r - The Hong Kong Polytechnic University

Peak displacement (m)
84, 50, 16 percentiles
1.2
0.8
0.4
LBin 1a
LBin 1b
Lyield displ.
0
0 0.4 0.8 1.2 1.6 2
Period (sec)
β
0.8
0.6
0.4
0.2
0
0 0.4 0.8 1.2 1.6 2
Period (sec)
a. Peak displ., Fy
= 40% W
b. β , Fy
= 40% W
1.2
0.8
Peak displacement (m)
84 , 5 0, 16 p erce ntile s
0.8
0.4
0
0 0.4 0.8 1.2 1.6 2
Period (sec)
β
0.6
0.4
0.2
0
0 0.4 0.8 1.2 1.6 2
Period (sec)
c. Peak displ., Fy
= 20% W
d. β , Fy
= 20% W
1.2
0.8
Peak displacement (m)
84, 50, 16 percentiles
0.8
0.4
0
2 2.4 2.8 3.2 3.6 4
Period (sec)
β
0.6
0.4
0.2
0
2 2.4 2.8 3.2 3.6 4
Period (sec)
e. Peak displ., F = 6% W
f. β , F = 6% W
y
Figure 22 Median, 84th and 16th percentiles and β of peak displacement response for Bins 1a and 1b
Method 2: Spectrum-Matching Method
Spectrally matched ground motions are often used to compute seismic demands in structural framing systems.
To judge the utility of spectrum-matched ground motions for predicting the response of nonlinear SDOF
framing systems (such as base-isolated structures), the NF seed motions of Table 1 were modified to match the
median spectrum of Bin 1a using the computer code RSPMATCH (Abrahamson 1998, Hancock et al. 2006).
The bin of 50 spectrally matched motions is labeled as Bin 1b. The 16th, 50th and 84th percentiles of elastic
spectral acceleration for Bin 1b are shown in Figure 20a. The median spectral accelerations for Bins 1a and 1b
are virtually identical. Figure 20b presents the dispersion in the spectral accelerations for the two bins of ground
motions. The dispersion in the spectral accelerations for Bin 1b is negligible.
The 16th, 50th and 84th percentiles and β of the inelastic peak displacement for Bin 1b are shown in Figure
22 together with those for Bin 1a. The results indicate that the use of spectrally matched ground motions
underestimate the median peak displacement demand in highly nonlinear SDOF systems and cannot capture the
dispersion in the displacement response. For Fy
= 0.06W
(see Figure 22e), the median responses are
underestimated by 20%. This observation is similar to that of Bazzurro and Luco (2006) for NF motions.
Earthquake ground motions that are spectrally matched to a target median spectrum should not be used for risk
computations of nonlinear SDOF systems and first-mode-dominated structures because a) the median
displacement response will be underestimated, and b) the dispersion in the displacement response is
underestimated by a wide margin.
y
-386-