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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 1
Simplified damage models applied in the numerical analysis of reinforced concrete structures
In the 1D analysis, a mesh with 20 elements and 10 layers has
been considered. On the other hand, in the 2D analyses performed
by Guello [15] with Mazars’ model, a mesh with 38 x 16 triangle
finite elements (6 nodes) has been used in order to represent the
concrete, while a mesh with 30 bar elements represents the steel.
On the other hand, in this work, a mesh with 100 constant strain
quadrilateral (4 nodes) elements divided into 10 layers of 10 el-
ements and placed in whole extension of the structural element
has been considered for the 2D analysis with Pituba’s model. Note
that, in this mesh, one layer represents the reinforcement bar, see
Figure [4]. The results are described in the Figure [10].
In the 1D analysis, once again the stiffness degradation is observed
in a more evident way in the anisotropic model by the reasons previ-
ously explained. However, that difference is more evident after the
adherence loss stage between the reinforcement bar and concrete
presented in the Fig. [10] about 28 kN. Note that the 1D models pres-
ent a stiffness recovery after to total concrete cracking. That new re-
sistance is just owed to the reinforcement bar that presents an elastic
behavior up to yielding resistance be achieved. Those observations
are in agreement with others works (Mazars [1] and Guello [15]).
On the other hand, in the 2D analysis, the anisotropic model has
presented locking problems related to numerical responses due to
the distortion of the finite element that should be partly responsible
for the excessive stiffness, what does not happen with the Mazars’
model (triangular element). Therefore, there was not possibility
of more intense stiffness degradation by the anisotropic model.
Note that in this analysis the elastic behavior for reinforcement
bar has been assumed leading to the increase of difference about
numerical responses given by the models, due mainly to the finite
elements. Besides, in the 2D analysis the strain localization is an
important phenomenon in the behavior of concrete structures. In
particular, this structure is mainly tensioned presenting a localized
cracking configuration
[15]
.
4.3 Reinforced Concrete Beam
The third numerical application is about a reinforced concrete beam
submitted to monotonic loading. This beam was tested by Delal-
ibera [17]. The elastic parameters of the concrete are f
ck
=25MPa
and E
c
=32.3MPa. For the reinforcement has been adopted E
a
=
205 GPa, yielding stress 590 MPa and ultimate stress 750 MPa.
The geometric characteristics of the beam are given in Figure [11].
The loading is composed by two equal forces applied on the beam.
The uniaxial stress tests that were performed by Delalibera [17]
and they were used in order to identify the models parameters, see
Table 2 – Parameter values – reinforced concrete bar structure
Mazars’ model
Pituba’s model
Tension
Compression
Tension
Compression
A = 0,8
T
A = 1,4
C
-4
Y = 0,25x10 MPa
01
-3
Y = 0,1x10 MPa
02
-3
Y = 0,5x10 MPa
03
B = 20000
T
B = 1850
C
A = 130
1
A = 3
2
A = -0,6
3
e = 0,00001
d0
-1
B = 1000 MPa
1
-1
B = 11 MPa
2
-1
B = 1305 MPa
3
Figure 10 – 1D and 2D numerical responses
for reinforced concrete bar strucuture
Figure 11 – Geometry details of the reinforced concrete beam, dimensions in meters
0,3
2Ø6,3mm
2Ø12,5mm
2Ø20mm
0,15
2,85
0,3
F
F
0,1
0,1