Basic HTML Version
4
IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 1
RC T beams strengthened to shear with carbon fiber composites
or
(8)
21.0
75.0
95.16 67.2
0
0
fw
sw
fw
sw
c
u
h
s
for
The distance
x
in original paper [10] is given by equation 9, and
the proposed in this paper is given by equation 10:
(9)
c sw
c
f
h x
2
(10)
c fw
sw
c
f
h x
2
The angle of idealized diagonal crack
CIN
q
is given by:
(11)
x
h
tg
CIN
The equations 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11 indicate that
the effectiveness factor
0
ν
is an important parameter in this theo-
retical formulation. It governs the concrete shear resistance and
transverse reinforcement contributions for shear capacity. A ratio-
nal choice of one adequate expression for this parameter is funda-
mental for the predicted results. The value of the effectiveness fac-
tor depends on the material, size effect, geometry, reinforcement,
loading of the structures, and on the internal cracking process.
3.2 Bond model
The bond between carbon fiber composites and concrete is a
fundamental hypothesis that requires special attention for it repre-
sents the means by which stress is transferred between concrete
and CFC.
Significant advances in experimental studies into bond have been
achieved in recent years, and research shows that this technique
cannot mobilize the full tensile strength of CFC, due to the debond-
ing and the peeling phenomenon.
The bond between CFC U vertical stirrups and concrete is the
key factor in this study. The proposed formulation adopts a bond
model for the concrete-CFC interface, in which the CFC effective
mechanical properties should be carefully analyzed. The theoreti-
cal model adopted is the debonding failure mode ([13]), and the
effective axial CFC stress is given by:
(12)
ef f f
ef f
E f
,
,
verse reinforcement can be seen as the sum of two terms ([12]).
(1)
fw
sw
(2)
c
yw
w
sw
sw
f
f
db
A
0
(3)
c
fu
f w
f
f
fw
f
f
sb
wt
0
,
2
Concrete strengths of tested beams are very different to the
strength measured on 15
cm
x 30
cm
cylinder specimens be-
cause the concrete is cracked and the cracking reduces the
strength. It is essential to consider a reduced concrete strength
and, in the models of Plasticity Theory, it is indispensable to in-
sert a concrete effectiveness factor
1
0
≤
ν
into the theoretical
solution. Concrete is regarded as a perfectly plastic material,
which has a brittle behavior with poor ductility in compression.
The effectiveness factor
0
ν
decreases with the increase of the
concrete compressive strength.
The effectiveness factor is given by:
(4)
D
c
h
f
26 1 1 1 88.0
0
and the shear capacity of cracked concrete is:
(5)
0
64.11
fw
sw
c
u
with
(6)
c
c
f
0
059 .0
The upper-bound solution for the shear capacity of the cracked
concrete taking into account finite stirrups spacing is given by:
(7)
21.0
95.16
64.11
0
0
0
fw
sw
fw
sw
fw
sw
c
u
h
s
for