Optimal Placement of Controller for Seismic Structures - Design Optimization of Active and Passive Structural Control Systems - page 17

The base shear coefficient normalized with
respect to the total weight of the building is shown
in Figure 13, comparing the uncontrolled structure
with the uniformly distributed dampers and the
two optimal distributions obtained using the
maximum interstory drift ( J4 ) and the maximum
absolute acceleration ( J3 ) performance indices.
A reduction of the base shear is observed for all
the earthquake records that is slightly improved
when also the optimal damper distributions are
considered.
When considering a 10 story building there is
no difference among SS, WOBI and ESPS when
using the maximum drift (J4) or the maximum
absolute acceleration (J3) as index when El Cen-
tro earthquake is used as shown in Figure 14. In
this particular case using J3 or J4 does not bring
to substantial improvements in the performance
of the building.
This conclusion can be generalized, because
the distribution is independent from the earthquake
record selected, as shown in Figure 15, where
there is almost no difference among SS, WOBI
and ESPS when using the maximum drift (J4) as
index, while small differences can be found when
index J3 is adopted as shown in Figure 16.
Figure 17 shows that the algorithm that
maximize the energy dissipated by the viscous

dampers (J1) is the ESPS, regardless the earth-
quake record selected, however when comparing
the maximum interstory drift obtained with ESPS,
the performance of the obtained damper distribu-
tion is worst (Figure 17b), therefore this bring to
the conclusion that the objective function J1 might
not be a good candidate to find a practical damp-
er distribution that is able to reduce the damage
in the building.

Thirty Story Building

In order to show the applicability of the method-
ology for tall buildings, a 2D model of 30-story
shear building has been considered for determin-
ing the optimal locations of viscous dampers, by
optimizing the objective functions described in
previous paragraph. The properties of the lateral
story stiffness are summarized below

k = 150 10 ×

3

kN m i = 1 ,  , 4 k = 125 10 ×

3

kN m i = 5 ,  , 10

i i

3 3

k = 100 10 × kN m i = 11 ,  , 14 k = × 85 10 kN m i = 15 ,  , 18

i i

k = 72 5 10 . ×

3

kN m i = 19 ,  , 22 k = × 62 10

3

kN m i = 23 ,  , 26

i i

3

k = × 53 10 kN m i = 27 ,  , 30

i

while the story mass is assumed constant and equal
to 51.2 kN•sec 2 /m . The first natural frequency is
ω 0 =2.36 rad/sec that correspond to a period of
T=2.65sec and it is assumed a damping ratio equal
to 2 % on the first and the second mode. Dynamic
properties of the building, including the modal
damping ratio and the mass participation factor
are given in Table 6.
The story height considered is h = 3.0 m , the
same in all levels, while the total weight of the
building is 15063.01 kN . The structural response
in term of interstory drifts and absolute accelera-
tions for the uncontrolled structures (unbraced)
are shown in Table 7.
In the first step, a viscous damper was designed
and used such that the fundamental mode has 25%
damping ratio, when one damper is placed at
every story unit (uniform distribution).

Table 5. Dynamic properties of the unbraced ten
story building

Story ω [rad/s] T [s] ζ [%] ϵ [%]

1 22.64 0.277 5.00 80.29

2 56.42 0.111 4.08 11.16

3 91.72 0.069 5.00 3.99

4 127.21 0.049 6.28 1.97

5 151.45 0.041 7.22 1.05

6 182.02 0.035 8.46 0.55

7 208.21 0.030 9.54 0.27

8 244.64 0.026 11.07 0.26

9 280.94 0.022 12.61 0.23

10 323.38 0.019 14.42 0.21