Geology Reference
In-Depth Information
Based on the prescriptive seismic design for-
mulation, both buildings have been designed for
minimum initial cost following an optimization
strategy proposed by Mitropoulou
et al.
(2010).
In particular, for the solution of the single objec-
tive optimization problem formulated as shown
in Eq. (4) the EA(μ + λ) optimization scheme is
employed (Lagaros et al. 2004) with ten parent
and offspring (μ=λ=10) design vectors for both
test examples. On the other hand, the second op-
timization problem is formulated as a two-criteria
design optimization problem, as presented in Eq.
(5) where the initial construction cost C
IN
and the
life-cycle cost C
LS
are the two objectives both to
be minimized, while for solving the problem the
NSES-II(100+100) optimization scheme was
employed.
Solving the optimization problem of Eq. (4)
results to a single design denoted as D
descr
corre-
sponding to the prescriptive design procedure. On
the other hand, solving the optimization problem of
Eq. (5) results to a group of designs that define the
Pareto curve. In order to compare the behavior of
the different designs of the Pareto front curve two
characteristic designs were selected, correspond-
ing to the PBD optimum designs, which they are
denoted as D
PBD1
obtained from the region where
the initial cost is the dominant criterion and D
PBD2
obtained from the region where the life-cycle cost
is the dominant criterion. The steel and concrete
quantities for the columns and the beams along
with the RC frame cost and total initial cost, for
the three optimum designs, are presented in Tables
2 and 3 corresponding to the designs of the eight-
story and five-story test example, respectively.
For the eight-story symmetric test example,
as shown in Table 2, it can be said that compared
to D
descr
the D
PBD1
requires 9% more concrete both
for beams and columns while it requires 22% and
31% more longitudinal steel reinforcement for
the beams and the columns, respectively. On the
other hand, D
PBD2
requires 37% and 30% more
concrete for beams and columns, respectively;
while it requires 70% and 56% 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
PBD1
is by
10% more expensive compared to D
descr
; while
D
PBD2
is by 26% more expensive. On the other
hand though, with reference to the initial cost, the
three designs vary by 2% and 4% only.
The five-story non-symmetric test example has
a similar trend. Based on the concrete and steel
Table 2. Eight-story test example: comparison of steel and concrete quantities in the three designs
Columns
Beams
Design
procedure
C
IN, RC Frame
(10
3
MU)
C
IN
(10
3
MU)
Concrete (m
3
)
Steel (kg.)
Concrete (m
3
)
Steel (kg.)
D
descr
1.68E+02
1.84E+04
2.27E+02
1.06E+04
2.40E+02
1.44E+03
D
PBD1
1.84E+02
2.41E+04
2.48E+02
1.29E+04
2.64E+02
1.46E+03
D
PBD2
2.19E+02
2.87E+04
3.11E+02
1.80E+04
3.03E+02
1.50E+03
Table 3. Five-story test example: comparison of steel and concrete quantities in the three designs
Columns
Beams
Design
procedure
C
IN, RC Frame
(10
3
MU)
C
IN
(10
3
MU)
Concrete (m
3
)
Steel (kg.)
Concrete (m
3
)
Steel (kg.)
D
descr
8.86E+01
5.20E+03
6.57E+01
1.45E+03
1.11E+02
7.36E+02
D
PBD1
1.04E+02
6.87E+03
7.40E+01
1.75E+03
1.20E+02
7.45E+02
D
PBD2
1.27E+02
8.24E+03
9.16E+01
2.50E+03
1.33E+02
7.58E+02
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