Civil Engineering Reference
In-Depth Information
crack, then the ordinary elastic beam theory applies. The effects of conduc-
tive admixtures on fl exural strength
M
u
/
W
(where
M
u
is ultimate
bending moment and
W
is the section modulus) are illustrated in Table 4.5.
It may be seen that the fl exural strength of a concrete beam increases with
the addition of conductive admixtures. Amongst these, the samples contain-
ing only NCB show a smaller increment of fl exural strength as the NCB
dosages are increased (between 1.8% and 8.8%). However, there is a clear
increase in fl exural strength when both the CF and BF dosages are increased.
When compared with a PC beam without any conductive admixture, the
increment of fl exural strength in beams containing CF and BF is between
10% and 19%.
σ
u
=
4.4
Infl uence of conductive admixtures on the
electrical properties of concrete beams
As described above, fl exural strains are produced when a beam is subjected
to bending. During the loading process, the strain near the top of the beam
in the compression zone, the strain of initial geometrical neutral axis
(IGNA) and the tensile strain near the bottom of the concrete beam (Fig.
4.5) are measured by strain gauges. The resistance of the beam is measured
simultaneously. The strains of IGNA are obtained by strain gauges (2) and
(5), and the FCR at each loading stage can also be measured. The relation-
ship between the force and electrical fi elds is used to investigate stress and
strain behaviour through analysis of physical quantities such as current,
voltage and resistance (Wu, 2005).
4.4.1 Feasibility of relationship between force fi eld
and electric fi eld
It is diffi cult to measure quantities such as stress or current density directly.
However, there are some experimentally measurable physical quantities,
such as resistance in the electric fi eld and strain in the force fi eld. The
stress can be calculated by stress-strain curves, while current and current
density can be calculated by Ohm's law. Once the resistance-strain correla-
tions are established through experimentation, the relationship between the
force and electric fi elds is determined, so making it possible to obtain
the immeasurable quantities in the force fi eld with the measurable voltage
and resistance of the electric fi eld. The corresponding parameters of the
electric fi eld and the force fi eld are illustrated in Table 4.6.
The Laplace Equation [4.1] is satisfi ed for both the electric and force
fi elds:
∂
∂
ϕϕϕ
x
2
+
∂
∂
2
+
∂
∂
2
=
0
[4.1]
2
y
2
z
2
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