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significantly necessary to identify the pattern and
level of damage and to understand the modes of
failure of structures during severe seismic events.
In assessing the nonlinear seismic behaviour of
framework structures, pushover analysis has
provided an effective means for distinguishing
between good and bad seismic performance of
structures (Krawinker 1994).
It has been recognized that the displacement or
lateral drift performance of a multi-story building
can be a good measure of structural and non-
structural damage of the building under various
levels of earthquake motions (Moehle and Mahin
1991). The performance-based seismic design
provisions for multi-story buildings can be based
upon controlling story drifts to prescribed limit
states under different design levels of earthquakes.
Lateral drift design requires the consideration of
a proper distribution of the stiffness of all struc-
tural elements and, in a severe seismic event, also
the occurrence and redistribution of plasticity in
structure elements.
Numerous studies on structural optimization
in the seismic design of structures have been pub-
lished in the past two decades, including Cheng
and Botkin (1976), Feng et al. (1977), Bhatti and
Pister (1981), Balling et al. (1983), Cheng and
Truman (1982), Arora (1999). However, most of
these previous research efforts were concerned
with optimization through prescriptive-based
design concepts. Recently, Beck and his associates
(1998) developed an optimization methodology
for performance-based design of structural sys-
tems operating in an uncertain dynamic environ-
ment. Foley (2002) provided a comprehensive
literature review of current state-of-the-art
seismic performance-based design procedures
and presented a vision for the development of
performance-based design optimization. It has
been recognized that there is a pressing need for
developing optimized performance-based design
procedures for seismic engineering of structures
(Charney 2000; Foley 2002). Zou (2002), Chan
and Zou (2004), Zou and Chan (2001, 2005a,
b), Zou et al (2007a, b), Zou (2008), Wang et al
(2010) and Zou et al (2010) had been working at
the performance-based seismic design optimi-
zation of RC building structure and developed
an effective method for design optimization of
buildings subject to seismic elastic and inelastic
seismic drift performance criteria.
The traditional prescriptive design optimiza-
tion based on linear elastic techniques has been
researched for many years. One major drawback of
these elastic techniques is that it does not directly
address structural inelastic seismic responses
and thus cannot effectively deal with damage
loss due to structural and non-structural failure
during earthquakes. As a result, the long-term
risk and benefit implications cannot be assessed
using the traditional linear elastic design method.
In seismic performance-based design, the design
objective function may consist of two main parts:
initial construction cost and expected future failure
loss caused by earthquakes (SEAOC 1995; Foley
2002). The final design should be established
considering a good balance between the initial
structural cost and its loss expectation in the design
life period. Due to the fact that the life-cycle cost
involves the consideration of construction cost and
damage loss which are inherently conflicting, the
minimum life-cycle cost design can be viewed as a
multi-objective optimization problem. Given with
the initial conditions of a building project, it is,
in general, a relatively easy task to estimate the
construction cost of the building. However, the
estimation of the seismic damage to a building is
such a complex problem that it involves not only
engineering cost but also costs associated with
social, economic, political, cultural and ethical
aspects. A number of different damage loss models,
established by numerous researchers (Park and
Ang 1985; Gao and Bao 1985; Park et al. 1987;
Ang et al. 1997; Wen and Kang 1997, 2001), in-
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