Performance-Based Seismic Design - Structural Seismic Design Optimization and Earthquake Engineering - page 37

6.3 Preliminary Design: Initial
Values for the Design Parameters

Each of the question marks (?) in this Table
indicates an optimization design parameter (the
mean values for the depth of the beams and col-
umns, and for the longitudinal steel reinforcement
ratios).
The reliability assigned to each performance
level corresponds to a series system reliability for
all the performance functions G included in that
performance. Thus, the reliability for collapse cor-
responds to that of a series system consisting of the
three limit states given by Eqs.(41) through (43).
Databases for achieved reliabilities are devel-
oped, as described, as a function of the design
parameters, utilizing the performance functions
and the response neural networks, These databases
are themselves represented by neural networks,
permitting the efficient estimation of reliabilities
achieved for any choice of input design parameters
(within their bounds). The databases included
data from 180 design parameter combinations.
Neural network agreement with the input data is
shown in Figure 5 for the reliability índices β 1 , β 2 ,
β 3 corresponding to the three performance levels.
The dispersion or lack of agreement error is
represented by a normal distribution following
the same approach as described for Eq.(34). Fig-
ure 5 shows the very good approximation of the
reliability data by means of the trained neural
networks.

The preliminary design for the portal frame was
achieved according to the procedure described by
Rubinstein et al. (2006), followed by application
of the capacity design guidelines specified in the
Argentine norms INPRES-CIRSOC 103, Parte II
(2005). The results of this preliminary calculation
are shown in Table 3, and provide the first anchor
combination x d 0 for the optimization.
The design parameters satisfy additional con-
straints to provide adequate resistance to the
gravitational loads on the top beam. Thus, fol-
lowing Argentina's norm requirements,

2

1 4
6 48

. q l

b h f

ρ + ρ ≥

b

(46)

span end

2

.

b b y

Furthermore, to ensure a minimum ductility in
the beam cross-sections, the steel reinforcement
ratios satisfy

0 5 . ρ ≤ ρ ≤ 2 ρ (47)

end span end

Figure 5. Neural network agreement with data for the reliability indices β 1 , β 2 , β 3