Page 147 - Riem-Vol6_nº2
Basic HTML Version
318
IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 2
Influence of steel fibers on the reinforcement bond of straight steel bars
In order to represent the tensile behavior of the concrete with fi-
bers, the Hordijk constitutive model was used, which is available in
the DIANA
®
9.3 software, and which uses an exponential curve to
represent the concrete’s softening. In this case, the fracture energy
of the fibrous concrete (G
F
f
) was calculated using Equation (10),
available in literature [40].
(10)
f
f0
fF
V41,27 1
G
G
Here, G
0
f
is the fracture energy for the concrete without added fi-
bers and V
f
is the fibers volume, in percentage.
For the concrete without fibers, a constitutive tensile model with
linear softening was used, where the value of fracture energy was
determined in a three-point bend tests on notched beams (G
0
f
).
In order to represent the steel’s behavior, a constitutive model
with perfect elasto-plastic behavior was used, with the yield stress
equal to the experimentally determined values.
Table 6 shows the maximum strengths obtained in the test and
from the computer model. In general, the maximum strength ob-
tained from the computer model represented approximately 70%
of the maximum strength obtained in the test. This is due to the
fact that in the model there was intense cracking of the concrete in
the region close to the bar, which resulted in lack of convergence
of the numerical process. Despite this, it can be noted that in the
model with bonding length equal to 5
φ
, the fibers showed a small
influence on the bonding strength, with a 12% increase when com-
paring the model with 1% fibers with the model without fibers, and
a 14% increase when comparing the model with 2% fibers with
the model with 1% fibers. On the other hand, upon analyzing the
Figure 10 – Finite element mesh of models with bar of 10 mm diameter
Model with bonding length equal to 10
(10 cm)
A
Boundary conditions in displacement
in z-direction – concrete block base
B
Table 6 – Results of computer models with bar of 10 mm diameter
Bonding
length
Fiber
volume (%)
(1)
f
b,n
(MPa)
(2)
f
bm
(MPa)
Average maximum
experimental strength
F (kN)
exp
Maximum
numerical strength
F (kN)
u
5
10
0
1
2
0
1
2
13.8
15.4
17.4
9.6
9.8
9.9
18.7
20.9
23.8
9.6
9.9
10.3
32.2
35.0
31.7
45.6
50.4
48.6
23.0
25.7
29.3
30.9
31.5
33.0
0.71
0.73
0.92
0.68
0.63
0.68
(1) f is the average bonding stress, corresponding to the maximum numerical strength, determined by means of Equation
b,n
(12); (2) f is the bonding stress, corresponding to the maximum numerical strength, determined by means of the CQ48I
bm
interface element between bar and concrete.
F
exp
F
u
