Civil Engineering Reference
In-Depth Information
0.7
0.6
Splash
0.5
Atmospheric
0.4
0.3
0.2
0.1
0
0
50
100
150
200
250
300
t
(years)
16.8
Cumulative distribution function for
T
corr
.
in the table correspond to water-binder ratio of 0.4 for concrete. Figure 16.8
shows the CDFs for the variable
T
corr
for atmospheric and splash conditions.
The CDFs for
T
corr
are found to be asymptotic to a value less than 1.0
because there is a positive probability that
T
corr
.
Using Eq. (16.31),
C
t
is computed by using
d
b
(
t
|
T
corr
) in computing
C
d
(
x
t
,
=
∞
Θ
C
). We use the reduced cross-sectional area for longitudinal and transverse
steel to compute
C
d
(
x
t
,
Θ
C
). It is found that:
()
=
(
)
−
(
)
2
Rt C
⎣
1 4
.
×
10
−
6
tT
−
3 516
.
×
10
−
4
tT
−
⎦
[16.33]
C
0
corr
corr
To assess the effect of corrosion on seismic deformation demand, we
compute the natural period
T
N
of the deteriorated structure as a function
of time
t
. This is computed by conducting pushover analysis with reduced
steel area at different values of
t
. It is found that for the bent
T
′
′
N
=
5.0
×
10
−4
(
t
T
N
. As observed in the case of stiffness degradation due to
earthquakes, the change in natural period can be used to compute
−
T
corr
)
+
t
. The
type of deterioration process (i.e., corrosion or earthquakes) does not affect
the relation between
α
α
t
and
T
′
N
/
T
N
as long as the deteriorated state is the
same (in this case
T
′
N
/
T
N
). Therefore, the previously developed relation
α
t
=
ln[1
+
1.75(
T
′
N
/
T
N
−
1)] can be used with the difference that in this case
α
t
n
is replaced with
α
t
. Now, we obtain
[
]
α
()
=+× −
(
)
Rt
ln
112510
4
.
−
tT
C
[16.34]
corr
0
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