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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2018, Vol. 12 Issue (4) : 439-453
Non linear modeling of three-dimensional reinforced and fiber concrete structures
Fatiha IGUETOULENE(), Youcef BOUAFIA, Mohand Said KACHI
University Mouloud Mammeri of Tizi-Ouzou, 15000, Algeria
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Under the effect of the ascending loading, the behavior of reinforced concrete structures is rather non linear. Research in industry and science aims to extend forward the use of non-linear calculation of fiber concrete for structural parts such as columns, veils and pious, as the fiber concrete is more ductile behavior then the classical concrete behavior. The formulation of the element has been established for modeling the nonlinear behavior of elastic structures in three dimensions, based on the displacement method. For the behavior of concrete and fiber concrete compressive and tensile strength (stress-strain) the uniaxial formulation is used. For steel bi-linear relationship is used. The approach is based on the discretization of the cross section trapezoidal tables. Forming the stiffness matrix of the section, the integral of the surface is calculated as the sum of the integrals on each of the cutting trapezoids. To integrate on the trapeze we have adopted the type of Simpson integration scheme.

Keywords numerical modeling      column and beam      nonlinear analysis      fibers      pious      reinforcement      3D formulation      response load-deflection     
Corresponding Authors: Fatiha IGUETOULENE   
Online First Date: 31 October 2017    Issue Date: 20 November 2018
 Cite this article:   
Fatiha IGUETOULENE,Youcef BOUAFIA,Mohand Said KACHI. Non linear modeling of three-dimensional reinforced and fiber concrete structures[J]. Front. Struct. Civ. Eng., 2018, 12(4): 439-453.
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Fig.1  Uniaxial constitutive law of the concrete compression
Fig.2  Stress-Strain behavior of tensile concrete
Fig.3  Stress-strain of fiber concrete [13]
Fig.4  Discretization of the concrete section into trapezoidal tables
Fig.5  Flow chart of the procedure for the research of equilibrium section
Fig.6  Axis system of an element in 3D- initial and deformed state of the element
Fig.7  Flow chart of the procedure for the research of equilibrium structure
Fig.8  The portico modeling of Vecchio and Emara
Fig.9  Evolution lateral displacement according to lateral load
Fig.10  Composed bending test for reinforced concrete pile with circular section
Index of the test piecefcj
Tab.1  Mechanical properties (measuring cylinders (ZHAN)) of the reinforced concrete (BA), measured at 350 kg/m3 of cement; and control concrete (BT), measured at 400 kg/m3 of cement
Index of the test piecefcj
Index of the test pieceEa
Tab.2  Mechanical properties of the composite (reinforced concrete with steel fibers). Measuring cylinders (ZHAN)
Fig.11  Comparison of the load-deflection curve between simulation and experiment (BT)
Fig.12  Comparison of results calculated with the result experimental BA pile
Fig.13  Comparison of results calculated with the result experimental BFAC pile
Fig.14  OG3 beam
Fig.15  Detail of reinforcement for beam OG3 and the Section A-A of the OG3 beam
Elasticity limit
Stress of rupture
Tab.3  Mechanical characteristics of the sample
MixedAge j (day)CompressionTraction (Bending)
fcj(Mpa)Eij(MPa)Ed (MPa)εb(‰)ftj(MPa)
Tab.4  Mechanical characteristics of concrete measured on specimens
Fig.16  Load-deflection curve for the beam OG3
[K]Stiffness matrix
{ΔU} Vector of nodes displacements increase
{ΔF}Vector nodes forces increase
{ΔP} Vector of applied loads increase
{ΔS} Vector of nodes displacements increase
[Ks]Sections Stiffness matrix
[Ss]Sections flexibility matrix
[B], [D]Matrix of geometrical transformations
[RT]Matrix linking the local coordinates and the absolute coordinates
eLongitudinal stretching of the element
EaElastic modulus of passive reinforcement
Eb0Elastic modulus of concrete
fcjConcrete compressive strength at j day
ftjConcrete tensile strength at j day
εb0Peak of the strains corresponding to fcj
G Shear modulus
Kband KbDimensionless parameters of the Sargin low
LoBar length before deformation
LBar length after deformation
MBending moment
NNormal load
u, vLongitudinal displacements of the nodes
q, zRotations of the elements
εLongitudinal deformation
σeElastic stress from passive steel
σrTensile strength of steel reinforcement
EctInitial modulus of the composite in tension
fftTensile strength of the composite
εuUltimate strain of the composite
εrFracture strain of the composite
εsuUltimate steel strain
σucResidual stress
ω¯Percentage of fibers
θoFiber orientation coefficient
lfLength of the fiber
τuUltimate bounding stress of the fiber
φDiameter of the fiber
GShear modulus
Ay, AzReduced sections
Ix Torsion inertia of section
γy,γzThe shear strains in the plane xy and xz
θxThe angle of torsion
α Angle between the center line of the reinforcement and the axis Gx
β Angle between the reinforcement, projection in the plane of the section and the axis Gy
( yf, zf)The reinforcement crossing point in the coordinate Gyz axis system
{Δεn}Normal strains increase
{Δεt}Shear strains increase
Em(y,z) Concrete modulus
[Ss] The flexibility matrix of the section, βi The angle between the projection of the reinforcement bare i in the plan Gyz, and the axis Gy
(yfi, zfi)The coordinate of the reinforcement bare i in the axis system Gyz
αithe angle between of the reinforcement bare i and the axis Gx
sfi The cross-section of the reinforcement bare i
EfiThe elastic modulus of the reinforcement
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