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limited to 20% of the floor weight. The maximum
amplifying lever ratio used in this study was as-
sumed to be 4. Distribution of active controlled
devices in the structure for various “active” floors
number is shown in Table 1. Following this table,
when the number of “active” floors is low, con-
necting the devices to lever arms decreases the
number of dampers by three times and more. The
benefit decreases to about 2 times as the number
of active floors increases.
At the next stage the earlier defined efficiency
criteria (Equations 2, 3, 4, 5, 6, and 7) were cal-
culated. Figure 4 demonstrates efficiency of
control systems with various numbers of “active”
floors in reduction of structural responses to the
white noise ground motion compared to that
obtained in the case when all floors are active. As
it follows from the figure and from Table 1, when
control devices are connected to Chevron braces,
if half of the floors in the structure are active (23
devices are used), it is possible to achieve an af-
fect of 70 - 85%, compared with that obtained by
a control system with optimally distributed damp-
ers located at all floors (37 devices). When the
control devices are connected to lever arms, the
same effect may be achieved using just 11 de-
vices.
A similar effect was observed when the struc-
ture was subjected to natural ground motions. The
following natural earthquake records, scaled to
PGA = 0⋅3 g, were used: El Centro (1940), Kobe
(1995) and Hachinohe (1968).
Structural response to these earthquakes was
obtained for the following four cases:
•
Case 4:
Structure with a control system in-
cluding a limited set of optimally distribut-
ed dampers, located at
m
active floors and
connected to lever arms.
It was assumed that in the frame of this study
the number of active floors,
m
is equal to 8. This
number of active floors allows an economical solu-
tion yielding according to the selected efficiency
criteria about 70 - 85% of the effect that may be
achieved by an optimal set of active controlled
devices located at all floors (see Figure 4). Fol-
lowing Table 1, the optimal solution requires 21
devices connected to Chevron braces or 9 devices
connected to lever arms.
Peak floor displacements in the structure under
the artificial and natural earthquake records for
the four study cases specified above are shown in
Figure 5. As it follows from this figure, reduction
in peak values of floor displacements under the
natural earthquakes were very significant. Using
amplifiers allowed reduction of control devices
number to 9 and resulted in an effect that was
equivalent to that obtained by 21 devices con-
nected to Chevron braces.
Peak values of roof accelerations in the struc-
ture are presented in Table 2. Following this table,
adding active control devices at all floors (case
2) significantly decreases the peak roof accelera-
tions, compared to the uncontrolled structure (case
1). For the limited set of active control devices
(case 3) the decrease in peak roof accelerations
was less effective than for case 2.
Roof acceleration time histories are shown in
Figure 6. As it follows from this figure, using an
optimal set of active controlled devices yields a
significant reduction in peak roof accelerations
of the structure under all ground motions that
were used in the study. Like in the case of peak
displacements, also roof accelerations for cases
3 and 4 were equivalent. It proves that using lever
arms as amplifiers for connection of active con-
trolled devices (Case 4) yields the same reduction
in structural response like an optimal limited set
•
Case 1:
Structure without dampers;
•
Case 2:
Structure with a control system
including optimally distributed damp-
ers, located at all floors and connected to
Chevron braces;
•
Case 3:
Structure with a control system in-
cluding a limited set of optimally distribut-
ed dampers, located at
m
active floors and
connected to Chevron braces;
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