Performance-Based Seismic Design - Structural Seismic Design Optimization and Earthquake Engineering - page 48

Table 12. Performance-based design

Hysteresis: Finite element

Optimal Mean Mass (kN.sec 2 /m) Performing criterion λ Target reliability β Achieved reliability β

0.4 2.5 2.59

139.83

1.0 4.5 4.51

Hysteresis: BWBN
Optimal Mean Mass (kN.sec 2 /m) Performing criterion λ Target reliability β Achieved reliability β

102.19 0.4 2.5 2.76

1.0 4.5 4.42

The optimization is then a problem which
could admit multiple solutions. In practi-
cal terms, the design engineer has then
the possibility of choosing from differ-
ent alternatives, taking into account other
practical requirements. It is also possible
to add to the optimization additional con-
straints among the design parameters, ori-
enting the optimum solution towards, for
example, desired mechanisms for energy
dissipation.

gree with which each minimum reliability
constraint is met may vary, the relationship
between the optimal solution and the pre-
scribed targets is not simple. Increasing or
decreasing a single target may affect the
importance of another constraint, and the
total cost for the optimal solution may or
may not be affected.

• The assessment of reliability, and the op-

timization itself, are conditional on the
quality of the response analysis model,
particularly the quantification of the hys-
teretic energy dissipation during the shak-
ing. In order to illustrate this influence, a
second application example has been dis-
cussed involving the earthquake response
of a steel pile foundation in a sandy soil.
Two hysteretic representations are used:
one implementing a calculation of the
soil-structure interaction and the hyster-
etic force by means of a nonlinear finite
element model; the other using a hysteresis
model fitted to results from a cyclic dis-
placement of the pile-cap. While the first
model can self-adapt to different excitation
histories or different earthquakes, the sec-
ond approach can only be said to provide
a good representation for the history to
which it was fitted. The example consid-
ered the question of how significant is the
influence of these different analyses on the
reliability and optimization results. It was

• Data are required on the relationship be-

tween a calculated damage and the corre-
sponding repair cost. There is substantial
uncertainty in this relationship, and the
Chapter has also explored the sensitivity
of the optimal solution to the form of the
damage-cost function. For the first applica-
tion example, it has been shown that there
is a significant influence in the optimum
minimum total cost, while the optimum
design parameters are not affected. Further
research is therefore needed to quantify the
relationship, a task that must be guided by
experiments and expert assessments.

• The Chapter has also explored the sensitiv-

ity of the optimal solution to the minimum
target reliability levels prescribed for each
performance criteria. In general, it can be
concluded that the results show higher total
costs as the minimum targets are increased.
This is expected. However, since the de-