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Figure 7. Base shear comparison with uniformly braced structure
when the maximum acceleration (
J3
) is used as
objective function (Figure 10).
For both indices instead different damper
distributions can be obtained using different
earthquake records that can be caused by the dif-
ferent frequency content of each earthquake
(Figure 4). Hence it has been found that the op-
timal distributions obtained with
J3
and
J4
as
objective functions strongly depend on the nature
of the earthquake record at the site. Hence, the
optimal damper distribution for seismic excited
buildings can be obtained by minimizing
J4
using
the design earthquake of the particular site.
The index that maximizes the energy dissi-
pated by the viscous dampers (
J1
) tends to locate
dampers where the velocity is higher and this
usually happens in the upper floors. Therefore
this performance index moves the dampers in the
uppers floors. Instead the index that maximizes
the damping ratio (
J2
) is not very sensitive and it
does not bring to realistic distributions.
In summary, it has been observed that when the
DOFs of the building are reduced such as in the 6
story building, then SS, WOBI and ESPS search
methods bring to the same damper distribution
for the various objective functions considered.
Ten Story Building
A ten story shear building with story mass of
m
i
=
20786
and lateral stiffness of
kg
k
687 1 10
.
5
kN m i
1
,
,
2
=
×
=
i
5
k
=
540 1 10
.
×
kN m i
=
3
,
,
4
i
5
k
=
421 7
.
×
10
kN
m i
=
5
,
,
6
i
5
k
=
286 6 10
.
×
kN m i
=
7
,
,
8
i
5
k
=
164 5 10
.
×
kN m i
=
9
,
,
10
i
and it has been considered for determining the
optimal locations of viscous dampers, by opti-
mizing the objective functions described in the
previous paragraph. The natural periods of the
first three modes of the building are:
T=0.66,
0.22, 0.13, 0.10, 0.08
and
0.07 sec
, and it is as-
sumed a damping ratio of 5% on the first and the
third mode. Dynamic properties of the building,
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