Civil Engineering Reference
In-Depth Information
study contain the minimum longitudinal reinforcement ratio of 0.8% based
on the 2010 CHBDC. For the transverse reinforcement a confi nement rein-
forcement ratio of 1.2% was required.
The fi rst mode of the bridge is a torsional mode with
T
1.43 s (with
effective modal mass ratio close to zero). The fundamental period in the
transverse direction is 1.30 s (with 60% contribution) and the period in the
longitudinal direction is 0.92 s. In the transverse direction a third mode with
T
=
0.75 s (with about 40% contribution) is also important. For the three-
dimensional analyses the geometric mean period of 1.09 s was used to
compute the spectral acceleration of the records. It should be noted that
after performing the IDA, using a fi xed record set, the IM values can be
computed at any desired period using the elastic response spectra of the
records and therefore there is no need to perform the analyses again for
different periods. In this study only the results at the fundamental period
of the structure (which was found the most critical) are presented. Similarly
the evaluations can be carried out at the other periods. However, it should
be noted that for the record selection methods which are dependent on the
period of the structure, the evaluations need to be carried out using differ-
ent record sets at different periods and therefore the IDA should be per-
formed for each period independently. The periods are computed using the
effective stiffness of the columns (i.e.,
K
e
=
=
M
y
/
θ
y
where
M
y
and
θ
y
are the
moment and rotation at yield, respectively).
The modifi ed Takeda hysteresis model (Otani, 1981) was used in this
study to model the behavior of the reinforced concrete (RC) columns using
Ruaumoko software (Carr, 2009). However, the hysteresis model developed
by Ibarra
et al.
(2005) is recommended to be used when this model becomes
available in the computer program. The modifi ed Takeda model has two
main parameters, alpha and beta, which control the unloading and the
reloading stiffness, respectively. The values of alpha
0.3
were adopted to comply with both the recommended values in practice
(Priestley
et al.
, 2007) and the median values from the tests (more details
are available in Tehrani
et al.
, 2012). The structural modelling considered in
this study is similar to that used by Priestley
et al.
(2007), except that the
backbone curve shown in Fig. 21.2, including the post-peak response was
used. More details concerning the modelling of the bridge are available in
Tehrani
et al.
(2012) and Tehrani and Mitchell (2012a).
For the 3D analyses the yield interaction surface developed by Tseng and
Penzien (1973) was used in the Ruaumoko program (Carr, 2009). The inter-
action factors for the fl exural term (i.e.,
a
and
b
factors in the original model
by Tseng and Penzien, 1973) were considered as 2 for the circular bridge
columns. The use of the beam elements in modelling (i.e., interaction of
moments only) also resulted in similar predictions with about 15% differ-
ences on average. The small differences are due to the fact that the effects
=
0.3 and beta
=
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