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22
IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 1
Steel fibre reinforced concrete pipes. Part 2: Numerical model to simulate the crushing test
which lately is losing its market share in favor of the plastic pipes.
Therefore, new alternatives and improvements are necessary for
the concrete pipe to be competitive once again (Viñolas
et al
. [1]).
For the analysis, a range of
C
f
between 0 kg/m
3
and 30 kg/m
3
was
established. The first amount would correspond to an unreinforced
concrete pipe (UCP), and the second one has been established as
a maximum value because of economic criteria.
Likewise, the requirement of a minimum early compressive
strength is necessary for demolding and to manipulate the pipe. In
order to satisfy this requirement an
f
ck
of 45 MPa at age of 28 days
has been assumed in order to carry out the analysis.
Table 3
presents the values for the mechanical parameters used
to simulate the tension behavior of SFRC.
The values of
F
c
and
F
u
fixed in NBR 8890:2007 for the strength
classes EA2, EA3 and EA4 for pipes with
D
i
= 400 mm are gath-
ered in the
Table 4
.
Table 4 – Design loads for each strength class
for pipes with D = 400 mm
i
EA2
EA3
EA4
F (kN)
c
60
90
120
F (kN)
u
90
135
180
F (kN)
min,pos
63
94.5
126
Figure 7 – F-v curves for the pipes with D = 400 mm and different reinforcement configurations
c
i
Fig. 7 shows the curves
F
-
v
c
obtained with the MAP model. From
those curves, it is deduced that:
n
The load
F
cr
obtained in the four cases (96 kN) is enough to
reach the load
F
c
stipulated in classes EA2 (60 kN) and EA3
(90 kN). However, the value of
F
c
for class EA4 (120 kN) can-
not be reached by means of the addition of metallic fibres only
(stress
σ
1
is independent from
C
f
).
n
The 90 kN established for
F
u
in class EA2 are exceeded if a
fibre dosage of 10 kg/m
3
(93 kN) is used. But, in order to reach
the 135 kN stipulated for class EA3, according to the numerical
model, at least 30 kg/m
3
of fibres (136 kN) are required. On the
other hand, the
C
f
necessary to achieve the 180 kN established
for class EA4 is not under the economically competitive values.
n
In order to reach the 63 kN specified for the
F
min,pos
of classEA2
and the 94.5 kN of class EA3, 10 kg/m
3
(64 kN) and 20 kg/m
3
(99 kN) are required, respectively.
Therefore, keeping in mind that the three strength requirements
must be fulfilled simultaneously for a fixed
C
f
, it is possible to con-
clude that 10 kg/m
3
of fibres would be required to achieve the EA2
class requirements, and 30 kg/m
3
would be required for class EA3,
according to the numerical model.
Alternatively, in order to achieve class EA4 with an economically
attractive reinforcement configuration, a composite solution could
be proposed (fibres + bars). On one hand, the load
F
c
(
F
w
=0.25mm
in
case of SBFRCP) would be reached thanks to the use of fibres.
On the other hand, the steel bars would guarantee higher failure
strength due to their higher efficiency and strategic position within
the section.