Optimal Performance- Based Seismic Design - Structural Seismic Design Optimization and Earthquake Engineering - page 176

analysis does. Moharrami and Alavinasab (2006)
proposed a method for structural optimization
under equivalent static and pseudo-dynamic
earthquake loading. In their method, the effect of
change of structural components on the amplitude
of equivalent static loading (because of change in
natural period of the structure) was accounted for.
In this way, they could end up to a solution that
had maximum ductility leading to minimum lateral
earthquake loads and consequently lowest cost.
A different approach to seismic-related op-
timization was also followed in seismic design,
by considering the uncertainties that encounter
in demand and capacity assessment. This topic
attracted considerable research works in differ-
ent branches. Some researchers considered the
uncertainties involved in the response and per-
formance prediction of a structure during its life.
This type of problem formulation that is called
life-cycle design optimization is a more general
aspect of optimal design, and may be considered
as an overall performance-based design optimiza-
tion. The optimization of the structural system on
life-cycle performance has to consider the initial
cost of construction of a building, vulnerability
of damage to structural components, its expected
costs of preventive maintenance, the expected
costs of inspection, the estimated costs of repair or
rehabilitation, and predicted costs of consequences
of failure. This in turn, requires some deep study
on risk-related engineering applications including
studies about risk analysis on system survival and
possibilities of partial or total collapse of a structure
and corresponding damage assessment. It is also
necessary to have a highly efficient and robust
algorithm to estimate the deformation capacity
of the structure and evaluate the damage to the
structure for given deformation. To that end, some
vulnerability and damage functions have to be
defined in monetary terms that take into account
not only the damage and rehabilitation-related
costs, but also the cost of social consequences of
structural collapse related to human life.

Since the goal of this chapter is to promote
the readers in particular young researchers and
practicing engineers to become acquainted with
practical performance-based design optimization,
and on the other hand, from the practical point of
view the life-cycle design optimization requires
development of quantitative definitions for quali-
tative subjects that are not yet well documented,
this second type of performance-based design,
despite its generality, is not covered in this chapter.
However, for those readers who are interested in
having more information in this field, among many
others, the papers by Frangopol (2011), Fragia-
dakis and Lagaros (2011), Lagaros et al (2008),
Jalayer and Cornell (2009), Cornell(2008), and
Esteva et al. (2010) are suggested to start with.
With the promotion of deterministic perfor-
mance-based design philosophy, some researchers
in the field of structural optimization focused their
attention to various aspects of this new subject
with different approaches to the problem. Since
optimal performance-based design is the main
subject of this chapter, some selected research
works in the field will be reviewed in more detail
in the forthcoming sections.
When we seek the optimum performance-based
seismic design (OPBSD), we need to know: how
to formulate our optimization problem, what are
the prerequisites of the problem formulation,
how to choose the design variables and how to
choose the optimization algorithm to solve it. In
this chapter, all these items will be discussed.
The prerequisites of the OPBSD will be briefly
explained to enable the reader write his own com-
puter program for his especial type of structure and
material properties. Special attention will be paid
to the sensitivity analysis that is a fundamental
tool for classical optimization algorithms. Two
types of formulations of sensitivity analysis for
2D steel and reinforced concrete structures will be
discussed. The differences between the sensitivity
analyses will be presented by some samples from
the literature.