Metaheuristic Optimization in Seismic Structural Design and Inspection Scheduling of Buildings - Structural Seismic Design Optimization and Earthquake Engineering - page 158

reinforcement quantities and initial costs given
in Table 3, it can be said that compared to D descr
the D PBD1 requires 13% and 18% more concrete
for beams and columns, respectively; while it
requires 21% and 32% more longitudinal steel
reinforcement for the beams and the columns,
respectively. On the other hand, D PBD2 requires 39%
and 43% more concrete for beams and columns,
respectively; while it requires 72% and 59% more
longitudinal steel reinforcement for the beams
and the columns, respectively. Furthermore, with
reference to the RC frame initial cost, where the
cost of the plates is also included, it can be said
that D PBD 1 is by 8% more expensive compared to
D descr ; while D PBD2 is by 19% more expensive. On
the other hand though, with reference to the initial
cost, the three designs vary by 1% and 3% only.

elastic response. Thus, the seismic design loads
are reduced by the behavior factor q. According
to EC8, the nonlinear deformation of the structure
caused by the seismic load is equal to q times the
corresponding deformation of the linear analysis.
In accordance to the previous section, the three
designs are also considered for the comparative
study with reference to the life-cycle cost and the
impact of the various sources of randomness of
the LCCA procedure. The median values of the
life-cycle cost of the three designs are shown in
Tables 4 to 7 corresponding to the deterministic and
probabilistic formulations, while the histograms of
Figures 2 and 3 show the probabilistic distribution
of the life-cycle cost values for the deterministic
and probabilistic formulations implemented into
the Multi-Stripe Dynamic Analysis (MSDA) for
the three different designs along with the 90%
confidence bounds.
For the eight-story symmetric test example,
comparing the histograms of Figures 2(a) and
2(b) it can be noticed that the width of the 90%
confidence bounds of the life-cycle cost values
of design D PBD2 , is much narrower compared to
the other two confidence bounds both for the
deterministic and probabilistic formulations.
Furthermore, it can be said that with reference to
the mean value of the life-cycle cost (as shown
in Table 4) D PBD1 is by 18% less expensive com-
pared to D descr ; while D PBD2 is by 52% less expen-
sive when the deterministic formulation is imple-
mented for 60 records. On the other hand, as
shown in Table 5, it can be said that design D PBD1
is by 5% less expensive compared to D descr ; while

Prescriptive vs Performance-
Based Design

The difference between EC8 and PBD formula-
tions is demonstrated in terms of the life-cycle
cost analysis of selected designs. The EC8 for-
mulation implements a linear analysis procedure
where the behavioral factor q is used to take into
account the inelastic behavior of the structure.
Most of the contemporary seismic design codes
rely on the ability of the structure to absorb energy
through inelastic deformation using the reduction
or behavior factor q. The capacity of a structure
to resist seismic actions in the nonlinear range
generally permits the design seismic loads to be
smaller than the loads corresponding to a linear

Table 4. Eight-story test example: median value of the life-cycle cost (10 3 MU) for the four cases and
the three designs for the deterministic formulation

Number of records

Design

10 20 40 60

D descr 3.13E+03 2.73E+03 2.61E+03 2.72E+03

D PBD1 2.87E+03 2.02E+03 1.83E+03 2.30E+03

D PBD2 1.91E+03 1.82E+03 1.79E+03 1.79E+03