Civil Engineering Reference
In-Depth Information
v
1
v
2
Progressive
deterioration
v
0
Y
1
Shocks
Y
2
Serviceability
limit
k*
i
Early
replacement
Ultimate limit
state
s*
Replacement
only after failure
Time
X
1
X
2
X
3
X
4
...
Cycle 1
Cycle 2
Cycle 3
15.4
Description of the degradation for regenerative process.
where the second term on the right hand side of equation 15.13, for
(
t
)
>
1, is the history of demands since the last replacement. Note that the accu-
mulation of damage is defi ned by assuming statistically identical cycles.
Then, the loss of remaining lifetime at a given cycle
(
t
) is computed by
subtracting the accumulated damage caused by shocks in the cycle from
ν
(
t
)−1
. Then,
()
=
()
=
()
t
Vt
v
−
Q
;
t
12
, ,...
[15.14]
()
−
t
1
(
t
)-th cycle, an intervention takes place once the remaining capac-
ity/resistence falls below
k*
(or
s
*), i.e.,
V
(
t
)
(
t
)
In the
k
* (Fig. 15.3); and if the
structure is not abandoned, it is put back in service immediately. In other
words, intervention times are negligible and the 'off' times non-existent. If
the structure is either reconstructed after failure or preventive maintenance
is carried out, the instantaneous intervention rate (equation 15.7) can be
rewritten as (Sánchez-Silva
et al.
, 2011):
<
[
]
()
=
()
()
()
>
d
Pt
λ
tPQ
t
t
v
−
k
* d
t
[15.15]
()
−
t
1
∞
⎡
⎢
(
)
⎤
⎥
∫
Vt kn
t
()
=
λ
tGx
d
⋅
1
d
t
Zt
<≤
Z
()
−
(
)
t
1
t
(
)
,
*
()
where
V
(
t
)
(
t
,
k
*,
n
)
k
*. Note that at the beginning of every
cycle the remaining lifetime is reset to a random value
=
V
(
t
)
(
t
,
n
)
−
ν
(
t
)−1
.
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