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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 1
Steel fibre reinforced concrete pipes. Part 2: Numerical model to simulate the crushing test
A., MOLINS, C.; VIÑOLAS, B. Análise da viabilidade
do uso de fibras metálicas em tubos de concreto.
Parte 1: campanha experimental, 52° Congresso
Brasileiro do Concreto, IBRACON, Fortaleza, 2010.
[14] PARROT, J. Sustainability research in sewage pipes,
Minor Thesis, UPC, Barcelona, España, 2009.
[15] HILLERBORG, A., MODÉER, M., Petersson, P.E.
Analysis of crack formation and crack growth in
concrete by means of fracture mechanics and finite
elements. Cement and Concrete Research, 1976,
Vol. 6, pp. 773-782.
[16] VANDEWALLE, L. et al. Test and design methods for
steel fibre reinforced concrete. σ-ε design method.
RILEM Materials and Structures, 2003, vol. 36,
p. 560-567.
[17] LARANJEIRA, F., AGUADO, A., MOLINS, C. Equação
constitutiva de betão reforçado com fibras,
2° Congresso Nacional de Prefabricação em Betão,
Lisboa, Portugal, 2008.
[18] PEDERSEN, C. Fibre reinforced concrete pipes.
UNICON beton I/S. December 1992.
[19] FIGUEIREDO, A.D. de, et al. Steel fibre reinforced
concrete pipes. Part 1: technological analysis of the
mechanical behavior. Revista RIEM, 2011, no prelo.
[20] ASSOCIAÇÃO BRASILEIRA DE NORMAS
TÉCNICAS. Tubo de concreto de seção circular, para
águas pñuviais e esgotos sanitarios. NBR 8890,
ABNT, Rio de Janeiro. 2007.
[21] DE LA FUENTE, A., AGUADO, A., MOLINS, C.
Numerical model for the non linear analysis of precast
and sequentially constructed sections. Hormigón y
Acero, 2008, Vol. 57, n° 247, p. 69-87.
[22] PEDERSEN, C. Calculation of FRC pipes based
on the fictius crack model. Department of Structural
Engineering. Technical University of Denmark, 1995.
[23] MARÍ, A., BAIRÁN J. Evaluación de los efectos
estructurales del deterioro, reparación y refuerzo,
mediante análisis no lineal evolutivo. Hormigón y
Acero, 2009, Vol. 60, n° 254, p. 51-63.
[24] HEGER, F.J. A theory for the structural behavior of
reinforced concrete pipes, PhD Thesis, Department
of Civil and Sanitary Engineering, Massachusetts
Institute of Technology, MIT, Massachusetts,
USA, 1962.
[25] THORENFELDT, E., TOMASZEWICZ, A., JENSEN
J.J. Mechanical properties of high–strength concrete
and application in design, Proceedings of the
Symposium Utilization of High Strength Concrete,
Stavanger, Norway, 1987.
[26] COLLINS M.P.; MITCHELL, D. Prestressed concrete
basics. Canadian Prestressed Institute, Ontario
(Canada), 1987.
[27] BENCARDINO, F.; RIZZUTI, L.; SPADEA, G.;
SWAMY, R.N. Stress-strain behavior of steel
fibre-reinforced concrete in compression. ASCE J.
of Materials in Civil Enineering 2008, 20(3):255-63.
[28] BARROS, J.A.O., FIGUEIRAS, J.A. Flexural behavior
of SFRC: Testing and modelling. ASCE Journal of
Materials in Civil Enineering, 1999, Vol. 11, nº 4, p. 331-339.
[29] PUJADAS, P. Durability of polypropilene fibre reinforced
concrete. Minor Thesis, UPC, Barcelona, España, 2008.
[30] PEDERSEN, C. The moment-rotation relationship with
implementation of stress-crack width relationships.
Department of Structural Engineering. Technical
University of Denmark, 1995.
[31] OLESEN, J.F. Fictious crack propagation in
fibre-reinforced concrete beams. J. of Engineering
Mechanics, 2001, Vol. 127, n° 3, p. 272-280.
[32] CASANOVA, P., ROSSI, P. Analysis and design of
steel fibre reinforced concrete beams. ACI Structural
J., 1997, Vol. 94, n° 5, p. 595-602.
[33] YANG W.Y., WENWU C., CHUNG T.S., MORRIS
J. Applied numerical methods using Matlab. John
Wiley & Sons Inc., Hoboken, New Jersey, 2005.
[34] TIMOSHENKO, S. Strength of Materials: Part 1:
Elementary Theory and Problems. D. Van Nostrand
Inc., New York, N.Y. 1940.
[35] VANDEWALLE, L. et al., Recommendations of RILEM
TC162-TDF: Test and design methods for steel fibre
reinforced concrete: Bending test (final
recommendation). Materials and Structures, 2002,
Vol. 35, p. 579-582.
[36] BARROS, J.A.O., CUNHA, V.M.C.F., RIBEIRO,
A.F., ANTUNES, J.A.B. Post-cracking behavior of
steel fibre reinforced concrete. Materials and
Structures, 2005, Vol. 38, p. 47-56.
[37] COMISIÓN PERMANENTE DEL HORMIGÓN
(Ministerio de Fomento). EHE 2008 Instrucción del
Hormigón Estructural, 2008.
[38] DE LA FUENTE, A., AGUADO, A., MOLINS, C.
Aplicaciones del HRFA: Tuberías de hormigón.
IV Congreso de la asociación científico – técnica
del hormigón estrutural, Valencia, España, 2008.
[39] LARANJEIRA, F. Design-oriented constitutive model
for steel fibre reinforced concrete. PhD Thesis, UPC,
Barcelona, España, 2010.
9. Nomenclature
A
:
Pipe spigot.
A
c
:
Concrete area.
A
s,i
:
Area of the
i
-th steel bar.
B
:
Pipe socket.
dA
c
:
Differential concrete area.
C
f
:
Fibre dosage.
D
i
:
Internal diameter of the pipe.
D
o
:
Outside diameter of the pipe.
E
cm
:
Average Young modulus of the concrete.
E
s
:
Young modulus of the steel.
F
:
Applied load on the pipe.
F
c
:
Proof load of the pipe.
F
cr
:
First cracking load of the pipe.
F
n
:
Minimum failure load (established) of the pipe.
F
max,pos
: Maximum post-failure load (simulated) of the pipe.
F
min,pos
: Minimum post-failure load (established) of the pipe.
F
u
:
Ultimate failure load of the pipe.
F
3mm
:
Post-failure load for a 3.0 mm vertical displacement of the
key (2
st
series of the tested pipes).