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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 1
A. D. de Figueiredo | A. de la Fuente | A. Aguado | C. Molins | P. J. Chama Neto
Fig. 7 also shows a simulation considering a reinforcement con-
sisting of 10 kg/m
3
of fibres and 7Ф5/ml of CA60 steel bars. This
strategy leads to an
F
w=0.25mm
= 125 kN (
F
c
= 120 kN) and also to
an ultimate failure load
F
u
strictly equal to 180 kN. Consequently,
class EA4 would be reached, with
F
u
being in this case the critical
parameter in the design process.
When comparing the curve
F
-
v
c
obtained SFRCP with 30 kg/m
3
of
fibres and the one obtained for the SBFRCP (10 kg/m
3
+ 7Ф5/m)
for values of
v
c
up to 1.2 mm (service range), it can be observed
that the behavior of the former is better. This highlights the fact that
the normative prescription which refers to the load
F
c
is much more
restrictive for FRCP, if compared with the conventional SBRCP.
While FRCP are not allowed any cracking symptoms (
F
cr
>
F
c
), the
SBRCP are allowed to reach cracking with a width of up to 0.25
mm (
F
w=0.25mm
>
F
c
). In the opinion of the authors, this criterion re-
stricts the range of application of fibres to this product. Besides, it
is not in accordance with the experimental and numerical results,
especially when it is known that the inclusion of the suitable type
and volume of fibres improves considerably the cracking behavior
of the concrete structures.
6. Conclusions
This paper introduces the MAP model for the analysis of concrete
pipes with mid-low diameters (lower than 1000 mm) and reinforced
with traditional steel rebars and/or steel fibres. The bases for this
model were already introduced by Pedersen [22], but this paper
uses the most recent constitutive equations to simulate the behavior
of SFRC. The obtained degree of correlation between experimen-
tal and model results can be considered excellent, having obtained
numerical results with an average relative error of 7.0% in the safe
of safety. To improve this aspect, the constitutive equation of ten-
sioned SFRC could be adjusted taking into account that the fibres
are oriented towards a preferential direction within the wall of the
pipe. In short, the MAP model can be considered to be a suitable
tool for designing the optimal configuration of the reinforcement for
this type of pipes. It is intended to be used in precast plants where
the required technology to manufacture and test pipes is available.
It leads to savings as regards both time and economical resources,
since it avoids the extensive test programs required in order to find
the optimal amount of reinforcement. This model is especially inter-
esting when a geometrical condition of the pipe, the type of fibres or
the strength class is modified, or simply if the factory wishes to make
the design tables of the most commercial pipes.
With the aim of illustrating the model capability, an example of
optimal design for a pipe with a diameter of 400 mm has been
included. The conclusions established were that, according to the
model, class EA2 would be obtained with 10 kg/m
3
of fibres; class
EA3, with 30 kg/m
3
; and with 10 kg/m
3
+ 7Ф5/m of CA60 steel,
class EA4 from the NBR 8890:2007 would be also reached.
Nowadays, several experimental campaigns are being carried out
with the purpose of expanding the data bank used to contrast the
model and adjust, if necessary, the convenient bases or parameters.
7. Acknowledgements
The authors of this document wish to express their appreciation for the
financial support received through the Research Project BIA2010-17478:
Procesos constructivos mediante hormigones reforzados con fibras.
Likewise, Professor Antonio D. de Figueiredo wishes to thank the
support provided by CAPES -Coordenação de Aperfeiçoamento
de Pessoal de Nível Superior– for having awarded him the post-
doctoral grant that allowed him to participate in this work.
8. References
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