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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 theoretical results for the beams with inclined stirrups should
be carefully analyzed in the future because the original upper-
bound model was formulated for vertical stirrups only.
Finally, it is necessary to verify the proposed model comparing the
theoretical results with more experimental data, as well as adopt
other expressions for the concrete effectiveness factor.
8. References
[01] American Concrete Institute −ACI 318. Building code
requirements for structural concrete. USA. 2005.
[02] American Concrete Institute − ACI 440. Guide for the
design and construction of the externally bonded FRP
systems for strengthening concrete structures. USA.
2001.
[03] FIB (CEB-FIP). Externally bonded FRP reinforcement
for RC structures. Bulletin 14. Lausanne. 2010.
[04] SIKA – Electronic catalogue, www.sika.com.br; visited
in 2006.
[05] SALLES NETO, M. Shear behavior of reinforced
concrete T beams strengthening with carbon fiber
composites (in Portuguese). M.Sc. Dissertation. UnB.
Brazil. 2000.
[06] JAYAPRAKASH, J.; SAMAD, A. A. A.; ALI, A. A. A.;
ABBASOVICH, A. A. An experimental investigation on
shear enhancement cracked RC beams with
bi-directional carbon fabrics. Cement Combination for
Durable Concrete, Thomas Telford. UK. 2005. pp.537-546.
[07] BEBER, A. Structural behavior of reinforced concrete
beams strengthening with carbon fiber composites
(in Portuguese). PhD Thesis. UFRGS. Brazil. 2003.
[08] KHALIFA, A.; NANNI, A. Rehabilitation of rectangular
simply supported RC beams with shear deficiencies
using CFRP composites. Constructions and Building
Materials, Vol. 6, No 3. 2002.
[09] ADHIKARY, B. B.; MUTSUYOSHI, H.; ASHRAF,
M. Shear strengthening of RC beams using FRP
sheets with bonded anchorage. ACI Structural
Journal. Vol. 1001, No 5. 2004. p.660-668.
[10] HOANG, L. C. Shear strength of non-shear reinforced
concrete elements. Department of Structural
Engineering and Materials. Technical University of
Denmark, Report No 29. 1997.
[11] HOANG, L. C.; NIELSEN, M. P. Plasticity approach to
shear design. Cement and Concrete Composites, 20.
1998. p.437-453.
[12] NIELSEN, M. P. Limit analysis and concrete plasticity.
CRC Press. USA. 1999.
[13] CHEN, J. F.; TENG, J. G. Shear capacity of
FRP-strengthened RC beams: FRP debonding.
Construction and Building Materials, 17. 2003. p.27-41.
[14] SPAGNOLO JUNIOR, L. A. Experimental study of
reinforced concrete beams strengthened for shear
force with carbon fiber composites. Master Science
Dissertation (in Portuguese). PUC-Rio. 2008.
[15] American Society for Testing and Materials – ASTM
D3039/D3039M. Standard test method for tensile
properties of polymer matrix composite materials.
USA. 2000.
9. Notation
a
= shear span
f
A
= CFC longitudinal area
ft
A
= CFC transverse area
sw
A
= total cross sectional area of steel stirrups in web
b
= flange width
w
b
= web width of beam
d
= effective deep of beam
f
D
= stress distribution factor
f
E
= CFC elastic modulus
c
f
= uniaxial standard compressive strength of concrete
f
f
= CFC tension
ef f
f
,
= effective axial CFC stress
ef t
f
,
= effective tensile strength of concrete
uf
f
,
= CFC ultimate tensile strength
s
f
= steel tension
yw
f
= yield steel strength
h
= depth of beam
e
L
= effective bond length
max
L
= maximum bond length
P
= applied load
CR
P
= crack load
exp u,
P
= experimental ultimate load
s
= steel stirrup spacing
f
s
= CFC stirrup spacing
f
t
= CFC thickness
u
= displacement
V
= shear force
c
V
= concrete shear contribution
exp u,
V
= ultimate shear strength
ref u,
V
= ultimate shear strength of reference beam
theor u,
V
= ultimate theoretical shear strength
f
w
= stirrup width
x
= horizontal projections of yield line/critical diagonal crack
= angle between yield line and displacement direction
= angle of the CFC stirrup with horizontal axis
L
= non-dimensional coefficient
w
= non-dimensional coefficient
ef f
,
= CFC effective strain
f
=
l
it i
l
ft
=
t
sw
= t t l
ti
l
f t l ti
i
fl
i t
i t f
d
ff ti
f
f
= t
i t i
ti
f t
f
E
l ti
l
c
i i l t
i t
t f
t
f
t
i
ef f
,
ff ti i l
t
ef t
,
ff ti t
il t
t f
t
f
,
=
lti
t t
il t
t
s
f
t l t
i
i l t l t
t
t f
ff ti
l
t
i
l
t
li
l
l
,
i
t l lti
t l
t l ti
i
f
ti
ing
f
t
t i
i l
t
f
t
t i
ti
,
lti
t
t
t
f ,
lti
t
t
t f f
theor u,
V
lti
t t
ti l
t
t
f
ti
i th
i
t l
j ti
f i l li
/ iti l i
l
l between i l li
i l
t i
ti
l f t
ti
it
i
t l i
i
i
l
ffi i
t
i
i
l
ffi i
t
ef f
,
ff ti t i