FRP Shear Strengthening of RC Beams
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Transcript of FRP Shear Strengthening of RC Beams
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ACI
WEB SESSIONS
Influencing Parameters
The following parameters that influence deboning ofFRP are studied:
Bond Model Effective Strain
FRP Effective Anchorage Length
FRP Effective Width
Strip-Width to Strip-Spacing Ratio
Crack Pattern
Transverse Steel
ACI
WEB SESSIONS
Status of influencing factors on shear strengtheningof RC beams in the current design guidelines.
International Design Codes and Guidelines
ACI
WEB SESSIONS
to study the effect of parameters which have
been proven to influence the shear resistance
of EB FRP, but which have not been sufficiently
documented in the guidelines,
The main impetus to carry out current study are;
Research Significance
to develop a transparent and evolutive design
model for the shear resistance of FRP-
strengthened beams which fail by FRP
debonding.ACI
WEB SESSIONS
Influencing Parameters (cont'd)
Bond Model:To study the mechanism of FRP debonding from concrete, a reliablebonding model is required.
frp frp e effP =w L
Maeda et al. (1997)
Holzenkmpfer (1994)
Khalifa et al. (1998)
Neubauer and Rostsy(1997)
Chen and Teng (2001)
The origin of mostcurrent NLFM modelsthat calculate bondstrength between FRP
and concrete,
The model uses correctconcept and variables.
The model is designedto calculate bondstrength between steelplates and concrete,
The model producesconservative results inpredicting the effectivebond length,Le.
The origin of current
ACI 440.2R model tocalculateVfrp,
Introduced theeffective length conceptfor FRP bonded toconcrete,Le,
Calculated Pfrp is
relatively accurate forl im it ed concretestrengths.
The effect off'c is not
considered,
Fails to pred ictaccurately Le and effwhen thesepa ra me ters a reconsidered separately.
Fails to pred ictaccurately Le and effwhen thesepa ra me ters a reconsidered separately.
The current HB 305code (previously knownas CIDAR) model tocalculateVfrp,
Considers a ll thecorrect variables in thebond model,
Calculated Le is
relatively accurate.
The modified version ofHolzenkmpfer (1994)model for FRP bondedto concrete,
The bond model usescorrect concept andvariables.
CalculatesPfrp andLe are
rather accurate.
Produces conservative
results in predictingthe bond strength,Pfrp.
The Modified version of
Maeda et al. (1997)model and the currentACI 440.2R model tocalculatedVfrp,
Considers a ll the
correct variables in thebond model,
Calculated Pfrp is
relatively accurate.
The model have notbe en originallydeveloped for RCbeams strengthened in
shear with FRP.
Advantage disadvantage
ACI
WEB SESSIONS
Influencing Parameters (cont'd)
Effective Strain:
2 (cot cot ) sinf f fe f ff
f
t w E d V
s
All the FRP strips intersected by the selectedshear crack are assumed to contribute the sameFRP effective strain.
Assuming that FRP carries only normal stresses inthe principal direction, FRP may be treated byanalogy to internal steel.
Most of design models or equations basically usesimilar design analogy with different definitions ofthe effective strain.
ACI
WEB SESSIONS
Influencing Parameters (cont'd)
FRP Effective Anchorage Length: Beyond a certain FRP bond-length threshold,
increasing bond length does not result in an increasein the ultimate bond strength.
0
50
100
150
200
0 100 200
Le
(mm
)
Ef.tf (GPa.mm)
Maedaetal.(1997)ModifiedNLFM
Note: In NLFM equation fct isassumed to be equal to 5 MPa.
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ACI
WEB SESSIONS
Influencing Parameters (cont'd)
FRP Effective Width:
Effective width of FRP in RCbeam strengthened withside-bonded FRP
Only the FRP fibers that have an anchorage length
greater than the FRP effective length remainadequately anchored.
w = d - Le f ef
dfLe d
Le
The width of the FRP sheet, wf, is replaced by aneffective width, w
fe.
ACI
WEB SESSIONS
Influencing Parameters (cont'd)
Strip-Width to Strip-Spacing Ratio:
Previous FRP-to-concrete direct pull-out tests have
shown that the width of the FRP sheets bonded to aconcrete block has a significant effect on the maximumbond strength of the FRP.
According to experimental research studies as the FRPsheets become narrower, the bond strain increases.
Holzenkmpfer (1994)and Neubauer andRostsy (1997)
Chen and Teng (2001).
2
1
f
f
wf
f
w
s
w
s
21.125
1400
p
cp
p
b
bk
b
ACI
WEB SESSIONS
Influencing Parameters (cont'd)
Transverse Steel:
It has been clearly established that theeffectiveness of the strengtheningcontribution of FRP to shear resistancedepends on the amount of internal shear-steel reinforcement.
None of the guidelines has yet considered intheir formulae the effect of transverse steelonVf.
ACI
WEB SESSIONS
Influencing Parameters (cont'd)
Cracking Pattern:Experimental observations clearly showedthat in RC beams with transversereinforcement the shear-crack patterntends to be distributed over a large widthcompared with the pattern in RC beamswith no or low shear reinforcement. No transverse reinforceme nt
Transverse steel reinforcement EB U-Jacket FRP sheet Transverse steel reinforcemen t
+ EB U-Jacket FRP sheet
ACI
WEB SESSIONS
Influencing Parameters (cont'd)
Transverse
ReinforcementRatio
(Steel + FRP)
Crack PatternDistribution
FRP AnchorageLength
Amount of FRPfibers longerthan (or equalto) effectiveanchorage length
Bond Strengthbetween FRPand Concrete
EB FRPcontribution to
the shearresistance
ACI
WEB SESSIONS
Proposed Model (cont'd)
e
Le
Le
L
wfe
Equivalent rectangularbondarea
e
eL
Side bondedFRP effective width
Area withinadequate
FRP anchorage length
(c)
(d)
Area with inadequateFRP anchorage length
Side bonded FRPactual width
FRP U-jacketeffective width
L
e
wfe
Trapezoidal
bonding areaArea withinadequate
FRP anchorage length
FRP U-jacketactual width
Equivalent rectangular
bondarea
(a)
(b)
Trapezoidalbondingarea
L
ACI
WEB SESSIONS
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WEB SESSIONS
Proposed Model (cont'd)
y = 0.6x-0.5y = 0.43x -0.5
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50
kc=w
e/df
fEf+sEs
U-JacketFRP-debonded
Side-bonded FRP-debonded
U-Jacket-concrete crushing
In the calculation of wfe, it is assumed that the crackingpattern changes with the amount of internal steel and externalFRP shear reinforcement as measured by their respectiverigidities.
ACI
WEB SESSIONS
Proposed Model (cont'd)
The effective width is then calibrated as a function ofj for beams strengthened with a continuous
U-jacket and side-bonding configurations.
The cracking modification factor can then be calculated as:
( )f f s sE E
0.6 for U-Jacketfe f
f f s s
w dE E
0.43 for side bondedfe f
f f s s
w dE E
0.6 for U-Jackets
0.43 for side bonded
fec
f f f s s
fec
f f f s s
wk
d E E
wk
d E E
ACI
WEB SESSIONS
Proposed Model (cont'd)
The effects ofkcto consider the effect of cracking pattern
and that of kwto incorporate the wf/ sfratio of the FRP
strips are considered in the equation for effective strain:
The shear contribution of FRP, Vf, can be calculated as a
function of feusing the following equation:
0.31.
c L w eff e cfe c L w fu
f f f f
k k k L fk k k
t E t E
2 (cot cot ) sinf f fe f f
f
f
t w E d V
s
ACI
WEB SESSIONS
Validation of the Proposed Model
28
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0
Vf cal(kN)
Vf exp (kN)
Side bonded-Proposed model
U-Jacket-Proposed model
R2 = 0.61
ACI
WEB SESSIONS
ACI
WEB SESSIONS
Validation of the Proposed Model
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0
Vf cal(kN)
Vf exp(kN)
Side bonded-Proposed model
U-Jacket-Proposed model
R2 = 0.37
ACI
WEB SESSIONS
ACI
WEB SESSIONS
Validation of the Proposed Model (cont'd)
ApplyingkctoVfcalculated using the ACI 440.2R 2008, fib-TG 9.3 2001, CAN/CSA-S806 2002, HB 305 2008 (CIDAR2006), and CNR-DT200 2004 guidelines resulted in asignificant improvement on the accuracy of the calculatedresults for all the mentioned guidelines .
ACI
WEB SESSIONS
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ACI
WEB SESSIONS
Conclusions
A new design approach has been proposed for
calculating the shear contribution of FRP, taking into
consideration the effect of transverse steel on the EB
FRP contribution in shear.
The proposed model showed an acceptable correlation
with experimental results in comparison with the current
guidelines.
ACI
WEB SESSIONS
Acknowledgement
The financial support of the National Science and
Engineering Research Council of Canada (NSERC),
The Fonds qubcois de la recherche sur la
nature et les technologies (FQRNT),
The Ministre des Transports du Qubec (MTQ).
ACI
WEB SESSIONS
Thanks for your attention
ACI
WEB SESSIONS
Vincenzo Bianco is a Post Doc at the Department of Structural
Engineering and Geotechnics of the Sapienza University of
Rome, Italy. He received his PhD from the Sapienza University
of Rome. His research interests include seismic assessment and
retrofit of existing structures, mechanical modeling and use of
composite materials for structural rehabilitation.
University of Minho
at Guimares, Portugal
a Post Doc: [email protected] ciat e Prof.: [email protected] Full Prof.: [email protected]
PARAMETRIC STUDIES OF THE NSM FRP STRIPSSHEAR STRENGTH
CONTRIBUTION TO A RC BEAM
Vincenzo Bianco 1a, J.A.O. Barros 2b and Giorgio Monti 1c
FIBER-REINFORCED POLYMER REINFORCEMENT FOR CONCRETE STRUCTURESFRP-RCS10 April 2-4, 2011 - Tampa, Florida, USA
1 Dept. of Structural Engrg. and Geotechnics, SapienzaUniversity, Rome2 Dept. of Civil Engineering, University of Minho, Guimares, Portugal
ACI
WEB SESSIONS
ACI
WEB SESSIONS
MECHANICAL MODEL : 1 Physical AspectsPOSSIBLE FAILURE MODES OF A SINGLE NSM FRP STRIP
SCHEMATIZATION OF R.C.
BEAM WEB AND NSM FRPSTRIPS
The strengthened web can be seenas a prism divided in two parts bythe Critical Diagonal Crack (CDC)which can be sch ematized as aninclined plane intersecting thestrips.
The two resulting w eb parts aresawn together by the FRP strips.
In analogy with the fasteningtechnology, 4 possible failure
modes can be foressen.
Z O o
fs
X
1,f kx
wh
z
Y y web bottom surface
web top surfaceassumed CDC plane
strips
a)
O
beam flange
beam web
b)
1, ,; ;
f k f k nx N t
sfxf1,k
hw
stX
Xil
Lfi
Li
nt
Z fiX
liO
Lf
wb
x
E
a) b) c) d)
Loss of bond(debonding)
StripRupture
Concrete semi-conical fracture
Mixed shallowsemi-cone-plus
debonding
Parametric studies of the NSM FRP strips shear strengthcontribution to a RC beam
FRP-RCS10 - Tampa -Florida2-4 Aprile 2011
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ACI
WEB SESSIONS
DEVELOPED MECHANICAL MODEL: 2 Physical Aspects
; ;cf lfi ctm iV f X
; 45 ; 45 ;f
i s
l
iX
90
ctmf
sinctm
f
; lfi iC X
Semi-conical tensile fracture capacity is evaluated byspreading the average concrete tensile strength fctm
throughout the semi-conical surface Cfi and integrating.
SCHEME OF A SINGLE FRP STRIP
,
;
. sin .
fi fi fi
p cfctm fi fifi
C L
V f dC
INTERACTION AMONG ADJACENT STRIPS
By reducing the strips spacing,the adjacent strips semi-conicalfracture surfaces overlap andthe overall fracture surfaceprogressively becomes smallerthan the mere summation ofeach of them.
The components of fctmorthogonal to t he web faces are
balanced only from an overall
point of view but not locally.
This justifies the spalling of the
concrete cover which was
observed experimentally.
45 0.0f
s
sinc tm c tm
f f
ctmfcomponents of parallel and
orthogonal to the web faces
section CDC plane OXY 2wb
wh
section plane
Parametric studies of the NSM FRP strips shear str engthcontribution to a RC beam
FRP-RCS10 - Tampa -Florida2-4 Aprile 2011
ACI
WEB SESSIONS
MECHANICAL MODEL: 3 Some Computational Aspects
1k
1i
1i i
1k k
n
y
n
y
,f ki Ny
n
0 1 2 1 2 3 max; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;w w f cm fu f f f d h b s f f E a b n InputParameters
, 1, , 2, , ,
, , , ,,
, , ,
, , 1
2 with ; 0.0 1,.,
1 1,.,
1 with 0 1,..,
with ; 0.0 1,., ,.,
c
f k i k fi k i k fi k f kk
f k Rfi k fi k f kR k
f k i k f kk
f k s k n f k n sk
H N H x H L i N
L N L L i N
u N u i N
D N t D i t i N t t t
, , ,, 1 with 1,.,n f k Li k n f k L k t N t i N
, , 1 , 1 , 1; ; ; StripFunctionc
fi k n Rfi k n fi k n i k nV t L t L t u t
n st t
3k
,w it h 1, 2, 3 a n d
f kV k
, , ,
,
2 sin
up dat ematri ces: , , ,
f k n f k n fi k n
k R k k k
V t V t V t
H L u D
,
max
, 1,
define geometry in : 3 2 ; 2 1, 2,3
determinenum berofloadsteps: ;
initialize vector: 1 with 0.0 , ., 1,2,3
build vector: 1
f kk
s
s f k n n sf k
s
oxyz x F N k
t
V t V t t t t k
t
1n nt t
1nt t
Build andinitialize the followingmatrices:
Det.andstore generalinformations
Evaluate andstore imposedendslips
Incrementshearstrengthcontribution
O
beam flange
beam web
1, ,; ;f k f k nx N t
sfxf1,k
hw
stX
Xil
Lfi
Li
nt
Z
fiX
liO
Lf
E
During the loading process of a beam subject toshear, after the occurrence of the CriticalDiagonal Crack, the two parts of the beam startmoving apart by pivoti ng around the CDC end(point E).
The strips oppose this movement by anchoringto the surrounding concrete to which theytransfer, through bond stresses, the forceoriginating at the intersection with the CDC anddue to the imposed end slip.
Main flow chart
Parametric studies of the NSM FRP strips shear strengthcontribution to a RC beam
FRP-RCS10 - Tampa -Florida2-4 Aprile 2011
ACI
WEB SESSIONS
Possible geometrical configurations taken into consideration
In order to single out the range [Vmin PM-VmaxPM] of analytical values, the following
three possible geometrical configurations were considered:
1. The first str ip is p laced at a d istance equal to the spacing sf from the
assumed crack origin O;
2. An even number of strips are placed symmetrically with respect to the axis
of the crack;
3. An odd number of strips are placed so that the central one gets the
maximum available bond length.
1st 2nd
3rd
MECHANICAL MODEL: 4 Computatio nal Aspects
Parametric studies of the NSM FRP strips shear str engthcontribution to a RC beam
FRP-RCS10 - Tampa -Florida2-4 Aprile 2011
ACI
WEB SESSIONS
ACI
WEB SESSIONS
MECHANICAL MODEL: 5 Single Strip Contrib ution
90
a)Z O o
s
X
1,f kx
wh
z
Y y web bottomsurface
web topsurfaceassumed
CDC plane
strips
wb
x
Z O o
s
X
1,f kx
wh
z
Y y web bottomsurface
web topsurfaceassumed
CDC plane
strips
wb
x
b)
d)c)
;Rfi n eL t q
tri
x
trio
cV
1;Rfi nL t q
trio
trix
cf lfi iV X
1;cfi nL t q
cV
1; ;bd
fi Li n Rfi nV t L t q ; ;bd
fi Li n Rfi n eV t L t q
;c i n eL t qliO
liX
1; ; ;bd tr
fi Li n Rfi n iV t L t q x
Li nt Li nt
, 1; ;t r i L i n R fi nL t L t q , ; ;t r i L i n R fi n eL t L t q
2; ;n ei t q q1; ;ni t q
liX
ctm
sinctmf
cf lfi iV X
45 ; 45 ; ;f w ws b h
; li iC X
liO
Iteration and search for the equilibrium condition
It can also happen, mainly for small resisting bondlengths, and for low concrete strength, that the fracturemechanism reach the strips free end, so that theultimate configuration is c omposed of a semi-conewhose height is equal to the initial available bondlength.
It can happen that, for a certain value of the imposedend slip, after the formation of some successive andco-axial semi-conical fractures, the portion of the str ipstill adhered to concrete, fails by debonding since thediagram of the progressive bond-transferred forceremains confined beneath the diagram of theprogressive concrete fracture capacity.
Parametric studies of the NSM FRP strips shear strengthcontribution to a RC beam
FRP-RCS10 - Tampa -Florida2-4 Aprile 2011
ACI
WEB SESSIONS
ACI
WEB SESSIONS
MECHANICAL MODEL: 6 Concrete Fracture Capacity
2wb
wh
a)
45 ; 90 ; 0; 0f w ws b h
semi-conesalready formed
; lfi iC X
semi-conesalready formed
; lfi iC X
intersection withthe semi-cone ofthe adjacent strip
intersection withthe CDC plane
intersection with thesemi-cone of the stripon the opposite side ofthe web
strip
intersection with theCDC plane limit
b)
; lfi iC XXO
X
Y
2 13
21 3
32
X
O
O
Y
Y
2
wb
dL
wb
jb
ja 1je
2je
jo
ojX
2jv1jv
fjX
2Pje
1PjeP
a)
21q
X22q
X
wb
dL
wb
dL
21q
X22q
X
23p
X
2
b)
c)
; ; ;n m nt i q n
2n li n n li ni fA A
2li n lini fA A
General case: strips are not orthogonal to the CriticalDiagonal Crack
,
;
. sin .
fi fi fi
p cfctm fi fifi
C L
V f dC
,
;
sin .
fi fi fi
p cfctm fifi
E L
V f dE
;
lfi i
nl in l ini fi fi
E X
dE
A AThe evaluation of the concrete semi-conical fracture capacity c an bereduced the evaluation of the area of the semi-ellipse intersection o f
the semi-cone with the critical diagonal crack.
Parametric studies of the NSM FRP strips shear str engthcontribution to a RC beam
FRP-RCS10 - Tampa -Florida2-4 Aprile 2011
ACI
WEB SESSIONS
EMPLOYMENT OF BOND AND LOSS OF BOND(BOND; DEBONDING)
1) Local bond stress-slip relationship: physical phenomena occurring in sequence,within the adhesive layer, by increasing the imposed end slip
1
2
0
01 2
E las ti c S oft en ing Fr ic ti on
Softening Free Sli pping
The initial strength is due to the micro-mechanicaland chemical propertiesof the materials involved. Itis the average of the physical entities encountered insequence by stresses flowing from the strip to thesurrounding concrete: 1) adhesion at the strip-adhesive interface, 2) cohesion within the adhesiveand 3) adhesion at the adhesive-concrete interface.
2) The governing differential equation, considering apull-out scheme, has been written fulfilling equilibrium,kinematic compatibility and constitutive laws.
3) Governing differential equation for aninfinite resisting bond length:
0122
Jxdx
d
cc
f
ff
p
EA
A
EA
LJ
11with:
Equilibrium:
Constitutive laws:
Kinematic compatibility:
0
f
pf
A
Lx
dx
xd
0 ccff AxAx
dx
duE
fff
dx
duE ccc
xuxux cf
strip-adhesive adhesionCohesion within the adhesive
adhesive-concrete adhesion 0Initial bond strength
Parametric studies of the NSM FRP strips shear strengthcontribution to a RC beam
FRP-RCS10 - Tampa -Florida2-4 Aprile 2011
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ACI
WEB SESSIONS
PROCESS OF LOSS OF BOND FOR ANINFINITE RESISTING BOND LENGTH
By imposing the boundary conditions and solving the differential equation for the several phases of the bondconstitutive law, we obtain: slip distribution; dist ribution of tangential stresses; distribution of the strip axialstress and of the progressive force t ransferred to the surrounding concrete.
1) ElasticPhase
2)Softening
Phase
3) Softening FrictionPhase
4) Free Slipping Phase
eo ex sx sfxex sxeo ex
so eo so sfo
e ex e e
x s sx s sx e ex sf sfx
sf sfx s sx e ex
10 2
sf sfx s sx e ex
,b d s f s f V x ,b d s sV x ,b d e eV x
s sx e ex
10
s sx e ex
,b d s sV x ,b d e eV x
1
0
2
e ex
,b d e eV x
1
1trL 2trL1trL
e ex
a) b) c)
fsxsfxex
sx
fsoeo
so
sfo
s sx e ex sf sfx
sf sfx
2
sf sfx
,b d s f s f V x
s sx
1
s sx
,b d s sV x
3
0
2
e ex
,b d e eV x
1
3trL2trL1trL
e ex
fs fsx
fs fsx
fs fsx
Parametric studies of the NSM FRP strips shear str engthcontribution to a RC beam
FRP-RCS10 - Tampa -Florida2-4 Aprile 2011
ACI
WEB SESSIONS
PROCESS OF LOSS OF BOND FOR A FINITERESISTING BOND LENGTH
Once the Debonding Process hasbeen solved for an infiniteresisting bond length, debondingpropagation is schematized as an
invariant wave that, increasing theimposed end slip, progressesfrom the loaded end to the freeend.
Thus, with geometrical relations,the trend of slip, tangential stress,axial stress in both the strip andsurrounding concrete can bedetermined for whatever value ofboth resisting bond length andimposed end slip.
fsx
sfx
ex
sx
fso
eo
so
sfo
sf sfx
sf sfx
2
1
3
0
2
1
3trL2trL1trL
2
0 2
RfiL
2 3Li mt 1Li it 2 3Li jt 2 3Li nt 3Li pt 2 3Li mt
3
fs fsx
fs fsx
e ex s sx
e ex s sx
i>j>n>m>p
trio
trix
a)
b) c)
Parametric studies of the NSM FRP strips shear strengthcontribution to a RC beam
FRP-RCS10 - Tampa -Florida2-4 Aprile 2011
ACI
WEB SESSIONS
MECHANICAL MODEL: APPRAISAL (1)
0 0.1 0.2 0.3 0.4 0.5 0.60
10
20
30
40
50
60
70
CDC opening angle []
NSMshearcontrib.Vf,k
[kN]
k 1
k 2
k 3
Exp.
Beam2S-7LI45-II
Exp.k 1k 2k 3
1k 2k
3k
The typical trend of the contribution tothe shear strength provided by asystem of NSM FRP strips, as functionof the CDC opening angle, ischaracterized by abrupt decays whichcorrespond to the strips failure.
Parametric studies of the NSM FRP strips shear str engthcontribution to a RC beam
FRP-RCS10 - Tampa -Florida2-4 Aprile 2011
ACI
WEB SESSIONS
MECHANICAL MODEL: APPRAISAL (2)
0 0.1 0.2 0.3 0.4 0.5 0.60
10
20
30
40
50
60
70
CDCopeningangle []
NSMshearcontrib.Vf,k
[kN]
Beam4S-4LI45-II
k1k2
k3
Exp.
Exp.k1k2k3
0 0.1 0.2 0.3 0.4 0.5 0.60
10
20
30
40
50
60
70
CDCopeningangle []
NSMshearcontrib.Vf,k
[kN]
k1k2
k3
Exp.
Beam4S-7LI45-II
Exp.k1k2k3
0 0.1 0.2 0.3 0.4 0.5 0.60
10
20
30
40
50
60
70
CDCopeningangle []
NSMshearcontrib.Vf,k[kN]
Beam2S-4LI45-II
k1
k2
k3
Exp.
Exp.k1k2k3
0 0.1 0.2 0.3 0.4 0.5 0.60
10
20
30
40
50
60
70
CDCopeningangle []
NSMshearcontrib.Vf,k
[kN]
k1
k2
k3
Exp.
Beam2S-7LI45-II
Exp.k1k2k3
0 0.1 0.2 0.3 0.4 0.5 0.60
10
20
30
40
50
60
70
CDCopeningangle []
NSMshearcontrib.Vf,k[kN]
Beam2S-3LI60-I
k1
k2
k3
Exp.
Exp.k1k2k3
0 0.1 0.2 0.3 0.4 0.5 0.60
10
20
30
40
50
60
70
CDCopeningangle []
NSMshearcontrib.Vf,k
[kN]
k1
k2 k3
Exp.
Beam2S-7LI60-I
Exp.k1k2k3
0 0.1 0.2 0.3 0.4 0.5 0.60
10
20
30
40
50
60
70
CDCopeningangle []
NSMshearcontrib.Vf,k
[kN]
Beam2S-5LV-I
k1
k2
k3
Exp.
Exp.k1k2k3
0 0.1 0.2 0.3 0.4 0.5 0.60
10
20
30
40
50
60
70
CDCopeningangle []
NSMshearcontrib.Vf,k[kN] k1
k2
k3
Exp.
Beam2S-8LV-I
Exp.k1k2k3
The developed mechanical model allows the maximum con tribution to the shear strength provided by asystem of NSM FRP strips to be predicted with a satisfactory level of accuracy and ragardless of: amount ofexisting steel stirrups, concrete mechanical properties, number and inclination of the strips.
Parametric studies of the NSM FRP strips shear strengthcontribution to a RC beam
FRP-RCS10 - Tampa -Florida2-4 Aprile 2011
ACI
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5 10 15 20 25 30 350
25
50
75
100
125
Spacingsf[cm]
NSMshearcontrib.Vf,3[kN]
=60;fcm
=31.1MPa;k =3
RealMax. Ideal
5 10 15 20 25 30 350
25
50
75
100
125
Spacingin theideal configurationsf[cm]
NSMshearcontrib.Vf[kN]
=60;fcm
=31.1 MPa;sf=75.0mm
Ideal
5 10 15 20 25 30 350
25
50
75
100
125
Spacingsf[cm]
NSMshearcontrib.Vf,k
[kN]
=60;fcm
=31.1 MPa
k1k2
k3
Exp.k1k2k3
5 10 15 20 25 30 350
25
50
75
100
125
Spacingsf[cm]
NSMshearcontrib.Vf,k
[kN]
=60;fcm
=18.6 MPa
k1k2
k3
Exp.k1k2k3
a) b)
c) d)
MECHANICAL MODEL: APPRAISAL (3)Reducing the strips spacing, the NSMFRP strips shear strength contributionincreases, the more as higher theconcrete mechanical propertiesare.
Group effect: the reduction of the shearstrength contribution provided by a realsystem of NSM strips with respect to an idealsystem in which the same system of strips,subjected to the same system of i mposed endslips, are spaced out at such an extent thatthey do not interact with each other anylonger. The group effect increases bydecreasing the strips spacing.
,f reals
,f ideals
1L nt
2L nt
3L nt 4L nt
5L nt
1L
2L
3L
4L
5L
2nt
1fL 2fL
3fL
4fL
5fL
1fL
2fL
3fL
4fL
5fL
c)
b)a)
,0.5 f reals
Parametric studies of the NSM FRP strips shear str engthcontribution to a RC beam
FRP-RCS10 - Tampa -Florida2-4 Aprile 2011
ACI
WEB SESSIONS
ACI
WEB SESSIONS
PARAMETRIC STUDIES: RANGE OF VALUES ASSUMED FOREACH PARAMETER
Parametric studies of the NSM FRP strips shear strengthcontribution to a RC beam
FRP-RCS10 - Tampa -Florida2-4 Aprile 2011
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8/13/2019 FRP Shear Strengthening of RC Beams
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10/14/20
ACI
WEB SESSIONS
MECHANICAL MODEL: PARAMETRIC STUDIES (1)
0 0.05 0.10
100
200
300
Load step
Vfkm
ax[
kN]
k1
k2
k3
0 15 30 45 600
100
200
300
CDCAngle[]
Vfkm
ax[
kN]
k1
k2k3
a) b) a) b)
0 20 40 60 800
100
200
300
Cross sectiondepthhw
[cm]
Vfkm
ax[
kN]
k1
k2
k3
0 10 20 30 40 500
100
200
300
Cross sectionwidthbw
[cm]
Vfkm
ax[
kN]
k1
k2
k3
0 2 4 60
100
200
300
Strip cross sectionthickness af[mm]
Vfkm
ax[
kN]
k1
k2
k3
0 10 20 30 400
100
200
300
Strip cross sectionwidth bf[mm]
Vfkm
ax[
kN]
k1
k2
k3
a) b)
0 25 50 75 1000
100
200
300
Concretecompressive strengthfcm
[MPa]
Vfkm
ax[
kN]
k1
k2
k3
0 15 30 45 600
100
200
300
Concreteangle[]
Vfkm
ax[
kN]
k1
k2
k3
a) b)
Parametric studies of the NSM FRP strips shear str engthcontribution to a RC beam
FRP-RCS10 - Tampa -Florida2-4 Aprile 2011
ACI
WEB SESSIONS
MECHANICAL MODEL: PARAMETRIC STUDIES (2)
0 30 60 900
100
200
300
Strip spacingsf[cm]
Vfkm
ax[
kN]
k1
k2
k3
40 55 70 85 1000
100
200
300
Strip inclinationangle[]
Vfkm
ax[
kN]
k1
k2
k3
a) b)
0 100 200 3000
100
200
300
Strip Youngs ModulusEf[GPa]
Vfkm
ax[
kN]
k1
k2
k3
0 2 4 60
100
200
300
Strip Strengthffu
[GPa]
Vfkm
ax[
kN]
k1
k2
k3
c) d)
Parametric studies of the NSM FRP strips shear strengthcontribution to a RC beam
FRP-RCS10 - Tampa -Florida2-4 Aprile 2011
ACI
WEB SESSIONS
MECHANICAL MODEL: PARAMETRIC STUDIES (3)
0 2 4 60
100
200
300
Bond parameter0[MPa]
Vfkm
ax[
kN]
k1
k2
k3
5 15 25 350
100
200
300
Bond parameter1[MPa]
Vfkm
ax[
kN]
k1
k2
k3
a) b)
0 3 6 9 120
100
200
300
Bond parameter 2[mm]
Vfkm
ax[
kN]
0 5 15 20 250
100
200
300
Bond parameter 3[mm]
Vfkm
ax[
kN]
k1
k2
k3
k1
k2
k3
e) f)
0 5 10 15 200
100
200
300
Localbond parameter2[MPa]
Vfkm
ax[
kN]
k1
k2
k3
c)
0 0.2 0.4 0.6 0.8 10
100
200
300
Localbond parameter 1[mm]
Vfkm
ax[
kN]
k1
k2
k3
d)
Due to both the high-performance of the currently available structural adhesives and the premature
occurrence of other failure modes such as either concrete tensile fracture or strip rupture, a variation of
each of the bond parameters does affect the peak NSM shear strength contribution.
Parametric studies of the NSM FRP strips shear str engthcontribution to a RC beam
FRP-RCS10 - Tampa -Florida2-4 Aprile 2011
ACI
WEB SESSIONS
Thank you for your attention
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Let me invite you to attend the 6th International Conferenceon FRP Composites in Civil Engineering CICE2012
which will be held in the Eternal City of Rome, in ITALY
Further information at www.cice2012.it
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Thank you for your attention
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8/13/2019 FRP Shear Strengthening of RC Beams
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ACI
WEB SESSIONS
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