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IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 1
RC T beams strengthened to shear with carbon fiber composites
The deformation field angle
q
e
was obtained by classical formulas of
Solids Mechanics, with the aid of readings of the strain gauge rosettes.
The basic hypothesis of the CSM is evaluated by means of com-
paring the
crack angle
q
CR
, the deformation field angle
e
q
, and
the angle of idealized diagonal crack sliding
CIN
q
,
because the
yield line is assumed to be equal to the crack in this model. This
shows that this model furnishes good agreement with the experi-
mental data of this test program. The suitability of this theoretical
model can also be assessed by analysis of the ratios
q
CR
/
q
CIN
and
CIN
q
q
e
, which gives good statistical results.
Table [4] shows the different types of angle measured in tests, the
crack angle
q
CR
, the deformation field angle
e
q
and the theoreti-
cal values for the ultimate shear given by the CSM
CIN
q
. The cal-
culated shear theoretical capacity is not limited by the bond model
adopted. As shown in the last column, the mean strength ratio is
07.1
,
.
theor
u
exp u,
V V
with a coefficient of variation of 6.79 %.
6.3 Comparison between experimental data
and upper-bound solution
The ultimate theoretical shear strength of each beam was comput-
ed using equations 1 to 19, as discussed earlier. The predictions of
the CSM are very close to the test beam results.
A very good agreement is obtained in terms of strength, but ad-
ditional study into this theoretical approach is necessary, focusing
on different reinforcement ratios and other stirrup configurations.
7. Conclusions
The results confirm that the technique of strengthening with CFC
sheets significantly increases shear capacity. None of the beams
presented bending failure, and the ultimate load of the strength-
ened beams was 36 % to 54 % greater than the reference beams.
All the beams showed good ductile behavior.
The CFC strips glued on top of CFC
U
stirrups are an effective way of
guaranteeing the bond between the CFC and the concrete surface.
The proposed upper-bound model provides good results and the
ratio
.
exp u,
theor
u
V V
,
has a coefficient of variation of 6.79 %, but
the following considerations should be made:
n
the theoretical results depend on the values assumed by the
concrete effectiveness factor, i.e., the adoption of an appropri-
ate expression for
0
ν
governs the results;
n
the equation
fw
sw
is susceptible to criticism, be-
cause the CFC external stirrups do not have the same mechani-
cal behavior as the steel stirrups, due, mainly, to the fact that
they are not completely enveloped by the concrete or provide
a dowel action. The assumption that the total shear strength
is the sum of the steel and CFC reinforcement strengths (i.e.,
the additive approach for reinforcements) is the fundamental
hypothesis for all theoretical models.
Figure 12 – Crack angle in the shear span of VR1
(digital measurement)
A
B
Figure 11 – Beam failure: a) VR2; b) VII-1