 2-D frame.
For this 2-D idealized frame, the governing
equations of motion are obtained by considering
the equilibrium of forces at the location of each
degree of freedom, in which for a fixed base
building (without any isolation system) can be
written as (Naeim & Kelly, 1999):
b
2
k
1
are taken about 2.50 cm and 0.142, respectively
(Matsagar & Jangid, 2004; Rodellar & Manosa,
2003).
b
High-Damping Natural Rubber
Systems (HDNR)
High damping rubber bearings are another cat-
egory of elastomeric bearings. These bearings
are made from a blend of filled natural rubber.
The bearings are designed with flange type end
plates to permit bolted structure and foundation
connections. The natural rubber compound with
enough inherent damping is developed in 1982
by the Malaysian Rubber Producers' Research
Association (MRPRA) of the United Kingdom
(Derham et al. 1985). The damping in this type
of bearings is neither viscous nor hysteretic, but
somewhat in between (Kelly & Naeim 1999).
M X
+
C X
+
K X
= −
M R x
g
(5)
{ }
{ }
{ }
{ }
where
M
,
C
and
K
are the
n
×
mass, damp-
ing and stiffness matrices of the main structure,
respectively;
{
X
is the
n
×1
displacement vec-
tor of the building with respect to the ground;
{
R
is the
n
×1
influence vector with unit ele-
ments in the direction of the earthquake motion;
x
g
is the longitudinal acceleration of earthquake,
acting on base of the main structure; and dot
Search WWH ::
Custom Search