Geology Reference
In-Depth Information
Maximum Peak Interstory Drifts (J4)
Hence, Milman and Chu (1994) proposed to
use the Ritz reduction method to calculate damp-
ing ratio.
Generally the structures are dominated by
the first
q
modes of vibration, consequently the
objective function can be written as
Buildings are usually planned by using the design
earthquakes for a particular site. Since the objec-
tive of installing dampers on buildings is to reduce
the interstory drifts, it may be interesting to in-
vestigate the optimal location of dampers for an
objective function which represents the maximum
of the peak drift of all story units which will be
minimized. For the system in Equation 5, for a
design earthquake ground acceleration
x t
q
∑
ψ ζ
J
=
(16)
i
i
2
j
=
1
0
( )
, the
where
q
indicates the first dominant modes,
ψ
i
is the scalar weighting factor for the i
th
mode.
J
2
objective function represents the weight average
damping ratios, which it is necessary to maximize,
to determine the optimal placement of passive
energy dissipation systems.
equation of motion can be expressed as
z
( )
t
=
(
A BG z
−
) ( )
t
+
E
x t
( )
(19)
0 0
−
( , )
,
n v
Equation 19 can be integrated for a particular
ground acceleration time-history, obtaining
x t
1
where
E
=
0
−
M m
0
1
Maximum Peak Absolute
Accelerations (J3)
i
( )
, from which peak interstory drift can be written
as
For particular type of buildings such as health care
facilities, control towers, etc., the goal of installing
dampers is to reduce the absolute accelerations
to reduce damage to mechanical equipments,
computers etc. Therefore it may be interesting
to investigate the optimal location of dampers
for an objective function which represents the
maximum of the peak absolute accelerations of
all story units, which will be minimized. Then the
objective function, representing the maximum of
all peak absolute accelerations, can be defined as
x
=
max
x t
( )
(20)
pi
i
t
Then the objective function, representing the
maximum of all peak interstory drifts, can be
defined as
{
}
J
=
J
=
max
x
, i=1,2,...,n
(21)
4
4
Dbe
pi
{
}
J
3
=
max
x
pi
i=1,2,...,n
,
(17)
INTEGER HEURISTIC
PROGRAMMING
where the maximum accelerations can be written as
Once the objective functions are defined in previ-
ous paragraph then the optimal location of energy
dissipation dampers needs be determined. Three
types of heuristic search algorithms can be used
in order to solve the nonlinear constrained opti-
mization problem:
x
=
max
x t
( )
(18)
pi
i
t
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