Optimal Seismic Performance- Based Design of Reinforced Concrete Buildings - Structural Seismic Design Optimization and Earthquake Engineering - page 228

reinforcement ratios of beams are largely increased
from the first to the eighth floors from Point C 0 to
Point C* (i.e., an increase of 17%~47%), while
there is no change of steel reinforcement ratios
in most columns due to no occurrence of plastic
hinges. Such an increase indicates that steel rein-
forcement has a significant effect on improving
inelastic drift performance and further reducing
damage loss.
Figure 7(c) presents the results of the inter-
story drift ratios at Points C 0 and C*, respectively.
It is found that all the inelastic inter-story drift
constraints are satisfied corresponding to either
Point C 0 or Point C*. In the optimal solution (i.e.,
corresponding to Point C 0 ) of the single objective
design optimization, the inter-story inelastic drift
constraints from the second to the seventh floors
are close to the limiting ratio of 1%. However, in
the multi-objective design optimization (i.e., Point
C*), all final drift constraints are not necessarily
found to be close to the limiting ratio 1%. This
is due to the fact that steel ratios of the structure
members are further enhanced in order to meet the
best balance between the initial structure cost and
damage loss. Such a result seems to indicate that
for the multi-objective design optimization, the
lateral load resisting system can be automatically
improved by the OC procedure to seek the best
balance so that lateral drift constraints are satis-
fied simultaneously with the least life-cycle cost.

found necessary to ensure a smooth and steady
convergence of the inelastic drift design process.
It has been demonstrated that steel reinforce-
ment plays a significant role in controlling the
lateral drift beyond first yielding and in providing
ductility to an RC building framework. It is also
demonstrated that the OC design method is able
to attain automatically and gradually the optimal
performance-based inter-story drift design. At op-
timum, a uniform lateral drift or ductility demand
over all stories of the building with the minimum
cost is achieved, thus preventing the occurrence
of soft story mechanisms in such structures.
The optimization technique developed for the
nonlinear multi-objective design of inelastic drift
performance of RC frameworks under pushover
loadings provides a very effective way to simul-
taneously optimize the structural life-cycle cost
while satisfying all drift performance design cri-
teria. A multi-objective optimization algorithm,
the ε-constraint method, has been effectively
applied to handle the conflicts between the initial
structure cost and damage loss by producing a
Pareto optimal set, from which a decision maker
can directly select the best compromise solution.
It is believed that the single- and multi-
objective optimization methodology provides a
powerful computer-based technique for seismic
performance-based design of multi-story RC
building structures. The proposed optimization
methodology provides a good basis for more
comprehensive performance-based optimization
of structures as multiple levels of performance
criteria and design objectives are to be considered.

5. CONCLUSION

Using the principle of virtual work, both the elastic
spectral drift constraints and the nonlinear push-
over inelastic drift constraints have been explicitly
formulated in terms of the design variables. Rapid
and steady convergence for elastic drift optimi-
zation has been found. In contrast, the inelastic
optimal design process converges quite slowly
but steadily. The restrictive move limit imposed
on the steel reinforcement design variables is

ACKNOWLEDGMENT

The author would acknowledge the thoughtful
suggestions and support from Prof. C.M. Chan of
the Department of Civil Engineering, the Hong
Kong University of Science and Technology.