Civil Engineering Reference
In-Depth Information
Table 4.6
Comparison of electrical and mechanical parameters
Electric fi eld variable
Force fi eld variable
Current:
I
Load:
N
Voltage:
V
Deformation:
U
Current density:
i
=
I/A
=
Ce
Stress:
σ
=
N/A
=
E
ε
Generated voltage:
e
=
V/L
Strain:
ε
=
U/L
Ohm's law:
I
=
V/R
Hooke's law:
N
=
U/
δ
=
EA
ε
Resistivity:
ρ
=
RA/L
Stiffness coeffi cient:
B
=
EA/L
=
1/
δ
Conductivity:
C
=
1/
ρ
=
L/RA
Elastic modulus:
E
=
L/(A
δ
)
Sensitivity:
λ
= Δ
R/(R
ε
)
Damage degree:
D
= Δ
E/E
For the electric fi eld:
∂
∂
2
V
x
+
∂
∂
2
V
y
+
∂
∂
2
V
z
=
0
[4.2]
2
2
2
For the force fi eld:
2
2
2
∂
∂
∂
∂
∂
∂
(
)
=
+
+
σσσ
++
0
[4.3]
x
y
z
2
2
2
x
y
z
where
x
,
y
and
z
are space coordinates; j and
are respectively the poten-
tial function and stress. The Laplace equations presented here are based on
the assumption that both the electric fi eld (see Fig. 4.6a) and the force fi eld
(see Fig. 4.6b) comply with the same boundary conditions. In the force fi eld,
the beam is subjected to three loading points (A and E are the support
points, and C is the mid-span point with an applied external load
N
, see Fig.
4.5 and Fig. 4.6b). In the electric fi eld, the beam is taken as being in a similar
situation as voltage is provided through three points, B, C and D. As illus-
trated in Fig. 4.6a, electric potential points B and D are used to provide the
same voltage, while point C at the mid-span is the ground terminal. Thus if
the beam section does not crack (the ordinary elastic beam theory applies),
the boundary condition of the electric fi eld will be comparable with that of
the force fi eld.
The variation of strain on the IGNA, along with the load, is shown in Fig.
4.7 as a function of time during the loading process prior to cracking. Figure
4.8 shows the relationship between the resistance and strain of IGNA
obtained simultaneously from the same specimen. It can be seen that the
resistance decreases along with the strain of the IGNA due to the sensitivity
of conductive concrete as previously reported. The relationship between
the IGNA strain in the force fi eld and the resistance in the electric fi eld can
therefore be established.
σ
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