FRP Shear Strengthening of RC Beams

8/13/2019 FRP Shear Strengthening of RC Beams

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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

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Status of influencing factors on shear strengtheningof RC beams in the current design guidelines.

International Design Codes and Guidelines

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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

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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

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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.

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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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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.

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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

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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.

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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

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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

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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

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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.

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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

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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

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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

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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

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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 .

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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.

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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).

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Thanks for your attention

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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

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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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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


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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



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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



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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.



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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.



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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




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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



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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)



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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.



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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 []


[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 []


[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 []


[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 []


[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 []


[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.



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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]


[kN]

=60;fcm

=31.1 MPa

k1k2

k3

Exp.k1k2k3

5 10 15 20 25 30 350

25

50

75

100

125

Spacingsf[cm]


[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



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PARAMETRIC STUDIES: RANGE OF VALUES ASSUMED FOREACH PARAMETER




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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)



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WEB SESSIONS


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)



ACI

WEB SESSIONS


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.



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