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predefined hazard level(s) is sufficient. A brief
review of existing literature on LCC optimization
of structures is provided in the following section.
The objective of this chapter is to emphasize the
importance of the following in LCC optimization:
The second item is critical to the evaluation of
LCC in that the repair cost (after an earthquake
event) is more directly related to the local behavior,
rather than the global. There is existing literature
on relating the global structural response to local
parameters (an example is predicting the damage
state of a vertical member based on the interstory
drift); however, it is not accurate to generalize
these relationships to structural configurations
other than that they are derived for. Therefore,
in order to accurately evaluate the LCC proper
response metrics need to be chosen.
As for the third item, the capacity of a structure
depends on various factors, most importantly on
the force resisting system employed in design.
The limit state values for a bearing wall system
will be significantly different from those for a
frame system. It is simpler to use generic limit
states, which also reduces computational demand;
however, accurate evaluation of the structural ca-
pacity is key to seismic design and it warrants full
consideration. In other words, structural capacity
has to be evaluated specifically for the considered
structural configuration.
Finally, for the fourth item, the sources of
uncertainty have to be defined clearly. The uncer-
tainty in exceedance probabilities of the structural
damage states is mainly governed by the vari-
ability in ground motion processes; nevertheless,
it is required to take into account the variability
in material properties, and other capacity related
parameters.
In the following, first the background informa-
tion on structural optimization that will allow the
reader to follow the rest of the chapter is provided.
Then a framework for LCC optimization of struc-
tures that includes the definition of seismic hazard,
evaluation of structural capacity and earthquake
demand, LCC model and optimization algorithm,
is proposed. Finally, the framework is applied to
an example RC structural frame.
1. Use of advanced analysis, which provides
the most rigorous assessment of structural
capacity and earthquake demand,
2. Evaluation of the structural capacity (that
has direct impact on the LCC) by taking
into account not only the global behavior
of the structure but also the local response,
such as reinforcement yielding and concrete
crushing,
3. Use of system-specific limit states (rather
than fixed value or generic limit states) to
define the structural capacity,
4. Consideration of all major sources of
uncertainty, from seismogenic source
characteristics to material properties and
structural modeling in calculating the limit
state exceedance probabilities.
The majority of existing work on structural op-
timization uses either elastic dynamic or nonlinear
static analysis for seismic performance assessment
of structures. In cases where inelasticity is mod-
eled, lumped plasticity models are adopted. The
first item in the list above is significant because
the oversimplification of the structural assess-
ment, even though the optimization framework is
robust and sound, might yield unrealistic results.
This chapter highlights the importance of utiliz-
ing distributed inelasticity approach using which
structural capacity and earthquake demand are
evaluated through nonlinear pushover analysis and
inelastic dynamic time history analysis, respec-
tively. Widespread use of optimization tools for
seismic design of structures can only be achieved
by having practical and reliable approaches that
can predict the structural performance with rea-
sonable accuracy.
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