Civil Engineering Reference
In-Depth Information
In the equations above, the factors such as strain (
ε
1
,
ε
3
) and the corre-
sponding effective stress (
σ
˜
1
and
σ
˜
3
) may be given as follows:
(
)
6
0 944
NLy h y
Ebh h
+
cr
0
0
ε
1
=
[4.21]
(
)
3
.
−
y
0
(
)
6
0 944
NLy h y
bh h
+
cr
0
0
σ
=
[4.22]
1
(
)
3
.
−
y
0
−
NLy
Ebh h
6
cr
0
ε
3
=
[4.23]
(
)
2
0 944
.
−
y
0
6
0 944
−
NLy
bh h
cr
0
σ
=
[4.24]
3
(
)
2
.
−
y
0
The relationship between the strain of IGNA (
ε
2
) and the degree of
damage
D
may be written as follows:
11
2
3
−−
D
NL
Ebh
cr
[
]
ε
=
⋅
D
0
≤≤
D
0 5
.
[4.25]
2
0 944
.
2
2
It may be seen that the degree of damage
D
increases in a monotonic
manner with an increase in the strain of IGNA
ε
2
.
Where
R
0
denotes the initial electric resistance of a concrete beam before
loading,
R
denotes the electric resistance of a beam subjected to external
loading at different times and the First Order Exponential Decay function
Y
=
m
exp(
−
X
/
n
)
+
p
,
Y
is replaced by 100
Δ
R
/
R
0
and
X
by
ε
2
, the relationship
between the strain of IGNA (
ε
2
) and the FCR is obtained, which may be
demonstrated as:
(
)
−
100
RR
mR
−
p
m
⎡
⎢
⎤
⎥
0
[
]
ε
=−
n
ln
10
6
RR
≤
[4.26]
2
0
0
It may be seen that
ε
2
increases with an increase in the absolute value of
FCR.
The relationship between the degree of damage (
D
) and the FCR may
be written as:
11
2
3
−−
D
(
)
−
100
RR
mR
−
p
m
NL
Ebh
⎡
⎢
⎤
⎥
0
cr
−
n
ln
10
6
=
⋅
D
[4.27]
2
0 944
.
2
0
It may be seen that the degree of damage
D
increases monotonically with
an increase in the absolute value of FCR.
When the elastic modulus
E
, beam dimensions (
b
,
2h
,
L
) and the cracking
load (
N
cr
) are given, the electrical resistance (both the initial
R
0
before
loading and
R
under loading) can be measured. The stress-strain state
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