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.
. [J]. Frontiers of Structural and Civil Engineering, 2018, 12(4): 439-453.
Fatiha IGUETOULENE, Youcef BOUAFIA, Mohand Said KACHI. Non linear modeling of three-dimensional reinforced and fiber concrete structures. Front. Struct. Civ. Eng., 2018, 12(4): 439-453.
Matrix linking the local coordinates and the absolute coordinates
e
Longitudinal stretching of the element
Elastic modulus of passive reinforcement
Elastic modulus of concrete
Concrete compressive strength at j day
Concrete tensile strength at j day
Peak of the strains corresponding to
Shear modulus
and
Dimensionless parameters of the Sargin low
Lo
Bar length before deformation
L
Bar length after deformation
M
Bending moment
N
Normal load
T
Shear
u, v
Longitudinal displacements of the nodes
q, z
Rotations of the elements
Longitudinal deformation
Elastic stress from passive steel
Tensile strength of steel reinforcement
Initial modulus of the composite in tension
Tensile strength of the composite
Ultimate strain of the composite
Fracture strain of the composite
Ultimate steel strain
Residual stress
Percentage of fibers
Fiber orientation coefficient
Length of the fiber
Ultimate bounding stress of the fiber
Diameter of the fiber
G
Shear modulus
,
Reduced sections
Torsion inertia of section
,
The shear strains in the plane xy and xz
The angle of torsion
Angle between the center line of the reinforcement and the axis Gx
Angle between the reinforcement, projection in the plane of the section and the axis Gy
(, )
The reinforcement crossing point in the coordinate Gyz axis system
Normal strains increase
Shear strains increase
Concrete modulus
The flexibility matrix of the section, The angle between the projection of the reinforcement bare i in the plan , and the axis
The coordinate of the reinforcement bare i in the axis system
the angle between of the reinforcement bare i and the axis
The cross-section of the reinforcement bare i
The elastic modulus of the reinforcement
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