Optimal Placement of Viscous Dampers for Seismic Building Design - Design Optimization of Active and Passive Structural Control Systems - page 42

equipment. Residual interstory drift indicates the
permanent damage to the structural members and
feasibility of economic repair of the building after
the earthquake. Residual drifts were determined
by continuing analyses for at least 20 seconds
beyond the end of the ground motion record, until
the structure was stationary. The residual drifts
were then calculated as the difference between
the final displacements of adjacent floors.

with little disparity between the three schemes.
Drifts in millimetres particularly highlight the
small differences between the methods.
The peak interstory drifts for the regular build-
ing are analysed further in Figure 4. The standard
deviations of drift under the DBE are similar
amongst the damper placement methods at each
floor (an average of 0.24% maximum standard
deviation, with all methods within 8% of the
average maximum standard deviation) and great-
est for the bare frame (0.40% and 0.84% maximum
standard deviations under the DBE and MCE,
respectively).
A larger dispersion of drifts occurs in the
damped frame under the MCE, with an average
of 0.39% maximum standard deviation, with all
methods within 11% of the average maximum
standard deviation. The dispersion is largest in
the internal floors (2-7) corresponding to the larg-
est peak interstory drifts in the frame.
Figure 5 compares the placement techniques
in terms of absolute accelerations. For the DBE
(Figure 5(a)), all the damper placement schemes
reduce the absolute accelerations of the bare frame
at all floors except the 1 st floor. The maximum
peak accelerations in the damped frames occur
at the first floor and are within a narrow range of
6.17 m/s 2 to 6.30 m/s 2 . Similar distributions and
narrow maximum peak acceleration range (9.25
m/s 2 to 9.46 m/s 2 ) are exhibited in the damped

Performance of Regular Building

The results of the regular building's performance
are presented in Figures 3-6. Figure 3 compares
the added damper placement schemes in terms
of the median peak interstory drift distributions
under both the DBE and the MCE. The drift design
objectives of the bare frame under the DBE (2.2%)
and of the frame with dampers (1.1%) are noted
with solid lines. Under the DBE (Figure 3(a)), all
the damper schemes achieve less than 1.10% peak
interstory drift, thereby meeting the DBE design
objective and reducing the bare frame drifts by
more than half. Both the Takewaki and Lavan
schemes result in peak interstory drifts best ap-
proaching a desirable, uniform drift distribution.
The stiffness-proportional and uniform distribu-
tions produce the least uniform drift profiles, with
the uniform scheme overdamping the upper floors
and the stiffness-proportional approach overdamp-
ing the first floor such that floors three and four
are not effectively damped. Figure 3(b) compares
the distributions under the MCE. The MCE drift
distributions mirror the DBE results, and display a
50% increase in the drifts of the damped frame, as
to be expected for a predominantly linear building
response. Under the MCE, the design objective
for added dampers (1.65% interstory drift) is met
by all of the damper placement schemes.
Table 4 presents the maximum interstory drifts
of all floors. The uniform and stiffness-propor-
tional damper schemes produce very similar
maximum interstory drifts, while the three ad-
vanced techniques all result in lower peak drifts,

Table 4. Regular building - Maximum of peak
interstory drifts

DBE Ground
Motion Suite

MCE Ground
Motion Suite

% mm % mm

No Dampers 2.27 72.5 3.28 104.9

Uniform 1.08 34.7 1.64 52.6

Stiffness
Proportional

1.07 34.3 1.62 52.0

SSSA 0.94 30.1 1.41 45.2

Takewaki 0.90 28.7 1.34 43.0

Lavan 0.87 27.7 1.30 41.6