Civil Engineering Reference
In-Depth Information
(iii) Matsumura Spectrum Intensities
Matsumura ( 1992) conducted a parametric study on the intensity measures of strong motions and their
correlation with structural damage. Four intensity measures of ground motion, namely PGA, PGV,
SI
M
and
V
e
, were examined by evaluating the inelastic response of SDOF systems. Both
SI
M
and
V
e
are
intensity measures suggested by Matsumura.
SI
M
is referred to as the ' Matsumura Spectrum Intensity '
and is defi ned as the mean spectral velocity between
T
y
and 2
T
y
, where
T
y
is the period corresponding
to yield of a SDOF structure with critical damping ratio
ξ
of 5%. On the other hand,
V
e
is the mean
equivalent velocity converted from the input energy
E
i
, between
T
y
and 2
T
y
, with conversion given
by:
2
E
m
i
V
=
(3.32)
e
where
m
is the mass of the SDOF system.
The adopted period interval, i.e.
T
y
to 2
T
y
, is based on the assumption that the response of the structure
in the inelastic range will be in the domain defi ned by its yield and twice its yield period. The bounds
of the period range were found by studying its correlation with
SI
M
and
V
e
for a ductility factor
μ
equal
to 2.0.
Based on the results obtained for four Californian and eight Japanese records, Matsumura confi rmed
that PGA and PGV are well correlated to damage in short- and long - period structures, respectively.
However, they are not reliable measures of intensity for other frequency ranges. It was also observed
that
V
e
and
SI
M
are measures of intensity that correlated well with damage for a wide range of frequen-
cies. The correlation coeffi cient for
V
e
was found to be slightly higher than that for
SI
M
. It should be
noted that in practice
SI
M
, as in the case of all spectrum intensity scales, can be directly used to defi ne
a scaling procedure since the pseudo-velocity spectrum could be derived from the acceleration spectrum
provided by the adopted seismic code. Conversely,
V
e
cannot be directly applied due to the fact that
the input energy
E
i
is not currently specifi ed in seismic design code provisions.
Although the study of Matsumura (1992) showed that
SI
M
is an adequate scaling parameter, a com-
parison of the effectiveness of Housner's spectrum intensity with that of the four parameters included
in his study was not performed. In addition, the post-yield stiffness ratio considered in the study was
0.5, which appears to be very high and not representative of typical earthquake- resistant structures with
signifi cant ductility demand.
(iv) Comparisons and Recommended Scaling Procedures
Martinez-Rueda (1997) carried out a preliminary evaluation by comparing the performance of the
Housner's intensity with the three-parameter system of spectrum intensities proposed by Nau and Hall
(1984). This indicated that the three-parameter system does not result in an improvement of the correla-
tion with displacement ductility demand. The spectrum intensity of Nau and Hall appeared to be mar-
ginally less stable, particularly for short-period structures. However, there was an improvement in the
velocity region when using Nau and Hall procedure. In addition, Housner's intensity involves a single
parameter for all period ranges and hence is simpler to use in practice. The discussion given below
focuses mainly on the comparison between the intensity scales of Housner
SI
H
and Matsumura
SI
M
as
well as a third intensity scale
SI
yh
suggested by Martinez- Rueda ( 1997 ).
The spectrum intensity scales were represented as average spectrum velocities for damping ratios
ξ
= 0.05, such that Housner average spectrum intensity is given by:
1
2.4
2.5
∫
SI
=
ST
(
, 0.05 d
)
T
(3.33.1)
H
v
0.1
