Prediction of bond failure and deflection of carbon fiber-reinforced plastic reinforced concrete beams
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Abstract
Carbon fiber-reinforced plastic (CFRP) reinforced concrete beams can fail due to interface debonding, due to the high tensile strength of such rebars. A set of 16 concrete beams reinforced with different amounts of CFRP reinforcement was subject to static three-point bending. The beam dimensions and CFRP reinforcements used were selected to demonstrate a transition from compression failure to bond failure with decreasing reinforcement ratio. It is shown that accurate bond strength data to predict such failures can be obtained from a “hinged-beam” test configuration, rather than the conventional direct “pull-out” tests. Deflection under service loads can also be predicted more accurately using a proposed equation that includes the reinforcement ratio and the elastic modulus of the reinforcement.
Key Words
Bond slip deflections pull-out failure strengthNomenclature
- f'c
concrete strength in compression
- Ef
E lb =E FRP =modulus of elasticity of the FRP
- ρf
ratio of tension reinforcement=A f /bd
- AFRP
A f =area of the FRP tension reinforcement
- b
width of the member
- d
distance from extreme compression fiber to centroid of tension reinforcement
- α1
ratio of the depth of the equivalent rectangular stress block to the depth to the neutral axis at ε cu
- ffd
0.65f fu
- cb
ε cu d/(ε cu +ε fd )
- εcu
maximum concrete strain in compression
- εfd
rebar strain=f fd /E f
- db
diameter of the rebar
- Ab
cross-sectional area of the rebar
- C
constant=πd b /E lb A b
- x
distance along the bar starting at the free end of the beam
- εb(x)
rebar strain variation along the distancex
- N(x)
normal force along the bar
- k
constant that multiplied by the effective depth of the section gives the neutral axis position from the compression
- fiber
\(\sqrt {(\rho n)^2 + 2(\rho n) - } (\rho n)\)
- Icr
cracked moment of inertia of a cross section=(kd) 3 (b)/3+nA FRP (d−kd) 2
- Ec
modulus of elasticity of the concrete
- n
modulus ratio=E FRP /E c
- Ig
gross moment of inertia
- fr
modulus of rupture of the concrete
- Mcr
cracking moment=f r (I tr )/y t
- Itr
moment of inertia of the transformed section
- yt
distance from centroidal axis to the extreme fiber in tension
- Ie
effective moment of inertia
- Ma
maximum moment in a member at the stage for which deflection is computed
- α
0.84
- β
7.0
- γ
reduction factor=E FRP /E s
- ŋ
100 π−0.2
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References
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