Optimal Seismic Performance- Based Design of Reinforced Concrete Buildings - Structural Seismic Design Optimization and Earthquake Engineering - page 224

Figure 5. Design history of structural cost

16% in the steel cost from the initial US$1693 to
US$1978.
Figure 6 presents the optimal steel reinforce-
ment ratios for Cases A and B. In the elastic phase,
the member sizes are increased after the elastic
design optimization since the initial design is
found to be infeasible. The starting strength-based
design, in the second inelastic design phase, is also
found to be infeasible in terms of the assumed
allowable inter-story drift limit. After the inelas-
tic design optimization, the steel reinforcement
ratios of the beams greatly increase particularly
in the lower levels of the structure, while those
of columns are found with little changes for Case
B. Reasons lie on that the columns of Case B are
found to be mainly controlled by the minimum
strength requirements with the final steel ratios
being set to the initial strength based limits,
whilst the beams are governed by the inelastic
inter-story drift performance requirements with
the final steel ratios being larger than the initial
strength based limits.

The initial and final inter-story drift ratios are
shown in Figure 7(a) for Case A and Figure 7(b)
for Case B. The initial inter-story drift constraints
at the second through the eighth floors are found
to violate substantially the allowable inter-story
drift ratio limit of 1/100 for both cases, resulting
in the occurrence of the weak stories on the these
floor levels of the building. However, these push-
over inter-story drift constraints are found to be
close to and within the allowable values after the
optimization, indicating that a rather uniform
inter-story drift distribution over the height of the
building has been achieved and the occurrence of
weak story has been prevented at the final per-
formance point.
Figure 8(a) includes a table showing the num-
ber of plastic hinges at three different performance
states, i.e., Immediate Occupancy (IO), Life
Safety (LS) and Collapse Prevention (CP) for
Case B. Figures 8(b)-(c) show the initial and final
plastic hinge distributions under the pushover
loading at the performance point of the structure.