Civil Engineering Reference
In-Depth Information
and Matsumura average spectrum intensity is given by:
1
2
T
y
∫
(
)
SI
=
ST
, 0.05 d
T
(3.33.2)
M
v
T
T
y
y
Martinez-Rueda (1997) also suggested changing the second integration limit of Matsumura to
T
h
,
which represents the hardening period of the structure. This was based on the assumption that the
ground-motion frequencies contributing to the failure of the structure are contained within the period
interval of
T
y
to
T
h
. Using these integration limits, average spectrum intensity may be represented as:
1
T
h
∫
(
)
SI
=
ST
, 0.05 d
T
(3.33.3)
yh
v
TT
−
T
y
h
y
In order to assess the effectiveness of the spectrum intensities considered, a large number of inelastic
time-history analyses were performed for a wide range of parameters of seismic input and dynamic
response using more than 100 earthquake records. The structural parameters were the yield force ratio
C
y
and the hardening parameter
α
. A sample of results is given in Table 3.22. From the extensive results,
it was concluded that the Matsumura defi nition is the most reliable regardless of the period range.
Within the intermediate period range, Housner's intensity gives higher coeffi cient of correlation, but
the improvements are not very signifi cant. Martinez- Rueda ( 1997 ) gives recommended scaling proce-
dures for each range of period, yield force ratio and hardening parameter. This is perhaps the most
comprehensive study of practical application of spectrum intensity scaling. However, one main concern
is that the spectra plotted for the yield force ratio do not control the ductility demand. Values in Table
3.22 show that the ductility demand imposed is up to 14. Hence, if the results are constrained to practi-
cal limits of ductility demand, i.e. up to about 6, the observations and conclusions may vary. Constant
ductility spectra are considered more appropriate for such applications, since the practical yield force
ratio is very wide, from structures that are not designed for seismic loading, to earthquake- resistant
structures exhibiting high overstrength values.
A parametric study was conducted by Elnashai (1998) with 30 earthquake records using constant
ductility spectra. The coeffi cients of variation (COVs) for elastic and inelastic spectral ordinates were
calculated. Comparison between the elastic and inelastic spectra of scaled records and a target smoothed
'code-like' spectrum was also undertaken, alongside comparison of the former with the elastic and
inelastic spectra of records compatible with the smoothed spectrum. A sample of the results is shown
in Figure 3.20 .
Table 3.22
Correlation coeffi cient for spectrum intensity scales (Yield force ratio,
C
y
= 0.3; hardening parameter,
α = 0.1).
T
y
(seconds)
I
nten
sity scale
0.4
1.4
2.4
0.84
0.91
0.70
SI
H
SI
M
0.93
0.84
0.92
0.92
0.79
0.88
SI
yh
Intensity range (g - sec)
0.0 - 0.20
0.0 - 0.20
0.0 - 0.20
Ductility demand range
0.0 - 14.0
0.0 - 2.5
0.0 - 2.0
Key
:
SI
H
= Average Housner spectrum intensity;
SI
M
= average Matsumura spectrum intensity;
SI
yh
= average
Martinez-Rueda spectrum intensity; T
y
= period at yielding
