315
IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 2
D. L. ARAÚJO | A. R. DANIN
|
M. B. MELO
|
P. F. RODRIGUES
of the bar during concreting (η
2
=1 for regions with good condition); and
η
3
is related to the bar diameter (η
3
=1 for φ < 32 mm). For reasons of
comparison, the design value of the concrete tensile strength (f
ctd
) was
taken equal to 90% of the concrete’s splitting tensile strength (f
ctm,sp
).
The basic anchorage length (
l
b
) is calculated following Equation
(5). In this case, for the steel’s yield stress (f
y
), the experimentally
obtained values were used.
(5)
bd
y
b
f
f
4

In line with item 12.2.3 of ACI 318M-08 [36], the anchorage length
of straight bars tensioned longitudinally must be calculated follow-
ing Equation (6).
(6)





tr
s e t
cm
y
b
Kc f 1,1
f
Using Equation (5), the design value of the ultimate bond stress fol-
lowing ACI 318M-08 [36] can be estimated by means of Equation (7).
(7)
s e t
tr
cm
bd
4
Kc
f 1,1
f



Here, λ is the coefficient that takes into consideration the con-
crete’s density (λ=1.0 for normal density concrete); K
tr
is the
coefficient that takes into account the confinement of the
concrete (K
tr
=1.0 in the absence of stirrups); the relation


 
tr
Kc
should not be higher than 2.5; ψ
t
=1.0 when less than
300 mm of fresh concrete is launched under the anchoring part; ψ
e
=1.0
when the reinforcement is not coated; ψ
s
=0.8 for bars with 10 mm diam-
eter. For the case of the realized tests, Equation (7) can be simplified into
Equation (8).
(8)
cm
cm
bd
f
859 ,0
8,04
5,2 f1,1
f
Upon comparing the results of Table 4, one notes that ACI
318M-08 is more conservative, proposing higher anchorage
lengths than those stipulated by the Brazilian and European
standards. These, on the other hand, present anchorage
lengths close to the value used in the test, i.e. 10 cm (or 10
φ
).
Furthermore, the bonding strength recommended by NBR
6118 and by Eurocode 2 happens to be close to the bonding
stress obtained in the test, with a difference of 25% less for the
concrete without fibers and of only 6% more for the concrete
with 1% fibers. This way, it can be deduced that the value of 10
cm (or 10
φ
) represents the straight basic anchorage length of
the tested bar and the expressions in these standards can be
used in order to evaluate the basic anchorage length of bars
immersed in fibrous concrete, as soon as the tensile strength
of the composite is known.
Special attention should be paid to the densification of the
fibrous concrete around the bar in order to avoid loss of
bonding stress. This happened in the bars of test specimens
CP10.10.2.A1 and CP10.10.2.A2, both with 2% fibers, which
did not reach the steel’s yield stress. This shows that the bond-
ing between the steel bar and the concrete in this case might
have been impaired, maybe because of problems during mold-
ing, such as the formation of a water film at the interface be-
tween bar and concrete, caused by excessive vibration. In the
other two test specimens in which the fibrous concrete has
less workability (Table 2), the bars failed without being pulled
out of the concrete.
3.3 Concrete splitting tests
The results of the concrete splitting tests, i.e. with bars with
diameters higher than 10 mm, as well as the concrete’s me-
chanical properties are shown in Table 5. In these tests, the
bonding length was kept constant and equal to 10
φ
, since the
anchorage’s failure due to splitting of the concrete was sought,
instead of the determination of the bonding stress between bar
and concrete.
Analyzing the influence of the concrete cover, it is noted that in
the tests with bars of 12.5 mm diameter (c/
φ
=5.5), all the test
specimens showed bond failure between bar and concrete,
since the bar was pulled out without any splitting of the con-
crete. In the tests with bars of 16 mm diameter (c/
φ
=4.2), two
test specimens showed splitting failure of the concrete cover
(Figure 8), and in one of these, the bar was pulled out without
splitting of the concrete cover.
Since the previous test was not conclusive with regard to split-
ting failure of the concrete cover, the reinforcement’s diameter
was increased by 20 mm, which represents a relation between
the concrete cover and the reinforcement’s diameter (c/
φ
)
equal to 3.25. In Table 5, it can be seen that due to the reduc-
Table 4 – Basic anchorage length for bars of 10 mm diameter
Fiber
volume (%)
NBR 6118 [34]/Eurocode 2 [35]
NBR 6118 [34]/Eurocode 2 [35]
ACI 318 [35]
ACI 318 [36]
Bonding strength – f (MPa)
bd
Basic anchorage length (cm)
f
cm
(MPa)
f
ctm,sp
(MPa)
0
1
2
58.90
58.70
66.98
73.20
69.96
67.80
4.84
5.98
8.74
8.12
9.17
10.80
9.80
12.11
17.70
16.44
18.57
21.87
6.59
6.58
7.03
7.35
7.18
7.07
15
12
8
9
8
7
22
22
21
20
21
21
1...,134,135,136,137,138,139,140,141,142,143 145,146,147,148,149,150,151,152,153,154,...190