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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 5
Flexural strengthening of reinforced concrete beams with carbon fibers reinforced polymer (CFRP) sheet
bonded to a transition layer of high performance cement-based composite
tion: 0.6×f
fct,L
. The post-peak behavior of the cement composite
was represented by an Exponential softening in tension diagram,
having in the high value attributed to the energy of fracturing, the
indication of the presence of fibers and microfibers of steel. The
energy of fracture was calculated up to a deflection for the pris-
matic specimen, equal to d = 2.65 mm.
5.2 Numerical analysis results
In the Figure [17] the curves load-deflection numerically obtained
are compared with the experimental results. Of the Figure [17-a] it
is observed that in the elastic phase, the numerical curve for the
control beam is identical to the experimental and after the concrete
cracking, the numerical is stiffer.
For the control beam, the first crack load obtained numerically is
24.6 kN, which is 17% higher than the load 21.01 kN, of first crack,
extracted from the experimental results. With the load of 85.3 kN,
it occurs the reinforcement yield, represented by the sharp drop of
stiffness of the numerical curve. This value exceeds the obtained
experimentally (79.80 kN) only in 6.89%.
In the Fig. 18-b, it can be observed that the similar behavior of the
Table � � �aterials and parameters �or the n�meri�al model o� the beams V1A� V1C and V2C
Parameters
Concrete
Steel
Beams
V1A
V1C
V2C
Elastic modulus
30,034 MPa
26,553 MPa
29,380 MPa
Poisson�s ratio
0.20
0.20
0.20
Tensile strength
2.04 MPa
1.93 MPa
2.06 MPa
Fracture energy
0.151 N/mm
0.123 N/mm
0.155 N/mm
Width of the crack band 19.61 mm
20.12 mm
20.03 mm
Compression strength
37.84 MPa
33.95 MPa
38.68 MPa
Tensile behavior
Exponential model
Elastic modulus
210,921 MPa
199,677 MPa
210,921 MPa
Yield stress
547.99 MPa
532.44 MPa
547.99 MPa
Behavior after yield
Elastic-perfectly plastic model
Table � � �aterials an� �arameters referring to the transition layer of the beam V2C
N�merical mo�el V2C � Com�osite cement�base� C����2C
Linear Elasticity
Isotropic, Young´s modulus = 28,700 MPa, Poisson´s ratio = 0.20
Static Nonlinearity
Concrete and Brittle Materials, Total Strain Rotating Crack, Direct Input, Exponential Softening in
Tension, Ideal in compression, Tensile strength = 2.24 MPa, Mode-I tensile fracture energy = 0.526
2
0,5
N.mm/mm , Crack bandwidth = (finite element area) = 20.03 mm, Compressive strength = 28.07 MPa.
numerical and experimental curves. After the concrete cracking
and up to the load of 75 kN, the numerical curve is slightly more
stiffen than the experimental. After this strength value, the curves
develop again very similarly up to approximately 128.62 kN, and
then up to the failure, the numerical curve develops with a stiffness
lower than the experimental curve.
The first concrete crack obtained through the FE occurred with
load equal to 26.96 kN, being this value 7.15% higher than the
obtained experimentally. The reinforcement yield, according to the
numerical model was given by a load of 122.4 kN, i.e., only 3.33%
above the experimental value which is 118.45 kN. In addition, the
load value corresponding to the failure pointed by the numerical
model is 134.34 kN, while the experimental is 147.37 kN.
The Figure [18-c] shows that until the reinforcement yield, the
numerical curve shows a higher stiffness than the experimental
curve. After the reinforcement yield, the numerical curve begins to
show higher values of vertical displacements than the experimen-
tal curve, within a same level of loading.
The first crack appearance according to the experimental results
was given by the load of 34.92 kN, while by the numerical model
was given by a load of 32.16 kN. The reinforcement yield according