Performance-Based Seismic Design - Structural Seismic Design Optimization and Earthquake Engineering - page 43

Figure 7. Evolution of the total cost for different minimum target betas

native, a different formulation could be used in
describing the hysteresis behavior. Thus, it could
be matched to the response of the pile to a given
cyclic displacement history for the pile-cap. This
history, obtained by either experiments or by cal-
culation, can then be fitted with a set of rules that
permit the reproduction of the hysteresis observed
for the specific cyclic displacements.
Many such set of rules are contained in dynamic
analysis software packages. However, although a

good fit can be obtained for the cyclic response
used for the matching, there is no guarantee that
a similar good representation would be achieved
when using the same fitted rules for any other
cyclic history or earthquake record. Perhaps the
most sophisticated of these calibrated approaches
to hysteresis representation is to use cyclic data to
determine parameters of a first-order differential
equation, the solution of which, for a given history,
can represent loops with pinching and degradation

Figure 8. Influence of β 2 and β 3 in the total cost