Geology Reference
In-Depth Information
Table 3. Nomenclature of constraint scenarios
considered
examined by comparing maximum response from
these accelerations with those from past recorded
ground motions. Thus, the maximum ductility
factor of the structure from the worst earthquake
is about 3.9 (case 1) and 2.6 (case 4) times that
from the Kobe earthquake and is 2.7 (case 1) and
1.5 (case 4) times that from the San Fernando
earthquake.
To examine the effect of the strain harden-
ing ratio on the design earthquake acceleration
computed, limited studies were carried out. The
value of α was changed and the critical input
was determined by solving a new optimization
problem. Namely, α was taken as 0.20, 0.10, 0.05,
and 0.01. The strain hardening ratio was not seen
to significantly influence the frequency content
of the critical earthquake input. It was observed,
however, that the inelastic structure with lower
values of α yields more frequently compared to the
same system with higher α values. Accordingly,
the cumulative hysteretic energy dissipated was
observed to decrease for higher values of α (Fig-
ure 8(a)). This feature is particularly remarkable
at the end of the earthquake duration. It was also
observed that the results on critical earthquake
accelerations for bilinear inelastic structure with
α = 0.01 are close to those for the elastic-plastic
structure (Abbas, 2006).
Case
Constraints imposed
1
2
3
4
Energy and PGA
Energy, PGA, PGV and PGD
Energy, PGA and UBFAS
Energy, PGA, UBFAS and LBFAS
age index for case 4 is 0.37 which is substan-
tially smaller than 1.15 for case 1 (Table 4). The
constraints on PGV and PGD were not found to
be significant in producing realistic critical inputs
compared to the constraints on UBFAS and LB-
FAS. Also, the realism of the critical acceleration
for case 4 can be examined by comparing the
Fourier amplitude spectra and frequency content
of the worst acceleration (Figures 4, 5) with the
Fourier amplitude spectra of past recorded earth-
quakes (Figure 7). Note that, while the constraint
scenario 1 leads to pulse-like ground motion, such
scenario is observable in past recorded earthquakes
(e.g., 1971 San Fernando, 1985 Mexico, and 1995
Kobe earthquakes). Resonant or pulse-like earth-
quakes are also observable in near-field ground
motion with directivity focusing, known as for-
ward- and backward-directivity ground motion
(Housner & Hudson, 1958, Kalkan & Kunnath,
2006, He & Agrawal, 2008, Moustafa 2008). The
realism of worst earthquake loads can be also
Figure 3. Convergence of objective function in terms of frequency terms N f (a) Case 1 (b) Case 4
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