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8/4/2019 09 Strengthening 2009 Nov9
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Flexure and Shear
using EB FRP Reinforcement
Tams NAGY-GYRGYLecturer, CE, Ph.D.
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fib
Initial load Mo = service moment acting during strengthening
Mo
is typically larger than the cracking moment Mcr
the calculation is based on a cracked section
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fib
1. full composite action of concrete and FRP is maintained
until the concrete reaches crushing in compression or the
FRP fails in tension (such failure modes may also be characterized as
2. composite action is lost prior to class 1 failure, e.g. due to
pee ng-o o e
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fib
Steel yielding followed by concrete crushing
Steel yielding followed by FRP fracture
Concrete crushing(high reinforcement ratios brittle and undesirable failure mode)
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Debonding and bond failure modes
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Bond behaviour of RC members strengthened with FRP
Most failures observed caused by peelingoff of the EBR element.These depends on the starting point:
in an uncrackedanchorage zone
caused atflexural cracks
caused atshear cracks
caused by the unevennessof the concrete surface
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fib
Bond behaviour of RC members strengthened with FRP
Also was observed FRP end shear failure (or concrete ripoff)
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fib
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fib
VRd = min (Vcd + Vwd + Vfd , VRd2 )
Vfd = 0.9 fd,e Efu fbw d (cot + cot ) sin
fd,e = design value of effective FRP strain=w
d = effective depth of cross section
f = FRP reinforcement ratio equal to 2tfsin / bw for continuously bonded shearreinforcement of thickness tf or (2tf/bw)(bf/sf) for FRP reinforcement in the form of
f
Efu = elastic modulus of FRP in the principal fibre orientation
= angle of diagonal crack with respect to the member axis, assumed equal to 45 = angle between principal fibre orientation and longitudinal axis of member
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fib
Vfd = 0.9 fd,e Efu fbw d (cot + cot ) sin
= k k = 0.8
fd,e = fk,e / f f= 1.3
, ,
fu
.
ffu
/
cme,f
E
f.
30032
170 Fully wrapped (or properly anchored) CFRP - FRP fracture controls:
Side or U-shaped CFRP jackets:
fu
.
ffu
/
cm
.
ffu
/
cme,f
E
f.;x
E
f.min
30032
3
56032
17010650
Fully wrapped AFRP (FRP fracture controls):fu
.
ffu
/
cme,f
E
f.
47032
0480
Note that in the equations () fcm is in MPa and Efu is in GPa.
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Taljsten
Where f= 0.6fu
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fib
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Comparison of the axial compressive stress as a function of the
axial strain for an unreinforced, reinforced with steel stirrups and
- , , .
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fib
(c
/
fck
)
(c / cc )
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fib
Circular column
Continuous confinement Confinement with gaps
f = fu
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Teng et. al.
Rectangular column