Page 43 - Riem-Vol6_nº2

214 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 2
Numerical analysis of reinforced concrete beams strengthened with high strength cement-based
composite material
tween the two materials. These stresses may lead to the premature
debonding of the PBO-FRCM system and consequent structure fail-
ure with little mobilization of its resistance capacity, indicating that the
material was underutilized. Slipping between reinforcement and con-
crete was calculated using a six-node one-dimensional interface ele-
ment with quadratic interpolation functions, according to Adhikary and
Mutsuyoshi [9]. The constitutive model applied is that recommended
by the CEB-FIP Model Code 1990 [10], with bond stress (τ) to slip (s)
relationship parameters obtained by Silva [11] and shown in Figure 3.
3.5 Finite element mesh used for numerical analyses
Due to the loading symmetry, mechanical properties, and geom-
etry, only half of the beams were used in the numerical simula-
tions. The finite element mesh used in the numerical simulations
is presented in Figure 4. Concrete was discretized by 18 two-di-
mensional plane stress elements, and the external reinforcement
and the interface concrete/strengthening were discretized by eight
one-dimensional elements.
Further details of the finite element model used in the numerical
simulations are described by Paliga et al. [12].
4. Results
In this section, the results obtained using numerical simulations are
presented, discussed and compared with the results of the experi-
mental program (Ombres[1]). It must be mentioned that the finite
element model was able to follow up beam performance from initial
loading to ultimate load. The numerical model was also able to
detect beam failure mode. Failure may be ductile, due to excessive
elongation of the tensioned reinforcement or to failure caused by
PBO-FRCM material tension, or fragile, resulting from crushing of
the compressed concrete or from PBO-FRCM system debonding.
4.1 Series S1
In this series, two beams were reinforced at a tension reinforcement
as a stiffer line inside the concrete that resists only to axial forces.
It was assumed perfect bonding between the reinforcement and the
concrete that involves it. Therefore, the reinforcement stiffness matrix
has the same dimensions as the concrete element. The adopted steel
constitutive equation is bilinear both for tension and compression.
3.3 Model for the strengthening composite material
The strengthening material was modeled by quadratic elements of
plane truss with three nodes. The element is fixed to the remain-
ing finite element mesh by an interface element. These materials
are modeled as having linear elastic behavior until rupture stress
is achieved, and are able to absorb only tension forces parallel to
their longitudinal axis.
3.4 Model for the interface between the concrete
substrate and the PBO- FRCM system
The transference of forces between the external strengthening sys-
tem and the concrete generates bond stresses at the interface be-
Figure 3 – Constitutive model for the interface
concrete/strengthening system
Figure 4 – Finite elements mesh