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the life cycle costs. Zou et al. (2007) used the
method of virtual work to achieve an explicit
formulation for multi-objective optimization of
RC frames. Then, optimality criteria method was
used to minimize the initial material cost and the
expected damage loss in a Pareto optimal sense.
The method was formulated in two stages: first
elastic response spectrum analysis was performed
where the cross-sectional dimensions were consid-
ered as the only design variables, second section
sizes were kept constant and the reinforcement
ratio was taken as the design variable for the
static pushover analysis through which inelastic
drift responses were calculated.
Although, LCC was not considered in the fol-
lowing studies, these studies are mentioned here
because they are related to methods or derivations
in this chapter by considering uncertainty, multiple
hazard levels or advanced structural analysis to
obtain the seismic demand on structures. In Liu
et al. (2005) conflicting objectives were defined
as the initial material cost (including the cost due
to design complexity as a function of the number
of different structural shapes) and the seismic
performance. Two hazard levels were used and
the performance criterion was selected as the
maximum interstory drift. Structural assessment
was conducted using static pushover analysis
determined from seismic code provisions. GA
were employed to solve the optimization prob-
lem. Fragiadakis et al. (2006a) used evolutionary
strategies for optimal PBSD of steel structures.
Minimization of cost subjected to constraints on
interstory drift was targeted. Both inelastic static
and inelastic dynamic analysis were employed.
Discrete beam and column sections were selected
as design variables. 10 earthquake records were
used to represent each hazard level and mean
structural response was taken as the performance
measure. Uncertainty associated with structural
modeling was also taken into account. Lagaros et
al. (2006) evaluated modal, elastic and inelastic
dynamic time history analysis in an optimization
framework taking the European seismic design
code as a basis. Steel structures were considered
and evolutionary strategies were used to solve the
optimization problem. A fiber-based finite element
modeling approach was adopted. Either 10 natural
or 5 artificial records were used to represent the
hazard. Material weight was selected as the design
objective. It was observed that lighter structures
could be obtained when inelastic dynamic time
history analysis (instead of elastic dynamic time
history or modal analysis) and natural records
(instead of artificial records that were compatible
with a certain design spectrum) were used. Fragia-
dakis and Papadrakakis (2008) studied the optimal
design of RC structures. Both deterministic and
reliability-based approaches were evaluated and
the latter was found to provide more economical
solutions as well as more flexibility to designer.
The total cost of the structure was taken as the
objective function and compliance with Euro-
pean design codes was applied as a condition.
Evolutionary strategies were used to solve the
optimization problem. Three hazard levels were
considered. To reduce the computational time,
fiber-based beam-column elements were used only
at the member ends and inelastic dynamic analysis
was performed only if non-seismic checks per-
formed through a linear elastic analysis were met.
LCC oriented seismic design optimization of
structures is a relatively new subject, a review of
existing literature, as provided above, indicates
that there is still need for further research due to
following: (1) only a limited number of studies
utilized advanced computational tools, structural
performance assessment was usually performed
using code-based formulations or elastic analysis,
simplified modeling techniques were adopted
whenever inelastic analysis was conducted; (2)
existing studies overwhelmingly focused on the
optimization of steel structures due to well defined
design variables (i.e. section types) and availabil-
ity of structural modeling tools; (3) most of the
research effort was devoted to the development
of optimization methods; the real engineering
problem to be solved remained faint.
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