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frame under the MCE (Figure 5(b)). The maximum
peak accelerations of the bare frame (at the roof)
are reduced by an average of 30% under the DBE
and 14% under the MCE with the added dampers
(peak occurring at the first floor).
In terms of overall distribution, the uniform
and stiffness-proportional schemes are the most
effective at reducing accelerations at floors 5-10.
For example, under the MCE at the roof, the
uniform scheme achieves a 10% reduction and
the stiffness proportional approach a 14% reduc-
tion from the nearest of the advanced methods,
SSSA. This may be attributed to the standard
methods apportioning large damping at the base
and roof of the building.
Figure 6 presents residual interstory drifts.
The building with added dampers experiences
negligible residual interstory drifts under the DBE,
confirming that the addition of dampers has in all
cases resulted in linear building performance. This
compares favourably with the large residual drifts
in the bare frame, 0.42% at floor 6 (Figure 6(a)).
McCormick et al. (2008) recommend a permis-
sible residual drift limit of less than 0.5%, based
on realistic repair costs and human tolerance of
drifts. The bare frame under the MCE (Figure
6(b)) achieves peak residual drifts near 0.75%;
these would render the building economically
unsalvageable after the earthquake. However, the
addition of viscous dampers reduces the residual
drifts to less than 0.15% for the standard placement
methods and less than 0.05% for the advanced
placement methods.
Finally, we offer some comments on the ease
of implementation of the schemes, based on
adherence to the damper placement methods'
procedures as outlined in literature. The uniform
and stiffness proportional methods are the simplest
to apply while still achieving the desired drift
limit. Although requiring the use of only three
time histories, the SSSA method is the most time
consuming because it requires three time domain
analyses at each of the twenty steps used in our
analysis (i.e. a total of sixty linear time history
analyses). The Takewaki technique requires sig-
nificant up-front effort in developing the neces-
sary programming script; once this is achieved
the method is reasonably efficient, requiring only
minimal inputs and operating independently from
ground motions. Selection of the correct step-size
greatly influences convergence time. Of the three
optimisation techniques, the Lavan technique is
the easiest to implement from scratch. Although it
does depend on an iterative analysis with specific
ground motions, this can be conducted with the
same tools used for the SSSA method and requires
fewer ground motions and steps; for our structures,
convergence occurred in less than 10 iterations.
While controlling the total added damping per-
mits a fair comparison of the placement methods,
the advanced placement schemes could achieve
a reduced damping while still meeting the drift
performance objectives. Further research is needed
to conduct thorough comparisons of the existing
damper placement methods that consider both the
optimal placement of dampers and reduction of
total damping to meet specific performance crite-
ria. In addition, investigation of a wider range of
effective damping ratios and structural properties
would provide additional insight into the efficiency
and robustness of the damper placement methods.
CONCLUSION
The effectiveness and usability of five damper
placement methods has been evaluated by using
them to achieve response reductions in ten-story,
moment-resisting frames. It was shown that
even the simplest methods can provide substan-
tial improvements in building performance, as
demonstrated by the median responses to a suite
of 20 ground motions. In our example, all the
schemes considered were able to meet the de-
sign drift limits, reduce floor accelerations and
eliminate non-linearity at the DBE, resulting in
zero residual drift.
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