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Figure 5. Optimal earthquake input and associated structural responses for case 4 (a) Fourier ampli-
tude of the ground acceleration (b) Normalized inelastic deformation (c) Hysteretic restoring force (d)
Dissipated energy
,
µ
are taken as 0.10 m and 2.64, respec-
tively.
The value of
µ
u
was taken as 6 in Figures. 9(a)
and 8 in Figure 9(b). It was found that the damage
index for the structure with initial natural fre-
quency smaller than 1.65 is higher than 0.40 and
thus either total collapse or damage beyond repair
x
max
of the structure is expected. The value of DIPA
for the structure with
ω
0
greater than about 1.70
Hz is less than 0.40 and thus the structure does
not experience total damage but repairable dam-
age. This observation is consistent since the site
dominant frequency is around 1.65 Hz and since
the Fourier amplitude of the ground acceleration
max
Figure 6. Optimal earthquake acceleration and velocity (a) Case 1 (b) Case 4
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