Page 145 - Riem-Vol6_nº2

316 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 2
Influence of steel fibers on the reinforcement bond of straight steel bars
tion of the concrete cover, in all the tests splitting of the con-
crete was observed. For this reason, this diameter was used
to analyze the influence of the fibers on the concrete’s splitting
strength.
It is worth noting that with the bar of 20 mm diameter, the bond-
ing length was 20 cm, and equal to the test specimen’s length.
As such, there was no part without bonding of the bar with the
concrete. Previous test results with this same test specimen
and bar of 20 mm diameter, but with bonding length equal to
10 cm (or 5φ), showed a bonding stress that was much higher
than the real values. This happened due to the test speci-
men’s way of molding, which introduced additional resisting
mechanism next to the bonding between bar and concrete [37].
For this reason, it was opted to maintain the test specimen’s
height, even without the non-bonding part.
From the test results, it can be concluded that the addition
of 1% steel fibers propitiated an average increase of 100%
in the maximum load, while the addition of 2% increased
this maximum load by 157%. When an analysis of variance
is carried out on these results (with a 95% confidence inter-
val), it can be concluded that the addition of fibers as well
as its volume significantly influenced the concrete’s splitting
strength.
This increase in the splitting strength of the concrete cover
is related to the increase in the concrete’s splitting tensile
strength. Starting from theory of elasticity [38], it is possible
to write Equation (9), giving us the maximum circumferen-
tial stress (σθ,max ) in a circular section with radius b, with a
circular hole with radius a, to which is applied an internal
pressure pi, distributed along the internal hole. In this case,
the maximum stress occurs on the side of the internal hole.
(9)  
2 2
2 2
i
max , a b
b aP


 

When in this expression the test specimen’s dimensions are sub-
stituted, i.e. a=10 mm (half of the bar’s diameter), and b=75 mm
(shortest distance from the bar’s surface to the test specimen’s
surface, being the cover), the result is σ θ,max=1.036pi. The radial
pressure acting on the internal hole can be related to the bar’s
bonding stress (fb) starting from the knowledge of the inclination
of the bar’s ribs (β), i.e. pi=fb/tg β. Assuming that the bar has the
lowest rib inclination allowed for high-bonding bars, i.e. β=45° [1],
pi =fb is reached. For the test specimen without fibers, the bonding
stress can be calculated by means of Equation (1) and is equal to
5.1 MPa, from which it can be concluded that the maximum circum-
ferential stress in this model is equal to 5.3 MPa. This value is only
2% lower than the average splitting tensile strength of the concrete
used for the test specimens, i.e. 5.41 MPa (Table 5). This indicates
a good correlation between the load measured during the test and
the concrete’s tensile strength.
In the case of the models with steel fibers, the maximum circumfer-
ential stress is 10.7 MPa for the test specimen with 1% fibers and
13.8 MPa for the test specimen with 2% fibers. These values are
18% and 32% higher than the average splitting tensile strength of
the concrete (Table 5). However, the fibrous concretes showed a
strength increase after the matrix’s cracking, which justifies this dif-
ference, since Equation (9) is valid for fragile materials.
Table 5 – Results of concrete properties and splitting test
Test
specimen
fcm
(MPa)
fctm,sp
(MPa)
Ecm
(MPa)
G f
2 (N.m/m )
F max
(1) (kN)
Failure
type
CP12,5.10.0.A1
CP12,5.10.0.A2
CP12,5.10.0.A3
CP16.10.0.A1
CP16.10.0.A2
CP16.10.0.A3
CP20.10.0.A1
CP20.10.0.A2
CP20.10.0.A3
CP20.10.1.A1
CP20.10.1.A2
CP20.10.1.A3
CP20.10.2.A1
CP20.10.2.A2
CP20.10.2.A3
53.0±7.67
60.77±4.71
58.90±3.32
58.70±3.86
73.20±2.72
73.07±3.43
77.97±2.02
67.80±0.98
4.99±0.95
5.94±0.28
4.84±0.44
5.98±0.05
8.76±0.24
9.38±0.04
9.84±1.23
11.10±0.46
29.60±0.62
31.00±0.82
29.03±0.48
28.33±0.35
30.83±0.23
30.15±0.49
31.10±0.53
30.27±0.32
0.080±0.034
0.040±0.012
ND
0.062±0.019
–
–
–
–
61.2
55.7
58.4
95.1
81.0
88.6
64.2
61.3
68.9
119.7
131.1
139.1
179.7
180.1
140.0
Pull-out
Pull-out
Pull-out
Splitting
Splitting
Pull-out
Splitting
Splitting
Splitting
Splitting
Splitting
Splitting
Splitting with yield of steel
Splitting with yield of steel
Splitting
ND: non-determined value. (1) Represents the last strength obtained during the test, which in case of fibrous concrete is higher
than the matrix' cracking strength.