m UNIVERSITED SHERBROOKE E

m UNIVERSITEDE SHERBROOKE

Faculte de genie

Departement de genie civil

SHEAR BEHAVIOUR OF CONCRETE BEAMS REINFORCED

WITH FIBRE-REINFORCED POLYMER (FRP) STIRRUPS

ETUDE DU COMPORTEMENT A L'EFFORT TRANCHANT DE

POUTRES EN BETON ARME AVEC DES ETRIERS EN

POLYMERE RENFORCE DE FIBRES (PRF)

These de doctorat es sciences appliquees

Specialite : genie civil

Jury:

Richard Gagne

Pierre Labossiere

Brahim Benmokrane

Ehab El-Salakawy

Mark F. Green

David Lai

President

Rapporteur

Directeur de recherche

Codirecteur

Examinateur

Examinateur

Ehab Abdul-Mageed AHMED

Sherbrooke (Quebec) Canada June 2009

w~m>

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Abstract

ABSTRACT

Corrosion of steel reinforcement is a major cause of deterioration in reinforced concrete

structures especially those exposed to harsh environmental conditions such as bridges,

concrete pavements, and parking garages. The climatic conditions may have a hand in

accelerating the corrosion process when large amounts of salts are used for ice removal during

winter season. These conditions normally accelerate the need of costly repairs and may lead,

ultimately, to catastrophic failure. Therefore, using the non-corrodible fibre-reinforced

polymer (FRP) materials as an alternative reinforcement in prestressed and reinforced

concrete structures is becoming a more accepted practice in structural members subjected to

severe environmental exposure. This, in turn, eliminates the potential of corrosion and the

associated deterioration.

Stirrups for shear reinforcement normally enclose the longitudinal reinforcement and

are thus the closest reinforcement to the outer concrete surface. Consequently, they are more

susceptible to severe environmental conditions and may be subjected to related deterioration,

which reduces the service life of the structure. Thus, replacing the conventional stirrups with

the non-corrodible FRP ones is a promising aspect to provide more protection for structural

members subjected to severe environmental exposure. However, from the design point of

view, the direct replacement of steel with FRP bars is not possible due to various differences

in the mechanical and physical properties of the FRP materials compared to steel. These

differences include higher tensile strength, lower modulus of elasticity, different bond

characteristics, and absence of a yielding plateau in the stress-strain relationships of FRP

materials. Moreover, the use of FRP as shear reinforcement (stirrups) for concrete members

has not been sufficiently explored to provide a rational model and satisfactory guidelines to

predict the shear strength of concrete members reinforced with such type of stirrups.

An experimental program to investigate the structural performance of FRP stirrups as

shear reinforcement for concrete beams was conducted. The experimental program included

seven large-scale T-beams reinforced with FRP and steel stirrups. Three beams were

reinforced with CFRP stirrups, three beams reinforced with GFRP stirrups, and one beam

reinforced with steel stirrups. The geometry of the T-beam was selected to simulate the New

England Bulb Tee Beam (NEBT) that is being used by the Ministry of Transportation of

i

Abstract

Quebec (MTQ), Canada. The beams were 7.0 m long with a T-shaped cross section measuring

a total height of 700 mm, web width of 180 mm, flange width of 750 mm, and flange

thickness of 85 mm. The large-scale T-beams were constructed using normal-strength

concrete and tested in four-point bending over a clear span of 6.0 m till failure to investigate

the modes of failure and the ultimate capacity of the FRP stirrups in beam action. The test

variables considered in this investigation were the material of the stirrups, shear reinforcement

ratio, and stirrup spacing. The specimens were designed to fail in shear to utilize the full

capacity of the FRP stirrups. Six beams failed in shear due to FRP (carbon and glass) stirrup

rupture or steel stirrup yielding. The seventh beam, reinforced with CFRP stirrups spaced at

d/4, failed in flexure due to yielding of the longitudinal reinforcement followed by crushing of

concrete. The effects of the different test parameters on the shear behaviour of the concrete

beams reinforced with FRP stirrups were presented and discussed. The test results contributed

to amending the shear provisions incorporated in the Canadian Highway Bridge Design Code

(CAN/CSA-S6) and the updated provisions were approved in the CSA-S6-Addendum (CSA

2009).

An analytical investigation was conducted to evaluate the validity and accuracy of

available FRP codes and guidelines in Japan, Europe, and North America. The predictions of

the codes and the guidelines were verified against the results of the tested beams as well as 24

other beams reinforced with FRP stirrups from the literature. The tested beams were also

analysed using various shear theories including the modified compression field theory

(MCFT), the shear friction model (SFM), and the unified shear strength model (USSM). A

simple equation for predicting the shear crack width in concrete beams reinforced with FRP

stirrups is proposed and verified against the experimentally measured values.

n

Resume

RESUME

Etude du comportement a l'effort tranchant de poutres en beton arme avec

des etriers en polymere renforce de fibres (PRF)

La corrosion des armatures en acier est une des plus importantes causes de deterioration des

ouvrages en beton arme exposes a des environnements agressifs, comme les ponts, chaussees

et stationnements. Les conditions climatiques peuvent accelerer le processus de degradation

par corrosion, surtout lors de l'utilisation du sel de deglacage, et engendrer des reparations

couteuses, ou dans 1'extreme, des effondrements de structures. Pour ces raisons, le

remplacement des armatures en acier par des armatures en PRF, materiaux non corrodables, se

fait de plus en plus, surtout dans les elements structuraux exposes a des environnements

agressifs.

Les etriers constituent les armatures les plus proches de la surface exterieure du beton.

Par consequent, ils sont plus exposes aux conditions environnementales severes qui peuvent

les deteriorer plus rapidement (comparativement a 1'armature longitudinale par exemple) et

ainsi reduire de facon prematuree la duree de vie des ouvrages. II devient alors evident que

l'utilisation des etriers non corrodables en PRF au lieu de ceux en acier, permet aux structures

exposees a des environnements agressifs des longevites plus accrues. Cependant, le

dimensionnement a l'effort tranchant avec des etriers en PRF est different de celui de ceux

d'acier a cause des differences sur les proprietes mecaniques de ces deux materiaux. En effet,

les PRF ont une resistance en traction plus elevee que celle de 1'acier, un module plus faible et

un comportement en traction elastique lineaire jusqu'a la rupture. De plus, la litterature

rapporte peu de travaux et d'etudes sur l'utilisation des etriers en PRF comme armature de

cisaillement.

Afin de combler ce besoin, un programme de recherche, constitue d'etudes

experimentales et d'etudes theoriques, a ete entrepris a l'Universite de Sherbrooke, dans le

cadre de la Chaire de recherche du CRSNG sur les «Materiaux composites novateurs de PRF

pour les infrastructures», pour investiguer les performances des etriers en PRF comme

armature de cisaillement (etiers) dans des poutres. Les etudes experimentales comprennent

1'evaluation du comportement a 1'effort tranchant de sept poutres de section en T de grandes

dimensions, renforcees en cisaillement par des etriers en PRF et en acier. Parmi ces poutres,

iii

Resume

trois ont ete renforcees avec des etriers en PRF de carbone, trois avec des etriers en PRF de

verre et une avec des etriers en acier. La geometrie des poutres en T est celle utilisee par le

ministere des Transports du Quebec (MTQ). La longueur des poutres est de 7,0 m, avec une

section en T de 700 mm de hauteur, une ame de 180 mm de largeur et une dalle (aile) de

compression de 750 mm de largeur et 85 mm d'epaisseur. Les sept poutres d'essais ont ete

armees en flexion (armature longitudinale de traction) a l'aide de cables de precontrainte

torsades tres legerement tendus lors de la mise en place du beton. Aussi, toutes les poutres ont

ete construites en utilisant un beton normal et ont ete testees en flexion quatre point sur une

portee de 6.0 m jusqu'a la rupture. Les modes de rupture en cisaillement et les capacites des

etriers ont ete investigues. Les parametres etudies sont le type d'etriers (PRFC, PRFV et

acier), le taux d'armature de cisaillement et l'espacement des etriers. Les poutres d'essais ont

ete concues pour rompre en cisaillement afin de sollicker les etriers a leur pleine capacite. Les

resultats obtenus ont montre que la rupture de six poutres s'est produite comme prevu par

cisaillement ayant conduit a la rupture en traction des etriers pour ceux de PRP (carbone et

verre) (carbone et verre) ou en traction par plastification pour ceux en acier. La septieme

poutre renforcee avec des etriers en PRFC ayant un espacement de dIA a rompu, quant a elle,

en flexion par la plastification des armatures longitudinales d'acier (cables de precontrainte

torsadees) et de l'ecrasement du beton. Ces essais ont ainsi permis l'etude et l'analyse de

differents parametres sur le comportement en cisaillement de poutres renforcees avec des

etriers de PRF.

En parallele aux etudes experimentales, des etudes analytiques ont ete effectuees pour

ameliorer et ou optimiser les equations de calcul proposees par les differents codes et guides

de calcul traitant de membrures en beton arme de PRF actuellement en usage (CSA, ACI,

JSCE). Les predictions des codes et guides ont ete comparees aux resultats des sept poutres

testees, ainsi qu'a ceux de 24 autres poutres renforcees avec des etriers en PRF, trouves dans

la litterature. Les poutres testees ont aussi ete analysees avec differentes theories de

cisaillement, incluant la MCFT ((Modified Compression Field Theory», la SFM «Shear

Friction Model» et le ((Unified Shear Strength Model». Une equation simple pour predire la

largeur de fissures de cisaillement dans les poutres en beton renforcees par des etriers en PRF

a ete proposee et validee avec les resultats experimentaux.

Mots-cles: Materiaux composites, polymeres renforces de fibres, beton, etriers, cisaillement,

effort tranchant, fissures de cisaillement, modeles de prediction, conception, codes de calcul,

resistance, poutres de ponts.

IV

Bibliography

AUTHOR'S RESEARCH CONTRIBUTIONS

The candidate has conduced experimental and analytical investigations concerning the shear

behaviour of concrete beams reinforced with carbon and glass FRP stirrups. In addition, the

candidate has participated in some research activities and publications concerning the bond

behaviour of FRP bars, characterization of FRP bent bars/stirrups, GFRP post-installed

adhesive anchors and FRP stirrups as shear reinforcement for concrete structures. During this

research work at the University of Sherbrooke the following papers were published/accepted

or submitted for publications:

Journal Papers:

Direct results from PhD work

1. Ahmed, E. A., El-Salakawy, E. F., and Benmokrane, B., (2009), "Shear Performance

of RC Bridge Girders Reinforced with Carbon FRP Stirrups," ASCE Journal of Bridge

Engineering, (BEENG-57), in press.

2. Ahmed, E. A., El-Salakawy, E. F., and Benmokrane, B., (2009), "Performance

Evaluation of GFRP Shear Reinforcement for Concrete Beams," Submitted to ACI

Structural Journal, (ID S-2008-358), in press.

3. Ahmed, E. A., El-Salakawy, E. F., and Benmokrane, B., (2009), "Shear Behaviour of

Concrete Beams Reinforced with FRP Stirrups: Comparative Study and Evaluation,"

submitted to the Canadian Journal of Civil Engineering, June.

Results from other research work

4. Ahmed, E. A., El-Salakawy, E. F., and Benmokrane, B., (2008), "Tensile Capacity of

GFRP Post-Installed Adhesive Anchors in Concrete," ASCE Journal of Composites

for Construction, Vol. 12, No. 6, November-December, pp. 596-607.

5. Ahmed, E. A., El-Sayed, A. K., El-Salakawy, E. F., and Benmokrane, B., (2009),

"Bend Strength of FRP Stirrups: Comparison and Evaluation of Testing Methods,"

ASCE Journal of Composites for Construction, (CCENG-104), in press.

v

Bibliography

6. Ahmed, E., El-Salakawy, E., and Benmokrane, B., (2008), "Bond Stress-Slip

Relationship and Development Length of FRP Bars Embedded in Concrete," The

Housing and Building National Research Center (HBRC) Journal, Vol. 4, No.3, 17p.

Conference Papers:

Direct results from PhD work

7. Ahmed, E. A., El-Salakawy, E. F., Benmokrane, B., (2008), "Shear Strength of RC

Beams Reinforced with FRP Stirrups," 5l International Conference in Advanced

Composite Materials in Bridges and Structures (ACMBS-V), Winnipeg, Manitoba,

Canada, September 22-24, lOp.

8. Ahmed, E. A., El-Salakawy, E. F., Benmokrane, B., (2008), "Shear Behaviour of

Concrete Bridge Girders Reinforced with Carbon FRP Stirrups," 4th International

Conference on FRP Composites in Civil Engineering (CICE2008), Zurich,

Switzerland, July 22-24, 8p.

9. Ahmed, E. A., El-Salakawy, E. F., Benmokrane, B., and Goulet S., (2008),

"Performance Evaluation of CFRP Stirrups as Shear Reinforcement for Concrete

Beams," CSCE Annual Conference, Quebec City, Quebec, June 10-13, lOp.

10. Ahmed, E. A., El-Salakawy, E. F., Benmokrane, B., (2007), "Strain-Based Shear

Strength Analysis of FRP RC Beams without Transverse Reinforcement," 12th

International Colloquium on Structural and Geotechnical Engineering (ICSGE), Ain

Shams University, Egypt, December 10-12, pp. 258-269.

11. Ahmed, E. A., El-Salakawy, E. F., Benmokrane, B., (2007), "Structural Behaviour of

Concrete Beams Reinforced with Carbon FRP Stirrups," 12 International Colloquium

on Structural and Geotechnical Engineering (ICSGE), Ain Shams University, Egypt,

December 10-12, pp. 295-305.

12. Ahmed, E. A., El-Sayed, A. K., El-Salakawy, E. F., Benmokrane, B., (2006), "Shear

Behaviour of Concrete Bridge Girders Reinforced with Carbon FRP Stirrups," 7th

International Conference on Short and Medium Span Bridges, Montreal, Quebec,

Canada, August 23-26, CD-ROM, lOp.

VI

Bibliography

Results from other research work

13. Ahmed, E. A., El-Salakawy, E. F., Benmokrane, B., (2008), "Bond Behaviour of

GFRP Bars Embedded in Normal Strength Concrete," 5 Middle East Symposium on

Structural Composites for Infrastructure Applications, Hurghada, Egypt, May 23-25,

lOp.

14. Ahmed, E. A., El-Salakawy, E. F., Benmokrane, B., (2007), "Pullout Strength of Post-

Installed Adhesive Anchors Using Glass FRP Reinforcing Bars," CSCE Annual

Conference, Yellowknife, North Territories, June 6-9, CD-ROM, lOp.

15. Ahmed, E. A., El-Salakawy, E. F., Benmokrane, B., (2006), "Bond Characteristics of

GFRP Post-Installed Anchors," 3rd International Conference on FRP Composites in

Civil Engineering (CICE 2006), Miami, Florida, USA, December 13-15, pp. 87-90.

Technical Reports:

16. Ahmed, E. A., El-Salakawy, E., and Benmokrane, B., (2008), "Tensile Properties of

GFRP Bent Bars for RC Bridge Barriers," Technical Report, submitted to the Ministry

of Transportation of Quebec, August, 16p.

17. Ahmed, E. A., El-Salakawy, E. F., Massicotte, B., and Benmokrane, B., (2007),

"Shear Behaviour of NEBT-Bridge Girders Reinforced with Carbon FRP Stirrups,"

Technical Report (Phase Il-b), submitted to the Ministry of Transportation of Quebec,

August, 34p.

18. Benmokrane, B., Ahmed, E. A., El-Salakawy, E. F., (2006), "Conception de poutres

de ponts en beton precontract renforcees avec des etriers en materiaux composites,"

Rapport d'Etape Il-a « Resultats d'essai sur poutre a grande echelle de 7 m de long »,

soumis au ministere des Transports du Quebec, Mars, 36p.

19. El-Sayed, A. K., Ahmed, E. A., El-Salakawy, E. F., Benmokrane, B., (2006), "Tensile

Capacity of Glass FRP Bent Bars Used as Reinforcement for Concrete Bridge

Barriers," Technical Report, Submitted to Ministry of Transportation of Quebec, June,

37p.

vii

A cknowledgement

ACKNOWLEDGEMENTS

I'd like to express my sincere gratitude to my supervisors professor Brahim Benmokrane,

NSERC Research Chair Professor in Innovative FRP Composites for Infrastructures,

Department of Civil Engineering, University of Sherbrooke, and professor Ehab El-Salakawy,

Canada Research Chair Professor in Advanced FRP Composite Materials and Monitoring of

Civil Infrastructures, Department of Civil Engineering, University of Manitoba, for their

support, guidance, encouragement, and valuable advice during this research program.

I'd like to thank the structural laboratory technical staff in the Department of Civil

Engineering at the University of Sherbrooke, especially, Mr. Francois Ntacorigira and Nicolas

Simard for their help in constructing and testing the specimens.

The financial support received form the Natural Sciences and Engineering Research

Council of Canada (NSERC), Fonds quebecois de la recherche sur la nature et les

technologies (FQRNT), Pultrall Inc. (Thetford Mines, Quebec, Canada), the Ministry of

Transportation of Quebec (MTQ), the Network of Centers of Excellence on the Intelligent

Sensing of Innovative Structures (ISIS Canada), and the University of Sherbrooke is greatly

acknowledged.

The patience, love, support, and encouragement of my father, my mother, my family

(Ghada, Ahmed, and Mohamed) and my sisters cannot be praised enough; to them this thesis

is dedicated.

viii

Table of Contents

TABLE OF CONTENTS

ABSTRACT i

RESUME iii

AUTHOR'S RESEARCH CONTRIBUTIONS v

ACKNOWLEDGEMENTS viii

TABLE OF CONTENTS ix

LIST OF FIGURES xiv

LIST OF TABLES xxii

CHAPTER 1: INTRODUCTION 1

1.1 Background and Problem Definition 1

1.2 Objectives and Originality 4

1.3 Methodology 5

1.4 Structure of the Thesis 5

CHAPTER 2: SHEAR BEHAVIOUR OF CONCRETE BEAMS REINFORCED

WITH STEEL: BACKGROUND AND REVIEW 8

2.1 General 8

2.2 Shear in Reinforced Concrete Beams without Shear Reinforcement 9

2.2.1 Shear resisting mechanisms 9

2.2.2 Pattern of inclined cracking and modes of shear failure 9

2.2.3 Factors affecting shear strength 15

2.3 Shear in Reinforced Concrete Beams with Shear Reinforcement 15

2.3.1 Internal forces in a concrete beam with shear reinforcement 15

2.3.2 Role of shear reinforcement in concrete beams 17

2.3.3 Modes of shear failure 18

2.4 Shear Strength Analysis of Reinforced Concrete Beams 18

2.4.1 Historical background 19

ix

Table of Contents

2.4.2 The 45° truss model 21

2.4.3 Variable-angle truss model 24

2.4.4 Modified truss model 24

2.4.5 Compression field theory 26

2.4.6 Modified compression field theory 30

2.4.7 Rotating-angle softened truss model 35

2.4.8 Fixed-angle softened truss model 39

2.4.9 Disturbed stress field model 41

2.4.10 Shear friction model 47

2.4.11 Unified shear strength model for reinforced concrete beams 49

2.5 Shear Design Provisions in North American Codes 53

2.5.1 American Concrete Institute, ACI 318-08 (ACI 2008) Code 53

2.5.2 The Canadian Highway Bridge Design Code, CHBDC, CAN/CSA-S6-06

(CSA2006) 55

2.5.3 The Canadian Standard Association CSA-A23.3-04 (CSA 2004) 59

2.5.4 AASHTO LRFD Bride Design Specification (2004) 60

2.6 Shear Crack Width 64

CHAPTER 3: SHEAR BEHAVIOUR OF CONCRETE BEAMS REINFORCED

WITH FRP STIRRUPS: BACKGROUND AND REVIEW 65

3.1 General 65

3.2 Fibre-Reinforced Polymers (FRP) 65

3.2.1 Reinforcing fibres 65

3.2.2 Resins 66

3.2.3 FRP reinforcing bars 66

3.3 FRP Product Certification 69

3.4 Strength of FRP Bent Bars/Stirrups 70

3.4.1 Bend strength of FRP bent bars/stirrups 71

3.4.2 Strength of FRP bars subjected to induced shear cracks 89

3.5 Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups 93

x

Table of Contents

3.6 Shear Design Provisions for FRP Reinforced Concrete Members 111

3.6.1 Japanese design recommendations 112

3.6.1.1 JSCE Design Recommendations (JSCE 1997) 112

3.6.1.2 Building Research Institute (BRI) (1997) 116

3.6.2 Canadian design codes and guidelines 118

3.6.2.1 The Canadian Highway Bridge Design Code CSA (2006) 119

3.6.2.2 The Canadian Highway Bridge Design Code CSA (2009)-Addendum 121

3.6.2.3 The Canadian Building Code S806-02 (CSA 2002) 122

3.6.2.4 ISIS Canada Design Manual No. 3 (ISIS Canada 2007) 124

3.6.3 American design codes and guidelines 125

3.6.3.1 ACI 440.1R-06 (ACI 2006) 125

3.6.3.2 AASHTO LRFD Specifications (AASHTO 2009) 126

3.6.4 European shear provisions 128

3.6.4.1 Institution of Structural Engineers (ISE 1999) 128

3.6.4.2 Italian National Research Council (CNR-DT 203) (2006) 129

CHAPTER 4: EXPERIMENTAL PROGRAM 131

4.1 General 131

4.2 Material Properties 131

4.2.1 FRP stirrups 131

4.2.1.1 Tensile characteristics 133

4.2.1.2 Bend strength of FRP stirrups 133

4.2.1.2.1 B.5 Method 135

4.2.1.2.2 B.12 Method 140

4.2.2 Steel bars 143

4.2.3 Concrete 144

4.3 Beam Specimens (Test Specimens) 146

4.4 Fabrication of Test Specimens 148

4.5 Instrumentation 161

4.6 Test Setup and Procedure 167

xi

Table of Contents

4.7 Summary 173

CHAPTER 5: TEST RESULS AND ANALYSIS 174

5.1 General 174

5.2 Test Results 174

5.2.1 Deflection 175

5.2.2 Flexural strains 175

5.2.3 Shear cracking load 178

5.2.4 Capacity and mode of failure 181

5.2.5 Cracking pattern and crack spacing 191

5.2.6 Strains in FRP stirrups 195

5.2.7 Effect of FRP stirrup spacing 205

5.2.8 Shear crack width 216

5.2.9 Serviceability limits 221

5.2.10 Effect of bend strength on the design shear capacity 223

5.3 Summary 225

CHAPTER 6: ANALYTICAL STUDY 227

6.1 General 227

6.2 Predictions using Design Codes and Guidelines 227

6.3 Predictions using MCFT 238

6.4 Shear Friction Model (SFM) 246

6.5 Unified Shear Strength Model 255

6.6 Theoretical Predictions of the Shear Crack Width 267

6.7 Summary 268

CHAPTER 7: SUMMARY AND CONCLUSIONS 271

7.1 Summary 271

7.2 Conclusions 273

xii

Table of Contents

7.2.1 FRP stirrup characterisation 273

7.2.2 FRP stirrup in beam specimens 273

7.2.3 Code predictions 276

7.2.4 Analytical investigation 277

7.3 Recommendations for Future Work 278

REFERENCES 279

xiii

List of Figures

LIST OF FIGURES

CHAPTER 1

Figure 1.1: Kinking of the innermost fibres at the bend zone of FRP stirrups 2

Figure 1.2: Effect of bend strength of FRP stirrups on the shear strength of beam

specimen 3

CHAPTER 2

Figure 2.1: Shear resistance component in a cracked concrete beam without shear

reinforcement 10

Figure 2.2: Flexural and diagonal tension cracks (Winter and Nilson 1979) 11

Figure 2.3: Effect of shear span-to-depth ratio {aid) on shear strength of beams

without shear reinforcement (MacGregor 1997) 12

Figure 2.4: Modes of failure of deep beams (ASCE-ACI1973) 13

Figure 2.5: Modes of failure of short shear spans with aid ranging from 1.5 to 2.5

(ASCE-ACI 1973) 14

Figure 2.6: Typical shear failure of a slender beam 14

Figure 2.7: Internal forces in a cracked concrete beam with stirrups (ASCE-ACI 1973) 16

Figure 2.8: Ritter and Morsch's truss models 22

Figure 2.9: Equilibrium consideration for 45° truss (Collins and Mitchell 1997) 23

Figure 2.10: Equilibrium conditions for variable-angle truss (Collins and Mitchell 1997) 25

Figure 2.11: Compression field theory aspects (Mitchell and Collins 1974) 28

Figure 2.12: Modified compression field theory aspects (Vecchio and Collins 1986) 31

Figure 2.13: Reinforced concrete membrane elements subjected to in-plane stresses

(Pang and Hsu 1996) 37

Figure 2.14: Reinforced concrete element: (a) Reinforcement and loading conditions;

and (b) Mohr's circle for average stresses in concrete (Vecchio 2000) 42

Figure 2.15: Equilibrium conditions: (a) External conditions; (b) Perpendicular to crack

direction; (c) Parallel to crack direction; and (d) Along crack surface

(Vecchio 2000) 43

xiv

List of Figures

Figure 2.16: Compatibility conditions: (a) Deformations due to average (smeared)

constitutive response; (b) Deformations due to local rigid body slip along

crack; and (c) Combined deformations (Vecchio 2000) 45

Figure 2.17: Shear friction model in a concrete beam by Kriski and Loov (1996) 48

Figure 2.18: Rankine's failure criteria for reinforced concrete (Chen 1982) 50

Figure 2.19: Critical sections and strain distribution of a cracked beam (Park et al. 2006) 52

CHAPTER 3

Figure 3.1: Typical FRP products (fib 2006) 67

Figure 3.2: Typical stress-tensile strain of FRPs compared to steel 69

Figure 3.3: Test setup and specimen dimension tested by Maruyama et al. (1993) 72

Figure 3.4: The relationship between the tensile and bend strengths

(Maruyama et al. 1993) 73

Figure 3.5: Relationship between bend and concrete strengths (Maruyama et al. 1993) 73

Figure 3.6: The test specimens for bend strength evaluation by Nagasaka et al. (1993) 74

Figure 3.7: Specimen details, test setup, and tested stirrups by Currier et al. (1994) 75

Figure 3.8: Details of the test specimens for hooked bars (Ehsani et al. 1995) 76

Figure 3.9: Influence of hook radius on load-slip relation (Ehsani et al. 1995) 76

Figure 3.10: Influence of concrete compressive strength on tensile strength

(Ehsani etal. 1995) 77

Figure 3.11: Effect of tail length and straight embedment length on tensile force at failure

(Ehsani etal. 1995) 77

Figure 3.12: Test specimen and setup details (Ueda et al. 1995 & Ishihara et al. 1997) 79

Figure 3.13: Model of FRP bent bar in concrete by Nakamura and Higai (1995) 81

Figure 3.14: Details of the test specimens for evaluating the bend strength (Morphy 1999)...82

Figure 3.15: CFRP U-shaped stirrups for Phase I (El-Sayed et al. 2007) 84

Figure 3.16: Details of the test specimens (Guadagnini et al. 2007) 87

Figure 3.17: Average of maximum stress: (a) Type 2; and (b) Type 3

(Guadagnini et al. 2007) 88

Figure 3.18: Testing FRP rod at crack intersection by Kanematsu et al. (1993) 89

Figure 3.19: Diagonal tension due to diagonal crack (Nakamura and Higai 1995) 90

xv

List of Figures

Figure 3.20: Comparison between the proposed equation results and experimental results

(Nakamura and Higai 1995) 91

Figure 3.21: Effect of the inclined crack on the FRP stirrup, Kinking effect,

(Morphy 1999) 92

Figure 3.22: Details of the test specimens for evaluating the kinking effect (Morphy 1999). .92

Figure 3.23: Test specimens and loading setup by Nagasaka et al. (1993) 95

Figure 3.24: Configuration of test specimens by Tottori and Wakui (1993) 97

Figure 3.25: Details of test specimens for shear by Yonekura et al. (1993) 98

Figure 3.26: Details of test specimens (Zhao et al. 1995) 99

Figure 3.27: Stirrup strain distribution model (Zhao et al. 1995) 100

Figure 3.28: Configuration of FRP Stirrups (Shehata 1999) 107

Figure 3.29: Details of beam specimens (Shehata 1999) 108

Figure 3.30: Beam specimens and instrumentations by Gudagnini et al. (2003 & 2006) 110

CHAPTER 4

Figure 4.1: Surface configuration of the carbon and glass FRP stirrups 132

Figure 4.2: Details of the FRP and steel stirrups: (a) FRP stirrups; and (b) Steel stirrups... 132

Figure 4.3: Typical tension testing of FRP straight portions: (a) Test setup;

and (b) Typical fibre-rupture of FRP straight portions 134

Figure 4.4: Typical stress-strain relationship for the reinforcing bars 135

Figure 4.5: Dimensions of the C-and U-shaped specimens for B.5 and B.12 methods 136

Figure 4.6: Schematic for B.5 method and specimen configuration 137

Figure 4.7: Attaching the debonding tubes to the FRP stirrups 137

Figure 4.8: Casting of the concrete blocks 138

Figure 4.9: Testing FRP stirrups in concrete blocks 139

Figure 4.10: Rupture of the FRP stirrup at the corner in concrete blocks followed

by stirrup slippage 139

Figure 4.11: Schematic for B.12 test method 141

Figure 4.12: Preparing No. 10 CFRP and GFRP U-specimens for B.12 test 141

Figure 4.13: Testing U-shaped FRP specimens using B.12 method 142

Figure 4.14: Typical fibre-rupture failure mode at the bend for U-shaped FRP specimens... 142

xvi

List of Figures

Figure 4.15: Typical tension testing of steel bars: (a) Test setup;

and (b) Failure of steel bars 143

Figure 4.16: Slump test of the fresh concrete before casting 144

Figure 4.17: Compression test of the standard concrete cylinders 145

Figure 4.18: Splitting test of the standard concrete cylinders 145

Figure 4.19: Stress-strain relationship for different concrete batches 146

Figure 4.20: Cross section of the New England Bulb Tee (NEBT) beams 147

Figure 4.21: Geometry and dimension of beam specimens 149

Figure 4.22: Reinforcement details and stirrup instrumentation of SC-9.5-2 151



Figure 4.25: Reinforcement details and stirrup instrumentation of SG-9.5-2 154

Figure 4.26: Reinforcement details and stirrup instrumentation of S4-9.5-3 155

Figure 4.27: Reinforcement details and stirrup instrumentation of SG-9.5-4 156

Figure 4.28: Reinforcement details and stirrup instrumentation of SS-9.5-2 157

Figure 4.29: Assembling the reinforcing cage of a beam specimen 159

Figure 4.30: Completed reinforcing cage and the formwork ready for casting 159

Figure 4.31: Concrete casting of abeam specimen 160

Figure 4.32: A concrete beam specimen just after casting and adjusting the surface 160

Figure 4.33: Curing of the beam specimens 161

Figure 4.34: Locations of the longitudinal reinforcement strain gauges for

the test specimens 163

Figure 4.35: Steel strands after attaching the strain gauges 164

Figure 4.36: CFRP stirrups instrumented with strain gauges 164

Figure 4.37: Deflection measurement using LVDTs 165

Figure 4.38: The demec gauges installed in both shear spans of each beam 165

Figure 4.39: Measuring the demec gauges using the digital extensometer 166

Figure 4.40: The data acquisition systems utilized in beam testing 166

Figure 4.41: Schematic for the setup used for testing the beams reinforced

with CFRP stirrups 168

xvii

List of Figures

Figure 4.42: Schematic for the setup used for testing the beams reinforced with GFRP

and steel stirrups 169

Figure 4.43: A photograph of the test setup for the beams reinforced with CFRP stirrups. ..170

Figure 4.44: A photograph of the test setup for the beams reinforced with GFRP stirrups. ..171

Figure 4.45: Measuring the initial shear crack widths using the hand-held microscope 172

Figure 4.46: Measuring the shear crack widths using high accuracy LVDTs 172

CHAPTER 5

Figure 5.1: Applied shear-deflection relationship for beams reinforced with

CFRP stirrups 176

Figure 5.2: Applied shear-deflection relationship for beams reinforced with

GFRP stirrups 176

Figure 5.3: Flexural strains of beam reinforced with CFRP stirrups 177

Figure 5.4: Flexural strains of beam reinforced with GFRP stirrups 177

Figure 5.5: Evaluating the shear cracking loads of the tested beams 179

Figure 5.6: Shear failure of beam SC-9.5-2 (CFRP@o?/2) 182

Figure 5.7: Shear failure of beam SC-9.5-3 (CFRP@tf/3) 183

Figure 5.8: Flexure failure of beam SC-9.5-4 (CFRP@J/4) 184

Figure 5.9: Shear failure of beam SG-9.5-2 (GFRP@rf/2) 185

Figure 5.10: Shear failure of beam SG-9.5-3 (GFRP@c//3) 186

Figure 5.11: Shear failure of beam SG-9.5-4 (GFRP@c//4) 187

Figure 5.12: Shear failure of control beam SS-9.5-2 (steel@d/2) 188

Figure 5.13: Load carrying capacity of beams reinforced with CFRP stirrups 189

Figure 5.14: Load carrying capacity of beams reinforced with GFRP stirrups 190

Figure 5.15: Effect of the shear reinforcement stiffness on the beams strength 190

Figure 5.16: Crack pattern at failure for beams reinforced with CFRP stirrups 192

Figure 5.17: Crack pattern at failure for beams reinforced with GFRP stirrups 193

Figure 5.18: Crack pattern at failure for the control beam SS-9.5-2 (steel@c//2) 194

Figure 5.19: Shear crack spacing versus stirrups spacing relationship 194

Figure 5.20: Typical applied shear force-stirrup strain relationship

(SC-9.5-2 and SS-9.5-2) 196

xviii

List of Figures

Figure 5.21: Typical applied shear force-stirrup strain at the bend of FRP stirrups

(SC-9.5-2) 196

Figure 5.22: Comparisons between the average stirrup strains calculated from both

shear spans of beams reinforced with CFRP stirrups 197

Figure 5.23: Applied shear force-average stirrup strain for beams with CFRP stirrups 199

Figure 5.24: Applied shear force-average stirrup strain for beams with GFRP stirrups 199

Figure 5.25: Comparison between the average stirrup strains for FRP stirrups with similar

stirrups spacing: (a) spacing=d/2; (b) spacing -dll>; and (c) spacing=d/4 200

Figure 5.26: Effect of the stiffness of the shear reinforcement on the average stirrup strain. 202

Figure 5.27: Applied shear force-maximum stirrup strain relationships for CFRP

stirrups in beam specimens comparing to the steel stirrup 203

Figure 5.28: Applied shear force-maximum stirrup strain relationships for GFRP

stirrups in beam specimens comparing to the steel stirrup 203

Figure 5.29: Stirrup strain distribution along the shear span of

SC-9.5-2 beam (CFRP@rf/2) 206


SC-9.5-3 beam (CFRP@<//3) 207


SC-9.5-4 beam (CFRP@<//4) 208


SG-9.5-2 beam (GFRP@<//2) 209


SG-9.5-3 beam (GFRP@J/3) 210


SG-9.5-4 beam (GFRP@<//4) 211

Figure 5.35: Effect of stirrup spacing on effective capacity of FRP stirrups

in beam action 212

Figure 5.36: Comparison of effective capacity of CFRP stirrups in beam action 212

Figure 5.37: Shear resisting components of beams reinforced with CFRP stirrups 214

Figure 5.38: Shear resisting components of beams reinforced with GFRP stirrups 214

xix

List of Figures

Figure 5.39: Comparison between the shear resisting components for FRP stirrups

in beams with similar stirrups spacing: (a) spacing=<i/2; (b) spacing

=d/3; and(c) spacing=t//4 215

Figure 5.40: Applied shear force-shear crack width relationships for beam

specimens reinforced with GFRP stirrups: (a) SG-9.5-2; (b) SG-9.5-3;

and (c) SG-9.5-3 218

Figure 5.41: Maximum shear crack width for beams reinforced with CFRP stirrups 219

Figure 5.42: Maximum shear crack width for beams reinforced with GFRP stirrups 219

Figure 5.43: Comparison between the maximum shear crack width for beams

reinforced with FRP stirrups at the same spacing: (a) spacing=J/2;

(b) spacing =d/3; and (c) spacing-J/4 220

Figure 5.44: Applied shear force-maximum stirrup strain across the critical shear crack-

serviceability requirements 222

CHAPTER 6

Figure 6.1: Predicted shear strength of beams reinforced with CFRP stirrup 231

Figure 6.2: Predicted shear strength of beams reinforced with GFRP stirrup 231

Figure 6.3: Comparison between measured and predicted shear strength 232

Figure 6.4: Experimental to predicted shear strength using JSCE (1997)

and CSA (2006) 236

Figure 6.5: Experimental to predicted shear strength using ACI (2006)

and CSA (2009) 237

Figure 6.6: Experimental to predicted shear strength using CNR DT-203 (2006) 238

Figure 6.7: Measured shear strength versus the predicted using the MCFT 239

Figure 6.8: Effect of stirrup spacing of the effective FRP stirrup capacity using MCFT. ...240

Figure 6.9: Comparison between measured average stirrup strain and the

predicted using the MCFT for beams reinforced with CFRP stirrups 241

Figure 6.10: Comparison between measured average stirrup strain and the

predicted using the MCFT for beams reinforced with GFRP stirrups 242

Figure 6.11: Measured shear crack width versus predicted using MCFT for

the control beam SS-9.5-2 243

xx

List of Figures

Figure 6.12: Measured shear crack width versus predicted using MCFT

for beams reinforced with CFRP stirrups 244

Figure 6.13: Measured shear crack width versus predicted using MCFT

for beams reinforced with GFRP stirrups 245

Figure 6.14: Internal forces at a potential failure plane using SFM 248

Figure 6.15: Potential failure planes for beams reinforced with CFRP stirrups for

SFM analysis 249

Figure 6.16: Potential failure planes for beams reinforced with GFRP stirrups for SFM

analysis 250

Figure 6.17: Measured shear strength versus predicted using SFM 254

Figure 6.18: Effect of stirrup spacing of the effective CFRP stirrup stress using SFM 254

Figure 6.19: Predicted shear strength according to the strain-based analysis 261

Figure 6.20: Predicted shear strength according to the JSCE (1997) 262

Figure 6.21: Predicted shear strength according to the CSA (2002) 263

Figure 6.22: Predicted shear strength according to the ACI (2006) 264

Figure 6.23: Predicted shear strength of beam specimens using the unified shear model 266

Figure 6.24: Prediction of shear crack width for the control beam (SS-9.5-2)

using Equation (6.8) 267

Figure 6.25: Prediction of shear crack width for beams reinforced with CFRP stirrups

using the proposed equation (Equation 6.9) 269

Figure 6.26: Prediction of shear crack width for beams reinforced with CFRP stirrups

using the proposed equation (Equation 6.9) 270

xxi

List of Tables

LIST OF TABLES

CHAPTER 2

Table 2.1: Values of 6 and /? for sections with transverse reinforcement

(AASHTO LRFD 2004) 62

Table 2.2: Values of 6 and ft for sections with less than minimum transverse

reinforcement (AASHTO LRFD 2004) 63

CHAPTER 3

Table 3.1: Mechanical properties of the most commonly used fibres

(ISIS Canada 2007) 66

Table 3.2: Typical properties of thermosetting resins (ISIS Canada 2007) 68

Table 3.3: Typical mechanical properties of FRP reinforcing bars (ISIS Canada 2007) 68

Table 3.4: Designation of some FRP reinforcing bars (ISIS Canada 2006) 70

Table 3.5: Details and test results of CFRP stirrups embedded in concrete blocks

(Phase II) (El-Sayed et al. 2007) 86

CHAPTER 4

Table 4.1

Table 4.2

Table 4.3

The test results of FRP straight portions 135

The bend strength of FRP C- and U-shaped stirrups 140

Concrete properties and reinforcement details of test specimens 150

CHAPTER 5

Table 5.1: Summary of the test results 180

Table 5.2: The stress at the bend zone of FRP stirrups corresponding to an

average strain equals 4000 microstrain in the straight portions 224

CHAPTER 6

Table 6.1

Table 6.2

Table 6.3

Predicted shear strength of test specimens 233

Shear strength prediction of beams reinforced with FRP stirrups 234

Shear friction analysis of tested beams reinforced with FRP stirrups 251

xxii

List of Tables

Table 6.4: Strain-based calculated shear strength for FRP RC beams without

stirrups in comparison to the experimental results 257

Table 6.5: The predicted shear strength of the beam specimens using the unified

shear strength model 265

xxiii

Chapter 1: Introduction

CHAPTER 1

INTRODUCTION

1.1 Background and Problem Definition

Corrosion of steel reinforcement is a major cause of deterioration in reinforced concrete

structures especially those exposed to harsh environmental conditions such as bridges,

concrete pavements, and parking garages. The use of concrete structures

reinforced/prestressed with fibre-reinforced polymer (FRP) composite materials has been

growing to overcome the common problems caused by corrosion of steel reinforcement and to

increase the anticipated service life of such structures. The climatic conditions may have a

hand in accelerating the corrosion process where large amounts of salts are used for ice

removal during the winter season. These conditions normally accelerate the need of costly

repairs and may lead, ultimately, to catastrophic failure. Therefore, using non-corrodible FRP

materials as an alternative reinforcement in prestressed and reinforced concrete structures is

becoming a more accepted practice in structural members subjected to severe environmental

exposure. This, in turn, eliminates the potential of corrosion and the associated deterioration.

Stirrups for shear reinforcement normally enclose the longitudinal reinforcement and

are thus the closest reinforcement to the outer concrete surface. Consequently, they are more

susceptible to severe environmental conditions and may be subjected to related deterioration

which reduces the service life of the structure. Thus, replacing the conventional stirrups with

the non-corrodible FRP ones is a promising aspect to provide more protection for structural

members subjected to severe environmental exposure. However, from the design point of

view, the direct replacement of steel with FRP bars is not possible due to various differences

in the mechanical properties of the FRP materials compared to steel. These differences include

higher tensile strength, the lower modulus of elasticity, the different bond characteristics, and

the absence of yielding plateau in the stress-strain relationships of FRP materials. Extensive

research programs have been conducted to investigate the flexural behaviour of concrete

members reinforced with FRP reinforcement (Benmokrane et al. 1996; El-Salakawy et al.

2003; El-Salakawy and Benmokrane 2004; Gravina and Smith 2008). On the other hand, the

use of FRP as shear reinforcement (stirrups) for concrete members has not been adequately

1


explored to provide a rational model and yield satisfactory guidelines to predict the shear

strength of concrete members reinforced with FRP stirrups.

FRP bars are made of anisotropic materials with weak lateral strength compared to

their longitudinal one. Bending FRP bars to form stirrups significantly reduces the strength at

the bend portions (Maruyama et al. 1993; Ishihara et al. 1997; Shehata 1999; El-Sayed et al.

2007; Ahmed et al. 2008). The strength reduction of the FRP stirrups was referred to as the

bending effect rather than the kinking effect (Morphy 1999; Shehata 1999). At the bend, the

stirrup resists lateral loads due to bearing against concrete, in addition to the stresses in their

longitudinal direction parallel to the fibre's direction. Besides, bending the FRP bars causes

the innermost fibres at the bend to be kinked compared to those at the outermost radius as

shown in Figure 1.1. The intrinsic weakness of fibres perpendicular to their axis accompanied

by the kinked fibres at the bend contributes to reduced strength at the bend portion of FRP

stirrups compared to straight bars. The bend capacity of FRP bars is influenced by bending

process, bend radius, r^, bar diameter, db, and type of reinforcing fibres (ACI 2006).

Moreover, the shear strength of concrete beams reinforced with FRP stirrups may be governed

by the reduced bend strength of the FRP stirrups, especially when diagonal shear cracks

intersect the FRP stirrups at the bend zone as shown in Figure 1.2.

S Type 1

\

vi

(a) Bare fibres after removing the resin (b) Fibre's orientation at the bend

Figure 1.1: Kinking of the innermost fibres at the bend zone of FRP stirrups.

2


i FRP Stirrups

( •

•

• •

*

• •

Bend Effect '

Figure 1.2: Effect of bend strength of FRP stirrups on the shear strength of beam specimen.

The FRP reinforcement is characterised by a linear elastic stress-strain relationship up

to failure. The shear failure of a concrete member reinforced with FRP stirrups occurs due to

either rupture of the FRP stirrups or to crushing of concrete in the compression zone. Failure

due to FRP stirrup rupture is more brittle than shear compression failure and occurs suddenly

when; at least, one of the FRP stirrups crossing the critical shear crack reaches its strength

capacity. This is contrary to steel stirrups when yielding of steel provides a more ductile

failure. When FRP stirrups are used as shear reinforcement, serviceability limits (cracking and

deflection) and have to be checked because of the lower modulus of elasticity of the FRP

materials in comparison with the steel. Although there is no limit for the shear crack width at

service, there are few recommended strain limits for the FRP stirrups at service and ultimate

which need to be verified. Moreover, the shear capacity of concrete sections reinforced with

FRP stirrups are unduly underestimated by some design codes and guidelines.

Recently, there have been a variety of commercially available FRP stirrups with bend

strength equal to almost to double the yield stress of the conventional steel bars. The

characterisation of these stirrups was determined through testing of C- and U-shaped FRP

stirrups in accordance with B.5 and B.12 (ACI 2004) test methods (El-Sayed et al. 2007;

Ahmed et al. 2008). However, the behaviour of these stirrups in beam specimens is still to be

investigated.

Based on the results from the literature and the aforementioned discussion, it is

obvious that the shear behaviour of concrete beams reinforced with FRP stirrups differs from

3


that reinforced with steel stirrups. Limited research has been conducted to quantify the

contribution of the FRP stirrups to the shear carrying capacity. However, the full response is

still in need to be completely understood. Therefore, the shear behaviour of concrete beams

reinforced with FRP stirrups is investigated through this research thesis.

1.2 Objectives and Originality

The use of FRP as reinforcement for concrete structures is rapidly increasing and it is

now being intensively researched as primary reinforcement for concrete. These efforts reflect

the urgent need for completely understanding the behaviour of FRP reinforced concrete

elements. However, limited research work has been carried out to investigate the shear

behaviour of the FRP-reinforced. Through the NSERC Research Chair in Innovative FRP

Composites for Infrastructures at the University of Sherbrooke, the shear behaviour of FRP

reinforced concrete members is being investigated. The investigation was initiated by

evaluating the concrete contribution of FRP-reinforced concrete beams (El-Sayed 2006).

Thereafter, the current study evaluates the contribution and the structure performance of the

FRP stirrups as shear reinforcement for concrete beams.

Many design codes and guidelines addressing the FRP as primary shear and flexural

reinforcement have been recently published. The shear design provisions incorporated in these

codes and guidelines are based on modifying the original equations used for steel reinforced

concrete sections to account for the substantial difference between FRP and steel

reinforcement. Thus, investigations are needed to examine the validity of these methods. The

main objectives of this investigation are:

1. To investigate the structural performance of FRP stirrups as shear reinforcement for

concrete members.

2. To investigate the shear behaviour of concrete beams reinforced with FRP stirrups and

to evaluate the contribution of the FRP stirrups, V„f, to the shear resistance.

3. To evaluate the validity of the current analytical and design approaches for shear

strength in the design codes and guidelines for concrete members reinforced with FRP

stirrups.

4. To establish design recommendations for the concrete members reinforced with FRP

stirrups.

4


1.3 Methodology

To achieve the aforementioned objectives, experimental and analytical programs were

designed. The experimental program included constructing and testing of seven large-scale T-

beams reinforced longitudinally with steel strands and transversally with FRP and steel

stirrups. These beams were designed to study the effect of the material type and spacing of

FRP stirrups on the shear behaviour and strength compared to the steel ones. The beam

specimens were divided into two groups concerning the FRP stirrup materials in addition to a

control beam reinforced with steel stirrups. The first group included three beams reinforced

with carbon FRP stirrups with three different stirrup spacing. The second group was

reinforced with GFRP stirrups with the same spacing in group one. The control beam

reinforced with steel stirrups was selected for comparison, when applicable. The test

parameters were the shear reinforcement type (CFRP, GFRP, and steel stirrups), the shear

reinforcement ratio (0.262 to 0.526%), and the stirrup spacing (150 to 300 mm).

The analytical investigation included analysis of the test results using the different

available shear design provisions pertinent to structural members reinforced with FRP

stirrups. The results of each beam specimen were compared to the predicted values using

different design codes and guidelines. Based on the comparisons and experimental findings, a

revised value for the FRP stirrup strain at service was proposed. The analytical investigation

included also theoretical prediction of the shear crack width and a simple equation for

predicting the shear crack width of concrete beams reinforced with FRP stirrups was

proposed. The proposed equation was based on modifying the equation proposed by Placas

and Regan (1971) to account for FRP stirrups instead of steel ones. The analytical

investigation extended to include the analysis of the beam specimens using well defined shear

theories including the modified compression field theory (MCFT), the shear friction model

(SFM) and the recently published unified shear strength model (USSM). The results of these

methods were compared to the experimentally measured values and the main findings were

verified.

1.4 Structure of the Thesis

The thesis is divided into seven chapters. The following is a brief description of each chapter's

content:

5


Chapter 1: This chapter defines the problem and presents the main objectives of this

investigation. The originality and methodology followed to achieve the objectives of this

research program is also highlighted.

Chapter 2: This chapter provides a review of the shear behaviour of reinforced concrete

beams either with or without shear reinforcement. This chapter also includes background and

review on the analytical methods and theories predicting the shear strength and behaviour of

concrete beams reinforced with conventional steel bars. The shear design provisions available

in North America are also presented and discussed.

Chapter 3: This chapter provides brief information on the FRP composite materials and their

characteristics. The available literature review focusing on the effect of the bend on the FRP

stirrup strength and the behaviour of concrete beams reinforced with FRP stirrups are also

presented in this chapter. The available shear design provisions for concrete members

reinforced with FRP composite materials recently published in Japan, Europe, Canada and

USA are also introduced and discussed.

Chapter 4: This chapter describes the experimental program which included the construction

and testing of seven large-scale T-beams reinforced with FRP and steel stirrups. In this

chapter, the geometry and reinforcement details of the test specimens, stirrup configuration,

test setups and procedures, and the instrumentation details are presented. This chapter also

provides detailed characteristics of the materials used in this research program.

Chapter 5: The results of the experimental investigation conducted in this research program

are presented in this chapter. The general behaviour of the tested beams is presented in terms

of flexural strains, load-deflection response and mode of failure. The shear behaviour of the

beams is also presented and discussed including shear cracking load, applied shear force-

stirrup strains relationships, applied shear force-shear crack width relationships, shear

cracking pattern, and the inclination angles of the major shear crack at failure (in case of shear

failure). The analysis of the results includes the effect of different parameters on the shear

response of beams reinforced with FRP stirrups such as, FRP stirrups material, shear

6

Chapter I: Introduction

reinforcement ratio (stirrup spacing), and the bend strength of the FRP stirrups relative to the

strength parallel to the fibre's direction. The serviceability issue regarding the FRP stirrups is

also discussed and a stirrup strain limit at the service load limit is proposed to keep the shear

crack width controlled.

Chapter 6: In this chapter, the shear strengths of the tested beams as well as 24 beams from

literature are predicted using shear design provisions in the available codes and guidelines and

the predicted values are compared with the experimental ones to evaluate the accuracy of the

design equations. The analytical study was extended to include the shear theories for

predicting the shear behaviour of the tested beams. The full response of the tested beams was

predicted using the modified compression field theory (MCFT). The shear strength of the

tested beams was also calculated using the shear friction model (SFM) as well as the unified

shear strength model (USSM). The proposed modifications were verified considering the

tested beams in addition to 73 beams from literature. A simple equation for estimating the

shear crack width in beams reinforced with FRP stirrups is also proposed in this chapter.

Chapter 7: This chapter presents the summary and conclusion of this investigation based on

the findings of the experimental and the analytical studies. Recommendations for future

research work are also presented.

7

Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review

CHAPTER 2

SHEAR BEHAVIOUR OF CONCRETE BEAMS REINFORCED WITH

STEEL: BACKGROUND AND REVIEW

2.1 General

The flexural behaviour of reinforced and prestressed concrete has been extensively

investigated and incorporated in many design codes with well-defined simple design

equations. On contrary, the shear behaviour of reinforced and prestressed concrete beams is

not completely understood despite of the extensive research work conducted in this area. This

is related to the complexity of this phenomenon, which involves many variables that can not

be simplified and rationalized into one model. Several models were introduced based on the

experimental and theoretical investigations. Some of these methods were adopted by different

codes and design procedures.

The shear failure of reinforced and prestressed concrete members is frequently sudden

and brittle so that the design must ensure that the shear strength equals or exceeds the flexural

strength at all points along the member. This is the main reason to consider the flexural design

first to determine the cross-section and the flexural reinforcement. Therefore, concrete beams

are generally reinforced with shear reinforcement to ensure that, upon on overloading, the

flexural failure will occur rather than shear failure. Most of the shear design provisions divide

the shear strength of the reinforced concrete members into two components: concrete

contribution, Vc, and shear reinforcement contribution, Vs. The design shear strength is based

on the summation of both contributions considering appropriate factors of safety.

The shear behaviour of steel-reinforced concrete beams has been extensively

investigated for decades and it is not reviewed because this is beyond the scope of this study.

A comprehensive review on Shear and Diagonal Tension in concrete beams with/without

shear reinforcement was provided by the Joint ASCE-ACI Task Committee 426 on Shear and

Diagonal Tension in 1973 and updated by the Committee 445 on Shear and Torsion in 1998.

However, this chapter presents a brief review on the shear behaviour of reinforced concrete

beams with a focus on the role of shear reinforcement in concrete, mechanisms of shear

transfer and modes of failure. The available analytical methods and design approaches for

8


shear in steel reinforced concrete are also reviewed in this chapter since some of the design

approached for FRP reinforced concrete beams are based on these methods. Furthermore, a

literature review on the shear behaviour and design provision of concrete beams reinforced

with FRP bars is presented in Chapter 3.

2.2 Shear in Reinforced Concrete Beams without Shear Reinforcement

The shear behaviour of reinforced concrete beams without shear reinforcement has been

extensively investigated. However, a well-understanding of shear behaviour of such beams is

still limited. This is referred to the complexity and sensitivity of the affecting parameters that

govern the shear strength of concrete beams without shear reinforcement.

2.2.1 Shear resisting mechanisms

The ASCE-ACI Committee 445 (1998) identified five components for shear transfer in

cracked concrete beams. These five components are: (i) shear resistance provided by the

uncracked concrete above the neutral axis; (ii) the interface shear transfer along the two faces

of the cracks after the appearance of shear cracks, which is sometimes noted as "aggregate

interlock;" (iii) dowel action of the longitudinal reinforcement; (iv) residual tensile stresses

across the crack because a "clean crack" does not occur and there are some connecting

bridges; and (v) arch action, which is significant in deep member with a shear span-to-depth

ratio, a/d, less than 2.5. Generally the aforementioned five components are lumped together

and referred to as concrete contribution to the shear strength, Vc. The shear resistance

components for a slender beam without shear reinforcement are shown in Figure 2.1.

2.2.2 Pattern of inclined cracking and modes of shear failure

When the principal tensile stress at any location exceeds the cracking strength of the concrete

a crack forms. Cracks usually form perpendicular to the directions of the principal stress. For

members with uniaxial stress the principal tress will be parallel to the longitudinal direction of

the member resulting in parallel cracks perpendicular to the member's axis. For members

subjected to biaxial stresses, as the case of flexural and shear stresses, the principal tensile

stress will be inclined at an angle with the member's axis. Therefore, the shear cracks are

usually inclined to the member's axis.

9


Vcz: Shear resisted y uncracked concrete

Va : Shear transferred by aggregage interlock

Vd : Dowel action

Vrt : Residual tensile stresses across the crack Vac: Arch action (in deep members)

Figure 2.1: Shear resistance component in a cracked concrete beam without shear

reinforcement.

Winter and Nilson (1979) specified two different modes of shear cracks: web-shear

cracks and flexure-shear cracks. When the flexural stresses are small at the particular location,

the diagonal tension stresses are inclined at about 45° and are numerically equal to the shear

stresses with a maximum at the neutral axis. Consequently, diagonal web-shear cracks start

mostly near the neutral axis and then propagate in both directions as shown in Figure 2.2(a).

The situation will be different when both shear forces and bending moments have large

values. The flexural cracks will appear and their widths are controlled by the presence of

longitudinal reinforcement. However, when the diagonal tension stress at the upper end of one

or more of these cracks exceeds the tensile strength of the concrete, the crack bends in

diagonal direction and continues to grow in length and width as shown in Figure 2.2(b). These

cracks are known as flexure-shear cracks and more are common than web-shear cracks.

10


Large V and Small M

(a) Web-shear cracks

Large V and Large M

Flexural-shear cracks Flexural cracks

(b) Flexure-shear cracks

Figure 2.2: Flexural and diagonal tension cracks (Winter and Nilson 1979).

The behaviour of beams failing in shear varies widely depending on the relative

contributions of beam action and arch action and the amount of shear reinforcement

(MacGregor 1997). The moments and shears at inclined cracking and failure of a rectangular

beam without shear reinforcement are shown in Figure 2.3. The shaded areas in the figure

show the reduction in strength due to shear. Thus, the shear reinforcement is provided to

achieve the full flexural capacity.

According to MacGregor (1997) classification, shown in Figure 2.3, the shear span can

be classified based on shear span-to-depth ratio, aid, into four types:

11


a v

1 v

a

T v

Deep

(a) Beam

T V

Very slender

^ Flexural capacity

Inclined cracking and failure

1.0 2.5 a/d

6.5

(b) Moment at cracking and failure

Shear failure

Flexural failure

Inclined cracking and failure

a/d 6.5

(c) Shear at cracking and failure

Figure 2.3: Effect of shear span-to-depth ratio (a/d) on shear strength of beams without shear

reinforcement (MacGregor 1997).

12


1. Very short: with shear span to depth ratio, aid, equals 0 to 1.0. These beams develop

inclined cracks joining the load and the support. The cracks, in turn, destroy the

horizontal shear flow from the longitudinal steel to the compression zone and the

behaviour changes from beam action to arch action. The failure of such beams, which

is commonly referred to as deep beams, is shown in Figure 2.4.

2. Short: with aid ranges from 1 to 2.5. These beams develop inclined cracks and after

redistribution of internal forces are able to carry additional load, in part by arch action.

The final failure of such beams will result from a bond failure, a splitting failure or a

dowel failure along the tension reinforcement as shown in Figure 2.5(a) or by crushing

of the compression zone over the shear crack as shown in Figure 2.5(b).

3. Slender: with aid ranges from 2.5 to about 6. In these beams the inclined cracks disturb

the equilibrium to such an extent that the beam fails at inclined cracking as shown in

Figure 2.6.

4. Very slender: with aid greater than about 6. These beams will fail in flexure prior to

the formation of inclined cracks.

I

Types of failure:

1: Anchorage failure

2: Bearing failure

3: Flexural failure

4,5: Crushing of compression

strut

Figure 2.4: Modes of failure of deep beams (ASCE-ACI 1973).

13


Loss of bond due to splitting crack i

(a) Shear-tension failure

Crushing I

(b) Shear-compression failure

Figure 2.5: Modes of failure of short shear spans with aid ranging from 1.5 to 2.5 (ASCE-ACI

1973).

Figure 2.6: Typical shear failure of a slender beam.

14


2.2.3 Factors affecting shear strength

For beams without shear reinforcement, the shear resisting capacity includes the five resisting

mechanisms listed earlier. The shear resisting capacity (shear strength) is influenced by the

following variables as introduced by the ASCE-ACI (1998):

1. The concrete tensile strength;

2. The longitudinal reinforcement ratio;

3. Shear span-to-depth ratio;

4. Axial forces; and

5. Depth of concrete members (size effect).

2.3 Shear in Reinforced Concrete Beams with Shear Reinforcement

The shear failure of the concrete beams is brittle and catastrophic in nature. This failure occurs

without sufficient advance warning. Thus, the purpose of using shear reinforcement is to

ensure that the full flexural capacity of the concrete member can be developed.

2.3.1 Internal forces in a concrete beam with shear reinforcement

The main purpose for providing shear reinforcement to a reinforced concrete element is to

achieve its flexural capacity, minimize the shear deformation, and keep the element away

from the brittle shear failure. The internal forces in a typical concrete beam reinforced with

steel stirrups and intersecting a diagonal shear crack are shown in Figure 2.7(a). The shear is

transferred across line A-B-C and consequently accumulate the following contributions: (i) the

shear in the compression zone, Vcz\ (ii) the vertical component of the shear transferred across

the crack by interlock of the aggregate particles on the two faces of the diagonal crack, Vay\

(iii) the dowel action of the longitudinal reinforcement, Vj, and (iv) the shear transferred by

tension in the stirrups, Vs. The loading history of such a beam is shown qualitatively in Figure

2.7(b). As shown in Figure 2.7(b) the summation of the internal shear resistance components

must equal the applied shear force which is represented by the uppermost line. Prior to

flexural cracking, all shear is carried by the uncracked concrete. Between flexural and

inclined cracking, the external shear is resisted by Vcz, Vay, and Vj (the concrete components).

As soon as the inclined cracks appear, the stirrups resist a portion of the applied shear and

noted as stirrup contribution, Vs. Eventually, the stirrups crossing the crack yield, and Vs

15


remains constant for higher applied shears. Once the stirrup yield, the inclined crack opens

more rapidly. As the inclined crack widens, the aggregate interlocking component, Vay,

decrease further, forcing Vj and Vcz (dowel action and uncracked concrete contributions) to

increase at accelerated rate until either splitting (dowel) failure occurs or the compression

zone fails due to combined shear and compressive stresses.

A

T R

(a) Shear resisting mechanisms.

Dowel splitting

Flexural Inclined cracking cracking

Yield of Failure stirrups

Applied shear

(b) Distribution of internal shear.

Figure 2.7: Internal forces in a cracked concrete beam with stirrups (ASCE-ACI 1973).

16


Each of three aforementioned shear resisting components of this process except Vs has

a brittle load-deflection response. As a result it is difficult to quantify the contribution of Vcz,

Vay, and Vd at ultimate. In design, these are lumped together as Vc referred to as "the shear

carried by concrete". Thus the nominal shear strength, V„, is assumed to be as follows:

V„=VC+VS (2.1)

Traditionally in North American design practice, Vc, is taken equal to the shear force at

the initiation of inclined shear cracking, Vcr, which approximately equals the ultimate shear

strength of slender concrete beams without stirrups.

2.3.2 Role of shear reinforcement in concrete beams

Prior to diagonal cracking, the strain in the stirrups is equal to the corresponding strain in

surrounding concrete. The stresses in the stirrups prior to diagonal cracking will not exceed 20

to 40 MPa (MacGregor 1997). Winter and Nilson (1979) reported that there is no noticeable

effect for the shear reinforcement prior to the formation of diagonal cracks and the shear

reinforcement could be free of stress until the diagonal cracking. Thus, the stirrups do not

prevent the appearance of the diagonal cracks; they come into play only after the cracks have

formed. The stirrups enhance to the shear performance of a beam, in addition to their

contribution to the shear strength, Vs, by the following means:

1. Improve the contribution of the dowel action. The stirrups effectively support the

longitudinal reinforcement that crossing the flexural shear cracks close to the stirrup.

2. Control the widths of the diagonal shear cracks and, in turn, maintain the contribution

provided by the aggregate interlock.

3. Confine the cross section when closely spaced stirrups are used. This increases the

compressive strength of the concrete and enhances the zones affected by the arch

action.

4. Enhance the bond and prevent the breakdown when splitting cracks develop in

anchorage zone due to dowel forces.

It can be summarized that the shear reinforcement in concrete beam maintain the

overall integrity of the concrete contribution, Vc, allowing the development of additional shear

forces, Vs, which increases the shear capacity and prevents the premature shear failure.

17


2.3.3 Modes of shear failure

There are various modes of failure that can be observed in concrete beams reinforced with

shear reinforcement. These modes of failure can be summarized as:

1. Failure of shear reinforcement (stirrups). When the steel stirrups reaches their yield

stress, the shear crack widths get wider resulting in breakdown of the aggregate

interlocking. Consequently, the beam fails in shear due to crushing or shearing of the

compression zone above the neutral axis.

2. Failure due to crushing of the beam web. This failure mode usually happens either

when the beam has thin web that may crush due to inclined compressive strength or

when the beam is provided with very high shear reinforcement ratio.

3. Failure of the stirrups anchorage. The functionality of the stirrups depends on their

mechanical anchorage. Loosing the anchorage before stirrup yielding will cause a

sudden failure of the beam without achieving the stirrup capacity.

4. Failure of the flexural reinforcement. The shear cracking yields more tensile stresses in

the flexural reinforcement which may lead to yielding of the longitudinal

reinforcement or anchorage failure.

5. Failure to meet the serviceability requirements. However, there is no specific shear

crack width specified in the design codes, but the larger shear crack widths at service

load my not be accepted.

2.4 Shear Strength Analysis of Reinforced Concrete Beams

The manner in which the shear failures occur varies widely depending on the dimensions,

geometry, loading and properties of the members. For this reason, there is no unique way to

design for shear (MacGregor 1997). Moreover, for complex phenomena influenced by many

variables understanding the meaning of particular experiments and the range of applicability

of the results is extremely difficult unless the research is guided by an adequate theory which

can identify the important parameters (Collins et al. 2007). Several attempts have been made

to rationalize the shear design procedures for reinforced and prestressed concrete members

decades ago. Some of these procedures were reviewed in the ASCE-ACI Committee 426

(1973) report. Recently, the ASCE-ACI Committee 445 (1998) has published an updated

report reviewing some of the shear models developed for concrete members. This section

18


provides summary of the shear models for reinforced concrete beams. Some of these models

are based on the equilibrium conditions and some others depend on the compression field

approach as follows:

1. Models based on equilibrium approach:

a. The 45° Truss Model.

b. Variable-Angle Truss Model.

c. The Modified Truss Model.

2. Methods based on compression field approach:

a. Compression Field Theory (CFT).

b. Modified Compression Field Theory (MCFT).

c. Rotating-Angle Softened Truss Model (RA-STM).

d. Fixed-Angle Softened Truss Model (FA-STM).

e. Disturbed Stress Field Model (DSFM).

3. Shear Friction Model (SFM).

4. Strain Based Shear Strength Model

2.4.1 Historical background

There were several attempts to analyse the shear behaviour of reinforced concrete beams.

Truss models were among the earliest methods that have been developed in the early 1900s

and used as conceptual tools in the analysis and design of reinforced concrete beams. Ritter

(1899) and Morsch (1902) postulated that after a reinforced concrete beam cracks due to

diagonal tension stresses, it can be idealized as two parallel longitudinal chords connected to

composite web made of shear reinforcement bars and diagonal concrete struts. The diagonal

concrete struts were assumed to be subjected to direct axial compression, while the shear

reinforcement bars were treated as the tensile web members of the truss. The inclination angle

of the diagonal cracks was assumed to be 45 degrees with respect to the longitudinal

reinforcement. Thus, this model was referred to as the "45-degree truss model." Withey (1907

& 1908) pointed out that Ritter's truss model yielded conservative predictions when compared

with test results and Talbot (1909) confirmed this finding. Morsch (1920 & 1922) introduced

the use of truss models for concrete members subjected to torsion.

19


Since then, there have been great efforts to enhance the model assumptions to yield

more reasonable predictions in comparison with experimental results, which can be

categorized in as three major developments. This first major development was presented by

Lampert and Thurlimann (1968) through assuming that the inclination angle of the concrete

struts may deviate from 45°. Their theory was known as variable-angle truss model. The

second development was achieved by Robinson and Demorieux (1968). They realized that a

reinforced concrete element subjected to shear stresses was actually subjected to biaxial

compression-tension stresses in the 45-degree direction. Besides, they discovered that the

compressive strength in one direction was reduced by cracking due to tension in the

perpendicular direction which is known as "softening effect." Based on testing of eight beams

with I-section, they were able to explain the equilibrium of stresses in the webs according to

the truss model but they were not able to quantify this reduction of strength in the concrete

struts. The third development was the derivation of the compatibility equation to determine

the inclination angle of the concrete struts (Collins 1973). Mitchell and Collins (1974)

presented the theory of diagonal compression field theory for members subjected to pure

torsion and they quantified the softening effect of the concrete were introduced. In this

theory, the formulation of equilibrium conditions, geometry of deformation, and the stress-

strain characteristics of the steel and the concrete. This model was capable of predicting the

complete post-cracking torsional behaviour of symmetrically loaded reinforced concrete

members. Following this, Collins (1978) and Vecchio and Collins (1981) presented the

compression filed theory for reinforced concrete members subjected to shear. The CFT

assumes that the inclination of the principal compressive stress in concrete coincides with the

inclination of the principal compressive strain, and cracks develop in the principal direction of

concrete. In this theory, the equilibrium conditions that relate the average stresses in the

beams to the applied loads and the compatibility conditions that exist between the average

strains in the various directions were considered, which represented a major breakthrough in

the prediction of shear behaviour of reinforced concrete elements. Through this study, the

softened stress-strain relationship was also introduced. Moving a step forward and based on

the compression field theory, Vecchio and Collins (1986 & 1988) presented the modified

compression field theory which accounts for the contribution of the tensile stresses in the

concrete between cracks, which was not considered in the compression field theory. However,

20


the theory had two deficiencies as pointed out by Hsu (1998). First, the MCFT violated the

basic principle of mechanics by imposing concrete shear stresses in the principal directions.

Second, it used the local stress-strain curve of steel bars embedded in concrete, rather than the

smeared (average) stress-strain curves.

A Rotating-Angle Softened Truss Model (RA-STM) was developed by Hsu (1988);

Belarbi and Hsu (1994) & (1995); Pang and Hsu (1995), and Hsu and Zhang (1996). This

theory treated the cracked reinforced concrete as a smeared and continuous material. In this

model, a new smeared stress-strain curve of steel bars embedded in concrete was proposed

(Belarbi and Hsu 1994). This model has two advantages: (i) it produces a unique solution

instead of multiple solutions as resulting from the modified compression field theory; and (ii)

there is no need to perform the "crack check" which is difficult to apply in finite element

methods. On the other hand, these studies confirmed that the rotating-angle could not logically

produce the concrete contribution, Vc, because shear stresses could not exist along the

rotating-angle cracks.

In order to predict the concrete contribution, Vc, Fixed-Angle Softened Truss Model

(FA-STM) was proposed by Pang and Hsu (1996); and Hsu and Zhang (1997). In this model

the direction of cracks is assumed to be perpendicular to the applied principal tensile stresses

at initial cracking and the concrete constitutive laws were set in the principal coordinate of the

applied stresses at initial cracking.

Based on the rotating-angle crack model, Vecchio (2000 & 2001) developed the

Disturbed Stress Field Model (DSFM). The DSFM was a partially smeared model, which

included shear slips along crack surfaces and required a crack check as specified in the

MCFT.

2.4.2 The 45° truss model

Ritter (1899) and Morsch (1902) explained the flow of forces in a cracked reinforced concrete

beam in term of truss models as shown in Figure 2.8. The internal forces in a reinforced

concrete beam forms the different members of the truss. The diagonal compressive stresses in

the concrete act as the diagonal members of the truss while the stirrups act as vertical tension

members. The longitudinal flexural reinforcement forms the bottom chord of the truss while

the flexural compressive concrete zone forms the top chord of the truss. In their models, Ritter

21


and Morsch neglected the tensile stresses in the cracked concrete and assumed that after

cracking the diagonal compression stresses would remain 45°.

/ /

(a) Ritter's truss model.

(b) Morsch's truss model.

Figure 2.8: Ritter and Morsch's truss models.

The equilibrium conditions for the 45° truss model are summarized in Figure 2.9.

Assuming uniformly distributed shear stresses over and effective shear area bw wide and dv

deep as shown in Figure 2.9(a), then from the free-body diagram shown in Figure 2.9(b) the

required magnitude of the principal compressive stress,^, is given by:

2V / 2 =

b..,d., (2.2)

The horizontal component of the diagonal compressive force will equal V as shown in

Figure 2.9(b) and this force must be balanced by an equal tensile force, Nv, in the direction of

the longitudinal flexural reinforcement.

22


N=V (2.3)

From the free-body diagram shown in Figure 2.9(c) and considering the force

equilibrium in the vertical direction, the force in the stirrups will equal to the vertical

component of the diagonal compression force ( = bwf2s sin 45). Thus:

^^ = — (2.4)

where Av is the cross-sectional area of the stirrups, s is the stirrup spacing, and/, is the tensile

stress in the stirrups.

M=0

•*

* • • < *

(a) Cross section (b) Diagonal stresses and longitudinal equilibrium

(c) Force in stirrups

Figure 2.9: Equilibrium consideration for 45° truss (Collins and Mitchell 1997).

23


2.4.3 Variable-angle truss model

Lampert and Thurlimann (1968) assumed that the inclination angle of the concrete struts may

deviate from 45°. The equilibrium conditions for the variable angle truss model are shown in

Figure 2.10. From this figure, the following relationships can be deduced which are similar to

that of the 45° truss model but the inclination angle is unknown:

V = Dsme = (bwf2dvcos6)smG (2.5a)

/ 2 = - ^ ( t a n < 9 + cot0) (2.5b) Kdv

Nv=Vcot0 (2.6)

4iA = — tan6> (2.7) s dv

It can be noticed that these three equilibrium equations are not enough to find the

stresses in a beam subjected to shearing force because there are four unknowns: fi,fv, Nv, and

6. A simple procedure to overcome this shortening is to assume the maximum compressive

stress in the concrete struts at failure and to solve Equations (2.5) and (2.7) to get the Fand 6.

Marti (1985) recommended a compressive stress limit of 0.6 fc\ where fc' is the concrete

compressive strength.

2.4.4 Modified truss model

Both of the 45° truss model and the variable angle truss model neglect the tensile stresses of

the cracked concrete and no stresses are transferred across the cracks. Ramirez and Breen

(1991) proposed a modified truss model approach for beams with shear reinforcement

incorporating additional term to account for concrete contribution. In this modified truss

model, the nominal shear strength of a prestressed or nonprestressed concrete beam with shear

reinforcement is represented as:

Vn=Vc + Vs (2.8)

where Vc is the additional concrete contribution and Vs is the strength provided by the shear

reinforcement.

According to Ramirez and Breen (1991) the additional term for the concrete

contribution, Vc, is a function of the shear stress level, v. This can be represented as follows:

24


M=0

(a) Cross section (b) Diagonal stresses and longitudinal equilibrium

(c) Force in stirrups

Figure 2.10: Equilibrium conditions for variable-angle truss (Collins and Mitchell 1997).

For nonprestressed concrete beams:

For uncracked state: Vc = 2y/c ' bw (0.9d) for v < 2^/J (psi; in. units)

For transition state: Vc = — 16 f'c -v\bw (0.9 d) for 2^fc < v < 6^fc (psi; in. units)

For full truss state: V = 0 for v > 2 J / j (psi units)

(2.9a)

(2.9b)

(2.9c)

25


where vcr is the shear stress resulting in the first diagonal tension cracking in the concrete, and

v is the stress level due to factored loads.

For prestressed concrete beams:

For the prestressed concrete an additional factor, K, is added to account for the beneficial

effect of the prestressing force on concrete diagonal tensile strength and further capacity after

cracking. Thus, the concrete contribution takes the following form:

Vc =K^2^Zyw(0.9d) (psi; in. units) (2.10)

K = f f \0-5

l + JPL (2.11) ft

where fpc is the compressive stress at the neutral axis and ft is the principal diagonal tension

stress.

The additional tensile force in the flexural reinforcement due to shear is calculated

from Equation (2.6) and the shear reinforcement contribution is calculated from Equation

(2.7). Ramirez and Breen (1991) proposed a limiting value of 30^/ c (psi) for the

compressive stress to avoid the web-crushing failure and the following limits for the

inclination angle of the diagonal trusts:

30° < 9 < 65° For reinforced concrete beams.

25° < 9 < 65° For prestressed concrete beams.

2.4.5 Compression field theory

In 1974 the diagonal compression field theory was developed for the analysis of concrete

beams subjected to torsion by Mitchell and Collins (1974) and noted as compression field

theory. There after, Collins (1978) extended this theory to account for the reinforced concrete

beams subjected to shear. In this theory, the cracked concrete is treated as a new material

which with its own stress-strain characteristics. The principal strain directions in the concrete

are assumed to coincide with the corresponding principal stress directions. The equilibrium,

compatibility (neglecting the tensile resistance of the concrete after cracking), and stress-strain

relationships are formulated in terms of average stresses and average strains.

26


Figure 2.11 shows the compression field theory aspects. The equilibrium equations are

formulated in a way similar to the variable angle truss model. From Figure 2.11 (a; b) the

following equilibrium equations can be deduced:

Pjsy= fey =vtan0 (2.12)

pjsx=fcx=v cote (2.13)

/ 2 = v ( t a n 0 + cot0) (2.14)

where fsx and fxy are tensile stresses in the longitudinal and transverse directions, px and/?v are

the reinforcement ratio in longitudinal and transverse directions, a n d ^ is the compressive

stress in cracked concrete, inclined at an angle 6 with the longitudinal direction.

For design, the inclination angle of the diagonal compression has to be known. To

determine the angle of inclination of the diagonal compression, Mitchell and Collins (1974)

introduced the compatibility equations neglecting the tensile resistance of the concrete after

cracking and assuming that the shear is carried by a field diagonal compression. This

assumption yielded the following expression for the inclination angle of the diagonal

compression which can be deduced form Mohr's circle of strain as shown in Figure 2.1 l(c; d).

2 „ £„+£ tan2 9 = x 2 (2.15)

ey+e2

where EX and ey are the strains of the longitudinal and transverse reinforcement, and £2 is the

concrete strain in the diagonal compression direction. The principal tensile strain in the

concrete, ei, and the shear strain, y^, can be derived also form Mohr's circle as follows:

EX =ex+(£x+e2)cot20 (2.16)

rxy=2{£x+£2)cot20 (2.17)

Before using Equation (2.15) to determine 0, however, the stress-stain relationships for

the reinforcement and the concrete are required. The simple bilinear stress-strain

approximations for the longitudinal and transverse were assumed as shown in Figure 2.1 l(e;

f). Collins (1978) suggested that the relationship between the principal compressive stress,^,

and the principal compressive strain, £2, for diagonally cracked concrete would differ from

that resulted from the standard cylinder test as shown in Figure 2.11(g).

27


Equilibrium conditions

Shear stress

(a) Free body diagram (b) Mohr's circle of stress

Compatibility relationships

(c) Strains in cracked elements

y/7,

2/

£2

\

Ey

^ l / > / \ \ £

2 0 / j

I . X

1 e\

0. 5rm

(d) Mohr's circle of strain

Jsx

fy

Stress-strain relationships for reinforcement

fsyi

/ J y

E,

(e) Longitudinal reinforcement

-y

(f) Transverse reinforcement

Figure 2.11: Compression field theory aspects (Mitchell and Collins 1974).

28


Stress-strain relationships for cracked concrete in compression

(g) Stress-strain relationship

1.0

/2max

/ ;

0

/ 3.6/:

2max 1 + ^•Ym/^c

A L

0 1 2 3 4 5

(h) Failure stress in cracked concrete

Figure 2.11 (Cont'd): Compression field theory aspects (Mitchell and Collins 1974).

Collins (1978) assumed that the cracked concrete would fail at a smaller compressive

stress, fimzx., than that of standard cylinder test as shown in Figure 2.11(h) because this stress

must be transmitted across relatively wide cracks. The following equations were proposed:

3.6/;

And for values of/2 less than/max:

8 - & -O2 t 1

/c£c

(2.18)

(2.19)

where ym is the diameter of the strain circle (£1+^2), and ec' the strain at the peak stress,/ ' in

the cylinder compression test.

By using the equilibrium and the compatibility conditions as well as the appropriate

stress-strain relationships for reinforcement and diagonally cracked concrete the load-

deformations response of members loaded in shear is found. However, because the

compression field theory neglects the contribution of tensile stresses in cracked concrete, it

overestimates deformations and gives conservative estimate of strength (Mitchell and Collins

1997).

29


2.4.6 Modified compression field theory

The modified compression field theory (MCFT) is a further development of the compression

field theory (CFT). While the original CFT ignored the tension in the cracked concrete, the

MCFT takes into account tensile stresses in the concrete between the cracks and employs

experimentally verified average stress-average strain relationships for the cracked concrete

(Vecchio and Collins 1986).

The MCFT aspects are shown in Figure 2.12. The shear on a section will be resisted by

the diagonal compressive stress,/, together with the diagonal tensile stresses,/:. It should be

noted that the tensile stresses in the diagonally cracked concrete vary in magnitude from zero

at the crack locations to maximum values between the cracks as shown in Figure 2.12(j). From

the equilibrium conditions which relate the concrete stresses and the reinforcement stresses to

the applied load and expressed in terms of average stresses, the following relationships can be

derived considering Figure 2.12(a; b):

fcy=pjsy=vtan0-fi (2.20)

fa=P,f»=v**0-fi (2-21)

/ 2 = v ( t a n 0 + c o t 0 ) - / (2.22)

V where v = (2.23)

The tensile force resisted by the web reinforcement is calculated as:

4 fv = (f2 sin2 0 + fx cos2 9)bw s (2.24)

where Av and/, are the area of the stirrups and the average stress in the stirrups, respectively.

Substituting for / in Equation (2.22) gives:

V = flbwdvcot0 + dvcot0 (2.25)

s

From Equation (2.25) it can be noticed that the shear resistance of a concrete member

can be expressed as the sum of the concrete contributions, which depends on the tensile

stresses in concrete, and the shear reinforcement contribution.

30


Equilibrium conditions

/ , Jsy f

L\ L \Z v\—I x \—K^—

Shear stress

(a) Free body diagram (b) Mohr's circle of stress

Compatibility relationships

y/i.

/

£2

Sy

^ ^ >

2 0 /

\Fx •

1 S\

1 £

0. 5r •* 1 m

(c) Strains in cracked elements (d) Mohr's circle of strain

Equilibrium in terms of local stresses at crack Shear stress

fs sycr

fs. sxcr

HH

(e) Free body diagram (f) Local concrete stresses

Figure 2.12: Modified compression field theory aspects (Vecchio and Collins 1986).

31


Stress-strain relationships for reinforcement

Jsx

fy

Jsy

fy

(g) Longitudinal reinforcement (h) Transverse reinforcement

Stress-strain relationships for cracked concrete in compression

t y h

• ' 2max

0 I I I I I L 0 -1 -2 -3 -4 -5

E\lE'c

(i) Stress-strain relationship (j) Failure stress in cracked concrete

Stress-strain relationships for concrete in tension

W=£\Sg

£X £,

(at crack slip)

Vci/

0.2

0.4

0.2

K -

a=20 mm

i I

0 1 2 w (mm)

(k) Average stress-strain relationship for (1) Allowable local shear stress on cracks as a

cracked concrete in tension function of crack width

Figure 2.12 (Cont'd): Modified compression field theory aspects (Vecchio and Collins 1986).

32


Considering the equilibrium in the direction of the longitudinal reinforcement, the

unbalanced component in the longitudinal direction must be resisted by an additional stress in

the longitudinal reinforcement as follows:

Kfs* = (fi cos2 9 + fx sin2 e) bw dv = V cot 9 - fx bwdv (2.26)

where Asx and fsx are the area and the average stress in the longitudinal reinforcement,

respectively. It should be mentioned that the Equation (2.26) shows the effect of the shear

force on the stresses in the longitudinal reinforcement.

The compatibility equations for the MCFT are the same as that of the CFT which are

defined in Equations (2.15) to (2.17). In order to relate the stresses and the strains shown in

Figure 2.12, the stress-strain curves for the reinforcement and the cracked concrete in

compression and tension are required. For the reinforcing steel bars and stirrups, typical

bilinear diagram is assumed as shown in Figure 2.12(g; h). However, the stress-strain

relationship of diagonally cracked concrete element in pure shear was investigated by Vecchio

and Collins (1986) and based on the these tests they concluded that the principal compressive

stress in concrete,^, is a function not only of the principal compressive strain, £2, but also of

the coexisting principal tensile strain, ei. Moreover, they suggested the following stress-strain

relationship and the maximum limit for the compressive stress in the compression diagonals

which are shown in Figure 2.12(i; j).

2 ( \

UJ -

( \ \£2

UJ 2~

/2=/2 max 2 ^ - -4- (2.27b) \£c J

<1.0 (2.27b) J2max

fc 0.8 + 17*.

On the other hand, Vecchio and Collins (1986), through experimental and analytical

investigations, proposed the following equation for the stress-strain relationship for cracked

concrete in tension:

(2.28a)

(2.28b)

f\ = Ec £\

, a\alfcr

for

for

*1 ^ £cr

£\>£cr 1 T •«/ J U U t ]

where a\ and ai are factors accounting for bond characteristics of the reinforcement and type

of loading, respectively, fcr and ecr are the tensile stress and the corresponding strain at the

33


concrete cracking, respectively, and Ec is the concrete modulus of elasticity. Figure 2.12(k)

shows the stress-strain relationships for concrete in tension represented by the aforementioned

equations.

As assumed in this theory and treated above, the strains and stresses are calculated on

average values. However, the failure of the reinforced concrete element may be governed by

local stresses at a crack rather than average stresses. At a crack the tensile stress in the

concrete goes to zero, while the tensile stresses in the reinforcement become larger. The shear

capacity of the member may be limited by the ability of the members to transmit forces across

the crack. At low shear values, tension is transmitted across the crack by local increase in

reinforcement. At certain shear force the stress in the web reinforcement will just reach yield

at crack locations. At higher shear forces transmitting tension across the crack will require

local shear stresses, vc„ on the crack surface which depends on the crack width. Vecchio and

Collins (1986) presented the following equation for the vc, which is based on Walraven (1981)

tests neglecting the compressive stresses across the crack as shown in Figure 2.12(1):

0.3 + ag+16

where w is the crack width and ag is the maximum aggregate size. The tensile stress must be

limited to:

y;=vc,.tan^ + - ( 4 - / v ) (2.30)

The use of the above equation requires estimating the crack width, w. It can be

estimated as the product of the principal tensile strain, e\, and the average spacing of the

diagonal cracks measured perpendicular to the crack, smg, as follows:

w = exsme (2.31)

The inclined crack spacing depends on the crack control characteristics of both the

longitudinal and transverse reinforcement which is represented as:

J " " = s i n 0 cos0 ( 2 ' 3 2 )

+ mx mv

' - - M , ( 1 2 9 >

34


where s^ and smv are crack spacing indicative of the crack control characteristic of the

longitudinal and vertical reinforcement, which are calculated respectively as follows:

Smx ~ ^

Smv *•

f O „ „ . d, c + — x V lOy

V v 10,

+ 0.25 A:,-^ (2.33) Px

+ 0.25 kx -&- (2.34) Pv

where cx and cv are the concrete covers for the longitudinal and transverse reinforcement,

respectively, sx and sv are the spacing between the reinforcing bars in longitudinal and

transverse direction, respectively, dbx and dbv are the bar diameter of the longitudinal and

transverse bar diameter, respectively, k\ is 0.4 for deformed steel bars and 0.8 for smooth steel

bars, and px and pv are the longitudinal and transverse reinforcement ratio, respectively.

Finally, the transmitted concrete tension is limited at a crack to the value

corresponding to the yielding of the longitudinal reinforcement:

sx Jsxy ~ sxcr J sxcr J\ w uv *x U eVW ^v) bwdvcot20 (2.35)

The above equation sets for equilibrium, compatibility, stress-strain relationships for

concrete in compression and tension provide a complete model to predict the response of a

reinforced concrete member in shear.

2.4.7 Rotating-angle softened truss model

A Rotating-Angle Softened Truss Model (RA-STM) was developed through an extensive

research work conducted at the University of Huston which was initiated by presenting the

Softening Truss Model Theory for Shear and Torsion by Hsu (1988). This work is continued

and the constitutive models were developed by Hsu (1991); Belarbi and Hsu (1994) & (1995);

Pang and Hsu (1995); and Hsu and Zhang (1996). This model treats the cracked reinforced

concrete as a smeared and continuous material. Like the MCFT this model satisfies the three

fundamental principals of the mechanics of materials: the two-dimensional stress equilibrium,

the strain compatibility, and the constitutive laws for concrete and reinforcement.

The stresses and the principal axes for a concrete membrane element in shear loading

are shown in Figure 2.13. The direction of the post cracking principal stress and strain in the

concrete is defined by the d-r coordinates as shown in Figure 2.13(e). The c/-axis which

35


represents the direction of the concrete strut is oriented at an angle a to the /-axis of the

longitudinal steel bars. Because the angle alpha decreases with increasing loading, it is

referred to as "rotating angle." Upon considering the softening effect for the concrete, this

model is referred to as rotating-angle softened truss model (RA-STM). The assumption of a

rotating angle makes the shear strength completely provided by steel. Considering the

illustration shown in Figure 2.13, the equilibrium and compatibility equations are derived by

transforming the concrete stresses and strains in the 2-1 coordinate to concrete stresses and

strains in l-t coordinate. The equilibrium equations are given by:

<j, = <Jd cos2 a + <rr sin2 a + p, ft (2.36)

at = ad sin2 a + <Jr cos2 a + pt ft (2.37)

xu ={-<7d +cr r)sinacos« (2.38)

where o\ and a, are the steel stresses in the /- and /-directions, respectively (positive for

tension), T/, is the applied shear stress in the l-t coordinate (positive as shown in Figure 2.13),

Od and ar are the principal stresses in the d-r directions, respectively (positive for tension), a is

the angle of the inclination of the d-axis with respect to the /-axis, pi and pt are the mild steel

ratios in the /- and /-coordinate, respectively, fi and ft are the average stresses in /- and /-

directions, respectively.

The compatibility equations are given by:

£, = sd cos2 a + sr sin2 a (2.39)

st = ed sin2 a + £r cos2 a (2.40)

— = (-sd+£r)smacosa (2-41)

where £/ and et are the average strains in the /- and /-directions, respectively (positive for

tension), 721 is the average shear strains in the l-t coordinate, pi and pt are the mild steel ratios

in the /- and /-coordinate, respectively (positive as shown in Figure 2.13), and e and er are the

average principal strains in the d- and r-direction, respectively (positive for tension).

36


^

r (a) Reinforced concrete

Tit 1 = - f P +

Th

T (b) Concrete

Pi ft

\

Plfl

(c) Reinforcement

(d) Principal axis 2-1 for applied stresses

(e) Principal axis d-r for stresses on concrete

(f) Assumed crack direction (g) Assumed crack direction in Fixed-Angle Model in Rotating-Angle Model

Figure 2.13: Reinforced concrete membrane elements subjected to in-plane stresses (Pang and

Hsu 1996).

The above listed six equations for equilibrium and compatibility require three

constitutive relationships for: (i) concrete in compression for aj and Ed in d-r direction; (ii)

concrete in tension for ar and er in d-r direction; and (iii) steel in tension foxfi and e/ oxft and

s,. The constitutive relationships for this model were developed by Belarbi and Hsu (1994) &

(1995); Pang and Hsu (1995) and will be summarized as follows:

37


Concrete in compression

°d=Zfc 2 M bd

2

1-

0.9

I 2AT-1 .

7T+400J

&o

<1 (2.42)

(2.43)

(2.44)

where fc' is the maximum compressive strength of a standard (152^305 mm) concrete

cylinder, e0 is the concrete peak strain at the maximum compressive strength (=0.002), and Cis

the softening effect.

Concrete in tension

°r = Ec £r

ar = for

/ \0.4 ' 0.00008

for er < 0.00008

for e. > 0.00008

(2.45a)

(2.45b)

where Ec is the modulus of elasticity of the concrete (~3900Jfc ; fc in MPa), mdfcr is the

concrete cracking stress (=0.3lJf ; fc in MPa).

Steel reinforcement

fs=Es£s for £•„ < £•„

Js J V (0.91-25) + A

0.02 + 0.255^-V 'yj

'x 2-« 2 / (45deg)

1000/?

en=ey{0m-2B)

f - V-5

P

J cr

\*y J

(2.46)

for es > sn (2.47)

(2.48)

(2.49)

where Es is the steel modulus of elasticity, fs and es are the stress in the steel bars and the

corresponding strain,^ is the cracking stress of concrete. This equation is applicable for both

38


longitudinal and transversal steel reinforcement where fs = fi or fi when applying for

longitudinal or transversal reinforcement, respectively.

By using this model, the full member response of a reinforced concrete member loaded

in shear could be predicted.

2.4.8 Fixed-angle softened truss model

The fixed angle softened truss model was developed by Pang and Hsu (1996). This model was

developed to overcome the incapability of the RA-STM to predict the concrete contribution.

This incapability is attributed to the RA-STM assumption that the concrete struts are oriented

in the direction of the post cracking principal compressive stress thus, shear stress is not

allowed to exist along the assumed cracks. To overcome this incapability, Pang and Hsu

(1996) assumed that the cracks in the concrete are oriented at a fixed angle, wi, with the /-

direction. The model assumptions are summarized as follows:

Equilibrium equations

<y, = cr2 cos2 a2 + acx sin2 a2 + r2l 2sin a2 cos a2 + pl f, (2.50)

<rt = G2 sin2 a2 + cr[ cos2 a2 - r21 2 s m aicos a2 + Pt ft (2.51)

TU =(-cr2 +cr1c)sina2cosa2 +r21(sin2a2 - cos 2 a 2 ) (2.52)

where fi and /J are the average steel stresses in /- and /-directions, respectively, a-i is the angle

of the inclination of the 2-axis with respect to the /-axis, pi and pt are the mild steel ratios in

the /- and /-coordinate, respectively, ai and at are the applied normal stresses in the /- and t-

directions, respectively, of and o\ are the average normal stresses of concrete in the 2- and 1-

directions, respectively, TI, is the applied shear stress in the l-t coordinate (positive as shown in

Figure 2.13), and X2\ is the average stresses of concrete in the 2-1 coordinate.

Compatibility equations

e, =s2cos2 a2 +sx sin2a2 +-^-2J-2sin«2cosa2 (2.53)

st = e2 sin2 a2 +£, cos2 a2 +-^-2sina2 cosa2 (2.54)

39


h 2 - = (~e2 + £\) sin a2 cos a2 +-^-(sin2 a2 - cos 2 a 2 ) (2.55)

where a2 is the angle of the inclination of the 2-axis with respect to the /-axis, £/ and et are the

average normal strains in the /- and /-directions, respectively (positive for tension), £2 and £1

are the average normal strain in the 2- and 1-direction, respectively, yn is the average shear

strains in the /-/ coordinate (positive as shown in Figure 2.13), 721 is the average shear strain in

the 2-1 coordinate.

In addition to the three constitutive laws of concrete and steel defined before for the

RA-STM, the FA-STM requires an additional constitutive law for the stress-strain relationship

of cracked concrete in shear. The constitutive laws defined by Equations (2.41) to (2.49) for

the RA-STM are valid for the FA-STM by replacing the stresses and strains in the d-r

coordinate by those in the 2-1 coordinate. However, the fourth required constitutive law relates

the two shear components (721 and r2] ) is defined as follows:

T21 ~T2U 1 1- r2\ Yi\ o J

T2lm ~ ~ {°i -Plfly)-{°t-Ptf'ty )] S i n 2«2 + *ltm C0S 2«2

(2.56)

(2.57)

2Clm i s t h e where rltm is the maximum shear stress of cracked concrete in l-t coordinate, r;

maximum shear stress of cracked concrete in the 2-1 coordinate, y2lo is the peak shear strain

corresponding to maximum shear stress in the 2-1 coordinate which is presented by Zhang

(1995) by the following empirical expression:

( n f - ^ / 2 1 o =-0.85* l o 1 - A 7 *' (2.58)

^ Pi fly -O/ J

where £i0 is the strain corresponding to zltm. The values of average steel stresses fly and/^,

are calculated using Equations (2.46) to (2.49).

In this model Pang and Hsu (1996) derived the following formula for evaluating the

shear strength at the local steel yielding:

Tllm ~ {T2\m ) / 7 —

2 VPi fly Ptfty

(2.59)

40


Equation (2.59) represents the shear strength in the form of two-term equation where

the first term caused by concrete shear stress x\Xm which denoted as the concrete contribution,

Vc, and the second term denoted as the steel contribution, Vs.

2.4.9 Disturbed stress Held model

Although the accuracy and reliability of the MCFT have been generally good, experience has

revealed some deficiencies in specific situations as observed from testing of panel elements

(Vecchio 2000): (i) Shear strength and stiffness generally underestimated for panels

containing heavy amounts of reinforcement in both directions; and (ii) shear strength and

stiffness are generally overestimated for uniaxially reinforced panels or for panels containing

very light reinforcement in transverse direction. Vecchio (2000) starting from the MCFT

proposed a conceptual model describing the behaviour of cracked reinforced concrete element

considering a hybrid formulation between fully rotating crack model and a fixed crack model.

Later, this model is validated by Vecchio et al. (2001).

The advancements in the formulation of this model comparing with the modified

compression field theory include: (i) a new approach to the orientation of concrete stress and

strain fields; (ii) removing the restriction for the coincidence of the average principal stresses

with the strains; and (iii) improving the treatment of shear stresses on crack surfaces. The

formulation of this model which is denoted as disturbed stress field model (DSFM), as

proposed by Vecchio (2000), is presented as follows:

Equilibrium equations

Considering the reinforced concrete element shown in Figure 2.14(a) and considering

the special case of orthogonally reinforced panel with reinforcement aligned with the

reference axes:

°x=fcx+Pxfsx (2-60)

°,=fv+PyfV (2-61)

^ = v c x y (2.62)

where the concrete stresses fcx, fey, and vcxy can be determined from Mohr's circle as shown in

Figure 2.14(b).

41


Reinforcement

2

vcxy

1

—ycy

y

(E vA fcZ —

I

vf. )

1 fc

—f«

(a) (b)

Figure 2.14: Reinforced concrete element: (a) Reinforcement and loading conditions; and (b)

Mohr's circle for average stresses in concrete (Vecchio 2000).

The equilibrium conditions of a cracked element employed in the DSFM are shown in

Figure 2.15. As the crack interfaces are considered planes of weakness, the average stresses

that can be transmitted across the cracks have to be checked. The component of the concrete

principal tensile stresses due to tension stiffening is assumed zero at crack location. To

transmit the average stress fc\, local increases in the reinforcement stresses are necessary. The

local stresses are shown in Figure 2.15(d) and noted as^cw- The magnitude ofîthtat can be

transmitted trough this mechanism is:

/C ,=ZAU, - / , ) C O S 2 ^ 1=1

(2.63)

where p, is the reinforcement ratio, fsi is the average stress, fyi is the yield stress for the f

reinforcement component, and 6ni is the difference between the angle of orientation of

reinforcement, a,, and the normal to crack surface 6:

eni=e-at (2.64)

The local reinforcement stress must satisfy the equilibrium condition that the average

concrete tensile stresses be transmissible across the cracks:

E Pi ifscri ~ fsi ) C O s 2 9ni = fci (2.65) i=i

where the stresses^,-, are determined from local reinforcement strains eS{

42


Bv

\

1 _tu

V \0

/A /

/

X

B

Average

*0y Section A

,J* I a Section B "xy \a Section C

(c) (d)

Figure 2.15: Equilibrium conditions: (a) External conditions; (b) Perpendicular to crack

direction; (c) Parallel to crack direction; and (d) Along crack surface (Vecchio 2000).

The local increase in reinforcement stresses at crack locations lead to the development

of shear stresses along the crack surface, vCJ. The equilibrium requirements yield the following

relationship:

Vci =YJP> ifscri ~ fsi ) C 0 S 6ni S i n On (2.66) i=i

Compatibility relations

Figure 2.16 summarizes the compatibility conditions of the DSFM. The apparent inclination

of the apparent principal strains ([e] = \£x sy yxy}) will be calculated as:

43


0e=-tan_I

E 2

xy

£x~£y (2.67)

The principal strains are determined form the net strains ([£•<,] = \£cx £cy ycxy\) as

follows:

£c\'£c2 ~

£cx + £cy + ^j{£cx+£cyf+rcxy (2.68a; b)

2 2

The actual inclination of the principal strains in the continuum, 6, and the assumed

inclination of the principal stresses, dd, will be:

i cxy 0 =0 = -ton~l

d 2 £cx £cy (2.69)

From Figure 2.16(b) assuming the cracks are inclined in the direction of net principal

tensile strain, 9, and the cracks have an average width equals w with average crack spacing

equals s, the average shear slip strain is calculated as:

Ys (2.70)

where the slip strains ( \e s \- \ssx ss

y Yxy\) a r e determined as follows:

* , '= -£-s in(20)

*;=*|-sin(20)

(2.71)

(2.72)

rxy=yscos{20) (2.73)

The "lag" in the rotation of the principal stresses in the continuum relative to the

rotation of the apparent principal strains is defined as:

A9 = 0£-0a (2.74)

The following relationship should be considered when relating the apparent strains

conditions to the actual orientation of stresses and strains:

ys=yvcos0tr+(ey-ex)sm20<f (2.75)

44


fV^^j

\ \ ^

-Ik, (a)

r/2*

26+90

(b) y^&sfc

yf2'

<

\

T jy

X

\ V2

l1''" (c)

Figure 2.16: Compatibility conditions: (a) Deformations due to average (smeared) constitutive

response; (b) Deformations due to local rigid body slip along crack; and (c) Combined

deformations (Vecchio 2000).

45


The average strain in a reinforcement component is calculated form the total strains as

follows:

£ + £ £ £ F = — + - - r. cos2<x +-^-[£„ -er)sin2a, + EI (2.76)

2 2 ' 2

where a, is the orientation of the reinforcement, and £°s( is the initial prestrain in the

reinforcement.

The average crack spacing and the average crack width are then defined as:

1 s = sin 9 cos 0

+

(2.77)

w = £cls (2.78)

Constitutive relations

The concrete compression response:

, . »(ec2/ep) Jc2 J p / \ I

(n-\) + (£c2/£f

where /i = 0 .80- / D /17

Jt = 1.0

k = (0.67-fp/62)

\nk

')

for

for

£p <£c2<0

£C2 > £P

(2.79a)

(2.79b)

(2.79c)

(2.79d)

fp and £p are the peak stress and the corresponding peak strain.

For concrete in tension before cracking:

fcl=Ec£c\ for 0<ec\<ecr

where Ec is the initial tangent modulus of elasticity, and ecr is the cracking strain.

(2.80)

For concrete in tension after cracking:

After cracking the concrete continues to carry tensile stresses as a result of two components,

which are tension softening and tension stiffening calculated as:

46


h\ ~ Jt ! i£cl-£cr)

(£tS-£cr)_

(2.81)

G, such that £ts = 2.0 , where Gy-=75 N/m and Lr is the characteristic length.

Jt^r

/ci = r (2-82) \ + yjCtEcX

such that c, =200 for relatively small elements or elements containing a closely spaced mesh

of reinforcement and =500 for larger-scale element. The tensile concrete tensile strength is

calculated as:

/ /=0 .65( / ; ) ° 3 3 (2.83)

Slip model

The following slip model is used in DSTM model:

v . S' = 1.8 MT 0 8 + (0.234 w-0 7 0 7- 0.20) fcc

( 2 ' 8 4 )

where vc, is the shear across the crack, w is the average cack width, a is the aggregate size,fcc

is the concrete cube strength. Once the slip displacement, S°, has been found, Equation (2.70)

is used to determine the crack slip shear strain, yas .

2.4.10 Shear friction model

The shear friction model (SFM) is based on the behaviour of the shear and longitudinal

reinforcement crossing a shear crack plane. The stirrups and the longitudinal reinforcement

are assumed to provide a clamping force and thereby increasing the friction force which can

be transferred a cross a potential failure crack. Loov (1978) proposed that the shear resistance,

v„, transferred across a crack is limited by the stress that can be sustained by bond and

anchorage and can be predicted as follows:

vn=k^c (2-85)

47


where a is the normal stress on the plane and k is the shear-fiction factor. The results of this

formula were in agreement with the results of the push-off tests conducted by Kumaraguru

(1992).

N-

Figure 2.17: Shear friction model in a concrete beam by Kriski and Loov (1996).

Starting from Equation (2.85), Kriski and Loov (1996) and Loov (1998) derived a

general equation based on shear friction as follows:

For any inclined crack as shown in Figure 2.17, with v=SIA and s=RIA

S = k^Rf'cA (2.86a)

A = bwh/sin6 (2.86b)

Solving for R and S using the equilibrium of the forces affecting the free body diagram

in Figure 2.17 the following values are obtained:

R = (T-N)sme-(Vn-Tv)cose (2.87)

s = (T-N)cos0-(vn-Tv)smO (2.88)

Inserting the R and S values from Equations (2.87) and (2.88) in Equation (2.85) and

solving for Vn, the following equation was derived for the shear strength of a reinforced

concrete beam:

7.0 ^ = 0.5k2 T-N

'o.25k2C • + cor6>-cot<9 C + cot20)-^—^cot9 + -^< .

' C C f *-» ^w Jc

(2.89)

48


Cw=fXh (2.90)

Tv=Afy (2-91)

where A is the area of the potential failure plane, Av is the are of stirrups, h is the overall

section height, fy is the yield stress of the steel stirrups, N is the axial force, R, is the normal

force acting on potential shear failure plane, and 6 is the inclination angle of the failure plane.

Kriski and Loov (1996) evaluated the shear strength of beam specimens using the

shear friction analysis considering the test results from literature and their tests. Based on this

study, they concluded that the shear friction analysis is capable of predicting the shear strength

of reinforced concrete beams. However, 0.6 value for the shear-friction parameter, k, may be

slightly unsafe if the beam area is considered. Loov and Peng (1998) presented the following

equation for calculating the shear-friction factor as follows:

* = 2.1 (/j)"04 (2.92)

where X ' is the concrete compressive strength.

2.4.11 Unified shear strength model for reinforced concrete beams

A theoretical model was recently developed to predict the shear strength of slender reinforced

concrete beams without web reinforcement by Park et al. (2006). Through this model, the

shear force applied to a cross section of the beam assumed to be resisted primarily by the

compression zone of intact concrete rather than by the tension zone and the shear capacity of

the cross section was defined based on the material failure criteria. Later, Choi et al. (2007)

and Choi and Park (2007) presented a unified shear strength model for reinforced concrete

beams which is based on the strain based calculations for the shear strength. The details of this

method will be presented in this section considering these three references: Park et al. (2006),

Choi et al. (2007) and Choi and Park (2007) as follows:

The compression zone of a beam is subjected to combined compressive normal stress

and shear stress. The interaction between these two stress components must be considered to

accurately evaluate the shear strength of the compression zone as shown in Figure 2.18. The

failure mechanism of the compression zone that is subjected to combined stresses is defined

using Rankine's failure criteria (Chen 1982). Accordingly, material failure occurs when the

principal stress resulting from the combined stresses reaches material strength. When the

49


principal tensile stresses reaches the tensile strength of concrete, ft', a failure controlled by

tension occurs, and when the principal compressive stress reaches the compressive strength,

fc', a failure controlled by compression occurs as shown in Figure 2.18. Thus the failure

criteria of the compression zone can be defined as follows:

<Ju

Tensile failure surface

Compression failure surface

Mohr circle

Tension

-fc

v__ ft 8 0

~-\Compression

s=(aso)

Figure 2.18: Rankine's failure criteria for reinforced concrete (Chen 1982).

For failure controlled by tension:

A2

" 2 = 2 + V l 2 +v u

2 </ ; (2.93)

For failure controlled by compression:

50


°l=- ' 2 " V l 2 + v„2>-/c ' (2.94)

where o\ and 02 equal the principal compressive and tensile stresses, respectively; cu and vu

equal the compressive stress and shear stress of concrete, respectively; and ft ' equals the

tensile strength of concrete affected by transverse compressive stress. In the critical section of

a simply supported beam that is susceptible to shear failure, however, the principal

compressive stress o~\ is usually not a large value. Therefore, the tensile strength of concrete

can be simplified as^J' =ft, the tensile strength of concrete in pure tension.

In a concrete beam, the normal stress in the compression zone is developed by flexural

moment. The normal stress ou varies according to its distance from the neutral axis of the

cross section. Therefore, using Equations (2.93) and (2.94), the allowable shear stress at each

location in the compression zone can be defined as a function of the distance from the neutral

axisz.

For failure controlled by tension

vut (z) = Jft[fl+cr(z)] (2.95)

For failure controlled by compression

v~(z) = Jfc[fc-<r(*)\ (2-96)

But in slender beams without transverse reinforcement, the failure mechanism is controlled by

tension rather compression (Al-Nahlawi and Wight 1992). For this reason the failure

controlled by tension is considered.

K = K\l\<{z)dz*ylf,[f,+*(axle0)] bwc(axls0) (2.97)

For an arbitrary location x0, where flexural crack initiates (Figure 2.19), the relation

between the moments at the location x0 and the loading point can be defined as:

MZL-M*. ( 2 . 9 8 )

x0 a

At cracking, the relationship between the moment Mxo and the normal strain at the

extreme compression fiber of the cross section is defined as:

Mxo = Mcr = "xo £o Ec

rbh2^ (2.99)

51


Strain ax\e0 aaz0

Atxo Atxl At a

Figure 2.19: Critical sections and strain distribution of a cracked beam (Park et al. 2006).

A previous assumption based on the test results of MacGregor et al. (1960) assumed

that an additional applied force of 0.05^ fc bw d is required to make a tensile crack reach the

neutral axis. Thus, when the tensile crack reaches the neutral axis the previous equation takes

the following form:

M„ _ Mc • + 0.05^M = ^ = ^ (2.100)

The moment at the location x0 and JCI are defined as:

Mxo=Mcr+0.05J7cbwdxo

^ . = <*xleoEc C(ax\£o) •\aX\£o) xk.

(2.101)

(2.102)

where ax\e0 equals compressive strain at the extreme compression fiber of the cross section at

location x\ and c(axls0) equals the depth of the compression zone at location x\. Following

the 45 degree angle for the tensile crack, leads to xl=x0+h-c(axls0). The normal strain

ax\e0 at the extreme compression fiber at location xi is defined as:

<xxie0=-

x„ =

frh2/(6xo) + 0.05jZd](xo+h-c(axi£o))

Ecc{ax\£o)'(-[d-c{axXs0)l'i\

\0a frh2

60(aa-a2

a/3)xc(axl£0)x£xdv-3jfcad <a

(2.103)

(2.104)

52


where fr is the concrete modulus of rupture = 0.625y/J and h is the cross section height.

K=^ylf,[f,+^{ax^0)]bwc(axle0) (2.105)

where <r = axl s0 Ec/2 and ft = 0.292y/c . Using these values in Equation (2.105), it takes

the following form:

Vc=^ylf,[f,+axle0Ee/2]bwc(axle0) (2.106)

Xs a factor to account for the size effect the previous shear stress which proposed by Zarais

and Papadakis (2001) and it equals:

Xs = 1.2 -0.2 (a/d)d > 0.65; d in meters (2.107)

Choi et al. (2007) and Choi and Park (2007) presented their unified model which

includes the strain-based evaluation of the concrete strength. A simplified design method was

provided including the contribution of the concrete and steel stirrups to the shear resistance.

The shear strength of a beam is defined as the sum of the contribution of the concrete and

shear reinforcement as follows:

Vn = Vc + Vs (2.108)

where, Vs, is calculated as follows considering the 45° diagonal cracking angle:

V, = P„fyKd (2.109)

However, for simplicity in calculating the concrete contribution, it was assumed that:

x}=0.6a-d for 2<a/d<5 (2.110a)

xx=a-2>d a/d>5 (2.110b)

axl = 1.0 - 0.44 a/d> 0.2 (2.111)

2.5 Shear Design Provisions in North American Codes

2.5.1 American Concrete Institute, ACI 318-08 (ACI 2008) Code

The ACI 318-08 (ACI 2008) Codes is based on the 45° truss model in addition to the concrete

contribution. The shear design is performed as follows:

Wn=Vf (2.112)

53


Vn=K+Vs (2.113)

where (j) is the material resistance factor (=0.75), V„ is the nominal shear strength, and I -is the

factored shear force at the section considered, Vc and Vs is the contribution of concrete and

shear reinforcement, respectively.

The shear strength is based on an average shear stress on the full effective cross-

section, bw d. For members without shear reinforcement, shear is assumed to be carried by the

concrete web while for members with shear reinforcement, a portion of the shear strength is

assumed to be provided by the concrete and the remaining portion by the shear reinforcement.

The shear strength provided by concrete, Vc, is assumed to be the same for beams with or

without shear reinforcement and is taken as the shear causing significant inclined cracking.

The ACI (2008) presents the following two equations for determining Vc as follows:

The simplified equation:

1. For sections subjected to shear and flexure only:

Vc=0MAjZbwd (2.114)

2. For sections subjected to axial compression in addition to shear and flexure:

( N, N

Fc=0.17 1 + -1 4 4y

Hfcbwd (2.115)

The detailed equation:

1. For members subjected to shear and flexure only

K = 0.16AV/ c+0.17pv-^ MfJ

bd (2.116a)

where Vc < 0.29 X fc bw d ,Vf dJMf < 1.0. (2.116b)

2. For members subjected to axial compression, Vc shall be computed using Equation

(2.115) substituting Mm for M/ which is calculated as:

Mm=Mf-Nf^-^- (2.117)

However, Vc shall not be taken greater than:

54


Vc<0.29Zjfc bwdj\ + —^- (2.118)

When Mm is negative, Vc shall be determined using Equation (2.118).

3. For members subjected to significant axial tension:

( 0.29 A ^ F =0.17 1 + -

Az J Ufcbwd>Q (2.119)

where A//-is negative for tension.

For calculating Vc, using Equations (2.114) to (2.119) ^fc shall not be greater than 8.3

MPa unless the section is provided with minimum shear reinforcement specified by the code.

The shear reinforcement contribution, Vs, is calculated as follows:

Affvd Vs=

f y (2.120) s

Minimum shear reinforcement

A minimum area of shear reinforcement that shall be provided in reinforced concrete flexural

members when Vj exceeds 0.5 </>Vc equals:

A „ = 0 . 0 6 2 ^ b-f>.^f± (2.121) J y J y

Spacing of shear reinforcement placed perpendicular to axis of member shall not

exceed d/2 in non prestressed members or 0.75/2 in prestressed members or 600 mm.

2.5.2 The Canadian Highway Bridge Design Code, CHBDC, CAN/CSA-S6-06 (CSA

2006)

The CHBDC (CSA 2006) provides a shear design method based on the modified compression

field theory (MCFT) for reinforced and prestressed concrete members. The nominal shear

strength is calculated as follows.

Vn=Vc + Vs + Vp<0.25<Pcf'bwdv+Vp (2.122)

Vc =2.5 <l>cPfcrbwdv (2.123)

/ c r = 0 . 4 J / c < 3 . 2 M P a (2.124)

55


^>s Avfvdv cot 0 Vs = (vertical stirrups) (2.125a)

s

6, A, /„ dv (cot 6 + cot a ) sin a Vs =

s W j > vV * (inclined stirrups) (2.125b) s

where Vc and Vs are the concrete and shear reinforcement contributions to the shear strength,

respectively; (j)c and <j>s are the material resistance reduction factors for concrete and

reinforcing steel, respectively (</>c = 0.75 and <j>s = 0.90); dv is the greater of 0.72/z where h is

the total depth of the cross-section, or 0.9d,fc' is the specified compressive strength concrete,

Av is the area of shear reinforcement, and s is the stirrup spacing. To determine the factor /?

and the angle 6 the CHBDC CSA (2006) Code recommends two methods which can be

described as follows:

Simplified method for determining fi and 0

For non-prestressed components not subjected to axial tension, and provided that the specified

yield strength of the longitudinal reinforcement does not exceed 400 MPa and the design

concrete strength does not exceed 60 MPa, the value of the angle of inclination, 6, shall be

taken as 42° and the value of /? shall be determined as follows:

1. For sections with at least the minimum amount of transverse reinforcement, /? shall

equal 0.18.

2. For sections not containing transverse reinforcement but having a specified nominal

maximum size of coarse aggregate (ag) not less than 20 mm, /? shall be calculated as:

230 (2.126)

1000 + c/v

3. Alternatively, for sections containing no transverse reinforcement, /? may be

determined for all aggregate sizes from the following equation:

230 1000 + sze

where the equivalent crack spacing parameter, sze, is calculated as:

35J„ 15 + ag

(2.127)

(2.128)

56


However, sze shall not be taken as less than 0.85.sz, where the crack spacing parameter,

sz, shall be taken as dv or as the distance between layers of distributed longitudinal

reinforcement where each intermediate layer of such reinforcement has an area at least equal

to 0.0036^.

General method for determining p and 0

1. The factor /? shall be determined from the following equation:

« = -™° ^ 0 _ (1 + 1500*,) (\000 + sze)

2. For sections containing at least the minimum transverse reinforcement required by the

code, sze shall be taken as 300 mm; otherwise, sze shall be calculated using Equation

(2.128). The value of ag Equation (2.128) shall be taken as zero iffc is greater than 70

MPa and shall be linearly equal to zero asfc' goes from 60 to 70 MPa.

3. The angle of inclination, 6, in degrees shall be calculated as:

(29 + 7000*,) 0.88-Sze ^ (2.130)

2500,

4. The value of the longitudinal strain at the mid-height of the cross-section, ex, is

calculated from the following equation:

(Mf/dv) + V,-Vp+0.5Nf-Af s=K fl v) / p- 4- — <0.003 (2.131)

2(E,A, + EpAp)

where As is the area of longitudinal steel reinforcement, Es is the tensile modulus of

elasticity of steel, fpo is the stress in tendons when the stress in the surrounding

concrete is zero (MPa), Mj is the factored moment at a section (N.mm), N/ is the

factored axial load normal to the cross-section occurring simultaneously with Vj ,

including the effects of tension due to creep and shrinkage (N), Ap is the area of the

prestressing steel tendons, Ep is the elastic modulus of the prestressing tendons, Vp is

the component in the direction of the applied shear of all of the effective prestressing

forces factored by (j)p (material resistance factor for FRP tendons).

The following notes should be considered when calculating ex:

(a) Vf and JWf are positive quantities and M/shall not be less than (Vf-Vp)dv.

57


(b) N/ shall be taken as positive for tension and negative for compression. For rigid

frames and rectangular culverts, the value of N/ used to determine ex may be

taken as twice the compressive axial thrust calculated by elastic analysis.

(c) As and Ap are the areas of reinforcing bars and prestressing tendons in the half-

depth of the section containing the flexural tension zone.

(d)fp0 may be taken as 0.7fpu, where fpu is the specified tensile strength of

prestressing steel (MPa) for bonded tendons outside the transfer length andfpe

for unbonded tendons.

(e) In calculating As, the area of bars that terminate less than their development

length from the section under consideration shall be reduced in proportion to

their lack of full development.

(f) If the value of ex is negative, it shall be taken as zero or recalculated with the

denominator replaced by 2{ES As+Ep Aps+Ec Act), where Act is the area of

concrete on the flexural tension side of a member (mm2). However, sx shall not

be less than-0.20x10"3.

(g) For sections closer than dv to the face of the support, the value of ex calculated

at dv from the face of the support may be used in evaluating 9 and /?.

(h) If the axial tension is large enough to crack the flexural compression face of the

section, the resulting increase in ex shall be taken into account. In lieu of more

accurate calculations, the value calculated from Equation (2.131) shall be

doubled.


When transverse shear reinforcement is required, Avmm shall not be less than:

Amm=0.l5fcr^f (2.132) Jy

where^,. is determined from Equation (2.124).

The spacing of the transverse reinforcement, s, measured in the longitudinal direction

shall not exceed the lesser of

1. 600 mm or 0.75dv if the nominal shear stress is less than 0.1 <j>c fc; and

58


2. 300 mm or 0.33dv if the nominal shear stress equals or exceeds 0. \</>cfc-

2.5.3 The Canadian Standard Association CSA-A23.3-04 (CSA 2004)

The CSA-A23.3-04 (CSA 2004) Code provides a shear design method based on the MCFT for

reinforced and prestressed concrete members. The nominal shear strength is calculated as

follows:

VH=Ve + V, + VpZ0.25*efebwdv + Vp (2.133)

Vc=<l>cXpJfcbwdv where 7 Z ^ 8 M P a (2.134)

<f>s A. fvdv cot 9 y = YS >vjy v (vertical stirrups) (2.135a)

s

d>. A, /„ dv (cot 6 + cot a) Vs =

s ^ y vV '- (inclined stirrups) (2.135b)

s

where Vc and Vs are the concrete and shear reinforcement contributions to the shear strength,

respectively; <j)c and <f>s are the material resistance reduction factors for concrete and

reinforcing steel, respectively (^c = 0.65 and <j>s = 0.85); dv is the greater of 0.72/z where h is

the total depth of the cross-section, or 0.9d,fc' is the specified compressive strength concrete,

Av is the area of shear reinforcement, and s is the stirrup spacing. To determine the factor /?

and the angle 6 the CSA (2004) Code recommends the same two methods specified by the

CHBDC CSA (2006). However, minor differences are summarized as follows.

1. The recommended 6 in the simplified method is 35° instead of 42° specified by the

CHBDC CSA (2006).

2. Equation (2.130) in the general method takes the following format: (29 + 7000*,) (2.136)

3. /? and 6 shall be taken as 0.21 and 42° for any of the following member types:

a. Slabs and footings with an overall thickness not greater than 350 mm.

b. Footings in which the distance form the point of zero shear to the face of the

column, pedestal, or wall is less than three times the effective shear depth of

the footing.

c. Beams with an overall thickness not greater than 250 mm.

59


d. Beams cast integrally with slabs where the depth of the beam below the slab is

not greater than one-half the width of web or 350 mm.


A minimum area of shear reinforcement shall be provided in the following regions:

1. In regions of flexural members where the factored shear, Vj, exceeds Vc+Vp.

2. In regions of beams with an overall thickness greater than 750 mm.

When calculations show that transverse shear reinforcement is required, Avm\n shall not

be less than:

Amm =0.06^7:^ (2-137) Jy

The spacing of the shear reinforcement, s, placed perpendicular to the axis of the

member shall not exceed 0.7 dv or 600 mm.

2.5.4 AASHTO LRFD Bride Design Specification (2004)

The American Association of State Highway and Transportation Officials (AASHTO) in its

Load and Resistance Factor Design (LRFD) Bridge Design Specifications (2004) adopts the

MCFT for shear design of reinforced and prestressed concrete beams. As usual in most of the

design codes and guidelines, the nominal shear resistance for a reinforced concrete section is

the summation of concrete contribution, Vc, and shear reinforcement contribution, Vs, in

addition to the prestressing component, if any. The nominal shear strength is calculated as

follows:

4>VH=Vf (2.138)

Vn=Vc+Vs+Vp<0.25y[7;bwdv+Vp (2.139)

where <j> is the material resistance factor (= 0.90 for normal strength concrete and 0.7 for low

density concrete), Vn is the nominal shear strength, and Vj is the factored shear force at the

section considered, Vp is the component in the direction of the applied shear of the effective

prestressing force (positive if resisting the applied shear), and Vc and Vs are the contributions

of concrete and shear reinforcement, respectively determined as follows:

VC=0.0S3 pjfcbwdv where ^ < 8 M P a (2.140)

60


<^s Avfvdv cot 0 Vs = (vertical stirrups) (2.141a)

s

6, Av fvdv{co\0 + coXa)sma Vs= ^Jy vV '- (inclined stirrups) (2.141b)

s

where a is the angle of the transverse reinforcement to the longitudinal reinforcement in

degrees.

Similar to the CHBDC CSA-S6 (CSA 2006) and CSA-A23.3-4 (CSA 2004) there are

two methods to determine the values of /? and 6. Moreover, like the aforementioned codes,

those two methods are simplified and general method and they can be described as follows.

Simplified method for determining fi and 0

This method is applicable for concrete footings in which the distance from point of zero shear

to the face of the column, pier, or wall is less than three times the effective shear depth of the

footing, and for other nonprestressed concrete sections not subjected to axial tension and

containing at least the minimum amount of transverse reinforcement according to Equation

(2.144), or having an overall depth less than 400 mm. according to this method, the following

values for the parameter /? and the angle 6 may be used:

P = 2.0 and 0 = 45°

General method for determining p and 6

For sections containing at least the minimum amount of transverse reinforcement as given by

Equation (2.144), the values of/? and 6 shall be as specified in Table 2.1. To use this table, the

longitudinal strain at the mid-height of the cross-section, ex, and the crack spacing parameter,

sze, shall be calculated. In lieu of more accurate calculations, ex shall be determined as follows:

e - {Mfldv)^.SNf^Vf-Vp)coiG-Apfpo

2(EslAsl+EpAp)

If the value of ex from Equation 22 is negative the strain shall be taken as:

e SH,iO+™«Ay,-r.)«*°-*.f~ (2,42b)

2{EcAa+Et,A„ + EpAp)

where Act is the area concrete on the flexural tension side of the member.

61


Table 2.1: Values of 6 and/? for sections with transverse reinforcement (AASHTO LRFD

2004).

fc

<

0.075

<

0.100

<

0.125

<

0.150

<

0.175

<

0.200

<

0.225

<

0.250

sx x 1000

<

-0.20

22.3°

6.32

18.1°

3.79

19.9°

3.18

21.6°

2.88

23.2°

2.73

24.7°

2.63

26.1°

2.53

27.5°

2.39

<

-0.10

20.4°

4.75

20.4°

3.38

21.9°

2.99

23.3°

2.79

24.7°

2.66

26.1°

2.59

27.3°

2.45

28.6°

2.39

<

-0.05

21.0°

4.10

21.4°

3.24

22.8°

2.94

24.2°

2.78

25.5°

2.65

26.7°

2.52

27.9°

2.42

29.1°

2.33

<

0

21.8°

3.75

22.5°

3.14

23.7°

2.87

25.0°

2.72

26.2°

2.60

27.4°

2.51

28.5°

2.40

29.7°

2.33

<

0.125

24.3°

3.24

24.9°

2.91

25.9°

2.74

26.9°

2.60

28.0°

2.52

29.0°

2.43

30.0°

2.34

30.6°

2.12

<

0.25

26.6°

2.94

27.1°

2.75

27.9°

2.62

28.8°

2.52

29.7°

2.44

30.6°

2.37

30.8°

2.14

31.3°

1.93

<

0.50

30.5°

2.59

30.8°

2.50

31.4°

2.42

32.1°

2.36

32.7°

2.28

32.8°

2.14

32.3°

1.86

32.8°

1.70

<

0.75

33.7°

2.38

34.0°

2.32

34.4°

2.26

34.9°

2.21

35.2°

2.14

34.5°

1.94

34.0°

1.73

34.3°

1.58

<

1.00

36.4°

2.23

36.7°

2.18

37.0°

2.13

37.3°

2.08

36.8°

1.96

36.1°

1.79

35.7°

1.64

35.8°

1.50

* v/is the factored shear stress = V/(bw dv).

For sections containing transverse reinforcement less than calculated using Equation

(2.144), the values of /? and 6 shall be as specified in Table 2.2 where the value of the strain at

the mid height of the cross-section, ex, is calculated from Equation (2.142). The crack spacing

parameter, sze, is calculated from the following equation:

35v s„= z < 2000 mm (2.143)

16 + a„

62


where the parameter sz shall be taken as the smaller of dv or the maximum distance between

layers of longitudinal crack control reinforcement provided that each layer of such

reinforcement has an area al least equals 0.003bwsz.

Table 2.2: Values of 8 and/? for sections with less than minimum transverse reinforcement

(AASHTO LRFD 2004).

&ze

(mm)

<

130

<

250

<

380

<

500

<

750

<

1000

<

1500

<

2000

ex x 1000

<

-0.20

25.4°

6.36

27.6°

5.78

29.5°

5.34

31.2°

4.99

34.1°

4.46

36.6°

4.06

40.8°

3.50

44.3°

3.10

<

-0.10

25.5°

6.06

27.6°

5.78

29.5°

5.34

31.2°

4.99

34.1°

4.46

36.6°

4.06

40.8°

3.50

44.3°

3.10

<

-0.05

25.9°

5.56

28.3°

5.38

29.7°

5.27

31.2°

4.99

34.1°

4.46

36.6°

4.06

40.8°

3.50

44.3°

3.10

<

0

26.4°

5.15

29.3°

4.89

31.1°

4.73

32.3°

4.61

34.2°

4.43

36.6°

4.06

40.8°

3.50

44.3°

3.10

<

0.125

27.7°

4.41

31.6°

4.05

34.1°

3.82

36.0°

3.65

38.9°

3.39

41.2°

3.20

44.5°

2.92

47.1°

2.71

<

0.25

28.9°

3.91

33.5°

3.52

36.5°

3.28

38.8°

3.09

42.3°

2.82

45.0°

2.62

49.2°

2.32

52.3°

2.11

<

0.50

30.9°

3.26

36.3°

2.88

39.9°

2.64

42.7°

2.46

46.9°

2.19

50.2°

2.00

55.1°

1.72

58.7°

1.52

<

0.75

32.4°

2.86

38.4°

2.5

42.4°

2.26

45.5°

2.09

50.1°

1.84

53.7°

1.66

58.9°

1.40

62.8°

1.21

<

1.00

33.7°

2.58

40.1°

2.23

44.4°

2.01

47.6°

1.85

52.6°

1.60

56.3°

1.43

61.8°

1.18

65.7°

1.01

<

1.50

35.6°

2.21

42.7°

1.88

47.2°

1.68

50.9°

1.52

56.3°

1.30

60.2°

1.14

65.8°

0.92

69.7°

0.76

<

2.00

37.2°

1.96

44.7°

1.65

49.7°

1.46

53.4°

1.31

59.0°

1.10

63.0°

0.95

68.6°

0.75

72.4°

0.62


The AASHTO LRFD specifications (2004) require a minimum amount of shear reinforcement

vmin for non prestressed concrete members given by:

63


^ m i n = 0 . 0 8 3 ^ ^ (2.144) Jy

The spacing of the transverse reinforcement shall not exceed the maximum permitted

spacing, smax, determined as follows:

vf < 0.125 f'c then smax < 0.8 dv < 600 mm (2.145a)

vf >0.125/c'then smm <0Adv <300mm (2.145b)

where v/is the shear stress calculated as V//(bw dv) and dv is the effective shear depth.

2.6 Shear Crack Width

Many investigations were conducted to evaluate the flexural crack width and to introduce

design equations. Most of the design codes for steel reinforced concrete sections provide

equations to evaluate the flexural crack width. Besides, there are proposed limits for the

flexural crack width corresponding to the degree of exposure to the environmental conditions.

On contrary, a few researches attempted to evaluate the width of the inclined shear cracks.

Placas and Regan (1971) proposed an equation for the maximum shear crack width, w,

at any loading level after the appearance of the shear cracks (V>Vcr). This equation is

presented in the following format:

ssincc {V~Vcr) ... . . . / - , i ^ w = 7-r- -^ (lb; in. units) (2.146)

io6p„(/;r Kd

where s is the stirrup spacing, V is the applied shear force, Vcr is the shear forces causing shear

cracking, pCT is the shear reinforcement ratio, and a is the inclination angle of the stirrups.

64

Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review

CHAPTER 3

SHEAR BEHAVIOUR OF CONCRETE BEAMS REINFORCED WITH

FRP STIRRUPS: BACKGROUND AND REVIEW

3.1 General

This chapter provides brief information on the FRP materials, their characteristics and

applications in structural engineering. It is focusing on the use of FRP as shear reinforcement

for concrete structures. The studies conducted to investigate the strength capacity of FRP

stirrups and the shear strength of concrete beams reinforced with FRP stirrups are reviewed as

well. The shear design provisions for concrete members reinforced with FRP in Japan,

Canada, USA, and Europe are also discussed.

3.2 Fibre-Reinforced Polymers (FRP)

Fibre-reinforced polymer (FRP) is a composite material constitutes of reinforcing fibres and

the matrix (polymer resin) that binds the fibres together to form the composites. The

mechanical properties of the final FRP product depend on the fibre quality, orientation, shape,

volumetric ratio, adhesion to the matrix, and the manufacturing process. The common fibre

types are glass, aramid, polyvinyl and carbon whereas the common resin types are

thermosetting and thermoplastic resins. FRP products are manufactured in different forms

such as bars, fabrics, 2D grid, 3D grid or standard structural shapes. Figure 3.1 shows the

typical FRP products. The FRP reinforcements have favourable characteristics that can be

summarized as: resistance to corrosion and chemical attack, high strength-to-weight ratio,

magnetic transparency and non conductivity, and ease of handling.

3.2.1 Reinforcing fibres

Fibres are functioning as the main resistant component of the composite materials.

Consequently, fibres used for manufacturing composite must have strength, stiffness,

durability, sufficient elongation at failure, and preferably low cost. The performance of fibres

is affected by their length, cross-sectional shape, and chemical composition. Fibres are

available in different in different cross-sectional shapes and sizes. The most commonly used

65


fibres for producing FRPs are glass, aramid, and carbon. Table 3.1 presents the typical

mechanical properties for the most commonly used fibres.

Table 3.1: Mechanical properties of the most commonly used fibres (ISIS Canada 2007).

Fibre type

Carbon

Aramid

Glass

PAN

Pitch

Kevlar 29

Kevlar 49

E-Glass

S-Glass

Tensile strength

(MPa)

2500-4000

3000-3500

3620

2800

3500-3600

4900

Modulus of

elasticity (GPa)

350-650

400-800

82.7

130

74-75

87

Elongation

(%)

0.4-0.8

0.4-1.5

4.4

2.3

4.8

5.6

Poisson's

ratio

-0.20

N/A

0.35

0.35

0.20

0.22

3.2.2 Resins

A very important issue in the manufacture of composites is the selection of the proper matrix

because the physical and thermal properties of the matrix significantly affect the final

mechanical properties as well as the manufacturing process. The matrix not only coats the

fibres and protects them from mechanical abrasion and from alkaline degradation, but also

transfers stresses between the fibres. Another very important role of the matrix is to transfer

the inter-laminar and in-plane shear in the composite, and to provide the lateral support to

fibres against buckling when subjected to compressive loads (ISIS Canada 2007).

There are two types of polymeric matrices widely used for FRP composites:

thermosetting and thermoplastic. The thermosetting polymers are used more often than

thermoplastic ones because their good thermal stability and chemical resistance and low creep

relaxation. The most commonly used types of these thermosetting resins are the vinyl ester

and epoxies. Table 3.2 gives the typical properties of thermosetting resins.

3.2.3 FRP reinforcing bars

FRP reinforcing bars are manufactured from continuous fibres (such as carbon, glass, and

aramid) embedded in matrices (thermosetting or thermoplastic). Similar to steel

reinforcement, FRP bars are produced in different diameters, depending on the manufacturing

66


process. The surface of the rods can be spiral, straight, sanded-straight, sanded-braided, and

deformed. The mechanical properties of some commercially available FRP reinforcing bars

are given in Table 3.3. Figure 3.2 shows typical stress-tensile strain relationships for

commercially available carbon, aramid, and glass FRP bars compared to steel.

X

V

V.

V

k

(a) FRP products

.sr<«7

/ /'A'/?.. I

I'vtluuntt

CFCC

leadline

(c) FRP tendons

%-

m &

&?x*

* > « . . ' • " . 'sm'

(b) FRP fabrics

(d) FRP grids

(e) FRP ropes and bars (f) FRP pultruded shapes

Figure 3.1: Typical FRP products (fib 2006).

67


Table 3.2: Typical properties of thermosetting resins (ISIS Canada 2007).

Resin

Epoxy

Polyester

Vinyl Ester

Specific gravity

1.20-1.30

1.10-1.40

1.12-1.32

Tensile strength

(MPa)

55.0-130.0

34.5-103.5

73.0-81

Tensile modulus

(GPa)

2.75-4.10

2.10-3.45

3.00-3.35

Cure shrinkage

(%)

1.0-5.0

5.0-12.0

5.4-10.3

Unlike the steel bars, the FRP materials are linear material up to failure and the CFRP

has the highest modulus of elasticity which ranges from 60 to 75% of that for steel. While the

GFRP bars has the lowest modulus of elasticity which ranges from 20 to 25% of that for steel.

On the other hand, the tensile strength of all FRP bars is higher than the yield strength of the

conventional steel bars.

Table 3.3: Typical mechanical properties of FRP reinforcing bars (ISIS Canada 2007).

Trade name Tensile strength

(MPa)

Modulus of elasticity

(GPa)

Ultimate tensile

strain

Carbon Fibre

V-ROD

Asian

Leadline

NEFMAC

1596

2068

2250

1200

120.0

124.0

147.0

100.0

0.013

0.017

0.015

0.012

Glass Fibre

V-ROD

Asian

NEFMAC

710

690

600

46.4

40.8

30.0

0.017

0.017

0.020

68


(MP

a)

Str

ess

1800

1600

1400

1200

1000

800

600

400

200

/

/ C a r b o n FRP

/

/ / ^ / / ^ ^ ^ ^ ^

Aramid FRP

- Glass FRP

Steel

r ^ — • i i i i "• i • • ' • •

0.0 0.5 1.0 1.5 2.0

Strain (%)

2.5 3.0

Figure 3.2: Typical stress-tensile strain of FRPs compared to steel.

3.3 FRP Product Certification

Unlike steel reinforcement, there are no available governing standards for the production of

the FRP reinforcing bars or their mechanical properties. ISIS Canada moved a step forward

regarding this issue and published its FRP Product Certification (ISIS Canada 2006) and there

are parallel efforts now to adopt and update this certification as a standard by the Canadian

Standard Association (CSA-S807): FRP Product Specification (CSA 2008). Corresponding to

ISIS Canada Specifications (2006), FRPs are designated according to their fibres, minimum

tensile strength, minimum modulus of elasticity and durability as follows: Xa-Eb-Dc, where X

is A, C or G for aramid, carbon or glass; a is the tensile strength of the FRP in MPa; E is the

modulus of elasticity; b is the grade of the FRP; D stands for durability; and c is the durability

designation. In drawings, FRP bars shall be identified by an uppercase letter and the nominal

bar diameter; the letter shall be A, C or G for aramid, carbon or glass, respectively.

Table 3.4 provides the ISIS Canada (2006) designation for some aramid, glass, and

carbon FRP bars, receptively. From Table 3.4 it can be noted that corresponding to modulus

of elasticity there are three FRP Grades: Grade I; Grade II; and Grade III. Grade I FRPs is

characterized by the highest value of £ and Grade III by the lowest.

69


3.4 Strength of FRP Bent Bars/Stirrups

Due to the unidirectional properties of the FRP materials, they have lower transverse strength

and dowel resistance. Consequently, there are two main factors affecting the strength of FRP

bent bars/stirrups. The first factor is the bending of FRP bar into stirrup configuration to

provide sufficient anchorage. This results in significant reduction in the bent bar/stirrup

strength at the bend location. The second factor is effect of inclined shear cracks on the

straight portions of the FRP stirrups. At the intersections, induced shear forces affect the FRP

stirrups at an angle with the fibres' direction which, in turn, results in reduction in the strength

of the FRP stirrups. Through the following section the conducted studies from literature for

investigating the performance and strength of FRP bent bars/stirrups and the FRP bars

subjected to inclined cracks in comparison with the strength in the fibres' direction will be

reviewed.

Table 3.4: Designation of some FRP reinforcing bars (ISIS Canada 2006).

Fibre in

FRP

Aramid

Carbon

Carbon

Nominal

diameter

(mm)

6

8

10

13

15

20

6

8

10

13

15

20

Cross-

sectional

area

(mm2)

32

50

71

129

199

284

32

50

71

129

199

284

Min.

tensile

strength

(MPa)

*

*

*

*

*

*

*

*

*

*

*

*

Min. E,

for

Grade III

(GPa)

50

80

Min. E,

for

Grade II

(GPa)

70

110

Min. E,

for

Grade I

(GPa)

90

140

Designation

Aa-Eb-Dc

Ca-Eb-Dc

70


Table 3.4 (Cont'd): Designation of some FRP reinforcing bars (ISIS Canada 2006).

Fibre in

FRP

Glass

Nominal

diameter

(mm)

6

8

10

13

15

20

22

25

Cross-

sectional

area

(mm2)

32

50

71

129

199

284

387

510

Min.

tensile

strength

(MPa)

*

*

*

*

*

*

*

*

Min. E,

for

Grade III

(GPa)

35

Min. E,

for

Grade II

(GPa)

40

Min. E,

for

Grade I

(GPa)

50

Designation

G750-EZ>-Dc

G650-E6-Dc

G600-E6-Dc

G550-E6-Dc

T o be provided by manufacturer.

3.4.1 Bend strength of FRP bent bars/stirrups

The tensile strength of the bent bar at bend location (bend strength) is significantly less than

that parallel to the fibres. At the bend, the stirrup resists lateral loads due to bearing against

concrete, in addition to the stresses in their longitudinal direction parallel to the fibre's

direction. Besides, bending the FRP bars causes the innermost fibres at the bend to be kinked

compared to those at the outermost radius. The intrinsic weakness of fibres perpendicular to

their axis accompanied by the kinked fibres at the bend contribute to reduced strength at the

bend portion of FRP stirrups compared to straight bars.

Maruyama et al. (1993) investigated the tensile strength of the FRP bent rods at the

bend locations (bend strength) using the loading system and test specimen illustrated in Figure

3.3. In this study three different FRP bent rods were tested. Those types were 7-strand CFRP

(Carbon Fibre-Reinforced Plastic) rods, pultrusion CFRP rods, and braided AFRP (Aramid

Fibre-Reinforced Plastic) rods, and steel bars for comparison. The diameters of the used FRP

and steel bars were 7.5, 6.0, 8.0, and 6.0 mm for 7-strand CFRP, pultrusion CFRP, braided

AFRP, and steel, respectively. Three different bend radii for each type of FRP rods were used

71


and they were 5, 15, and 25 mm; however, the steel bars were tested only with 5 mm bend

radius. Besides, the effect of the concrete strength on the bend radius was also investigated

using two different concrete strengths: high strength concrete (about 50 MPa), and ultra high

strength concrete (about 100 MPa). The main findings of this investigation can be summarized

as follows:

1. Unlike the steel specimens (control), all FRP rods ruptured at the bent portion at the

beginning of the bend on the loading side and the corresponding bend strength was

lower than the tensile strengths of the straight portions.

2. The tensile strength of the bent portion of FRP rods tends to decrease hyperbolically as

the curvature of the bend increases as shown in Figure 3.4.

3. The difference in bend strength between the 50 and 100 MPa concrete strengths varied

to some degree with the type of rod, though the higher strength concrete did produce

higher bend strengths as shown in Figure 3.5.

m

^ r -

Grip

Load Cell

Jack

FRP Rod

o o

o

o

- * -

^k

ft Strain Gauge (Loading Side)

Strain Gauge ^ X

(Loading Side) Anchor

M-70

-*-80

-*-100

*

Figure 3.3: Test setup and specimen dimension tested by Maruyama et al. (1993).

72


«> 0.4

o

I 0.2

I.. . -fc=50MPa -fc=100MPa

1.0

0.8

0.6

0.4

0.2

0.0

^-<

-» - fc=50MPa -Q-fc=100MPa

1.0

0.8

0.6

0.4

0.2

0.0

-

- • - f c = 5 0 M P a

-O-fc=100MPa

0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 0.20

Curvature of Bent Portions (mm'1)

(a) CFRP Pultrusion (b) CFRP strands (c) AFRP Braided

Figure 3.4: The relationship between the tensile and bend strengths (Maruyama et al. 1993).

Au

s >

i -

1800

1600

1400

1200

1000

800

600

400

200

0

h A

-A-r = 5 mm

1800

1600

1400

1200

1000

800

600

400

200

0

€• - * - r = 5 mm -O—r= 15 mm - •— r = 25 mm

- . 1

1800

1600

1400

1200

1000

800

600

400

200

0

-

--A— r = 5 mm -Q— r= 15 mm -•— r = 25 mm

. 50 100 150 50 100 150 50 100 150

(a) CFRP Pultrusion

Concrete Strength (MPa)

(b) CFRP strands (c) AFRP Braided

Figure 3.5: Relationship between bend and concrete strengths (Maruyama et al. 1993).

Nagasaka et al. (1993) conducted an experimental study to evaluate the strength of the

curved sections of FRP stirrups using the specimens shown in Figure 3.6. The used FRP

materials were aramid FRP, carbon FRP, glass FRP and hybrid of glass and carbon FRP. The

FRP bars were left unbonded to the beginning of the bend zone and the bend radius of the

73


tested FRP stirrups was 2 times the bar diameter (rj= 2db). This study revealed that the tensile

strength of curved sections was reduced to 30-80% of that in the fibres direction.

Tensile Force

0 Shear Reinforcment ft Debonding

Main / j Reinforcment

100 100

200 mm

o o

Figure 3.6: The test specimens for bend strength evaluation by Nagasaka et al. (1993).

The bond development, stress distribution, and failure mode of thermoplastic FRP

used as shear reinforcement in concrete beams were investigated by Currier et al. (1994). The

tested FRP stirrups were nylon/carbon and nylon/aramid FRP bars as shear reinforcement that

were made using a thermoplastic pultrusion process by heating and bending the thermoplastic

bends into the desired shape with a heat gun. Hooks and bends were shaped around a 12 mm-

diameter rod. The stirrups were embedded in concrete blocks which, in turn, were pushed

apart till the failure of the FRP stirrups. The specimens and setup as well as the tested FRP

stirrups are shown in Figure 3.7. The main findings of this study can be summarized as

follows:

1. The strength of the FRP stirrup was only about 0.25 of the ultimate strength of the

tensile strength in fibres direction.

2. The main mode of failure for both nylon/carbon and nylon/aramid stirrups was due to

the stress concentration introduced at the bend of the stirrup. FRP stirrups with larger

bend radius may yield better performance and strength.

74


o

Hydraulic Jack

Concrete block

125 mm

(

]/•

FRP stirrups

^ Concrete block

3H

125 mm

600 mm

Figure 3.7: Specimen details, test setup, and tested stirrups by Currier et al. (1994).

The bond characteristics of hooked GFRP bars were investigated by Ehsani et al.

(1995). A total of thirty six 90-degree hooked GFRP bars embedded in concrete as shown in

Figure 3.8 were tested under static loading. The test parameters were: (i) the concrete

compressive strength (28 or 56 MPa); (ii) the GFRP diameter (9.5, 19.1, and 28.6 mm); (ii)

the bend radius to GFRP bar diameter (ri/db= 0 or 3); (iv) embedment length, Id, (0 to 15 db);

and (v) tail length beyond the hook, /,, (12 db or 20 db). The tensile load was applied to the

GFRP reinforcing bar till splitting of concrete or rupture of GFRP bar. The slip between the

reinforcing bars and concrete was measured at the loaded end for various load levels and the

effect of the bend radius on the slip of the bar is shown in Figure 3.9. The effect of the

concrete compressive strength on the tensile strength considering the two tested bend radii are

presented in Figure 3.10 and the effects of the tail and embedment lengths are shown in Figure

3.11.

75


R

cd

IL-

R

4 Unbonded Region

a

C=T

T

ld\embedment length

lt :tail length

Figure 3.8: Details of the test specimens for hooked bars (Ehsani et al. 1995).

120

100

Z £ , 60 •o

eS

40

20

0

1 1 1 1

1 / - ' 1 / 1/

7i / 1

/ i / i

i i i i

i i i

- - 4 -1 1 1 1

1 I

i i i

i i I i

i i i i

— + -i i i

— 4 - -1 1 1 1

1 1 1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1 1 1

/ i i i i i i / i i i i i i

/ i i i i i i / i i i i i i

\ i

r 1 1 1

1 I 1 I

! 1 T

1 1

+ -1 1

. 1 1

— - — J - — 1 1 1

1 1 1 1 1 1 1 1

0 3 4

Slip (mm)

Figure 3.9: Influence of hook radius on load-slip relation (Ehsani et al. 1995).

76


S. F

h

s

180

160

140

120

to 100 4

80

60

40-

20-

0

D No. 3 (9.5 mm) H No. 6 (19.1 mm) M No. 9 (28.6 mm)

28 56 Concrete Compressive Strength (MPa)

1200

I

28 56 Concrete Compressive Strength (MPa)

(a) n/db = 0 (b) rt/db = 3

Figure 3.10: Influence of concrete compressive strength on tensile strength (Ehsani et al.

1995).

<n

12 20 Ratios of Tail Length to Rebar Diameter

0 3 6 9 12 Ratios of Straight Length to Rebar Diameter

(a) Effect of tail length (b) Effect of embedment length

Figure 3.11: Effect of tail length and straight embedment length on tensile force at failure

(Ehsani etal. 1995).

The main findings of this study can be summarized as follows:

1. Higher concrete compressive strength resulted in little gain in the maximum tensile

stresses in the bars. For specimens with r\/db = 3; however, an increase in compressive

strength resulted in higher initial stiffness and lower maximum slip.

2. Strength and stiffness of the specimen with ri/dt = 0 were very low and a minimum

r\Jdb = 3 for GFRP hooks was recommended.

77


3. The use of a minimum tail length of 12 times the bar diameters is recommended (/, =

\2db).

4. The increase in the straight embedment length of the bars increases tensile stress and

initial stiffness and reduces the slip.

5. It is recommended that a development length equals to 16 times the bar diameter be

used for 90-deg GFRP hooks (ld = 16 db).

The failure criteria and the FRP stirrup capacity were investigated experimentally and

analytically by Ueda et al. (1995). The test specimens and setup were designed to model a

closed FRP stirrup intersecting a shear crack. The details of the test specimens are shown in

Figure 3.12. The tested stirrups were made of aramid FRP bars with a nominal diameter and

cross-sectional area of 6 mm and 25 mm , respectively. The simulated artificial shear crack

was created by inserting a plastic plate with a thickness of 0.5 mm. Three different distances

between the artificial crack and the bend were tested: 10, 60, and 110 mm which represent 1.7,

10, and 18.3 times the FRP bar diameter. The test specimens were simulated using 2-D finite

element model to investigate the local stresses at the bend portion of the FRP bar. The

findings of this study can be summarized as follows:

1. The longer the distance between the bend and the artificial crack (embedment length),

the lower the stress at the bend location. The specimens with embedment lengths equal

to 10 and 60 mm failed at the bend. Increasing the embedment length to 110 mm

resulted in achieving the capacity of the FRP stirrups parallel to the fibres and changed

the location of the failure to the straight portions at the intersection with the artificial

crack.

2. The finite element model based on the strain failure criteria was capable of predicting

the capacity of the test specimens and the mode of failure as well.

A finite element analysis and experimental investigation were conducted by Ishihara et

al. (1997) to predict the effect of bend radius and Young's modulus on the bond strength of

FRP rods. The used FRP bars used in this experiment was FiBRA, which consists of twisted

fibre soaked in resin and bonded sand on the surface. The reported tensile strengths in the

fibre's direction were 1577 and 2260 MPa for the AFRP and CFRP bars, respectively. The

78


nominal diameter for both AFRP and CFRP bars was 9 mm. The radii of the bent-up portion

of FRP rods were 9, 27, and 45 mm corresponding to bent radius to bar diameter of 1, 3, and 5

times the bars diameter (1 db, 3 db, and 5 db). The test specimens and setup was similar to

those used by Ueda et al. (1995) as shown in Figure 3.12. Four specimens for the AFRP

stirrups and four other specimens for CFRP stirrup were constructed and tested with bonded

and unbonded length measured from the artificial crack till the starting point of bend

locations. Besides, a 2-D finite element analysis was conducted to investigate the local

stresses in the FRP stirrups at the bend locations. The findings of this study can be

summarized as follows:

t t

Artificial Crack

Compressive Plate

Concrete

FRP Rod

Ui

& &

x:

Y W

I I Figure 3.12: Test specimen and setup details (Ueda et al. 1995 & Ishihara et al. 1997).

1. It was observed that the strength of the bend increases with the increase in the bend

radius. From the unbonded specimens, the bend strength of the specimens with 1 db

bend radius was 46.57 and 42.42% of the strength in the fibres' direction for the AFRP

and CFRP stirrups, respectively. From the bonded specimens, the bend strength ranged

79


from 60.16 to 85.97% of the strength in the fibres' direction for the AFRP stirrups and

49.20 to 66.06% for the CFRP stirrups.

2. The experimental results indicated that the strength reduction at bent-up portion was

different among the different types of FRP rods. The authors referred this to the

difference in the bond characteristics of the tested FRP stirrups.

3. the following equation was proposed, based on the finite element analysis, to predict

the bend strength of the FRP stirrups:

/w=//„v}ln(l + A) (3.1)

where In A = 0.90 + 0.73 In — and df, and rb are the bar diameter and the bend radius,

respectively.

A theoretical investigation of the bend capacity of FRP stirrups was carried out by

Nakamura and Hiagai (1995). In this study it was assumed that, when a tensile force is applied

to the FRP bend zone as shown in Figure 3.13, and there is no bond between FRP and

concrete, the FRP stretches Sx in the straight part subjected to uniform axial force as illustrated

in Figure 3.13. The findings of this study can be summarized as follows:

1. The radius of the bent corner is an important factor for the shear strength of a concrete

beam reinforced with FRP stirrups.

2. A proposed equation was introduced to evaluate the bend strength of FRP stirrups.

This equation was derived by assuming that the cross section deforms rotation angle of

^ maintaining the radius of the bent corner of r^ Then using Bernoulli assumption, the

strain distribution in the cross section was represented by a hyperbolic curve. The

stress distribution was calculated by multiplying the strain by the modulus of elasticity,

Efa. Integrating the stress distribution over the cross section resulted in the following

proposed equation for the bend strength of the FRP bent bars:

( J \ J bend ~ J fuv , m

b fuv d

ub

n . . d, 1 + ^ -

V rbJ (3.2)

where rj is the bend radius, db is the bar diameter andf/uv is the strength in the fibres'

direction.

80


y

/ /

/

^* y -- \ \ \ \ \

\ \ N

i \ V i \ \ ^ / \ ^ ^ f

\ ^ ^ ^ ^ / \ y

-v. S

- ~^ ~~ "~

Before deformation

Figure 3.13: Model of FRP bent bar in concrete by Nakamura and Higai (1995).

In 1997, the Japanese Society of Civil Engineers (JSCE 1997 recommendations)

provided a design equation for the bend strength of FRP bent bars/stirrups. This equation was

based on the findings of the experimental work carried out by the JSCE of the proportional

bend strength and the ratio between the bend radius and the bar diameter (ri/db). The equation

was presented in the following format:

ft 1 (

bend

r, mfb

>\ 0.05-^ + 0.3

V / , fuv (3.3)

J

where r* is the bend radius, db is the FRP diameter, f/uv is the tensile strength parallel to

the fibres, and ymjj, is the material factor of safety and generally is taken as 1.3.

In lieu of other accurate equations for estimating the bend strength of FRP stirrups,

Equation (3.3) was adopted by most of the available codes and design guidelines for FRP

reinforced concrete structures as ACI (2003 & 2006), CSA (2006 & 2009), ISIS Canada

(2007), AASHTO LRFD (2009).

An extensive study was performed by Morphy (1999) to determine the strength of FRP

stirrups as shear reinforcement for concrete structures due to the bending effect. The strength

of FRP stirrups was investigated and evaluated to quantify the reduction in the FRP stirrup

strength at the bend location. The variables considered in this study were the material type, the

effective diameter, db, the bend radius, rj, the configuration of the stirrup anchorage (Type A

81


or Type B), and the tail length, Id. The used FRP materials were: Carbon Fibres Composite

Cables (CFCC) stirrup, Leadline CFRP stirrups, and C-Bar GFRP stirrups. During this phase

101 specimens were tested. The configuration and dimensions of a typical bend specimen is

shown in Figure 3.14. The FRP stirrups were embedded in two concrete blocks measuring

200x250x200 mm with a clear distance between the two blocks measuring 200 mm. The

specimens were prepared and the embedment length was adjusted as required using debonding

tubes. The stirrups were tested by pushing apart the two concrete blocks using a hydraulic jack

till the failure occurred.

Id

y 200 mm ,, 200 mm

V

o in

^ v

(C

w

Debonding tube

t, 200 mm . ., -X 7f <& h

db

P

Y//////////A

V/////////A

n -^

^

ld=rb + db

X1'

Concrete block lt : tail length

fa: embedment length

ii II

'///////////*?

J-Debonding

V/////MWA.

rismmsk

^wwwws^t

Type A: standard hook Type B: continuous end

Figure 3.14: Details of the test specimens for evaluating the bend strength (Morphy 1999).

The main findings of this investigation can be summarized as follows:

1. In general Type B (continuous) anchorage is stronger than Type A (standard hook)

anchorage unless a sufficient tail length, /,, is provided.

2. The strength of the FRP stirrups was reduced due to the bend effect which is

influenced by: reduction in bend radius, rb, reduction in embedment length, U,

anchorage conditions, and reduction in tail length, /,.

82


3. The bend effect governs the strength of FRP stirrups in concrete structures rather than

the kinking effect. The bend effect reduces stirrup strength capacity to 35% of the

guaranteed strength in the direction of the fibres.

4. To achieve a stirrup capacity greater than 50% for the guaranteed strength in the

direction of the fibres a bend radius to bar diameter ratio (ri/db) of 4.0 for CFCC and

C-Bar stirrups and 7.0 for Leadline stirrups, respectively, is recommended.

5. The bend radius of the stirrup, r*, shall not be less than four times the effective bar

diameter or 50 mm, whichever is greater. The tail length, /,, shall not be less than six

times the effective bar diameter or 70 mm, whichever is greater.

6. The full guaranteed strength of the stirrups in the direction of the fibres can be

developed at embedment length to diameter ratios, l/db, of 20 for CFCC Type A

stirrups (minimum tail length /, of 6 db), 16 for the CFCC Type B stirrups and 42 for

the Leadline stirrups.

7. A tail length to diameter ratio, l/db, of 15 for CFCC Type A stirrups is sufficient to

achieve the full guaranteed strength in the direction of the fibres. A tail length to

diameter ratio, l/db, of 6 is sufficient to develop the guaranteed strength in the C-BAR

specimens.

8. The following equations were proposed for determining the capacity of the FRP

stirrups:

FRP CFCC

0.52 <^- = 0.35 + - ^ - < 1.00 "Type A" Anchorage (3.4a) ffuv 3 ( K

0.73 < ^ = 0.60 + - ^ - < 1.00 "Type B" Anchorage (3.4b) ffm 40<

However for CFCC stirrups with a tail length, /,, less than the limiting value, below 15

db, the following equation was proposed:

lt- = 0.24 + - ^ - < 1.00 (3.5) />v 17*.

CFRP Leadline

0.49 < ^ = 0.24 + - ^ - < 0.80 (3.6) U 20Je

83


A two-phase experimental study to characterize and evaluate the structural

performance of CFRP stirrup was conducted by El-Sayed et al. (2007). The first phase (Phase

I) included the characterization of five groups designated as Product A, B, C, D, and E of

carbon FRP stirrups in U-shaped configuration as shown in Figure 3.15. The main differences

between the five groups were the carbon fibre content (ranged from 55% for Product A to

75% for Product E), the method of fibre alignment, and the post-curing process. The entire

specimens in this phase were tested to determine their bend capacities according to the B. 12

(ACI 2004) test method. All the U-shaped specimens of the five groups were No. 13 CFRP

bars {db~\1.1 mm) with a bend radius of 75 mm (6 times the bar diameter) with five replicates

in each group. Straight CFRP bars from the five groups were tested using B.2 (ACI 2004) to

determine their strength in the fibres' direction. The results of this phase revealed that Product

E with the highest fibre content gave the maximum capacity. The observed bend capacities of

the tested specimens of Product E ranged from 408 to 534 MPa with an average strength of

460 MPa, which is comparable to the yield strength of the conventional steel stirrups. The

tensile strength and modulus of elasticity of straight portions of Product E failed at stress

ranged from 1101 to 1237 MPa with an average strength of 1185 MPa and an average

modulus of elasticity of 109 GPa.

a Strain gauge

Figure 3.15: CFRP U-shaped stirrups for Phase I (El-Sayed et al. 2007).

In Phase II, the CFRP stirrups, tested in phase I, were embedded in concrete blocks

and tested by pushing apart the two concrete blocks according to B.5 (ACI 2004) test method.

84


A total of 12 specimens included 6 specimens constructed using size No. 10 stirrups and 6

specimens constructed using size No. 13 stirrups with a constant bend radius, r&, equals four

times the bar diameter (4 db). The specimens of size No. 10 included five specimens of Type

A with a tail length ranging from 3 to 15 db and one specimen of Type B. While the specimens

of size No. 13 included four specimens of Type A with a tail length ranging from 3 to 9 db and

two specimens Type B. The details and results of this phase are presented in Table 3.5. The

main findings of this study can be summarized as follows:

1. A decrease in the embedment length, Id, of the FRP stirrup increases the possibility of

failure at the bent zone of the FRP stirrup. The lower bound of the tensile strength

capacity of the stirrups tested with the minimum embedment length {Id = rb+db) was

equivalent to 44% of the tensile strength parallel to the fibres.

2. For size No. 13 stirrups, increasing the embedment length from 5 to 20 db

approximately doubled the stirrup capacity. The 20 db embedment length was enough

to develop the strength parallel to the fibres.

3. The tail length beyond the bent portion should not be less than six times the bar

diameter to develop the stirrup capacity.

4. The FRP bent bars behaved similarly to the FRP straight bars considering the shear lag

phenomenon. A reduction in the longitudinal tensile strength of 7.8% was obtained by

increasing the bar diameter from 9.5 to 12.7 mm, whereas the corresponding reduction

in the bend capacity was 9.6%.

Guadagnini et al. (2007) conducted an experimental investigation to evaluate the

performance of the curved FRP reinforcement for concrete structures. Pullout tests were

conducted on curved, thermoplastic composite strips embedded in concrete cubes to

investigate the maximum strength that can be developed in their bent portion. In this study, a

total of 47 specimens and 19 different configurations were tested. The test parameters were:

(i) bend radius to strip thickness ratio, r\/t\ (ii) concrete strength; (iii) embedment length, Id',

(iv) tail length, /,; and (v) and surface treatments. The 10-mm wide reinforcing strips utilized

in this study were manufactured from unidirectional thermoplastic GFRP plates with a

nominal thickness, t, of 3 mm. the strips were bent to the desired shape by applying heat and

moulding them around a specially designed device equipped with interchangeable corner

85

Cha

pter

3: S

hear

Beh

avio

ur o

f Con

cret

e B

eam

s R

einf

orce

d w

ith

FR

P S

tirr

ups:

Bac

kgro

und

and

Rev

iew

Tab

le 3

.5:

Det

ails

and

test

res

ults

of

CFR

P st

irru

ps e

mbe

dded

in

conc

rete

blo

cks

(Pha

se I

I) (

El-

Saye

d et

al.

2007

).

db

(mm

)

9.5

12.7

* S-

RE

Ben

d ra

dius

n (m

m)

38.1

50.8

\: S

lipp

r b/d

b

4.0

4.0

age

of

Tai

l le

ngth

h

(mm

)

28.5

57.0

85.5

114.

0

142.

5

~ 38.1

38.1

76.2

114.

3

~ —

bond

ec

l t/d

b

3 6 9 12

15

« 3 3 6 9 —

—

port

ion

c

Em

bedm

ent

leng

th

(mm

)

r b +

db

= 4

7.6

r b +

db

= 6

3.5

250.

0

)f s

tirru

ps f

olk

h/d b

5 5 20

jwed

by

Stir

rup

anch

orag

e

type

A

B

A

B

B

Stre

ss a

t fa

ilure

(MPa

)

394

701

761

656

596

789

472

457

681

539

697

1236

rupt

ure

at t

he b

end;

R-B

: R

Lon

gitu

dina

l

tens

ile s

tren

gth,

jMM

Pa)

1328

1224

ffr/

fjuv

0.30

0.53

0.57

0.49

0.45

0.59

0.39

0.37

0.56

0.44

0.57

1.01

Mod

e of

failu

re1

S-R

B

R-B

R-B

R-B

R-B

R-B

S-R

B

S-R

B

R-B

R-B

R-B

R-S

uptu

re o

f st

irru

ps a

t th

e be

nd;

and

R-S

Rup

ture

of

stir

rups

alo

ng s

trai

ght

port

ion

betw

een

conc

rete

blo

cks.

86


inserts to allow for the fabrication of the required bend radius to thickness ratios. Nine of the

specimens were coated with silica sand, SC, to investigate the effect of surface treatment on

the bond properties between the composite and the concrete. Two types of concrete were used

in fabricating the test specimen: Normal strength concrete (N) with average cube strength of

45 MPa; and High strength concrete (H) with average cube strength of 95 MPa. The test

specimens are shown in Figure 3.16 and the summary of the test results are presented in

Figure 3.17.

t

o o

O

- * -

o V

X-200 mm

(a) Type 2 (b) Type 3

Figure 3.16: Details of the test specimens (Guadagnini et al. 2007).

In this study, the Type 2 specimens were able to sustain higher pullout load than Type

3 specimens, and specimens embedded in normal strength concrete generally failed at lower

load levels than those embedded in high strength concrete. The stress values developed in the

vertical leg of the strips was 25 and 60% of the ultimate strength of the composite for

specimens with an r\Jt value of 2 and 5, respectively. Besides, in this study a

macromechanical based failure model was proposed to could adequately capture the true

degradation of the strength of the bent composites. The main findings of this study can be

summarized as:

87


1. The capacity of the bent portion of the composite appeared to be mainly a function of

the bend radius.

2. The bend capacity of the test specimens varied between 25% and 64% of the ultimate

strength of the composite.

3. Values of r^/t greater than 4 are required to guarantee a minimum bend capacity of

40% of the ultimate strength of the composite.

4. The proposed macromechanical model adequately captures the strength degradation

due to the change in the geometry of the bent portion of the bar.

^

( U -

60 -

50 -

40 -

30 -

20 -

10 -

0 -

a)

i

V

1

*

1

l

V

.__ .

V •

A

S

Type 2, SM, N Type 2, SC, N Type 2, SM, H Type 2, SC, H

...

r/t

<4

70

60 -

50 -

40 -

30 -

20 -

10 -

0

b)

T

2

O Type 3, SM, N • Type 3, SM, H

T

4 r/t

Figure 3.17: Average of maximum stress: (a) Type 2; and (b) Type 3 (Guadagnini et al. 2007).

88


3.4.2 Strength of FRP bars subjected to induced shear cracks

The failure criteria of FRP bars subjected to combined tensile and shear forces was

investigated by Kanematsu et al. (1993) and Ueda et al. (1995). Aramid FRP bars with a

nominal diameter of 8 mm and tensile strength of 1280 MPa, and modulus of elasticity of 66

GPa were used in this investigation. Specially designed concrete specimens divided into three

blocks separated by stainless steel plate as shown in Figure 3.18 were used.

Concrete blocks

4— P/2 —•

4— P/2 —•

Stainless steel / plate

Plan

Q Q

i i

Elevation

Figure 3.18: Testing FRP rod at crack intersection by Kanematsu et al. (1993).

The FRP rod was tensioned by two hydraulic jacks between the two outer concrete

blocks until a target crack width which is a gap between the outer and central concrete blocks

was reached keeping the crack width constant. Then, the central block was pushed down by

another hydraulic jack, so that the FRP rod was subjected to shear force or shear displacement

at the crack intersections. A stainless steel plate with thickness of 0.2 mm was inserted

between the concrete blocks, so the aggregate interlocking was eliminated. The loading was

continued till the FRP rod fractured. The test variable in this study was the crack width

between the end and central blocks. In parallel to these experimental investigations, 2-D finite

element analysis was conducted to investigate the local stresses in the FRP bars at the crack

locations. The findings of these studies can be summarized as follows:

89


1. The experimental work showed that the tensile strength of the tested FRP bars were

reduced significantly at the crack location under the combined tensile and shear forces.

2. The shear crack width is a parameter affecting the strength of FRP bars subjected to

combined tension and shear forces.

A theoretical investigation was conducted by Nakamura and Higai (1995) to evaluate

the effect of the diagonal tensile forces induced due to diagonal shear cracks on the FRP bars

as shown in Figure 3.19. The study considered FRP bars with a length L subjected to a

diagonal tensile force with an inclination angle 6 with respect to the fibres' direction. Based

on the proposed model, the diagonal tensile strength of an FRP can be determined by the

following proposed equation for FRP with rectangular cross-sections:

U = / / w / ( cos0 + 6sin0tan0) (3.7)

However, for the FRP bars with circular cross-sections, the proposed equation was

presented as follows:

ffi =/fuv/(cos0 + Ssm0tm0) (3.8)

Nakamuara and Higai (1995) predicted and compared the proposed equation with the

experimental results from literature as shown in Figure 3.20. From this comparison, it was

concluded that the reduced strength of FRP bars subjected to diagonal tensile stresses could be

reasonably evaluated using the proposed equation.

Figure 3.19: Diagonal tension due to diagonal crack (Nakamura and Higai 1995).

90


1.0

0.9

0.8

0.7

> 0.6

v^ 0.4

0.3

0.2

0.1

0.0

- v% — \ s

\ \

— •

— • : Carbon

• : Aram id

• : Glass

l 1

\

l 1

\ ^ \ ~ \ ~ ~ • Proposed: \ ^ ^ \ ^ / Rectangualr

^ * ^ / ^ \ ^ section

Proposed: Circular section

1 1 1 1 10 20 30

Degree 40

Figure 3.20: Comparison between the proposed equation results and experimental results

(Nakamura and Higai 1995).

Morphy (1995) conducted an experimental investigation to evaluate the effect of

inclined cracks on the stirrup capacity (kinking effect) as shown in Figure 3.21. In this study,

12 specially designed specimens were constructed and tested to evaluate the effect of inclined

cracks on the stirrup capacity (kinking effect). The specimen was pre-cracked at the center by

the placement of metallic sheet between the two sides. A reduced concrete section measuring

75x235 mm was left in the center section (where the stirrups crossed) to allow for natural

crack development and transfer of the load from the concrete to the stirrups. Two indentations

were created on either side of the specimen at the center to allow room for a hydraulic jack

and load cell. These indentations were angled towards the center of the specimen to reduce the

amount of unnecessary concrete in the specimen near the critical center crack area and to

further control the specific crack location. The details of the test specimens are shown in

Figure 3.22. The parameters considered for the kinking samples were the material type and the

crack angle with respect to the stirrup. The used FRP materials were Leadline CFRP, C-Bar

GFRP, and reference steel bars with a cack angle ranging from 25 to 60°. The main findings of

this investigation can be summarized as follows:

91


1. The FRP stirrup strength is reduced as the angle is increased. The strength could be as

low as 65 % of the guaranteed strength in the direction of the fibres.

2. The bend effect reduces stirrup strength capacity to 35 % of the guaranteed strength in

the direction of the fibres whereas the inclined crack effect produces a capacity as low

as 65 % of the guaranteed strength. Therefore in beam action the bend effect is the

most critical and will govern the behaviour.

FRP Stirrup

Figure 3.21: Effect of the inclined crack on the FRP stirrup, Kinking effect, (Morphy 1999).

f 700 mm

Deformed Steel Cage

Figure 3.22: Details of the test specimens for evaluating the kinking effect (Morphy 1999).

92


3.5 Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups.

The use of FRP as internal flexural reinforcement for reinforced concrete structures has been

extensively investigated. Recently, the investigations of the flexural performance moved from

the small scale specimens to the full scale specimens and field applications for bridge deck

slabs (Benmokrane et al. 2006a; 2007), barrier walls (El-Salakawy et al. 2003; El-Gamal et al.

2008), parking garages (Benmokrane et al. 2006b), continuous pavement (Benmokrane et al.

2008) and other concrete structures. On the other hand, few studies were conducted on the

shear performance of concrete structures reinforced with FRP stirrups. Consequently, more

studies are needed to completely understand the structural performance and behaviour for

concrete members when FRP stirrups are used as shear reinforcement. The following section

reviews the available research work conducted to evaluate the performance of FRP as shear

reinforcement for concrete members.

An extensive experimental study was conducted by Nagasaka et al. (1993) to

investigate the shear performance of concrete beams reinforced with bar-shaped FRP

reinforcement (stirrups). Thirty-five concrete beams were constructed and tested under

monotonically increased load up to failure. The beams had a variable cross-section along the

beam length and the cross-section of the shear critical span under consideration measured

250x300 mm. Figure 3.23 shows the geometry and method of loading of the beam specimens.

The clear span of the test specimens, /0, ranged from 600 to 1200 mm (Figure 3.23). Four

types of FRP bars were employed in this study as shear reinforcement: aramid FRP, glass

FRP, carbon FRP, and hybrid of glass and carbon FRP. Control specimens were constructed

using steel stirrups for comparison. The AFRP, GFRP, and CFRP shear reinforcement were in

rectangular spiral stirrups format, however, the hybrid FRP was in the form of rectangular

closed stirrups. The main test variables were: (i) stirrup material (AFRP, GFRP, CFRP, and

Hybrid); (ii) shear reinforcement ratio (0, 0.5, 1.0 and 1.5%); (iii) concrete strength (target

strengths of 21 and 36 MPa); and (iv) the clear span (600, 900, and 1200 mm). The effect of

the FRP flexural reinforcement on the shear capacity was investigated as well. The main


1. The shear failure modes can be classified into two types: (i) shear-tension breaking

failure mode controlled by rupture of FRP stirrups at the curved sections of some

93


stirrups; and (ii) shear-compression failure mode due to crushing of concrete strut

between two adjacent diagonal cracks near either the ends of the clear span.

2. A shear reinforcement factor was proposed to distinguish between the tension and

compression shear failure = pjvfben/fc, where pj\, is the ratio of FRP shear

reinforcement, fbend is bend strength of FRP stirrup, and^ is the specified strength of

concrete. A threshold limit between rupture to crushing failure modes of 0.30 was

proposed. Below this limit, 0.3, a shear-tension is expected, otherwise a crushing

failure mode is expected to occur.

3. The ultimate shear capacity by the breaking failure mode increased almost linearly

with increasing stirrups ratio and decreases almost linearly with increasing the clear

span of the beam.

4. The shear strength of beams increased almost linearly with the ApÊ^ , which

demonstrates that the shear strength was affected by the axial rigidity of the shear

reinforcement.

5. The ultimate shear capacity of FRP reinforced concrete beams could be reasonably

estimated by modifying Arakawa's formula (Architectural Institute of Japan, AIJ) for

conventional reinforced concrete beams, where the yield strength was replaced by the

breaking strength at curved sections. The reduced reinforcement ratio was used for

both flexural and shear reinforcement = p EFRp/Esteei. The proposed modified equations

are:

For shear-tension breaking failure mode:

"o.ii5*B*;,(/;+i8o) VnX = 0.875 bw </, - + Ml J Pfr fbend (kgf; cm units)

(M/Vd) +0.12

where dv = (7/8) d and ku: Correction coefficient to account for size effect

* ; = 0.82(100 PfEj/E,)0

0.092*„*p(/c'+180)

(3.9a)

\0.23

Vn2 = 0.875 bwd, (M/Vd) + 0A2

• + 0-^^Pfofbend (kgf; cm units)

kp=0.S2(l00Pjl)02'

(3.9b)

(3.10a)

(3.10.b)

94


For shear-compression crushing failure mode:

o . i i 5 ^ ( / ; ) F,,=0.875A d • + 0-27'^p)jbmd (3.11a)

(M/Vd) + 0.\2

PP=PAE»/ES) ( 3 1 1 b >

Besides, in comparison with the experimental values, it was concluded that the shear

capacity predicted using Equation (3.10) was in slight better agreement with the measured

values than Equation (3.9). The mode of failure of the beam specimens has to be determined

using the proposed shear reinforcement factor. Thereafter, corresponding to the mode of

failure, the appropriate equation is to be used.

i Loading Beam

© o

I ClL I Test beam

825

1050 mm

loll 75

loll 75

lo (Clear Span)

825

1050 mm

M

M

Test Beam

4-1 Figure 3.23: Test specimens and loading setup by Nagasaka et al. (1993).

95


Tottori and Wakui (1993) investigated the shear capacity of rectangular beams

reinforced with FRP as flexural and shear. The concrete contribution, dowel action of FRP

reinforcement, and shear carrying capacity of FRP spiral stirrups were the main point of

interest in this study. The shear tests were conducted on RC beams reinforced with GFRP,

AFRP, CFRP and VFRP (Vynylon) spiral stirrups. The test specimens are shown in Figure

3.24. The main findings of this study can be summarized as follows:

1. The shear capacity of FRP reinforced concrete beam without stirrups could be

predicted using steel equations but considering the stiffness of the FRP bars relative to

the steel ones. Consequently, the following modified equations for the concrete

contribution were proposed:

Shear capacity, Vcj\, of reinforced concrete beams using FRP reinforcement:

F c / 1 = 2 0 0 ( / ; f (pJIEJI/Etf d-l/4[0J5 + \A/{a/d)]bwd (kN) (3.12)

Shear capacity, Vcji, of reinforced concrete deep beams using FRP reinforcement:

Vcn =244(/c ')2/3 (l + JpJ,EJ,/Es)[\ + 333/[l + (r/d)2]]bwd (kN) (3.13)

f'c in MPa; a, d, bw are in meters and r is the length of the loading plate in the direction

of the beam span.

2. That dowel capacity of the test specimens using FRP reinforcement was about 70% or

those using reinforcing steel with almost the same diameter. This value was

corresponding to the factor (Ej, jEs J which was included in Equation (3.12).

3. The observed stirrup strain at ultimate was more than 1% but the guaranteed value

corresponding to f/uv was not achieved.

4. The stirrup contribution to the shear carrying capacity of concrete beams reinforced

with FRP spiral stirrups could be estimated using the following equation:

AÊ^ ( i M )

s

where dv is the shear depth of the beam = dl 1.15 and e/v is the stirrup strain at ultimate

and it was recommended to be 0.01 for the shear-tension mode of failure.

96


10Q

• • • • • •

200

o 30

0

o 4 1

400

Figure 3.24: Configuration of test specimens by Tottori and Wakui (1993).

The fiexural and shear behaviour of prestressed concrete beams reinforced with carbon

or aramid FRP (CFRP or AFRP) were experimentally investigated by Yonekura et al. (1993).

The objectives of this study were to examine the fiexural strength, fiexural failure modes and

shear strength of FRP post-tensioned concrete beams in comparison with that reinforced with

conventional steel. The test specimens were prestressed using CFRP, AFRP, and steel. The

shear reinforcement was in form of spiral reinforcement of 5 mm-diameter CFRP and 4 mm-

diameter AFRP. A total of 32 prestressed beams were constructed in this study categorized

into two phases. Phase I included testing of 20 beams for flexure whereas Phase II included 12

beams tested for shear. The details of the beam specimens are shown in Figure 3.25. The test

parameters were: (i) the type of prestressing tendons; (ii) the type of axial reinforcement; (iii)

quantities of prestressing tendons; (iv) the amount of the initial prestressing force; and (v) the

amount and type of the shear reinforcement. The shear strength of the beam specimens

included in Phase II was predicted using the following equations:

V -V +V +V

Vp = 2M0/a

V,=Afi(EJI/EI)ffil,(dJs)bwd

(3.14a)

(3.14b)

(3.14c)

(3.14d)

(3.14e)

97


where Eji and Es are the modulus of elasticity of the FRP longitudinal reinforcement and steel,

respectively, /Tîs the flexural FRP reinforcement ratio, and M0 is the decompression

moment.

The findings of this investigation can be summarized as follows:

1. Nine beams of that tested for shear in Phase II failed either by shear compression

failure or tension failure of FRP spiral shear reinforcement. The other three beams

failed by flexural tension failure, flexure compression failure, and tendon failure.

2. The shear strength of the prestressed beams using FRP rods and FRP shear

reinforcement is smaller than those using prestressing steel bars when the same shear

strength is provided by shear reinforcement.

3. The predicted shear strength for the prestressed beams tested for shear, Phase II, was

in good agreement with the measured one. The observed-to-calculated shear strength

ranged from 1.03 to 1.48.

4. The ultimate flexural and shear strength of the prestressed beams using FRP

reinforcement were improved by increasing the prestressing force.

C.L 300 mm 400 mm

FRP Spiral Reinforcement

Pitch = 85, 110, 135 mm

Axial Reinforement 6

V

o -fc t) /

o o

o

< \

40| 70 |40

150 mm

o o

Figure 3.25: Details of test specimens for shear by Yonekura et al. (1993).

98


The shear behaviour of concrete beams reinforced by FRP bars for flexural and shear

was investigated by Zhao et al. (1995). In particular, the contribution of FRP stirrups was

studied in terms of the stirrup strain, shear crack opening, and shear deformation. CFRP was

used for longitudinal reinforcement and CFRP and GFRP as well as steel were used for

stirrups. FRP stirrups were manufactured in the form of closed loop. The geometry details and

dimensions of the beam specimens used in this study are shown in Figure 3.26. As it can be

noticed from Figure 3.26, a notch was provided at the most probable location of diagonal

crack within the target region for measurements of crack opening and stirrup strain. Nineteen

beams were fabricated and tested and the test parameters were: (i) the flexural reinforcement

ratio; (ii) the location of stirrups; (iii) the material type of the stirrups; and (iv) and the shear

span-to-depth ratio (a/d). All the tested beams had cross-section of 150x300 mm with a total

length of 2600 mm and were tested in four-point bending over simply supported clear span of

1800 mm. All beam specimens had shear span-to-depth ratio, a/d, of 3 except two beams one

of them was 2 and the other was 4. The main findings of this investigation can be summarized

as follows:

v-^-

• u

150

680

D10@100

K60 30 90 y 90 y 200 t T> <£

1 ft 1 1 l p T U , i , ,

Figure 3.26: Details of test specimens (Zhao et al. 1995).

1. All beam specimens except two beams failed in shear. The failure mode was classified

as shear compression failure because none of the stirrups was ruptured except one

beam.

99


2. When the shear compression failure was dominant, the higher stiffness of stirrup

resulted in the higher shear capacity with smaller stirrup strain at ultimate.

3. The concrete contribution of FRP longitudinally reinforced beams was evaluated by

the conventional code equations as long as the ratio of the stiffness of the FRP to that

of steel was considered (Eji/Es). The following equation was used in this study to

predict the concrete contribution:

(3.15a) Vcf={02)(\ + f]p+Pd)[0J5 + \A/{a/d)](f;fbwd

^ = ( l 0 0 P ; ) , / 2 - l < 0 . 7 3

pp={\ooo/df-\

PJI = pfl{EftlE>)

(3.15b)

(3.15c)

(3.15d)

where Eji and Es are the modulus of elasticity of the FRP longitudinal reinforcement

and steel, respectively.

4. The strain distribution along a diagonal crack could be expressed by a cubic function,

= (l 11 V / 3

li~\ il o) ^ ^(-1 t n e stirrup strain, in turn, was evaluated by the functions as

illustrated in Figure 3.27.

0.6 0.8 1.0 : Lj/Lo

Figure 3.27: Stirrup strain distribution model (Zhao et al. 1995).

100


5. Considering the strain distribution shown in Figure 3.27, the contribution of FRP

stirrups, Vsf, was calculated using the following equation:

Vsf = Efi « > Z { ( ^ -n •rMLilLof) (3.16a)

where:

^=0.012/(36/^+1) (3.16b)

P*fl = Pfl\EfllEs) (3-16c)

yv =1.7/(520/7;+l) (3.16d)

p'fi=(Afi+300)/{bw Loy(Efi/E,) (3.16e)

ya = 3.3/(0.8 a/d + l) (3.16f)

{rp-yw-ya)mikT^fylEs For steel stirrup (3.16g)

(rP-rr,-ra)iL,/Lof * ffi./Efi mikf For FRP stirrup (3.16h)

such that: a^ is the cross-sectional area of one stirrup, Ap is the total cross-sectional are

of the stirrups in the target region. The Z, and L0 parameters are shown in Figure 3.27.

6. The predicted shear strengths of the tested beams were compared with the measured

values and the proposed equation seems to be able to predict the shear capacity of FRP

reinforced concrete beams.

Vijay et al. (1996) conducted an experimental study to investigate the shear behaviour

and ductility concrete beams reinforced with GFRP bars. Two types of GFRP bars were used

as flexural and shear reinforcement. The main issues addressed in this investigation were: (i)

the shear behaviour of concrete beams reinforced with FRP bars and stirrups in terms of

diagonal crack occurrence; (ii) applicability of the ACI-318 (1992) equations for shear

capacity to beams reinforced with GFRP stirrups; and (iii) review the failure modes and

ductility of FRP RC beams. A total of six concrete beams measuring 150x300x1500 mm were

constructed and tested in four-point bending up to failure. The main findings of this study can

be summarized as follows:

101


1. Concrete beams reinforced with FRP bars exhibited crack pattern similar to those of

steel reinforced concrete beams. The inclination angle of the diagonal shear crack

ranged from 35 to 40 degrees.

2. The FRP stirrups in concrete beams do provided shear resistance; however shear

failure in concrete beams is governed by tension failure of the stirrups or by bond

failure between concrete and stirrup. The observed mode of failure in the tested beams

was bond failure of GFRP stirrup legs with an effective embedment length ranging

from 4.2 to 5.6 times the bar diameter (4.2-5.6 db).

3. The ACI-318 (1992) shear equation (Vc =Q.\l^fcbwd) is conservative and adequate

for the design of concrete beams reinforced with FRP stirrups.

The size effect in shear behaviour of concrete beams reinforced with FRP was

investigated by Maruyama and Zhao (1996). Continuous fibre reinforcing materials made of

grid type carbon reinforcement was used for flexure. Three different diameters of glass fibre

reinforced plastic formed in loop configuration were used for shear reinforcement. The

experimental program included nine beams of three different sizes with a cross-section

measured 150 x300 mm, 300 x600 mm, and 450 x900 mm. The beam length was determined

to have a shear span-to-depth ratio of 2.5. The configuration of the test specimens is similar to

those tested by Zhao et al. (1995) as shown in Figure 3.26. The test parameters were: (i) size

of effective depth; (ii) with or without stirrups; (iii) amount of stirrups; and (iv) the effect of

the ditch on shear capacity. The main findings of this investigation can be summarized as:

1. The entire beam specimens failed in shear. The shear failure was classified as one of

the following: (i) diagonal tension failure for beams without stirrups; (ii) shear

compression failure for beams provided with large amount of stirrups; (iii) rupture of

stirrups; and (iv) shear compression with rupture of stirrups.

2. The shear capacity of FRP reinforced concrete beams without stirrups was calculated

using the following equation in which the longitudinal FRP reinforcement ratio is

multiplied by of E/j/Es:

Vlf=(0.2)(l + Pp+fill)[0.7S + lA/{a/d)](/efbwd (3.17a)

fip=(l00p'j,f (3.17b)

102


&= (1000/df (3.17c)

pfl = pfl(Efl/Es) (3.17d)

where EJJ and Es are the moduli of elasticity of the FRP longitudinal reinforcement and

steel, respectively.

3. The size effect could appear in the concrete contribution, Vc, as the ordinary reinforced

concrete beams. The size effect is included in the previous equation through the factor

pd defined by Equation (3.17c).

4. The existence of a ditch might reduce the shear crack initiation level a little, but it did

not affect the behaviour of beams after cracking.

Alsayed et al. (1996 & 1997) conducted an experimental study to investigate the shear

performance of concrete beams reinforced longitudinally and transversally with combinations

of GFRP and steel materials and propose a design procedure for such members. A total of

tested 21 concrete beams reinforced longitudinally and transversely by steel bars, GFRP bars,

or a combination of both types. The beam specimens were arranged into two series. The first

series included 12 beams categorized into four groups: (i) group "A" reinforced with

longitudinally with steel bars and transversally with steel stirrups and referred to as control

specimens; (ii) group "Bl" reinforced longitudinally and transversally with GFRP

reinforcement; (iii) group "CI" reinforced with longitudinally with steel bars and transversally

with GFRP stirrups; and (iv) group "Dl" reinforced longitudinally with GFRP bras and

transversally with steel stirrups. Each group comprised three identical beams. Specimens in

this series were 200x360 mm in cross-section and 2400 mm long, tested in four-point bending

(two concentrated loads 200 mm apart) over a simply supported clear span of 2200 mm.

The second series comprised nine beams categorized into three groups, with three

identical beams each: (i) group "B2" reinforced longitudinally by GFRP bars and transversally

with GFRP stirrups; (ii) group "C2" reinforced longitudinally with steel bars and transversally

with GFRP stirrups; (iii) and group "D2" reinforced longitudinally with GFRP bars and

transversally with steel stirrups. Specimens in the tested series had a 200x360 mm cross-

section and 1800 mm total length, tested under four-point bending (two concentrated loads

220 mm apart) over a simply supported over a clear span of 1680 mm. The specimens of both

103


series were designed using AC-318 (1992) procedure to fail in shear. The findings of this

investigation can be summarized as follows:

1. All beam failed in shear, however, the beams with GFRP stirrups failed due to the

GFRP stirrup slippage rather than rupture.

2. The following modifications were proposed to the ACI-318 (1992) shear equation:

K-ClVc+C2Vs (3.18a)

Vc=-McKd (3.18b) o

s

where Av is the area of the stirrups, fv is the stress in the stirrup, and the values of the

constants C\ and C2, respectively, are:

1.0 and 1.0 for beams reinforced with steel for flexure and shear.

0.5 and 0.5 for beams reinforced with GFRP for flexure and shear.

1.0 and 0.5 for beams reinforced with steel for flexure and GFRP for shear.

0.5 and 0.5 for beams reinforced with GFRP for flexure and steel for shear.

3. The proposed modifications to ACI-318 (1992) equation were checked against the

measured shear capacity and the comparison showed adequate agreement between the

predicted and the measured shear strengths.

An experimental study to investigate the shear strength and mode of failure of the

concrete beams reinforced longitudinally and transversally with GFRP bars was conducted by

Duranovic et al. (1997). A total of 9 beams comprised two beams reinforced with steel and

seven beams reinforced with GFRP including one beam without stirrup were constructed ant

tested till failure. The cross-section of the test beams was 150x250 mm and the beams

measured a total length of 2500 mm. The beams were tested in four-point bending over a clear

span of 2300 mm. The shear span of the specimens measured 767 mm corresponding to shear-

to-depth ratio, aid, of about 3.8. The GFRP bars used for flexure were of 13.5 mm-diameter

with tensile strength and modulus of elasticity of 1000 MPa and 45 GPa, respectively. The

GFRP stirrups (shear reinforcement) had a rectangular cross-section measured 10x4 mm. The

main findings of this study can be summarized as follows:

104


1. The beam specimens failed due to either by flexural compression of the concrete at

mid-span or shear failure. The observed shear failures were diagonal shear for the

beams without stirrups or shear tension failure due to rupture of GFRP stirrups. The

maximum stress in the GFRP stirrups measured by means of strain gauges did not

exceed 270 MPa.

2. The reduced strength at the corners (bends) is attributed to the geometry, material

properties, and manufacturing process.

3. The shear strength of the beam specimens was predicted using the modifications

proposed for EUROCRETE Project by Clarke et al. (1996) to the British Code

BS8110. The measured stain in the stirrups was greater than the 0.0025 proposed by

Clarke et al. (1996). Thus, the predicted values were conservative when compared with

the measured ones.

One of the earliest field applications in Canada using CFRP stirrups is the Taylor

Bridge (Rizkalla et al. 1998). The bridge is located over the Assiniboine River in the Parish of

Headingley, Winnipeg, Manitoba, Canada. The bridge consists of five spans, 32.5 m each

covering a total length of 165.1 m. The deck slab is 200 mm-thickness and supported by a

total of 40 precast prestressed (pretentioned) simply supported beams, eight for each span. A

total of four bridge girders reinforced with CFRP reinforcement were implemented in the

bridge. Two different types of CFRP reinforcement were used for flexural and shear

reinforcement. Carbon fibre composite cables (CFCC) of 15 mm diameter produced by Tokyo

Rope, Japan were used to pretension two girders while the other two were pretentioned using

10 mm indented Leadline bars produced by Mitsubishi Chemical Corporation of Japan. Two

of the four girders were reinforced for shear using 15.2 mm diameter CFCC stirrups and 10x5

mm Leadline CFRP bars. The two remaining beams were reinforced for shear using 15 mm

diameter epoxy coated steel reinforcing bars. The girders were designed based on the

AASHTO Code 1989 using a CFRP stirrup stress of 275 MPa at the factored load, compared

to 200 MPa for the steel stirrups. The stress in the CFRP stirrups is lower than 33% of the

bend strength of the CFRP stirrups, fbend-

At that time and due to the lack of codes and standards in this field, five I-girders

prototype, 9.3 m each reinforced for shear and prestressed by CFRP and one prestressed with

105


conventional steel and reinforced for shear with steel stirrups were constructed and tested by

Fam et al. (1997). The test beams were 1:3.6 scale models of the Taylor Bridge girders.

Various stirrups sizes and configurations were used to investigate their effect on shear and

flexural behaviour. The test parameters were: flexural prestressing material and ratio, and

CFRP shear reinforcement type and ratio. The used carbon shear reinforcement were: CFCC

of 5.0 and 7.5 mm diameter closed stirrups; and Leadline CFRP bars of 10x5 mm rectangular

section of the same area as 7 mm-diameter bars in the form of double-legged and single-

legged stirrups. The shear reinforcement ratio ranged from 0.262 to 1.0 %. The beams were

loaded using four concentrated loads to simulate and equivalent and equivalent AASHTO

HSS 25 truck loading condition and lateral supports were provided at four locations along the

span. Five beams failed in flexure due to rupture of the FRP strands, or yielding of the steel

strands. The last beam failed in shear due to straightening of the stirrup at the bent between

the web and the bottom flange causing sudden loss of stirrup resistance and transfer of the

forces to the cracked concrete and prestressing rods. However, all beams exhibited number of

diagonal cracks within the maximum shear span before failure. The diagonal crack patterns

were almost similar in number and spacing and covered about 50% of the maximum shear

span before failure. The main findings of this study can be summarized as follows:

1. The web reinforcement ratio certainly affected the induced stress level in stirrups and

the diagonal crack width; however, the effect was not directly proportional to the web

reinforcement ratio.

2. Due to the relatively high elastic modulus of CFRP compared to other FRP

reinforcements, the effect of the tensile modulus on the induced strain in the stirrups

and the diagonal crack width was insignificant and was not directly proportional to the

tensile modulus.

3. The ACI-318 (1989) predicted the shear cracking load well; however, it

underestimated the stirrup strain after diagonal cracking. This suggests that the

concrete contribution is gradually reduced after cracking.

4. The modified compression field theory (MCFT) predicted well the entire response of

the tested beams.

5. For beams controlled by flexural capacity, variation of the shear reinforcement ratio

did not significantly affect the flexural behaviour.

106


Shehata (1999) preformed an experimental investigation to explore the behaviour of

FRP stirrups as shear reinforcement for concrete beams. A total of ten reinforced concrete

beams were tested to investigate the contribution of the FRP stirrups in beam mechanism. The

ten beams included four beams reinforced with CFRP Leadline stirrups. Four beams

reinforced with GFRP C-Bar stirrups, one beam reinforced with steel stirrups, and one control

beam without shear reinforcement. Figure 3.28 shows the details of these stirrups while Figure

3.29 shows the details of beam specimens.

GFRP l\ C-BAR f

1 8

Used for panel specimens Used for beam and panel specimens '•

Figure 3.28: Configuration of FRP Stirrups (Shehata 1999).

The test beams had a T-shaped cross-section with a total depth of 560 mm and a flange

width of 600 mm. The test parameters were the material type of stirrups, the material type of

flexural reinforcement, and the stirrup spacing. Eight beams were reinforced for flexure with

six 15 mm, 7-wire steel strands. Two beams were reinforced for flexure using seven 15 mm,

7-wire CCFC stands. All beams were designed to fail in shear while the flexural steel strands

were designed to remain in the elastic range to simulate the linear behaviour of FRP. The

beam without stirrups was used as a control beam to determine the concrete contribution to the

shear resistance. Each beam consists of a 5.0 m simply supported span with 1.0 m projections

from each end to avoid bond-slip failure of the flexural reinforcement. Only one shear span

was reinforced with FRP stirrups, while the other shear span was reinforced using 6.35 mm

107


diameter closely spaced steel stirrups. The beams were tested in four-point bending, with 2.0

m constant moment region.

All the tested beams failed in shear before yielding of the flexural steel strands or

rupture of CFRP Strands. No slip of the longitudinal reinforcement was observed during any

of the beam tests. Shear failure of beams reinforced with FRP stirrups was initiated either by

rupture of the FRP stirrups at the bend (shear compression failure). The use of CFRP strands

as flexural reinforcement in two beams resulted in a reduction in the shear capacity, compared

to similar beams reinforced with steel strands. This could attribute to the reduction of the

concrete contribution component due to the use of CFRP as flexural.

Steel stirrups

+-FRP stirrups

P/2 Steel stirrups

P/2 Steel stirrups j . Steel stirrups .

@80mm s = variable @ 250 mm @ 8 0 m m @80mm

—k— Shear span

a = 1500

Shear span

a= 1500

600 mm 600 mm

r~T

A • •

-Beams with 7 CFCC strands

r~r

W w

|—Beams with 6 steel strands

P254

Figure 3.29: Details of beam specimens (Shehata 1999).

Shehata (1999) compared the crack width measured from thee beams reinforced with

the CFRP, GFRP, and steel stirrups with the same stirrup spacing (dl2). From this comparison

it was reported that large crack widths were observed for the beam with CFRP stirrups, even

though the shear stiffness index Ep pp was higher that of the one reinforced with GFRP

stirrups. Moreover, or the beam reinforced with GFRP stirrups with shear reinforcement

index, pp (Ep/Es), of 0.15% behaved similarly to the one with steel stirrup ratio, psv, of 0.4%.

This indicates that an increase in the shear reinforcement ratio, pp, of 80% minimizes the

effect of the low modulus ratio (Ep/Es=0.2\) due to the good bond of GFRP stirrups. The


108


1. All the beams failed in shear. The shear failure mode was classified as: diagonal

tension failure for the beam without stirrups; shear tension failure due to rupture of

FRP stirrups or yielding of steel stirrups; and shear compression failure.

2. Beams reinforced with CFRP strands for flexure showed less concrete contribution, Vc,

than beams reinforced with steel strands. This is attributed to the wide cracks, small

depth of the compression zone and poor dowel action associated with the use of FRP

as longitudinal reinforcement.

3. Shear deformations are affected by the bond characteristics and the elastic modulus of

the stirrup material. The beams with GFRP stirrups showed better performance than

those with CFRP stirrups for the same reinforcement index ratio.

4. Limiting strain of 0.002 is recommended for both CFRP and GFRP stirrups to control

the shear crack width in concrete beams.

Alkhrdaji et al. (2001) conducted an experimental investigation to evaluate the shear

strength of GFRP reinforced concrete beams. A total of four beams reinforced longitudinally

and transversally with GFRP bars were constructed and tested. The main variables were the

longitudinal and transversal reinforcement ratios. The used GFRP stirrups were closed stirrups

with 90-degree bents made of 9.5 mm-diameter deformed GFRP bars with a bend radius of 19

mm (2 db). The test specimens had a cross-sections measured 178x330 mm and a total length

of 2400 mm. The beam specimens were tested in one point loading over a simply supported

clear span of 1500 mm. The main findings of this study can be summarized as follows:

1. Three beams failed in flexure-shear mode and their actual shear strength was not

determined. The fourth one, failed in shear mode by rupture of GFRP stirrup at the

bend. However; the measured stress at the failure was below the strength of the bend,

Jbend-

2. The flexure-shear failure mode started as flexural failure that was followed by shear

failure due to GFRP stirrup rupture that was caused by the loss of the internal shear

resistance provided by the compression concrete, which led to failure of the stirrup due

to overloading.

3. The strain limit of 0.002 for the design of GFRP stirrups is very conservative and

could be relaxed to 0.004 while maintaining a reasonably conservative design.

109


Guadagnini et al. (2003 & 2006) conducted experimental studies to investigate the

shear behaviour of concrete beams reinforced with FRP reinforcement. Six beams were

subjected to two successive phases of testing. Three beams were reinforced in flexure with

conventional steel reinforcement, while the other three were reinforced with glass fibre bars.

The tested beams had a rectangular section measured 250 mm deep and 150 mm wide.

Different shear span to depth ratios, ranging from 1.1 to 3.3, were analyzed in order to study

the variation in the shear behaviour of beams characterized by different types of shear failure.

No shear reinforcement was provided in the first phase of testing. In the second phase, just

enough glass and carbon shear reinforcement was provided to enable the shear failure. Figure

3.30 shows some of the beam specimens in the two phases.

F/2

SB42R SB45R

T nfa

7T

500 250 1000

(a) Phase 1 (b) Phase 2

Figure 3.30: Beam specimens and instrumentations by Gudagnini et al. (2003 & 2006).

The results of these tests are presented and compared to predictions according to the

design recommendations proposed by the ACI (2003) and the Institution of Structural

Engineers (ISE 1999). The main findings of this study can be summarized as follows:

1. Both the concrete shear resistance and the resistance of the shear links were found to

be much higher, by up to almost 200%, than estimated by the current design equations.

2. The levels of strain in the GFRP flexural reinforcement was 6200 microstrain

exceeding the value of 2000/2500 microstrain imposed by the original formulation of

the strain approach.

110


3. Maximum strain values, ranging from 10000 to 20000 microstrain for GFRP and 8000

to 10000 microstrain for CFRP, were recorded in the shear reinforcement. These

values greatly exceed the limit of 0.004 imposed by the ACI (2003) recommendations.

4. The principle of strain control adopted by the current FRP design recommendations is

recognized as a valid approach but it is recommended that the maximum allowable

strain for both flexural and shear reinforcement should be increased to 0.0045 to

account for structural performance, serviceability, and economic viability. At these

levels of strain, cracking is effectively controlled, the shear resisting mechanisms

offered by both concrete and shear reinforcement are effectively mobilized, and their

contribution can be added together to estimate the total resistance.

Fico et al. (2008) conducted an analytical study for the assessment of Eurocode-like

design equations for the evaluation of the shear strength of FRP RC members, as proposed by

the guidelines of the Italian Research Council CNR-DT 203 (2006). Both the concrete and the

FRP stirrups contributions to shear were taken into account. The assessment was based on

experimental results for FRP reinforced concrete beams from literature. Throughout this study

the following concluding remarks were introduced:

1. The equation proposed by the CNR-DT 203 accounting for the stirrups contribution to

the shear strength seems to give rather good results; nevertheless, the jr^ factor

accounting for bending effects of stirrups should be replaced by a term accounting for

the limit strain not governed by rupture of bent portion.

2. The strength of stirrups bent portion seems not to be a significant factor affecting the

FRP stirrups contribution to shear; this result becomes more evident when the bend

strength of stirrup approaches that of the straight portion and justifies the larger

inaccuracy of some analytical results.

3.6 Shear Design Provisions for FRP Reinforced Concrete Members

There are continuous ongoing activities and research work to develop design guidelines and

optimize/update the current design codes for FRP reinforced concrete members. This section

reviews the shear design provisions in the current design codes and guidelines in North

America, Europe, and Japan.

I l l


3.6.1 Japanese design recommendations

There are two different design recommendations for FRP reinforced concrete members

introduced in Japan. The first one is the Japanese Society of Civil Engineering (JSCE)

Recommendations and the second one is that of the Building Research Institute (BRI). Both of

the two methods will be presented in this section.

3.6.1.1 JSCE Design Recommendations (JSCE 1997)

The JSCE recommendation presents two methods for the shear strength of FRP reinforced

concrete members as follows:

Method 1:

Shear capacity, Vd, is determined from the following equation:

Vd = Vcf+Vsf+Vped (3.19)

Vcf is the design shear capacity of members without shear reinforcement and is given by:

Vcf = PdPpPnfvcdbwdlYb (3.20a)

such that:

fv* = 0-2 [fcd f3 < 0.72 N/mm2 (3.20b)

# , = ( 1 0 0 0 / ^ < 1.5; (3.20c)

Pp=(\00p/lEJ1/Esfi<\.5 (3.20d)

P„=\ + MjMd<2 for Nd > 0 (3.20e)

PH = 1 + 2 MjMd > 0 for Nd < 0 (3.20f)

where jb is the safety factor =1.3, fed is the compressive strength of the concrete, pjj is the

flexural reinforcement ratio, M0 is the decompression moment, Md is the design bending

moment, N'd is the design axial compression force, EJI is the Young's modulus of longitudinal

reinforcement, and Es is the reference Young's modulus.

Vsf is the design shear capacity resisted by the shear reinforcement and is calculated

form thee following equation:

112


Vsf =[AjvE/v £fi(sinas + c o s a s ) / s s + APV Epv(

sin<*P + cosap)/sp]z/rb

efi =0.0001 fmcd PflE. fl

PfvEfi 1 + 2 'N

yJmcd J < fbend/E_ •fi

J bend

( 0.05-^ + 0.3

; /fin//, mfb

fft=°Vpe+EfpV£jv Zf/u/r, mfb

J mcd ( h

-1/10

fc cd

(3.21a)

(3.21b)

(3.21c)

(3.2 Id)

(3.21e)

(3.2 If)

Uooj

*N={K+Ped)/Ag <0Afmcd

where Ajy is the total cross-sectional area of shear reinforcement, pj\, is the shear reinforcement

ratio, Ejv is the Young's modulus of shear reinforcement, EJ\, is the design value of shear strain

at ultimate limit state, as is the angle between the shear reinforcement and axis of the beam, ss

is the spacing of shear reinforcement, Apv is the cross-sectional area of the draped prestressing

tendons, fpv is the effective tensile stress in the prestressing shear reinforcement tendons, ap is

the inclination angle of draped prestressing tendons, sp is the spacing of draped prestressing

tendons, z is the distance between points of action of the tensile and compressive resultant

forces and it is equal to dl\.\5,fmcd is the design compressive strength of concrete allowing

for size effect, E^ is the modulus of elasticity of the shear reinforcement, O'N is the average

axial compressive stress, fbend is the design strength of the bent portion of the FRP stirrups, r*

is the internal bend radius of the FRP-stirrups, d\, is the bar diameter, f/uv is the tensile strength

of the straight portion of the shear reinforcement, yOTyj is the safety factor for the bent portion

and it equals 1.3, h is the total depth of the member, Ped is the effective prestressing force in

axial tendons, and Ag is the total cross-sectional area of the member.

Vpecj is the component of effective tensile force of axial tendons parallel to shear forced

determined from the following equation:

yped=Ped^CCplyb (3.22)

The shear force in concrete members should not exceed the design diagonal

compressive capacity F^max determined as follows:

(3.23) ^rfmax _ fwcd K "IYb

113


fwcd=l.25Jfc cd < 0.72 N/mmz (3.24)

where fcd is the compressive strength of the concrete, yi, is the member factor of safety and it

equals 1.3.

Method 2;

The shear capacity resulted from this method is generally greater than that resulted form

method 1. It is a simplified, for instance by conservatively ignoring the effect of the shear

span-to-depth ratio on shear capacity, but in some instances it will give a lower shear capacity

than method 1 when the main reinforcement has high rigidity (JSCE 1997).

Case 1: Design shear capacity when shear reinforcement does not break is calculated as

follows:

Vd=Vcf + Vsf (3.25)

Vcf\s the design shear force carried by concrete calculated as follows:

Kfâd+Kid (3.26a)

Vczd is the design shear force carried by the concrete in compression zone and calculated as:

Vczd=PfmcdxebJyb (3.26b)

Vaid is the design shear force carried by concrete in diagonal cracking load, calculated as:

(3.26c) Kid = PPPPE [fined) (h~Xe) K /Vb

xe={l-0.s(Pj,Efiy2]l[\ + (*N/fmcd)

P = 0.2(r7N/fmcd)01

PP=\-5(*N/fmcd)>0

A * =0.24 PflEfl +10 PfvEfv

5000 k

<.o.i

\

+ 0.66 <0.4

k = l-(°N/fined)

where xe is the design bending moment, crN is the design axial compression force.

(3.26d)

(3.26e)

(3.26f)

(3.26g)

(3.26h)

114


Vsf is the design shear capacity resisted by the shear reinforcement and is calculated

from the following equation:

A/vEfi£fi(h-Xe) 1

Yb Vsf- standi

^ = 0 . 0 0 0 1 lfmcd pfl

Efl

pfiEfi

f _• \ 1 + 2

/ . \Jmcd J Jbendl Efv

0„ = 45 \-[°Nlfmcd)

(3.27a)

(3.27b)

(3.27c)

where 0cr is the angle of the diagonal cracking.

Case 2: Design shear capacity when shear reinforcement breaks by fibre ruptured is calculated

as follows:

Vd =K0-/3m(Vco-Vczd) + Pm Vaid+0m Vsfd

Ko=PoPdf;dXo/rb+/3po/}pEoPd{£df\h-x0)bw/yb

l + K//«*)°''

/3d=(l000/df4 <1.5

PPo=\-S{aNlfmcd) >0

0.17 ^ - ^ - + 0.66 'PEo ^5000A:

*=i-K/>i)0'7

Pm - fbend/{Efv £fv )

<0.28

(3.28a)

(3.28b)

(3.28c)

(3.28d)

(3.28e)

(3.28f)

(3-28g)

(3.28h)

where Vco is the load at which diagonal cracking occurs, Vczd, Vaid, and V, are calculated

using Equations (3.26b), (3.26c), and (3.27a), x0 is the depth of the compression zone in

concrete at onset of diagonal cracking.

115


The mode of failure of the reinforced concrete beam varies depending on the rigidity

of longitudinal and shear reinforcements (pflEfl + 10 pÊ^). As the rigidity of the

longitudinal and shear reinforcements increase, the failure mode shifts from diagonal tension

to shear compression failure. With values less than 5000 shear failure occurs due to rupture of

shear reinforcement and for a rigidity index higher than 5000, shear failure occurs due to

concrete crushing (JSCE 1997).

3.6.1.2 Building Research Institute (BRI) (1997)

The BRI recommendations for design of concrete structures using FRP were first published in

English on August 1997 in the Journal of Composites for Construction (Sonobe et al. 1997).

Two different shear design methods are proposed in the BRI recommendations for concrete

members reinforced longitudinally and transversally with FRP bars.

Shear Strength Given by Method 1: Adjustment ofArakawa 's Equation

The ultimate shear strength of FRP reinforced concrete member is given by:

Va = imn.(p.8Vni,0.9V,a)

~0.U5kuk'p(fc+^0) V„x=Kdv

Ki=Kdv

(M/Vd) + 0.12

'0.1lSkHk'p(/e)

• + 027J^Jb bend

(M/Vd) + 0A2

dv={7/S)d

ku = 0.72 when d > 40 cm

\0.23

+ O-nJpfifbend

(kgf; cm units)

(kgf; cm units)

(3.29a)

(3.29b)

(3.29c)

(3.29d)

(3.29e)

(3.29f)

(3-29g)

k'p =0.82(100 PflEfllEs)

Pfi=Pfi{EfilE>)

where Vu\ is the shear strength when the shear reinforcement rupture, VU2 is the shear strength

when the concrete undergoes compression failure, dv is the distance between centers of tension

and compression in a concrete cross-section, f'c is the concrete compressive strength, fbend is

the bend strength of the FRP shear reinforcement.

116


Sonobe et al. (1997) reported that Equation (3.29) was derived from the

correspondence between the calculated and test values, since criteria for distinguishing

between rupture and compression failure are not clearly established. The following are the

chrematistics of the test beams used to develop Equation (3.29):

Concrete compressive strength: 225 < f'c < 500 kgf/cm2

Bend strength of FRP stirrups: 3500 < fbend < 9200 kgf/cm2

Shear span-to-depth ratio: 1.67 <al d < 4.0

Shear reinforcement capacity: pv fbend < 150 kgf/cm2

Shear Strength Given by Method 2: Application of Evaluation Method of the Architectural

Institute of Japan (AIJ) Design Guidelines

The ultimate shear strength of FRP reinforced concrete member is given by (kgf; cm units):

Vn=KJxpfi{aJbend) + aa\me(vfc-2pfifbend)bwhl2 (3.30a)

tan0 = y](Lh)2+\-L/h (3.30b)

v = 0.7-/c ' /2000 (3.30c)

where L is the clear span of the member (cm), h is the total depth of the member (cm),y'i is the

distance between the top and bottom longitudinal reinforcement (cm), 6 is the angle of the

compressive strut in the truss mechanism, v is the effectiveness factor for compressive

strength of concrete and aw and aa are the effectiveness factor for truss mechanism and arch

mechanism, respectively.

When elastic materials like FRP are used as shear reinforcement, if the rupture of shear

reinforcement occurs first, the concrete compression strut will not have reached its limit at the

ultimate state, and if the compression failure occurs first, the shear reinforcement will not

have reached their ultimate tensile strength. The reinforcement efficiency of the shear

reinforcement at the ultimate state is represented by aw and aa and the concrete compression

section is assumed to resist shear forces up to aa times the maximum bearable compression

force. For the shear cracking angle, a constant angle of 45° is assumed. The following two

alternative methods are proposed using different values for the coefficients aw and aa (Sonobe

etal. 1997):

117


1. aw = 0.5 and aa = 1.0: when the ultimate state takes the form of shear tensile failure

involving the rupture of shear reinforcement (pfi,fbe„d ^ 0.5v/c J and Equation (3.30)

takes the following format:

K =Kj\P/v(fbend/2) + tand(vf;-2pfifbend)bwh/2 (3.30d)

When it takes the form of shear compression failure \P^fbend >0 .5v/ c ] , and

(Pfifbend = 0-5v/c') may be used and the equation takes the following format:

K=hJ\Pfv(0.5vf;)/2 (3.30e)

2. aw = 0.5 and aa = 0: when the ultimate state takes the form of shear tensile failure and

Equation (3.30) becomes in the following format:

K=bwJ\pfvf:/2 (3.30f)

Values calculated from the two alternatives were compared with the test values and it

was concluded that alternative 2, which ignores the arch mechanism, gives values on the safe

side. The agreement between the test and calculated values is low in the range of

Pfifbend <50. As (yc^/^^j increases; however, the difference between alternatives 1 and 2 is

reduced. The same values are given by the two alternatives for shear-compression failure

where the shear reinforcements do not rupture. The following are the characteristics of the test

beams used to develop Equation (3.30):

Concrete compressive strength: 225 < f'c < 500 kgf/cm2

Bend capacity: 3800 < fbend < 9200

Span ratio: 1.0<(^/Z)< 4.0

Shear reinforcement capacity: 25 < (pp fbend J < 150

Shear reinforcement pitch: 0.09 < s/j\ < 0.5

3.6.2 Canadian design codes and guidelines

There are two design codes for FRP reinforced concrete structures in Canada: The Canadian

Highway Bridge Design Code (CHBDC) which provides the design criteria for bridge

components; and the Design and Construction of Building Components with Fibre-Reinforced

118


Polymers Code. Besides those two codes, there is a design manual for FRP reinforced

concrete structures published by ISIS Canada. This section will provide the shear provisions

for FRP reinforced concrete structures in the following codes and guidelines:

1. CHBDC (CAN/CSA S6-06) published in 2006.

2. CHBDC-Addendum which is the first update of the 2006 version and it will be

published in 2009.

3. The Canadian Building Code (CAN/CSA S806-02) published in 2002.

4. The ISIS Canada Design Manual No.3 (ISIS Canada-M03) published in 2007.

3.6.2.1 The Canadian Highway Bridge Design Code CSA (2006)

The recently published version of the CHBDC (CSA 2006) included a new section for fibre-

reinforced structures. According to the CHBDC, the shear strength of concrete members is

based on the modified compression field theory as presented in Section 2.4.6 in this thesis. For

FRP reinforced concrete members the following modifications are introduced in the general

method to reflect using FRP reinforcement instead of steel reinforcement:

K=Kf+K/+Vp where Vcf+Vsf < 0.25 *efebwdv (3.31)

Vcf = 2.5p<l>c fcr bw d \ ^ - (N; mm units) (3.32)

<t>frn Afv ffi,dv COt 9 Vsf=

frp /v A (3.33) s

where Vcf is the concrete shear resistance of a member reinforced longitudinally with FRP

reinforcement, Vsj is the shear resistance provided by FRP shear reinforcement, EJJ is the

modulus of elasticity of the longitudinal FRP reinforcement, Es is the modulus of elasticity of

steel bars, fp is the stress in the FRP stirrups at ultimate, $frp is the FRP material resistance

factor, and (j)c is the concrete material resistance factor.

It can be noticed that Equation (3.32) is the same as Equation 2.123 except the term

JEJJ/ES which was added to account for the relative stiffness of the FRP material relative to

the steel. The parameters /? and 6 can be determined based on the general method as described

in Section 2.5.2. However the longitudinal strain at the mid-height of the cross-section is

calculated using the following equation:

119


£„ =

(M//dv) + Vf-Vp+0.5Nf-Apfpe<Qm

2(EsAs + EpAp)

(Mf/dv) + Vf-Vp+0.5Nf-Afrpff < 0.003

(3.34a)

(3.34b) 2{EsAs + EflAJ])

where AJJ is the area of the FRP longitudinal reinforcement, EJJ is the tensile modulus of

elasticity of the longitudinal FRP reinforcement, As is the area of longitudinal steel

reinforcement, Es is the tensile modulus of elasticity of steel, fpo is the stress in tendons when

the stress in the surrounding concrete is zero (MPa), Mj is the factored moment at a section

(N.mm), Nf is the factored axial load normal to the cross-section occurring simultaneously

with Vf, including the effects of tension due to creep and shrinkage (N), Ap is the area of the

prestressing steel tendons, Afrp is the area of the FRP prestressing tendons, Vp is the component

in the direction of the applied shear of all of the effective prestressing forces factored by <f>p

(material resistance factor for FRP tendons), and ffo is strength of the FRP stirrups and is

calculated considering the smaller of the following two equations:

/A=(0.05r4 / r f6+0.3)/> , / l .5 (3.35)

fP=E/v£Jv (336a)

sfv= 0.0001 / ; PfiE. fi>

0.5

1 + 2 fc

< 0.0025 (3.36b)


The minimum amount of FRP shear reinforcement, 4/vmin> is calculated as follows:

b... s ^ m i „=0 -06J / c

/ , A

(3.37)

The spacing of the transverse reinforcement, s, measured in the longitudinal direction

shall not exceed the lesser of

1. 600 mm or 0.75dv if the nominal shear stress is less than 0.1^c fc; and

2. 300 mm or 0.33dv if the nominal shear stress equals or exceeds 0. \(f>cfc.

120


3.6.2.2 The Canadian Highway Bridge Design Code CSA (2009)-Addendum

The CSA-S6 subcommittee for Section 16 (Fibre-Reinforced Structures) has already approved

the first update for the 2006 version of the CSA-S6 (2006) Code and it will be published as

Addendum in 2009 (CSA 2009) to the original version. The test results of the experimental

investigation conducted in this study contributed to amending the shear provisions (FRP

stirrup contribution) incorporated in the 2006 version of the Canadian Highway Bridge Design

Code (CAN/CSA-S6) which yielded the CSA-S6-Addendum (2009). In the updated version of

the Canadian Highway Bridge Design Code, revised contributions for the concrete and FRP

stirrup contribution to the shear resisting capacity were introduced.

Equation (3.32) for calculating the concrete contribution to the shear resistance, Vcf,

will be in the following format:

Vcf = 2.5 {]<f>cfcrbwdv (3.38)

As mentioned earlier, the design provisions of the CHBDC Code are based on the

modified compression field theory. The main reason that JE„/ES term is removed from

Equation (3.32) is the replicate considerations for the reduced FRP stiffness in comparison

with steel. This reduced stiffness is included in the longitudinal strain calculations in Equation

(3.34). Consequently, keeping this term as in the original 2006 version yielded very

conservative predictions for the concrete contribution. Adequate conservativeness level was

observed for the concrete contribution of FRP reinforced concrete beams considering the

updated equation (El-Sayed and Benmokrane 2007).

The stirrup stress at ultimate,^, is the least of the following two equations:

/ / v=(0.05rAM+0.3)/ / u v / l .5 (3.39)

ffi = 0.004 £A (3.40)

This equation for the FRP stirrup contribution to the shear strength was originally

provided by the ACI (2003) and re-approved in ACI (2006). There are many investigations

that recommend increasing the strain at ultimate to values more than 4000 microstrain,

however, this strain limit is justified as it represents the strain level at which the degradation

of aggregate interlock and corresponding concrete shear starts to sharply decrease (Priestley et

al. 1996).

121


3.6.2.3 The Canadian Building Code S806-02 (CSA 2002)

The shear design method specified by CSA S806-02 covers the following two cases:

1. Concrete members reinforced longitudinally and transversely with FRP reinforcement.

2. Concrete members reinforced longitudinally with FRP bars and transversely with steel

stirrups.

The design shear strengths, Vn, in both aforementioned cases are defined as follows:

For FRP stirrups V„ =Vcf + Vsf <Fc/ + 0.60 A<f>c Jfc bw d (3.41)

For steel stirrups V„ = Vcf + VS< Vcf + 0.80 A<pc^bwd (3.42)

where Vcf and Vsf are concrete and FRP stirrup contributions, respectively, Vs is the

contribution of the steel stirrups, bw is the beam web width, d is the effective beam depth, X is

a factor to account for concrete density, and <f>c is the concrete resistance factor.

The concrete contribution to the shear strength of an FRP longitudinally reinforced

concrete member is calculated as follows:

Vcf = 0.035 A <f>c (/J pfl Efl {Vf/Mf)df bw d (3.43a)

Q.\A<l>cJfcbwd<Vcf<02A<l>cJfcbwd (3.43b)

such that Vf d/Mf < 1.0 (3.43c)

where Efl and pji are the tensile modulus of elasticity and the reinforcement ratio of the

longitudinal FRP reinforcement, respectively, Vf and and Mf are the factored shear force and

the factored moment at the section under consideration, respectively.

The previous equation, Equation (3.43) is applicable for concrete sections provided

with minimum shear reinforcement corresponding to the code requirements and/or the

effective depth, d, does not exceed 300 mm. On the other hand, to account for the size effect

of concrete members with effective depth exceeds 300 mm and with no shear reinforcement or

less than the minimum specified by the code, the concrete contribution, Vcf, is calculated using

the following equation: f 130

viooo+j, Kf = A <?>c Jfe bwd> 0.08 A </>c Jfe bw d (3.44)

The contribution of FRP stirrups is given by the following equation:

122


OA(pfrDAfvffuvd y = Yfrp fiJM ( 3 4 5 )

s

where Ajv is the area of the FRP shear reinforcement, fj\, is the ultimate strength of the FRP

stirrups, s is the stirrup spacing, ^ is the material resistance factor for FRP. The factor 0.4

included in Equation (3.45) is the bend strength relative of FRP stirrups relative to the strength

in the fibres' direction of the FRP stirrups. The previous equation may be re-arranged as

follows:

JfrP^{^ffuV)d JfrPAAfber,d)d

S S

The contribution of the steel stirrups is given by the following equation:

d>. A„ fv d Vs=

svJy (3.47) s

where As is the area of the steel stirrups, fy is the yield strength of the steel stirrups, s is the

stirrup spacing, </>s is the material resistance factor for steel.

It should be noted that Equation (3.45) for steel stirrups and Equation (3.47) for FRP

stirrups are similar and the only difference between them is replacing the yield strength of the

steel stirrups with the bend strength of the FRP stirrups (=0.4 ffuv).


The minimum shear reinforcement, Ajvmm, specified by the code can be calculated from the

following equation:

7 b,„ s Afvmin=0.3,Jfc^ (3.48a)

J jh

where fjh is the design stress in the FRP shear reinforcement and its value is the least of the

following:

ffi =0.004 Efi (3.48b)

123


3.6.2.4 ISIS Canada Design Manual No. 3 (ISIS Canada 2007)

The ISIS Manual 3 considers the CSA-A23.3-94 simplified method for contribution concrete

while it considers the CHBDC (CSA 2006) for the FRP shear reinforcement contribution as

follows:

K = K/ + Kf (3-49)

For members which do not contain shear reinforcement, such as slabs and footings,

and beams with the effective depth not greater than 300 mm or members in which at least the

minimum stirrups are provided, the factored shear resistance attributed to concrete, Vc/, is

calculated according to the following equation:

-7? K,=a2A4V/cM«hf (3.50a)

where 'fl <1.0 (3.50b)

where X is the modification factor of density of concrete, <f>c is the material resistance factor for

concrete, and d is the distance from the extreme compression surface to the centroid of the

reinforcement.

For sections with an effective depth greater than 300 mm and not containing at least

the minimum transverse reinforcement the concrete resistance, Vcf, is taken as:

260 *V = ,* 4 47c K dl— * o.u <f>c J7c K d\—

1000 + rfJ cy c \ Es cy c \ Es

(3.51)

The contribution of the FRP stirrups to the shear strength, Vs/, is based on the criteria

given in the CHBDC (CSA 2006) as follows:

<f>frpAJvfjvdV

COt0

Kf=-

/A =(0.05^/^+0.3)^/1.5

Jfi = Efr £fi,

-|0.5

PfiEfl ^ = 0 . 0 0 0 1 fc pfiE. ft

1 + 2 fc

< 0.0025

(3.52a)

(3.52b)

(3.52c)

(3.52d)

124


To control the shear crack width in concrete beams reinforced with FRP stirrups, the

strain in the FRP stirrups at service load is limited to 0.002 as indicated form the following

equation:

S(V -V) = _±jer £ /£ 0.002 (3.53)

AfiEfid


Failure of a beam without shear reinforcement is sudden and brittle. Therefore, a minimum

amount of shear reinforcement is required when the factored shear force, Vf, exceeds 0.5 Vc.

However, this reinforcement is not necessary for slabs, footings, and beam with a total depth

not exceeding 300 mm. The minimum amount of FRP shear reinforcement, 4/wnin, is

calculated as follows:

Afvmm=0.06JI ^ (3.54) /vm,„ MJC Q Q 0 2 5 E^ )

The spacing of the transverse reinforcement, s, shall not exceed 0.7 dv or 600 mm.

3.6.3 American design codes and guidelines

3.6.3.1 ACI440.1R-06(ACI2006)

The shear resistance of FRP-reinforced concrete element specified by the ACI (2006) is given

as follows:

Vn = Vcf + Vsf (3.55)

2 Vcf=-4fcKc (3.56a)

c = kd (3.56b)

k = ^2pflnJ1+(pflnfl) -pflnfl (3.56c)

The shear resistance provided by FRP stirrups perpendicular to the axis of the member, Vsf, is

calculated as:

Afi, ff„d Vsf=

pJfv (3.57a)

125


ffi= 0.004 Efv<fbend (3.57)

fbend=(0.05rjdb+0.3)ffuv/l.5<ffm (3.57c)

where c is the neutral axis depth (mm), pjj is the FRP longitudinal reinforcement ratio, njj is the

modular ratio, and bw is the beam width (mm), d is the distance from extreme compression

fibre to centroid of tension reinforcement (mm), f'c is the specified compressive strength of

concrete (MPa), Ajy is the amount of FRP shear reinforcement within spacing s, rb is the radius

of the bend (mm), d\, is the diameter of reinforcing bar, fben<t is the strength of bent portion of

FRP bar (MPa), ffuv is the design tensile strength of FRP, considering reductions for service

environment.


The minimum are of FRP shear reinforcement, 4/vmin, is given by:

A**. = ° - ^ (3-58)

The spacing of the transverse reinforcement, s, shall not exceed 0.5 d or 27 in.

3.6.3.2 AASHTO LRFD Specifications (AASHTO 2009)

These specifications offer a description of the glass fibre reinforced polymer (GFRP)

composite materials as well as provisions for the design and construction of concrete bridge

decks and traffic railings reinforced with GFRP reinforcing bars. The shear provisions

specified by AASHTO LRFD (2009) consider the same ACI (2006) equations for evaluating

the contribution of the FRP shear to the shear strength. The factored shear resistance, Vr, shall

be taken as:

Vr=Wn (3-59)

where <j> is the resistance factor, and V„ is the he nominal shear resistance and it shall be

determined as follows:

K = Kf+Kf (3-60)

where Vcf is the nominal shear resistance provided by the concrete, Vs/ is the nominal shear

resistance provided by the shear reinforcement.

126


The nominal shear resistance provided by the concrete, Vcj, is calculated from the

following equation:

^ = 0 . 1 6 V / A c (3.61a)

but shall not be larger than 0.32^//c60c representing the punching shear capacity of a two-

way system subjected to a concentrated load that is either rectangular or circular in shape. For

singly reinforced, rectangular cross-sections bent in uniaxial bending:

c = kd (3.61b)

where bw is the width of web (in.), c is the distance from extreme compression fibre to neutral

axis (in.), k is the ratio of depth of neutral axis to reinforcement depth, d is the distance from

extreme compression fibre to centroid of tension reinforcement (in.), bo is the perimeter of

critical section computed at d/2 away from the concentrated load (in.).

The nominal shear resistance provided by the shear reinforcement perpendicular to the

axis of the member, Vs/, shall be calculated as:

Vsf = 4 ^ < 0.25{£bwd (3.62a)

ffi=0.004EJ,<fbend (3.62b)

/ * bend

( r ^ 0.05-^- + 0.3

V db J ffu^ffuv (3.62c)

where Af, is the area of shear reinforcement within spacing s, (in.2), fj\, is the design tensile

strength for shear (ksi), d is the distance from extreme compression fibre to centroid of tension

reinforcement (in.), s is the spacing of shear reinforcement (in.), Ep is the modulus of

elasticity of GFRP reinforcement (ksi), fbend is the strength of the bent portion of a GFRP bar

(ksi), rb is the internal radius of the bended GFRP bar (in.), db is the GFRP bar diameter (in.),

and ffuv is the design tensile strength of GFRP bars considering reductions for service

environment (ksi).


Where transverse GFRP reinforcement is required, the area of GFRP reinforcing bars, Aj\, m j n ,

shall satisfy:

127


_ 0.05 bw s Afimin- 7 C3-63)

Jfv

The spacing of the transverse reinforcement shall not exceed the maximum permitted

spacing determined as 0.5 d or 24 in., whichever is less.

3.6.4 European shear provisions

The EUROCRETE Project provisions for shear reinforcement as initially recommended by

Clark et al. (1996) consider the original equations for steel reinforced to determine the

concrete contribution but using the effective reinforcement ratio which equals:

Pfi=Pfl(EfllE.) <3-64)

where pjj is the flexural FRP reinforcement ratio, Eji is the modulus of elasticity of the flexural

FRP reinforcement, and Es is the steel modulus of elasticity (=200 GPa). On the other hand,

the FRP shear reinforcement is calculated considering 0.0025 strain limit in the FRP shear

reinforcement. Thus the stress in the FRP stirrups is limited to:

ffi= 0.0025 Efv (3.65)

where E^, is the modulus of elasticity of FRP stirrups. One of the direct methods for the shear

design of FRP reinforced concrete sections which is based on the previous assumptions is that

published by the Institution of Structural Engineers (ISE 1999).

3.6.4.1 Institution of Structural Engineers (ISE 1999)

The Institution of Structural Engineers (ISE 1999) published an "Interim guidance on the

design of reinforced concrete structures using fibre composite reinforcement". This guide is in

the form of suggested changes to the British Design Codes BS8110. The suggested

modifications consider the ratio between modulus of elasticity of the FRP material and steel to

account difference in the axial stiffness. Hence, the modified BS8110 equation for concrete

shear strength of sections reinforced with FRP, Vc/, is given in the following equation:

Vcf = 0.79 flOO . E„}

i / . i / , .,{

A _JL ybwd • /7200y

'3 (400Y4

V

V*f r>\ fc

K25j

'3

bwd (3.66) d

As far as the shear strength resisted by the vertical shear reinforcement is concerned,

this can be evaluated using the usual formulation derived according to the truss analogy theory

128


as reported for steel, but controlling the maximum strain developed in the vertical bars,

according to the strain approach. The specified limit for the stirrup strain is 0.0025; therefore

the shear strength resisted by the web reinforcement is given as follows:

0.0025 Eh Afv d Kf=

t - t - (3-67)

3.6.4.2 Italian National Research Council (CNR-DT 203) (2006)

The Italian National Research Council presents the following shear design provision which is

based on the Eurocode 2 (1992) approach with modifications to account for using FRP

materials instead of steel.

The shear capacity of FRP reinforced members without stirrups can be evaluated as

follows:

Vcf = mm{VRdct,VRdmax} (3.68)

where VR^CI represents the concrete contribution to shear capacity, and VRd>max. is the concrete

contribution corresponding to shear failure due to crashing of the web, as reported by the

current building code.

The concrete contribution, VR^CI, is calculated as follows:

*V-=l-3. KE,J

TRdk{\2 + AQpfl)bwd (3.69a)

such that 1.3. "HJL

\ E . j

<1.0 (3.69b)

^ = 0 . 2 5 / ^ (3.69c)

2\ where EJJ and Es are the Young's moduli of elasticity of the FRP and steel bars (N/mm ) 2N

respectively; TRJ is the design shear stress (N/mm ); fctd is the design tensile strength of

concrete; k , which represents a coefficient to be set equal to 1 for members where more than

50 % of the bottom reinforcement is interrupted; if this is not the case, k shall be assumed as

(1.6-d) > 1, where d is in m; and pfl =0.01 < Afl/(bv d) < 0.02.

Shear capacity of FRP reinforced elements using FRP stirrups can be computed using

the following equation:

129


Vn=mm{VRd,ct,Vsf,VRd^} (3.70)

where VMJ is the FRP contribution to the shear capacity and is calculated using the following

equation:

Afv f& d *V= fvJfr (3.71)

s

where Aj\, is the amount of FRP shear reinforcement within stirrups spacing s (sum of the area

of single stirrup legs), andj^. is the reduced tensile strength of the FRP reinforcement due to

the bend effect, defined as: ffdJYf^ a nd / / ^ = 2 .0 for FRP stirrups with bend radius equal to

six times the bar diameter (rj = 6 db).


Where shear reinforcement is required, the minimum area of shear reinforcement shall be

calculated form the following equation:

4>«in = ° - 0 6 V ^ o o o 4 £ <S t r e s s e s i n N / m m 2 > <3-7 2 )

^ > m i n > 0.35 bs/0.004 Efv (3.73)

FRP reinforced concrete beams shall have at least three stirrups per meter and the

stirrup spacing, s, must satisfy this condition: be s > 0.8 d.

130

Chapter 4: Experimental Program

CHAPTER 4

EXPERIMENTAL PROGRAM

4.1 General

The main objectives of the experimental program are to investigate the structural performance

of FRP stirrups as shear reinforcement for concrete structures as well as to validate and/or

improve the current analytical and design approaches for shear of concrete members

reinforced transversally with FRP stirrups.

This chapter presents the details of test specimens, fabrication, instrumentation, test

setup, and test procedure. Additionally, this chapter gives the detailed properties of the

different materials used in this experimental program based on testing representative samples

of each material.

Three materials were used in this study. These materials were FRP (in stirrups'

configuration), steel bars, and concrete. The FRP stirrups included carbon and glass FRP

(CFRP and GFRP) stirrups. As the strength of FRP stirrups at the bend zone (bend strength)

may be considered the limiting stress for the FRP bent bars, the evaluation of the bend

strength of the used FRP stirrups is also illustrated in this chapter. The following section

presents the characteristics of the materials used in this study.

4.2 Material Properties

4.2.1 FRP stirrups

Pre-fabricated carbon and glass FRP stirrups No. 10 (9.5-mm diameter) were used as shear

reinforcement for the beam specimens. The FRP bars were made of continuous longitudinal

carbon/glass fibres pre-impregnated in a thermosetting vinyl ester resin and winding process

with a fibre content of 74.2% and 78.8% (by weight) for carbon and glass FRPs, respectively.

The FRP stirrups had a sand-coated surface over a wire wrapping in two perpendicular

directions as shown in Figure 4.1 to enhance bond performance between FRP bars and

surrounding concrete. The FRP stirrups had a total width of 140 mm and 640 mm height and a

bend radius, r&, of 38.1 mm which represents 4 times the bar diameter (rt, = 4db). This

satisfied the requirements of both ACI guidelines (ACI 2008a & 2008b) to maintain a

131


minimum bend radius to bar diameter for FRP bent bars and stirrups equal to 3.0 {rb/db = 3)

for FRP bars No. 6 to 25 and equal to 4.0 (rb/db = 4) for FRP bars No. 29 and 32. Each FRP

stirrup consisted of two C-shaped parts. The two parts were tied together to form one stirrup.

Figure 4.2 shows the details of the FRP and steel stirrups. All the FRP reinforcement used in

this study were manufactured by Pultrall Inc., Thetford Mines, Quebec, Canada.

'& * § I I t V. „ 4

Figure 4.1: Surface configuration of the carbon and glass FRP stirrups.

I l\ I

!

a

01 *

J»

UU (a) (b)

Figure 4.2: Details of the FRP and steel stirrups: (a) FRP stirrups; and (b) Steel stirrups.

The characteristics of the FRP materials were determined using the B.2, B.5, and B.12

test methods specified by the ACI 440.3R-04 (ACI 2004) guidelines. To determine the tensile

132


strength and modulus of elasticity of straight portions (parallel to the fibre's direction), as well

as the reduced strength of FRP stirrups at the bend zone, two groups of CFRP and GFRP No.

10 (9.5 mm-diameter) were selected from the same batches of the CFRP and GFRP stirrups

fabricated for beam specimens. Each group consisted of six straight specimens to get the

tensile capacity and modulus of elasticity using B.2 test method, five U-shaped specimens

using B.12 test method, and four C-shaped specimens using B.5 test method. The main

purpose to utilize a complete set that includes straight, U-shaped, and C-shaped specimens

produced from the same batch is to evaluate the reduction in the strength due to bending the

FRP bars when either B.5 or B.12 test method is used. Besides, selecting the different

specimens from the same batch enables evaluating the difference between the bend strength

resulting from both ACI methods (B.5 and B.12) and comparing their bend strength with that

measured from beams. All the bent specimens (U-and C-shaped) had a bend radius equals four

times the FRP bar diameter (r^ = 4dt).

4.2.1.1 Tensile characteristics

The six straight specimens from each FRP type and diameter were directly cut from the FRP

stirrups and prepared by attaching the steel tubes at both ends as anchorages using

commercially available cement grout known as Bristar 10. Then, the specimens were tested in

tension using the BALDWIN machine up to failure. Figure 4.3 shows the typical tensile test of

FRP straight portion and the typical fibre-rupture failure mode. The results of the tension tests

are presented in Table 4.1. The average tensile strength for the straight portion of the FRP

stirrups was 1538±57 and 664±25 MPa for CFRP and GFRP, respectively. The modulus of

elasticity of the CFRP and GFRP bars was 130±6 and 45±2 GPa, respectively. The linear

elastic stress-strain relationship of the carbon and glass FRP bars as measured in tension tests

in accordance with the ACI (2004), B.2 method is shown in Figure 4.4.

4.2.1.2 Bend strength of FRP stirrups

There are two methods to evaluate the bend strength of FRP stirrups, namely B.5 and B.12 test

methods (ACI 2004). The B.5 test method evaluates the bend strength of C-shaped FRP

stirrups through embedment in two concrete blocks, which are pushed apart till the rupture of

the FRP stirrups. While the B.12 test method is used for testing the bare U-shaped FRP bars in

133


tension to determine the bend strength. ACI 440.6M-08 (ACI 2008b) reports that either B.5 or

B.12 (ACI 2004) test methods may be considered for determining the bend strength of FRP

bent bars/stirrups. ISIS Canada (2006) specifies the B.5 method for determining the strength

of FRP bent bars and stirrups at bend locations and B.12 method for determining the strength

and modulus of FRP bent bars at bend locations. However, it maintains the same limit of 35%

of the strength parallel to the fibres for both methods. It should be mentioned that the

CAN/CSA S806-02 (CSA 2002), Annex E, specifies the same method as the ACI (2004) B.5

for testing the FRP bent bars and stirrups. In this study, both methods were used to evaluate

the bend strength of the representative FRP specimens to compare the measured bend strength

of a single FRP stirrup and that resulted from beam specimens. Figure 4.5 shows the

dimensions of the C-and U-shaped specimens for both test methods.

Figure 4.3: Typical tension testing of FRP straight portions: (a) Test setup; and (b) Typical

fibre-rupture of FRP straight portions.

134


Table 4.1: The test results of FRP straight portions.

Specimen

No.

1

2

3

4

5

6

Average

SD

COV (%)

CFRPNo. 10 (9.5 mm)

Tensile

Strength, ffuv

(MPa)

1474

1630

1558

1484

1553

1527

1538

57

3.71

Modulus of

Elasticity, Ej\,

(GPa)

127

123

131

129

124

140

130

6

4.76

Strain at

Ultimate,

(%)

1.2

1.3

1.2

1.1

1.2

1.1

1.2

0.1

6.25

GFRPNo. 10 (9.5 mm)

Tensile

Strength^

(MPa)

687

649

686

624

679

657

664

25

3.75

Modulus of

Elasticity, Ej\,

(GPa)

45

45

43

43

46

48

45

2

4.36

Strain at

Ultimate,

(%)

1.5

1.5

1.6

1.5

1.5

1.4

1.5

0.1

4.81

!

Str

ess

1800 -,

1600

1400-

1200

1000-

800

600

400

200

Figure 4.4: Typical stress-strain relationship for the reinforcing bars.

4.2.1.2.1 B. 5 Method

Figure 4.6 shows a schematic drawing for the B.5 test method. The C-shaped FRP specimens

135

5000 10000 15000

Strain (microstrain)

20000


were prepared keeping the two sides of the stirrup as continuous end in the concrete block

(Type B). One side of the stirrup was provided with de-bonding tubes keeping a constant

embedment length, /</, equals 47.5 mm for FRP bars of 9.5 mm-diameter corresponding to an

embedment length-to-bar diameter, l/db = 5.0. These de-bonding tubes were secured into the

desired position with silicone and duct tape. The reason for choosing lj=5 db for the tested

stirrups was to ensure that all the applied tensile force was transferred directly to the bent

portions and no part of this force is transmitted through the embedded length of the bar before

the bend to the concrete by bond. Each concrete block was reinforced transversally with 10

mm-diameter steel stirrups spaced at 65 mm to prevent any premature splitting prior to the

rupture of the FRP stirrup. The test specimens were cast using ready-mixed normal weight

concrete (Type V, MTQ) with a target compressive strength of 35 MPa after 28 days. The

actual concrete strength obtained from standard cylinders at the day of the test was 39±1.2

MPa (average of four cylinders). Figure 4.7 shows the preparation of the specimens while

Figure 4.8 shows casting of the concrete blocks.

335 mm

db

db=9.5 mm rb~3i.\ mm

335 mm

db

Steel tubes

(a) (b)

Figure 4.5: Dimensions of the C-and U-shaped specimens for B.5 and B.12 methods.

136


Steel stirrups to prevent splitting

300 mm „ 400 mm X- -k-

S s o o i n

^ -

\

ir

IU

Debonding tube

db

P

Concrete block lt : to/7 length Id: embedment length

Debonding

II II

«= = = :

feW/W/y/K

W///S/////A ' $>

A . /fts\\\Ws\\4

vswwm^

Type A: standard hook Type B: continuous end

Figure 4.6: Schematic for B.5 method and specimen configuration.

Figure 4.7: Attaching the debonding tubes to the FRP stirrups.

137


Figure 4.8: Casting of the concrete blocks.

After casting and the curing of the concrete blocks, they were stored indoors for 28

days. After that, the two blocks (for each test) were adjusted on the horizontal testing bed and

the inner concrete surface of each block was cleaned. One of two blocks was placed over a

moving roller (the moving side) to allow for the horizontal movement and minimize the

friction between the block and the testing bed. Following the preparation and placing the

moving side block on the roller, two steel plates were placed in front of the inner faces of the

concrete bocks to distribute the hydraulic jack loading. The load was applied by pushing the

two concrete blocks apart till the failure of the bent specimen. Figure 4.9 shows the setup

during testing of FRP stirrup in concrete blocks (B.5). All the test specimens failed due to the

rupture of FRP bars at the bend which was followed by slippage of FRP bars out of the

concrete blocks as shown in Figure 4.10. The failure load was recorded and the bend strength

was calculated from Equation (4.1). The bend strength of No. 10 CFRP and GFRP C-shaped

specimens tested in concrete blocks are presented in Table 4.2.

Fu

J bend = T~7 V*-*)

where fbend is the bend strength (MPa), Fu is the failure load (N), and A is the FRP bar cross-

sectional area (mm").

138


Figure 4.9: Testing FRP stirrups in concrete blocks.

'-t I

> k- ' 'Li

W3n&**r *-

IV?' * m- "*

Figure 4.10: Rupture of the FRP stirrup at the corner in concrete blocks followed by stirrup

slippage.

139


Table 4.2: The bend strength of FRP C- and U-shaped stirrups.

Specimen No.

1

2

3

4

5

Average

SD

COV (%)

Jbend'Jfuv

fbendB.nl' fbend B.5

CFRPNo. 10 (9.5 mm)

Bend strength

B.5 (MPa)

661

714

773

702

-

712

46

6.53

0.46

Bend strength

B. 12 (MPa)

486

549

489

538

469

506

35

6.97

0.33

0.71

GFRPNo. 10 (9.5 mm)

Bend strength

B.5 (MPa)

382

385

373

409

-

387

15

3.92

0.58

Bend strength

B. 12 (MPa)

196

232

310

215

205

232

46

19.87

0.35

0.60

fbend- the bend strength of FRP stirrup (bent bar); f/uv: the tensile strength of FRP bars parallel

to the fibre's direction 2 fbend B.S: the bend strength based on B.5 test method; fbend B.n' the bend strength based on

B.12 test method.

4.2.1.2.2 B.12 Method

Figure 4.11 schematically shows the B.12 test method for FRP U-shaped specimens. The U-

shaped specimens for B.12 were prepared by attaching the anchorage system (steel tubes) for

both ends of the U-shaped stirrup as shown in Figure 4.12. The specimens were anchored at

each end using steel tubes filled with an expansive cement grout commercially known as

Bristar 10. Then, the U-specimens were installed on the testing setup and the load is applied

by moving apart the upper and lower test fixture. Testing of U-shaped FRP stirrups according

to B.12 method is shown in Figure 4.13. The typical failure mode due to rupture of FRP U-

shaped stirrups at the bend is illustrated in Figure 4.14. The failure load was recorded and the

bend strength was calculated from Equation (4.1). The bend strength of No. 10 CFRP and

GFRP U-shaped specimens tested in B.12 are also presented in Table 4.2.

140

http://fbendB.nl


Corner insert

Corner insert

Upper part

FRP U-specimen

Lower part

Anchorage

Anchorage

Figure 4.11: Schematic for B.12 test method.

I Figure 4.12: Preparing No. 10 CFRP and GFRP U-specimens for B.12 test.

141


Figure 4.13: Testing U-shaped FRP specimens using B.12 method.

- >

Figure 4.14: Typical fibre-rupture failure mode at the bend for U-shaped FRP specimens.

142


4.2.2 Steel bars

Deformed steel bars No. 15M (15.9 mm) and 10M (11.3 mm diameter) were used for top and

flange reinforcement, respectively. Based on the test results of three specimens, the yield

stress and modulus of elasticity were 450 MPa and 200 GPa, respectively. Additionally, 9.5

mm-diameter steel bars were used to fabricate the stirrups for the control beam. The yield

stress and modulus of elasticity were 576 MPa and 200 GPa, respectively. For the 7-wire steel

strands of 15.4 mm-diameter (140 mm2 cross-sectional area) used as flexural reinforcement of

the test specimens, the tensile strength was 1860 MPa and the modulus of elasticity was

200 GPa. Typical tension testing of steel bars and the typical failure of steel bars is shown in

Figure 4.15. Figure 4.4 additionally shows the measured stress-strain relationship for the

reinforcing steel bars.

(a) (b)

Figure 4.15: Typical tension testing of steel bars: (a) Test setup; and (b) Failure of steel bars.

143


4.2.3 Concrete

The beam specimens were constructed using concrete provided by a local ready-mix supplier

and cast in place in laboratory. The used concrete was MTQ Type-V with a target

compressive strength of 35 MPa after 28 days. The mixture proportion per a cubic meter of

concrete was as follows: coarse aggregate content of 646 kg with a size ranged between 10

and 20 mm, 341 kg with a size ranged between 2.5 and 10 mm and fine aggregate content of

717 kg, cement content of 455 kg, water-cement ratio (w/c) of 0.35, air entrained of 5.0-8.0%,

and water-reducing agent. The slump of the fresh concrete was measured before casting and

was about 100 mm (4.0 in.) as shown in Figure 4.16. Twelve concrete cylinders 150x300 mm

were cast from each concrete batch and cured under the same conditions as the test beams.

Four cylinders were tested in compression after 28 days, four cylinders were tested in

compression at the day of beam testing and the stress-strain relationship is measured, and the

last four cylinders were tested in tension by performing the split cylinder tests at the day of

beam testing. The compression and splitting testing of concrete cylinders are shown in Figures

4.17 and 4.18, respectively. The average compression strength ranged from 33.5 to 42.2 MPa

and the average tensile strength ranged from 2.65 to 3.22 MPa. The measured stress-strain

relationships for different batches are shown in Figure 4.19.

Figure 4.16: Slump test of the fresh concrete before casting.

144


Figure 4.17: Compression test of the standard concrete cylinders.

Figure 4.18: Splitting test of the standard concrete cylinders.

145


Pa)

S

tres

s (M

50 -i

45

40

35

30

25

20

15

10

5

0

0 1000 2000 3000 4000 5000 6000

Strain (Microstrain)

Figure 4.19: Stress-strain relationship for different concrete batches.

4.3 Beam Specimens (Test Specimens)

The MTQ is using a series of standard size New England Bulb Tee (NEBT) girders in

constructing bridges in Quebec, Canada with a total depth ranging from 1000 to 1800 mm.

The web width of such girders is constant and equals 180 mm. Figure 4.20 shows the details

of the NEBT cross section. However, these beams have different depths according to the

bridge span, which they cover.

Considering the fact that the web of such beams mainly provides the required shear

strength and that this study is focusing on studying the shear behaviour, the web width of the

test beam was selected to be the same as the NEBT series (180 mm). Nevertheless, due to

laboratory equipment limitations, the height of the test specimen can not be equal to any of the

NEBT series (1000-1800 mm). The designed test specimens had almost 1/3 the full scale of

the NEBT 1800 beam. To have shear failure, which is necessary to utilize and assess the full

capacity of the FRP stirrups, the test beams should have a flexural capacity greater than the

shear capacity. To meet this criterion, a concrete T-section reinforced with high strength

seven-wire steel strands was used to overcome the compression failure of the concrete or the

yielding of the flexural reinforcement.

146

fc=39.5MPa


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Tp *£,

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NEBT1800

NEBT 1000-1800 Dim. in mm

NEBT 1400

Figure 4.20: Cross section of the New England Bulb Tee (NEBT) beams.

The test specimens had a total length of 7.0 m with a T-shaped cross section measuring

a total height of 700 mm, web width of 180 mm, flange width of 750 mm, and flange

thickness of 85 mm. The total length of test beams included 500 mm overhanging length at

each end in order to insure the proper anchorage of the longitudinal reinforcement. The shear

span of the test specimens was kept constant at 2000 mm corresponding to a shear span-to-

depth ratio of 3.33. Besides, all beams were provided with the same longitudinal

reinforcement ratio (three layers of three 15.4 mm-diameter 7-wire steel strands) to keep the

effect of dowel action and longitudinal stiffness constant. As a result, changes in the observed

147


behaviour could be attributed to the performance of stirrups and their spacing. Figure 4.21

shows the geometry and dimensions of the test specimens.

A total of seven beams reinforced with CFRP and GFRP stirrups in addition to a

reference beam reinforced with steel stirrups. Three beams were reinforced with No. 10 CFRP

stirrups with a stirrup spacing equal 300, 200, and 150 mm which represent d/2, d/3, and d/4.

Three beams were reinforced with GFRP stirrups with the same spacing as the beams

reinforced with CFRP stirrups. The control beam was reinforced with 9.5-mm steel stirrups

spaced at 300 mm (d/2). The test specimens were designated in the form of AB-X-#. The first

letter denotes the longitudinal reinforcement type (S: steel) whereas the second letter denotes

the shear reinforcement type (C: carbon, G: glass). The following number indicates the

diameter of the used FRP stirrups (in mm) and the last number refers to the stirrup spacing as

a ratio of the beam effective depth (2: the stirrup's spacing equals d/2, 3: the stirrup's spacing

equals d/3, 4: the stirrup's spacing equal d/4). Table 4.3 gives the details of the test specimens

and the corresponding material properties as well. Besides, Figure 4.22 to Figure 4.28 present

the reinforcement details of each beam.

4.4 Fabrication of Test Specimens

The T-beams were cast in a wooden formwork which was designed to cast one T-beam each

time. The large-size of the T-beam specimens was the main reason to fabricate a formwork for

one beam to be able to handle the pieces and easily assemble the reinforcing cages. The

formwork was made of double plywood layers with 19-mm thickness each and was reused for

casting a total of seven T-beams.

Due to the flexibility of the seven-wire stands which was used as longitudinal

reinforcement and the T-shaped cross-section, it was very difficult to fabricate the cages

outside the formwork and then place it inside. Thus, the fabrication of the test specimens was

initiated by assembling only the rear side of the formwork keeping the other side open for

assembling the reinforcing cage. Before assembling the cage, the form work was lubricated to

provide ease in formwork removal after casting. Two end wooden plates with prefabricated

holes corresponding to the positions of the longitudinal strands were used at both beam ends

to facilitate arranging the layers keeping the strands in their desired positions and steel strands

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157


were placed inside the formwork passing through these end holes. The top reinforcement of

the web was placed on external steel supports and the FRP stirrups were placed enclosing both

top and bottom reinforcement. Then, the stirrups were attached to the top reinforcement to

assure their locations. The lower reinforcement was arranged row by row starting from the

bottommost row by attaching each strand to the enclosing FRP stirrups. During this, small

plastic chairs were used to maintain the cover requirements. After completing the cage of the

beam web, the formwork was closed and the wood wings supporting the top slab were

installed as well as their vertical supporting wood pieces. The slab reinforcement mesh was

added and attached to the beam web using and the concrete cover was maintained using small

plastic chairs. During the fabrication of the reinforcing cage and before casting, the wires

connecting the strain gauges were grouped in three bundles to keep these wires away of the

loading points and the concrete gauge locations. Figure 4.29 shows the assembly of the rear

side of the formwork and the reinforcing cage. Figure 4.30 shows the completed reinforcing

cage and the formwork ready for casting for one beam specimen.

The concrete was cast in the beam and was internally vibrated and when casting was

completed, the surface of the concrete beam was adjusted. Figure 4.31 shows the casting of a

beam specimens and Figure 4.32 shows a beam specimen just after casting and adjusting the

concrete surface. Twelve cylinders were cast simultaneously with the beams. Immediately

after casting, the beam and the control cylinders were covered with plastic sheets to avoid

moisture loss. Twenty-four hours after casting, the cylinders and the slab sides were removed

and the beam and the representative cylinders were covered with two layers of wet burlap and

plastic sheets over the burlap as shown in Figure 4.33. After 5 days, the beam specimen was

moved out from the formwork, placed indoors, and re-covered using the wet burlap and the

plastic sheets. The burlap moisture was kept by adding water twice a day during the curing

period which lasted 14 days. After the curing, the beams were stored in the laboratory until the

day of testing. The average concrete strength at the day of beam testing was determined based

on testing four standard cylinders as given in Table 4.3 for each beam specimen. The beams

were tested after at least 28 days from the date of casting.

Before testing, each beam was coated with whitewash to enhance the crack

monitoring and photographing. Besides, one face of the beam, after painting, was marked with

vertical and horizontal lines every 200 mm to enable the crack mapping of the beam specimen

158


at different loading stages and at the failure. Finally, the instrumentation and connecting wires

and the loading routine were re-checked and the acquisition systems were adjusted for data

recording.

Figure 4.29: Assembling the reinforcing cage of a beam specimen.

Figure 4.30: Completed reinforcing cage and the formwork ready for casting.

159


Figure 4.31: Concrete casting of a beam specimen.

Figure 4.32: A concrete beam specimen just after casting and adjusting the surface.

160


Figure 4.33: Curing of the beam specimens.

4.5 Instrumentation

To monitor the behaviour of the tested beams different instruments were used to measure the

deflection at the mid-span and mid-shear span, strains in shear and fiexural reinforcement,

strains in concrete, and the shear crack widths. Instrumentation of the beams included Linear

Variable Displacement Transducers (LVDTs) for deflection and crack widths measurement,

electrical strain gauges for strain measurements. Besides, demec gauges of 250 mm length for

verifying the shear crack widths were used. Detailed illustration of the concrete strain gauges,

LVDTs for the deflection, and the demec gauges are shown in Figure 4.21. Additionally, the

locations of the strain gauges attached to the longitudinal fiexural reinforcement were detailed

in Figure 4.34 and the stirrup strain gauge locations are described in Figure 4.22 to Figure

4.28 for all tested beams.

To measure the fiexural reinforcement strains, Electrical resistance strain gauges

produced by Kyowa Electronics Instruments Co., Ltd, Tokyo, Japan and Vishay

Intertechnology, Inc., USA with 120 ohms resistance were attached to the concrete and the

161


reinforcement. The concrete gauges had a total length of 70 mm and the reinforcement gauges

had a 6-mm length. In each beam, 9 gauges were attached to the longitudinal reinforcing bars

at the mid-shear span, loading point, and the mid-span as shown in Figure 4.34 and 8 gauges

were attached to the concrete surface to measure the compressive strain at the mid-span and

the mid-shear span of the tested beams as shown in Figure 4.21. In addition, many electrical

strain gauges were also attached to the stirrups located in the shear span with replicates at the

mid-shear span to capture the stirrups' strain and the strain distribution in stirrups along the

shear span as well. The detailed positions of the stirrups' strain gauges are described in Figure

4.22 to Figure 4.28. The strain gauges were glued to the reinforcement using M-bond 200 and

to the concrete using two-compound fast setting epoxy. The strain concrete gauges were

covered by a waterproof coating to protect them from water while the reinforcement gauges

were coved by a waterproof coating and heat proof coating to protect them from water and

damage during the concrete casting and the high temperature results from concrete. Figure

4.35 and shows the instrumented steel strands while Figure 4.36 shows the instrumented FRP

stirrups.

The deflection of the beam at the mid-span was measured using two LVDTs, one at

each side of the beam, whereas the deflection at mid-shear span was measured using one

LVDT at each section to monitor the deflection profile along the beam. Figure 4.37 shows the

LVDTs installed at the mid-span of the beam and the mid-shear span. The shear crack widths

were measured using six high accuracy small LVDTs (± 0.001), which were installed in the

position of the shear cracks as soon as they appeared (three in each shear span). Moreover, to

verify the crack width, 36 Demec points were installed on each beam to measure the shear

crack widths (18 for each shear crack that corresponds to 9 gauges with a 250-mm length).

The Demec gauges for both shear spans of a beam specimen are illustrated in Figure 4.38. The

readings of these Demec gauges were captured using the digital extensometer shown in Figure

4.39. Also, two automatic data acquisition systems connected to two computers were used to

monitor loading, deflection, strains in concrete and reinforcement (stirrups and longitudinal

stands). The formation and propagation of the cracks on the beams and corresponding loads

were marked and recorded during the test. Figure 4.40 shows the two data acquisition systems

utilized in the beam testing to capture and record the instrumentation readings.

162

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163


Figure 4.35: Steel strands after attaching the strain gauges.

Figure 4.36: CFRP stirrups instrumented with strain gauges.

164


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Figure 4.38: The demec gauges installed in both shear spans of each beam.

165


i f^ v? -•• , / / - • •

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Figure 4.40: The data acquisition systems utilized in beam testing.

166


4.6 Test Setup and Procedure

The beams were tested in four-point bending over a simply supported clear span of 6000 mm

with an overhang extra length of 500 mm at each end to provide a development length and

prevent bond slip failure of the flexural reinforcing bars. To prevent the local failure under the

loading plates, two 10-mm thick rubber sheets were used under the loading plates and over the

supports as well. For the beam specimens reinforced with carbon FRP stirrups the load was

monotonically applied using two actuators of 1000 kN capacity with a load controlled rate of

5 kN/min till about 90% of the expected failure load thereafter, the load was applied at a

displacement controlled rate of 0.6 mm/min to overcome any accidental problems of the

sudden and brittle shear failure. The two actuators were connected to the same pump and they

were adjusted to work simultaneously. The two actuators were attached to a very rigid beam

that tied to two steel frames fixed to the rigid floor of the laboratory. To prevent the in-plane

translation and out-of-plane movement of the two actuators they are connected together using

a rigid beam keeping a constant distance between the two actuators and each of them is

attached to one frame using two struts. The setup was modified for the beam specimens

reinforced with glass FRP stirrups by moving the rigid beam that was connecting the two

actuators to work as a spreader beam and apply the load through one actuator of 1000 kN

capacity. The actuator's load was distributed equally on the two loading points and the loading

rate was kept the same as that was used during testing the beam specimens reinforced with

CFRP stirrups. The configurations that which were used in both cases are shown in Figure

4.41 and Figure 4.42. Besides, the photos shown in Figure 4.43 and Figure 4.44 illustrate the

details of the setup during testing one beam reinforced CFRP stirrups and other one reinforced

with GFRP stirrups, respectively. During the test, the loading was stopped when the first three

shear cracks in each shear span appeared and the initial crack widths were measured using a

hand-held microscope with a magnifying power of 50X as shown in Figure 4.45. Then, six

high accuracy LVDTs were attached (three in each shear span) to measure the shear crack

widths continuously with increasing load. Figure 4.46 shows the three LVDTs attached to one

shear span of a test specimen after the appearance of the first shear cracks. The applied loads,

deflection, and strains in concrete and reinforcement were recorded using two data acquisition

systems connected to two computers as shown in Figure 4.40.

167


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168


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steel stirrups.

169


Figure 4.43: A photograph of the test setup for the beams reinforced with CFRP stirrups.

170


Figure 4.44: A photograph of the test setup for the beams reinforced with GFRP stirrups.

171


Figure 4.45: Measuring the initial shear crack widths using the hand-held microscope.

Figure 4.46: Measuring the shear crack widths using high accuracy LVDTs.

172


4.7 Summary

The characteristics of the different materials used in this investigation were presented. The

details of the test specimens, test setups and test procedures, as well as the instrumentation

details were also presented. The characteristics of the used carbon and glass FRP stirrups were

determined using the available test methods specified by the ACI (2004). The tensile strengths

of the straight portions of the stirrups are determined using B.2 method. However, the bend

strength was evaluated using both B.5 and B.12 method. From the comparison of the bond

strength based on both methods, it was noticed that:

1. Considering the comparison between the B.5 and B.12 methods to determine the bend

strength, the test results showed that the B.12 test method underestimates the bend

strength of FRP stirrups in comparison with the B.5 test method. The bend strength

measured according to B.12 method was 30 and 40% less than that based on B.5

method for carbon and glass FRP bent bars, respectively.

2. The ISIS Canada (2006) bend strength limit of 35% of the strength parallel to the

fibres, obtained using B.5 and B.12 test methods, seems to be conservative when B.5

method is used. This limit may be kept for B.12 method and a revised value ranging

from 40 to 45% of the strength parallel to the fibres may be used for B.5.

3. Since the bend capacities obtained by B.12 test method are consistently lower than

those obtained by B.5 test method, different limits for the acceptable bend capacity

should be presented for each test method.

173

Chapter 5: Experimental Results and Analysis

CHAPTER 5

EXPERIMENTAL RESULTS AND ANALYSIS

5.1 General

This chapter presents the test results of the experimental program. The general behaviour of

the tested beams is presented in terms of flexural strains, load-deflection response and mode

of failure. The shear behaviour of the beams is also presented and discussed including shear

cracking load, applied shear force-stirrup strains relationships, applied shear force-shear crack

width relationships, shear cracking pattern, and the inclination angles of the major shear crack

at failure (in case of shear failure). The analysis of the results includes the effect of different

parameters on the shear response of beams reinforced with FRP stirrups such as, FRP stirrups

material, shear reinforcement ratio, the shear reinforcement index, and the bend strength of the

FRP stirrups relative to the strength parallel to the fibre's direction. The serviceability issue

regarding the FRP stirrups is also discussed and a stirrup strain limit at the service load is

proposed to keep the shear crack width controlled.

5.2 Test Results

Seven concrete beams reinforced with FRP and steel stirrups were fabricated and tested in the

current study. Three beams were reinforced with CFRP stirrups, three beams were reinforced

with GFRP stirrups, and one beam was reinforced with steel stirrups. The details of the test

specimens and the used material properties were presented in Chapter 4. Six beams failed in

shear due to rupture of the FRP stirrups or yielding of the steel stirrups. The seventh beam

failed in flexure due to the yielding of the longitudinal steel strands. No slip of the flexural

reinforcement was observed during any of the beam tests. A summary of the beam test results

is presented in Table 5.1. The shear cracking load, the angle of the major shear crack at the

failure, the ultimate shear strength, the maximum stirrup strain at failure, the average stirrup

strain in the straight portion at failure, the maximum strain at the bend zone of FRP stirrups

and the mode of failure are given in Table 5.1.

174


5.2.1 Deflection

Figure 5.1 shows the applied shear force-deflection relationship for beams reinforced with

CFRP stirrups, however, Figure 5.2 shows the relationship for beams reinforced with GFRP

stirrups at mid-span and at middle of the shear span. Except SC-9.5-4, all specimens failed in

shear prior to reaching their flexural capacity, and hence the failure was brittle. The entire

specimens showed similar behaviour and there was no significant difference between the

beams with different FRP stirrup spacing or even the control one with steel stirrups except the

appearance of the yielding plateau in beam SC-9.5-4 followed by flexural failure. The

presence of shear reinforcement (stirrups) restrained the shear deformation and consequently

the shear induced deflection causing the beams to behave similarly in flexure. Thus, the

variation of the stirrup's material and spacing did not have a significant effect on the

deflection of the tested beams and the flexural deformation controlled the beam deflection.

On the other hand, beam SS-9.5-2 showed a curved relationship just before failure due

to the yielding of steel stirrups that affected the deflection of the beam. Additionally, beam

SG-9.5-2 showed higher deflection values than other beams at late loading stages before

failure. This is referred to the larger shear crack width which affects, in turn, the deflection of

the beam at the mid-shear span and the mid-span.

5.2.2 Flexural strains

The relationships between the applied shear force and the flexural strains (longitudinal

reinforcement and concrete) at the mid-span of the beams reinforced with CFRP stirrups are

shown in Figure 5.3 while the relationships for the beams reinforced with GFRP stirrups are

shown in Figure 5.4. As noticed form deflection, there was no significant difference between

the tested beams except the appearance of the yield plateau in specimen SC-9.5-4 because the

shear reinforcement was able to provide shear strength higher than its flexural strength.

175


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Figure 5.1: Applied shear-deflection relationship for beams reinforced with CFRP stirrups.

600

20 40 120 140 60 80 100

Deflection (mm)

Figure 5.2: Applied shear-deflection relationship for beams reinforced with GFRP stirrups.

176


SC-9.5-4

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8000 10000 12000

Figure 5.3: Flexural strains of beam reinforced with CFRP stirrups.

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Figure 5.4: Flexural strains of beam reinforced with GFRP stirrups.

177


5.2.3 Shear cracking load

At early loading stage, flexural cracks were observed in the middle region of the beam with

constant bending moment. With further increase in the load, additional flexural cracks were

formed in the shear spans between the applied load and the support. The shear cracking load

was determined based on the following:

1. Visual observation of cracks in shear spans of the test specimens during the loading.

2. The concrete strain gauges attached to the top surface of the beam specimens at the

mid-shear span. A typical relationship between the applied shear force and the

concrete strain in the shear span is given in Figure 5.5(a) for SC-9.5-2 beam. The

observed change in the concrete strain is attributed to the appearance of the shear

cracks and the variation of the shear carrying mechanism during the different loading

stages till the beam failure.

3. The strain in the stirrups measured by the means of the strain gauges attached to the

stirrups in the shear spans of the test specimens. At early loading stages and before the

shear crack appears, there is no change in the stirrup strains. As soon as the shear crack

appears, the stirrup strain increases instantaneously and continues to increase with the

load increase. Typical relationships for the stirrup strain versus the applied shear force

from the strain gauges attached to the FRP stirrups in SC-9.5-3 and SG-9.5-4 beams

are shown in Figure 5.5(b).

4. The strain in the longitudinal (flexural) reinforcement at the mid-shear span. Like the

flexural cracks effect on the flexural strains at the mid-span of the beam, the shear

crack appearance affects the flexural strains in the longitudinal reinforcement in the

shear span. Typical applied shear force-flexural strains relationships at the mid-shear

span of the SG-9.5-2 and SG-9.5-4 are shown in Figure 5.5(c).

The shear cracking load, Vcr, is considered as the concrete contribution to the shear

carrying mechanism (Vc=Vcr). The shear cracking loads of all tested beams are presented in

Table 5.1. There was no significant difference in the shear cracking load for all the tested

beams. The slight difference in the values is attributed to the difference in the concrete

strength for each beam specimen. It can be concluded that the stirrups material and spacing

does not affect the shear cracking load of the tested beams.

178


(a) From

concrete

strains

400

350

(b) From

stirrup strains

£ . 300 Q)

O 250 u.

8 200 (0

I 150

"H. £ 100

(c) From

xural strains

450

400

5 350

o 300 O

LL v. 250 ra

OT 2 0 0 •o •1 150 a a. < 100

50

0

SC-9.S-2

Vc,=61 kN

~450

400

350

300

250

200

150

100

"50

-400 -350 -300 -250 -200 -150 -100

Concrete Strain (Microstrain)

-50

SC-9.5-3 .

Shear Cracking Loads

2000 4000 6000 8000

Stirrup Strain (Microstrain)

SG-9.5-4.

1000 2000 3000 4000


Figure 5.5: Evaluating the shear cracking loads of the tested beams.

V) •a

a. <

10000

5000

179

Cha

pter

5:

Exp

erim

enta

l R

esul

ts a

nd A

naly

sis

Tab

le 5

.1:

Sum

mar

y of

the

test

res

ults

.

Tes

t

Spec

imen

SS-9

.5-2

SC-9

.5-2

SC-9

.5-3

SC-9

.5-4

SG-9

.5-2

SG-9

.5-3

SG-9

.5-4

Shea

r

crac

king

load

1, V

cr,

kN

64

61

49

50

60

57

56

vJU

10.0

2

9.39

8.28

8.36

9.55

8.90

9.68

Ulti

mat

e

shea

r, V

exp.

kN

272

376

440

536

259

337

416

Ang

le o

f

maj

or c

rack

,

e (d

egre

e)

44

45

44

~ 46

42

44

Vap

rVex

pJbd

(MPa

)

2.76

3.48

4.07

4.96

3.40

3.12

3.85

Max

imum

stir

rup

stra

in,

Mic

rost

rain

Stra

ight

port

ion

9330

1050

0

1054

0

7910

1340

0

1360

0

1310

0

Ben

d

-

6318

6530

1609

6840

5560

J

8000

Ave

rage

stir

rup

stra

in

at f

ailu

re

5361

7725

6670

5718

8890

8260

8350

Mod

e

of

failu

re2

SY

CR

CR

Flex

ure

GR

GR

GR

Bot

h sh

ear

crac

king

load

and

ulti

mat

e sh

ear

did

not

incl

ude

the

self

wei

ght

of th

e be

am.

1 Est

imat

ed f

orm

the

slo

pe c

hang

ing

of th

e sh

ear-

conc

rete

str

ain

rela

tions

hip

and

veri

fied

usi

ng th

e st

rain

gau

ge r

eadi

ngs.

2 S

Y:

Stee

l st

irru

p yi

eldi

ng, C

R:

CFR

P st

irru

p ru

ptur

e an

d G

R:

GFR

P st

irru

p ru

ptur

e.

3 the

gau

ge r

eadi

ng a

t the

con

nect

ion

betw

een

the

stra

ight

and

ben

d po

rtio

ns.

180


5.2.4 Capacity and mode of failure

Since the test specimens were designed to fail in shear to utilize the full capacity of, the

ultimate shear strength of the test specimens was governed by the stirrup's strength (except

SC-9.5-4). Despite the difference in the load level at which shear failure of beams took place,

a similar failure mechanism was observed in all beams reinforced with carbon and glass FRP

stirrups. The observed mode of failure was shear-tension failure due to rupture of FRP stirrups

or yielding of steel stirrups for the control beam. The failure of the beam specimens was very

brittle and occurred suddenly as soon as at least one of the FRP stirrups got ruptured. The

failure of beams due to stirrup rupture was verified using the strain gauge readings for the

straight portions as well as the bend zones. Figure 5.6 to Figure 5.12 show photos for the

failure of the test specimens reinforced with CFRP, GFRP, and steel stirrups.

For the beams reinforced with CFRP stirrups that failed in shear (SC-9.5-3 and SC-

9.5-4), the failure was initiated by the rupture of the CFRP stirrups at the bend. Consequently,

the remaining components of the shear resisting mechanism could not resist the applied shear

force and the beam failed in shear. The maximum strain gauge reading for straight portions of

CFRP stirrups was 10500 microstrain which represents 89% of the material capacity.

However, the strain at the bend was about 6500 microstrain which exceeds the material

strength with a ratio of 20% which confirms the observed mode of failure. The test specimens

failed at corresponding applied shear forces equal to 376 and 440 kN for SC-9.5-2 and SC-

9.5-3, respectively. The shear reinforcement ratio provided for beam SC-9.5-4 was enough to

provide shear strength greater than the flexural strength of the beam and hence, it failed at an

applied shear force equals 536 kN by steel yielding followed by concrete crushing at mid-

span. Figure 5.13 shows a comparison of the shear strength of the beams reinforced with

CFRP stirrups and the control one.

A similar failure mechanism was observed for the beams reinforced with GFRP

stirrups (SG-9.5-2, SG-9.5-3, and SG-9.5-4) due to rupture of GFRP stirrups. The maximum

measured strain in the straight portions of the GFRP stirrups was 13367 microstrain (average

181


Figure 5.6: Shear failure of beam SC-9.5-2 (CFRP@d/2).

182


Figure 5.7: Shear failure of beam SC-9.5-3 (CFRP@d/3).

183


Figure 5.8: Flexure failure of beam SC-9.5-4 (CFRP@d/4).

184


Figure 5.9: Shear failure of beam SG-9.5-2 (GFRP@o?/2).

185


Figure 5.10: Shear failure of beam SG-9.5-3 (GFRP@d/3).

186


Figure 5.11: Shear failure of beam SG-9.5-4 (GFRP@a?/4).

187


Figure 5.12: Shear failure of control beam SS-9.5-2 (steel@<i/2).

188


z •o re o

600

500

400 4-

ffi 300 o

p 200

100

272 38%

536

440

376

62%

97%

*»5^fi

SS-9.5-2 SC-9.5-2 SC-9.5-3 SC-9.5-4

Figure 5.13: Load carrying capacity of beams reinforced with CFRP stirrups.

for the three beams) which corresponds to 91% of the tensile capacity. On the other hand, the

maximum measured strain at the bend zones was 8500 microstrain which represents 99% of

the bend capacity based on B.5 method (ACI 2004). This indicates that the material strength

of the GFRP stirrups was fully utilized in the beam specimens. This is referred to the higher

bend strength of GFRP stirrups in comparison with the strength parallel to the fibre's direction

than that of the CFRP stirrups. The bend strength for both stirrup types was 0.58 and 0.46 of

the tensile strength in the fibre's direction for GFRP and CFRP stirrups, respectively. The test

specimens failed at applied shear forces equal to 259, 337, and 416 kN for SG-9.5-2 and SG-

9.5-3, and SG-9.5-4, respectively. Figure 5.14 shows the shear strength comparison for the

beams reinforced with GFRP stirrups and the control beam as well.

The control beam that was reinforced with steel stirrups (SS-9.5-2) failed also in shear;

however, the shear failure was initiated by stirrup yielding. Then, the shear cracks started to

widen rapidly as the applied load increases due to the post yielding plastic behaviour of the

steel bars. Finally, a concrete crushing at the top flange of the beam near the loading point

occurred at 272 kN applied shear force.

To investigate the effect of the shear reinforcement stiffness on the shear capacity of

the tested beams, the failure load is plotted against the stiffness of the shear reinforcement as

189


shown in Figure 5.15. It can be seen that the higher the shear reinforcement stiffness, the

higher the shear capacity of the beam specimens. The control beam, SS-9.5-2, showed lower

shear strength in comparison with the beam reinforced with CFRP stirrups spaced at d/3, SC-

9.5-3, although they have the same shear reinforcement stiffness. This is referred to the

limited capacity of the steel stirrups in comparison with the carbon FRP ones.

•a re o

600

500

400 4-

re 300 4) £

0)

re UL

200 4-

100

416

337

272 ^ § % 259

53%

SS-9.5-2 SG-9.5-2 SG-9.5-3 SG-9.5-4

Figure 5.14: Load carrying capacity of beams reinforced with GFRP stirrups.

I

600

500

400

300

re 200 u.

100

SG-9.5-4

SG-9.5-3 , ~ ~ ~ ~

• SG-9.5-2

""a

^ ^ - • ^ SC-9.5-4

„ , ' " " ' ° SC-9.5-3

SC-9.5-2

A SS-9.5-2

• GFRP Stirrups • CFRP Stirrups • Steel Stirrups

0.05 0.1 0.15 0.2 0.25

Pfv Efrp/Es

0.3 0.35 0.4

Figure 5.15: Effect of the shear reinforcement stiffness on the beams strength.

190


5.2.5 Cracking pattern and crack spacing

The cracking of each beam was monitored during each beam testing with greater attention to

the shear cracks in both shear spans of each beam. After the appearance of the shear cracks

they were marked successively and their propagation were traced during the beam testing till

the stabilization of the cracking pattern. After the stabilization of the shear cracks, no newer

shear cracks were observed but the already existing cracks were widening with the load

increase till the beam failure. As described in Chapter 4, the crack width of the first three

shear cracks in each shear span was measured using a hand microscope for the initial value

and six high accuracy LVDTs attached to the shear spans of each beam.

Figure 5.16 shows schematically the final crack pattern of the beams reinforced with

CFRP stirrups, while Figure 5.17 shows the crack pattern of the beams reinforced with GFRP

stirrups. The final crack pattern of the control beam reinforced with steel stirrups is shown in

Figure 5.18. The failure shear plane and its inclination angle are highlighted. The failure plane

of beam SG-9.5-2 was the closest to the loading point with the steepest inclination angle. The

other two beams reinforced with higher ratios of GFRP stirrups (SG-9.5-3 and SG-9.5-4)

failed at the same location and the failure plane passed through the mid-shear span. The two

beams reinforced with carbon FRP stirrups that failed in shear (SC-9.5-2, and SC-9.5-3) failed

at the same location and the failure plan was crossing the mid-shear span but it was closer to

the loading point. The inclination angle of the critical shear plane (failure) ranged from 42 to

46° which was in good agreement with the 45° truss model.

The main difference in final crack patterns between the tested beams was the number

and spacing of diagonal cracks developed in the shear spans. The higher the failure load the

greater the number of induced shear cracks. The maximum and average shear crack spacing

were measured and plotted versus the stirrup spacing for each type of FRP stirrups as shown

in Figure 5.19. As it can be noticed from this figure, the closer the stirrups the smaller the

crack spacing. The average shear crack width for all the tested beams reinforced with FRP

stirrups were less than 300 mm which is the equivalent crack spacing parameters specified by

the CSA (2006 and 2009). Thus, for concrete sections reinforced with FRP stirrups, with

minimum shear reinforcement according to the code, the 300 mm effective crack spacing

would yield conservative shear strength prediction for the beams reinforced with FRP stirrups.

191


£ £ o o

o o

6 £

© o r-

Figure 5.16: Crack pattern at failure for beams reinforced with CFRP stirrups.

192


B

s o o

a B

© o

o o

Figure 5.17: Crack pattern at failure for beams reinforced with GFRP stirrups.

193


s B

© o

Figure 5.18: Crack pattern at failure for the control beam SS-9.5-2 (steel@d/2).

450

400

E E D) C "o re Q. </> o re i _

O L .

re o

350

300

250

200

150

u> 100

50

0.1 0.2 0.3 0.4 0.5 0.6

s/d

Figure 5.19: Shear crack spacing versus stirrups spacing relationship.

194


5.2.6 Strains in FRP stirrups

The strains in the FRP stirrups in beam specimens as well as the steel stirrups of the control

beam were measured for almost all stirrups located in both shear spans of each tested beam up

to failure using electric strain gauges as described in Chapter 4. The average strains were

calculated from the stirrups located within a distance equals to 0.7 the shear span, a, measured

from the loading point. The stirrups close to the support were excluded from the average

because their strain was very small in comparison with the remaining stirrups in the shear

span. Besides, any shear cracks intersecting these stirrups usually appear at late loading stages

close to the beam failure. The maximum strain in the stirrups measured at the ultimate load in

the straight portions and bent zones of the FRP stirrups employed in all beam specimens is

presented in Table 5.1. The average stirrup strain based on the strain gauge readings is also

given in Table 5.1. Figure 5.20 shows typical applied shear-stirrup strain relationships for

selected strain gauges attached to the straight portion of the CFRP and steel stirrups in the

shear span of the beam SC-9.5-2 and SS-9.5-2, respectively. From this figure, the higher strain

capacity of the CFRP stirrups in comparison to the steel ones can be noticed. Figure 5.21

shows typical applied shear force versus stirrup strain at bend locations for the SC-9.5-2

beam.

Although all test conditions for all beams were identical, there was a small difference

between the average stirrup strains in the two shear spans of the same beam as shown in

Figure 5.22. The average stirrup strains resulted from the shear span where the shear failure

occurred was considered. The applied shear force versus the average stirrups strain for the

beam specimens reinforced with CFRP stirrups is shown in Figure 5.23, in comparison with

the control beam. While the applied shear force versus the average stirrup strain for the beams

reinforced with GFRP stirrups is shown in Figure 5.24, in comparison with the control beam.

Generally, for the same stirrup material, the larger the stirrup spacing the higher the stirrup

strain at all the same load level. A comparison between each two beams reinforced with FRP

stirrups spaced at the same distance, d/2, d/3, and dIA is presented in Figure 5.25. Generally,

when different FRP materials with the same bond characteristics are used as shear

reinforcement at the same with the same spacing, the higher the shear reinforcement index (or

the shear reinforcement stiffness), the smaller the average stirrup strain at the same load level.

From Figure 5.25, it is clear that each beam reinforced with the GFRP stirrups showed larger

195


average stirrup strains in comparison with that reinforced with CFRP stirrups at the same

spacing.

2000 4000 6000 8000 10000


12000

Figure 5.20: Typical applied shear force-stirrup strain relationship (SC-9.5-2 and SS-9.5-2).

Q>

p

re

•a .2 "5. Q. <

| 4 5 0 -

400

3 5 0 /

300j

25tt

200^

150

100

50

6 -

B4 / ^ —

i ' ' I

^ ^ B1

B4 B3 \ P 1 • i

-A- B2 Bl i

-2000 2000 4000 6000


8000 10000

Figure 5.21: Typical applied shear force-stirrup strain at the bend of FRP stirrups (SC-9.5-2).

196


(a) SC-9.5-2

(CFRP@flf/2)

600

500

SC-9.5-2 CFRP@t//2

Average Failure Side

2000 4000 6000 8000

Average Stirrup Strain (microstrain)

10000

(b) SC-9.5-3

(CFRP@<//3)

(c) SC-9.5-4

(CFRP@rf/4)

i

Fo

rce

Sh

ear

Ap

plie

d

D U U ~

500

400

300

200 -

100

0

SC-9.5-3 CFRP@d/3

^<^^'

y\y/.y'

//V'' Average * Failure Side l . , 1 ,

600

2000 4000 6000 8000


10000

SC-9.5-4 CFRP@d/4

Average

2000 4000 6000 8000


10000

Figure 5.22: Comparisons between the average stirrup strains calculated from both shear spans

of beams reinforced with CFRP stirrups.

197


For the beams reinforced with CFRP stirrups, the maximum stirrup strain in the

straight portion of the CFRP stirrups was 10500, 10540, 7910 microstrain for SC-9.5-2, SC-

9.5-3, and SC-9.5-4, respectively. These strain values correspond to about 83, 83, and 67% of

the CFRP straight portions strength, respectively. However, the maximum strain at the bend

was 6318, 6530, and 1609 microstrain for SC-9.5-2, SC-9.5-3, and SC-9.5-4, respectively.

The small strain value for SC-9.5-4 is attributed to the fact that the beam failed in flexure due

to the high shear reinforcement ratio provided for this beam. The average strain at the bend for

two beams failed in shear was 6424 microstrain which exceeds the strain at the bend

corresponding to the measured bend strength of CFRP stirrups based on the B.5 test method

(ACI 2004) with a ratio of 17%. Thus, it can be concluded the B.5 method is capable of

simulating the behaviour of the FRP stirrups in beam specimens and accurately evaluate its

bend strength. Table 5.1 presents the maximum stirrup strain for the test specimens at failure.

For the beams with GFRP stirrups, the maximum stirrup strain in the straight portion

of the GFRP stirrup, measured at failure, was 13400, 13600, and 13100 microstrain for SG-

9.5-2, SG-9.5-3, and SG-9.5-4, respectively. These strain values correspond to about 92% of

the GFRP straight portions strength. However, the maximum strain at the bend was 8000

microstrain from the beam SG-9.5-4 which corresponds to 93% of the bend strength. This is in

good agreement with the bend strength of the GFRP stirrups determined based on the B.5 test

method (ACI 2004) which was 387 MPa (corresponding to 8600 microstrain). This confirms

the previous findings from the beam reinforced with CFRP stirrups.

From the comparison presented in Figure 5.23, it can be noticed that SC-9.5-3 (CFRP

stirrups@flf/3) and SS-9.5-2 (steel stirrups@J/2) showed the same shear-average strain

relationship. This is related to the shear reinforcement index (the shear reinforcement ratio

multiplied the elastic modulus of elasticity = pfi Efi,/Es) because both beams have almost the

same shear reinforcement index (0.256 and 0.262 for SC-9.5-3 and SS-9.5-2, respectively).

Beams with the same shear reinforcement stiffness may yield the same average stirrups strain

at the same loading level.

From the comparison presented in Figure 5.24, it can be noticed that the beam SS-9.5-

2 (steel stirrups@c//2) showed the smallest average strain values compared to the other three

beams reinforced with GFRP stirrups (SG-9.5-2, SG-9.5-3, and SG-9.5-4). This is referred to

the higher shear reinforcement index (pÊ^fE,) for that beam compared to the others

198


0)

o LL ffi

£ CO

•D

"5. Q. <

600

500

400

300

200

100

-

-

/

fir s

2501

c

0 M

icro

stra

i 40

0i

SC-9.5-4 PltrEa- = 0.342 >/CFRP@d/4 £ .

> / SC-9.5-3 p ^ L = 0.256 / ^ . ^ C F R P @ d / 3 E,

^ ^ ^ ^ - ^ S C - 9 . 5 - 2 ^ ^ = 0.171 < ^ ^ CFRP@d/2 E .

_J><C™ SC-9.5-2 Steel@d/2

Pv= 0.262

Shear reinforcement index = P* ~ ~~

I 1 1 1 1 1

1000 2000 3000 4000 5000 6000 7000

Average Stirrup Strain (Microstrain)

8000 9000 10000

Figure 5.23: Applied shear force-average stirrup strain for beams with CFRP stirrups.

z

o

« 0) .c CO •a .22 "5. a. <

600

500

400

300

200

100

SS-9.5-2 Steel@d/2

pv= 0.262

SG-9.5-4 P ( v ^ = 0.120 GFRP@d/4 E -

p„-g- = 0.090

P(v-f- = 0.060 GFRP@d/2 Es

1000 2000 3000 4000 5000 6000 7000


8000 9000 10000

Figure 5.24: Applied shear force-average stirrup strain for beams with GFRP stirrups.

199


600

(a) Stirrups@ci/2

SC-9.5-2 p S t = 0.171 CFRP@d/2 E.

SG-9.5-2 p *&- = 0.060 GFRP@d/2 E,

2000 4000 6000 8000


10000

(b) Stirrups@d/3

600

Z 500

« t 400

300 n a> £

•o = 200 a. a. <

100

2500

Mic

rost

rain

SS-9.5-2 Steel@d/2

pv = 0 . 2 6 2 , /

r*"

4000

Mic

rost

rain

. ,

SC-9.5-3 p S t = 0.256 .•-^CFRP@d/3 £ .

• ••• -~ps>—" SG-9.5-3 p £&. = 0.090 _^^-"^ GFRP@d/3 £ .

Shear reinforcement index = P*~^~

2000 4000 6000 8000


10000

600

(c) Stirrups@J/4

SC-9.5-4 p S t = 0.342 CFRP@d/4 E .

SG-9.5-4 S t = 0.120 GFRP@d/4 * E.

p. =0.262

Shear reinforcement index = P/v"

2000 4000 6000 8000


10000

Figure 5.25: Comparison between the average stirrup strains for FRP stirrups with similar

stirrups spacing: (a) spacing=(i/2; (b) spacing =d/3; and (c) spacing^M.

200


reinforced with GFRP stirrups. The average stirrup strains resulted from the SG-9.5-4 beam

(GFRP stirrups@J/4) were very close to that of the control beam till the yielding of the steel

stirrups. Although the shear reinforcement index of SG-9.5-4 was about 50% of the SS-9.5-2

(0.12 and 0.26 for SG-9.5-4 and SS-9.5-2, respectively), they showed a very close applied

shear force-average stirrups strain relationship. This is referred to the good bond performance

of the sand-coated GFRP stirrups and the closer spacing (d/4 in comparison with d/2). Thus,

providing shear reinforcement at closer spacing is better than larger spacing even the closer

spacing was achieved using low modulus FRP stirrups as the used GFRP stirrups. The closer

stirrups with smaller diameter is recommended over the bigger diameter placed at larger

spacing.

To investigate the effect of modulus of elasticity and the reinforcement ratio on the

measured average stirrup strain the relationship between the average stirrup strain and the

shear reinforcement index (pÊÎEs) was plotted as shown in Figure 5.26 at an applied

shear force equal to 190 kN. The shear load of 190 kN was selected to assure the stabilization

of the shear cracks and also keeping the strain in the steel stirrups in the control beam below

the yield point. From Figure 5.28(a), considering the same stirrup material, it can be noticed

that the higher the shear reinforcement ratio, the lower the average stirrup strains at the same

loading level. This can be generalized for different stirrup materials considering the shear

reinforcement index in comparison as shown in Figure 5.28b. From this figure it can be

noticed that the increase in the shear reinforcement index resulted in reduction in the average

strain in the FRP stirrups at the same load level. Besides, it can be noticed that the SC-9.5-3

(CFRP stirrups@<i/3) and SS-9.5-2 (steel stirrups@c//2), with the same shear reinforcement

index, showed almost the same average stirrup strain.

The maximum strains in the CFRP stirrups crossing the critical shear crack in

comparison with that of steel stirrups are shown in Figure 5.27; however, the maximum

strains in the GFRP stirrups are shown in Figure 5.28. From the comparison it can be noticed

that at any loading level the maximum strain in the FRP (carbon and glass) stirrups were

higher than that in the steel stirrup. This occurs because the comparison here is based on a

single stirrup crossing the shear crack and of course the stiffness of a steel stirrup is higher

than that of CFRP and GFRP ones. Moreover, there was no significant difference between the

maximum strains in the FRP stirrups except that in beam SC-9.5-4 with closely spaced CFRP

201


stirrup till about 7000 microstrain. After this, the GFRP stirrups showed higher strains than

that of CFRP stirrups. The effect of the low modulus of GFRP stirrups on the stirrup strain

could be clearly identified at the early loading stages by the sudden increase in the GFRP

stirrup strain after the appearance of the shear crack comparing to the CFRP stirrups.

4000

_ 3500

ost

ra

i-

» S c (0 t-

*• (O 0 5P i > <

3000

2500

2000

1500

1000

500

„SG-9.5-2

' , « SG-9.5-3

O GFRP Stirrups

• CFRP Stirrups

A Steel Stirrups SC-9.5-2

SG-9.5-4

. , SC-9.5-3 * •-

A" ' . _

SS-9.5-2 SC-9.5-4

0.00 0.05 0.10 0.15 0.20 0.25

PfvEfrp/Es

0.30 0.35 0.40

(a) Effect of CFRP and GFRP stirrup stiffness of the average stirrup strain.

4000

_ 3500 c j= 3000 (0 o .a 2500

.E 2000 m

W 1500 0)

2 1000 > <

500

• SG-9.5-2

«• ^ » SG-9.5-3

SC-9.5-2

• GFRP Stirrups • CFRP Stirrups • Steel Stirrups

SG-9.5-4

SC-9.5-3

A " » ^

SS-9.5-2 SC-9.5-4

0.00 0.05 0.10 0.15 0.20 0.25

Pfv Efrp/Eg

0.30 0.35 0.40

(b) Effect of stirrup stiffness of the average stirrup strain.

Figure 5.26: Effect of the stiffness of the shear reinforcement on the average stirrup strain.

202


600

500 SC-9.5-4 CFRP @ of/4

SC-9.5-3 CFRP @ d/3

2000 4000 6000 8000


10000 12000

Figure 5.27: Applied shear force-maximum stirrup strain relationships for CFRP stirrups in

beam specimens comparing to the steel stirrup.

600

500

z "aT 400

g 300 i

SG-9.5-4 GFRP @ d/4

SG-9.5-3 GFRP @ d/3

2000 4000 6000 8000


10000 12000

Figure 5.28: Applied shear force-maximum stirrup strain relationships for GFRP stirrups in

beam specimens comparing to the steel stirrup.

203


Corresponding to an average strain value of 2500 microstrain in the CFRP stirrups (the

maximum stain specified by the CHBDC, (CSA 2006) for the FRP stirrups at ultimate), the

applied shear force was 188, 241 and 345 kN for SC-9.5-2, SC-9.5-3, and SC-9.5-4,

respectively (Figure 5.23). These values represent 50%, 55% and 64% of the observed failure

loads of the test specimens. On the other hand, the calculated stirrup strains using Equation

(3.36) (CSA 2006) which is adopted from the JSCE (1997) were 1703, 1265 and 1107

microstrain corresponding to an average stresses of 221.5, 164.4 and 143.9 MPa which

represent 14.4%, 10.7% and 9.4% of the CFRP stirrup strength parallel to the fibre direction

and 31.1%, 23.1% and 20.2% of the bend strength of the stirrups for SC-9.5-2, SC-9.5-3 and

SC-9.5-4, respectively. Therefore, it is evident that Equation (3.36) itself, rather than its limit

(2500 microstrain), yields very small strain values especially for FRP stirrups with relatively

high modulus (as CFRP stirrups). This resulted in limiting the contribution of the CFRP

stirrups in the tested beams to an average of 11.5% of its strength parallel to fibres (or 24.8%

of its bend strength). Moreover, the average ratio between the shear strength and applied

shear, which corresponds to the equation limit (2500 microstrain), for the two beams

reinforced with CFRP stirrups and failed in shear (SC-9.5-2 and SC-9.5-3) was 1.9. This

indicates that, even using the 2500 microstrain value (the upper limit for the stirrup strain)

yielded unduly conservative prediction for the shear capacity of the tested beams.

Corresponding to an average strain in the GFRP stirrups equal to 2500 microstrain, the

applied shear forces were 173, 185 and 218 kN for SG-9.5-2, SG-9.5-3, and SG-9.5-4,

respectively (Figure 5.24). These values represent 67, 55 and 52% of the observed failure

loads of the test specimens, respectively. On the other hand, the calculated stirrup strains using

Equation (3.36) of the CHBDC (CSA 2006) are 2500 (the code upper limit), 2104, and 2013

microstrain corresponding to an average stresses of 112.5, 94.7 and 90.6 MPa, respectively.

These average stresses represent 17%, 14% and 14% of the GFRP stirrup strength parallel to

the fibre direction and 30%, 24% and 23% of the bend strength of the stirrups for SG-9.5-2,

SG-9.5-3 and SG-9.5-4, respectively. This resulted in that the predicted contribution of the

CFRP stirrups in the tested beams was limited to an average of 15% of its strength parallel to

fibres (or 26% of its bend strength). This confirms the findings from the beams reinforced

with CFRP stirrups regarding Equation (3.36) and its limit.

204


Corresponding to an average strain value of 4000 microstrain in the CFRP stirrups (the

stirrup strain specified by the ACI (2006) and CSA (2009) at ultimate), the applied shear force

was 241, 309, and 415 kN which corresponds to 64, 70 and 77% of the observed failure load

for SC-9.5-2, SC-9.5-3, and SC-9.5-4, respectively. The average ratio between the shear

strength and applied shear that corresponds to the 4000 microstrain for the two beams failed in

shear (SC-9.5-2 and SC-9.5-3) was 1.5, which is yet conservative. For the beams with GFRP

stirrups and corresponding to the 4000 microstrain, the applied shear force was 241, 309, and

415 kN that corresponds to 64%, 70% and 77% of the observed failure load for SC-9.5-2, SC-

9.5-3, and SC-9.5-4, respectively. The average ratio between the shear strength and applied

shear that corresponds to the 4000 microstrain for the three beams (SG-9.5-2, SG-9.5-3, and

SG-9.5-4) was also equals tol.5.

The strain distribution in the shear span, where failure occurred, is plotted using the

strain gauge reading versus the stirrup position for the beam specimens reinforced with CFRP

stirrups in Figure 5.29 to Figure 5.31 and for the beam specimens reinforced with GFRP

stirrups in Figure 5.32 to Figure 5.34. The average strain value at the failure for each beam

specimen is marked on those figures. It can be noticed that the strain in the stirrups along the

shear span is affected by the cracking pattern and the position of the stirrup with respect to the

crack. Some of the stirrups did not show very high stress level at early loading stages,

however as soon the shear cracks are stabilized the same stirrups showed very high stress

levels. The highest stress levels were measured in the FRP stirrups located at the middle third

of the shear span with an average strain of 7198 and 8500 microstrain for the beams

reinforced with CFRP and GFRP stirrups that failed in shear, respectively.

5.2.7 Effect of FRP stirrup spacing

In general, the behaviour of the test specimens indicated, as expected, that beams with smaller

stirrups spacing showed higher shear capacity and lower transverse strain at any given load.

Based on the traditional 45° truss model, stress in the FRP stirrup at failure, fp, was

determined from the following equation (ACI 2006) considering the reduction factor (^)

equal to 1.0:

Afid

205


where Aj\, is the area of the FRP stirrups, s is the stirrup spacing, and d is the effective depth of

the beam. Figure 5.35 shows the effective stress in carbon and glass FRP stirrups at failure

with respect to the ultimate strength parallel to the fibres, ffi,v, for the different stirrup spacings

II II II II II II

—. 14000

•fc 12000 W

2 o 10000

s tn 8000 Q. 3 .b 6000 CO £ 4000 U_ O 2000 _c

.£ o 2 W -2000

J

Average

=300 kN

=250 kN

=200 kN

=150 kN

=100 kN

200 400 600 800 1000 1200 1400 1600 1800 2000

Distance from the Support (mm)

Figure 5.29: Stirrup strain distribution along the shear span of SC-9.5-2 beam (CFRP@d/2).

206


J

14000 'jo 2 12000 V)

£ 10000 H

^ 8000 Q. 3 t 6000 0) j£ 4000 u_ ® 2000

2 0

-2000

Average

P=300 kN

P=200 kN

— i 1 *

200 400 600 800 1000 1200 1400 1600 1800 20|00



207


J

14000

g 12000

</)

I 10000

i ^ 8000 Q. 3

t 6000 V) £ 4000 U_ CD c 2000 _c jo 0 (0

-2000

Average =500 kN =450 kN

=400 kN

=300 kN

200 400 600 800 1000 1200 1400 1600 1800 2000



208


II II II II II

<-. 14000 c £ 12000 in

8 o 10000

</> 8000 Q. 3 .h 6000 +•>

CO 0- 4000 CL u_ O 2000 _c .E 0

2 35 .2000

P=250 kN

Average

}P

200 400 600 800 1000 1200 1400 1600 1800 2000


Figure 5.32: Stirrup strain distribution along the shear span of SG-9.5-2 beam (GFRP@J/2).

209


14000 1c 2 12000 (/> p J; 10000

w 8000 Q. 3 t 6000

£ 4000 u_

® 2000

2 4-1

-2000

1

Average.

P=325 kN

200 400 600 800 1000 1200 1400 1600 1800 2000



210


C

'2 •4-> </> p

a.

V) a. at o c c 2 (0

14000

12000

10000

8000

6000

4000

2000

0

-2000

J *

Gauge went offscale

Average

200 400 600 800 1000 1200 1400 1600 1800 2000



211


1.2

0.8

!jf 0.6

0.4

0.2

0

X-

f Failed in Flexure

K = (Ks,orVn-<pVcr)s

\d

* . . . . . _ . . . . . _ .^ j , . . . . v , . .

0.2 0.3

XGFRP stirrups •CFRP stirrups

0.4

s/d

0.5 0.6

Figure 5.35: Effect of stirrup spacing on effective capacity of FRP stirrups in beam action.

1.2

1

0.8

J 0.6

0.4

0.2

f A • •

Failed in Flexure

K = (VtestorVn-<t>Vcr)s

\d

0.2 0.3

-A

• CFRP stirrups

• CFRP stirrups (Shehata 1999)

0.4

S/d

0.5 0.6

Figure 5.36: Comparison of effective capacity of CFRP stirrups in beam action.

212


used in this study. The effective CFRP stirrup stress,^, at failure with respect to the ultimate

strength of the stirrups parallel to the fibres, fjuv, was 72 and 60% for the beams SC-9.5-2 and

SC-9.5-3, respectively. This effective stress for the GFRP stirrups was 105, 99, and 95% for

beams SG-9.5-2, SG-9.5-3, and SG-9.5-4, respectively. The closer the FRP stirrups the lower

the effective stirrup stresses because there is a higher probability for the diagonal shear cracks

to intersect the bend zones of the FRP stirrups, as evident in Figure 5.35. This was verified

considering three beams reinforced with CFRP Leadline stirrups, manufactured by Mitsubishi

Chemical Corporation, Japan, with a rectangular cross-section (5x10 mm) spaced at d/2, d/3,

and d/4 (Shehata 1999). For the CFRP stirrups in that study, the effective stirrup stress at

failure with respect to the ultimate strength of the stirrups, fjuv, was 76%, 67%, and 56%

corresponding to stirrup spacings equal to d/2, d/3, and d/4, respectively, which is in good

agreement with the results of the current study. The comparison between the effective CFRP

stirrup stress form the current study and that of Shehata (1999) is presented in Figure 5.36.

On the other hand, the effective stirrup stresses resulted from the GFRP stirrups were

very high in comparison with that resulted form CFRP stirrups. The main reason for the

difference between the two results (CFRP and GFRP stirrups) may be referred to bend

strength relative to the straight portion strength. The tested GFRP stirrups had bend strength of

58% of the GFRP straight portion strength while the tested CFRP stirrups had bend strength

of 46% of the CFRP straight portion strength. As a result it can be concluded that providing

shear reinforcement with bend strength, fbend, equal to at least 60% of the ultimate strength of

the straight portions enables achieving the full capacity of FRP stirrups, both straight and bend

portions simultaneously. In other words, using FRP stirrups with lower bend strength

(fbend<0.6ffilv) results in a failure governed by the bend strength and the capacity of the straight

portions of the FRP stirrups could not be utilized. Other factors that may have impact on

effective stress values are the configuration of the stirrups, modulus of elasticity, and bond

characteristics.

To evaluate the effect of stirrup's material and spacing on the concrete shear

contribution after the appearance of the first shear cark, concrete contribution, Vc, is calculated

as Vc = Va - Vsj, where Va is the applied shear and Vsj is the FRP stirrups' contribution. The

contribution of the FRP stirrups, Vs/, was calculated based on the average strain values. The

relationship between the calculated Vc and the applied shear force for the beams reinforced

213


Z

c a> c o Q. E o o D) C * : ,<2 w <u

Q£ i_ <o a>

JC (0

DUU '

500

400

300

200

100

0

^ ^ SC-9.5-4

^>^ SS-9.5-2^^— k - U

^ SC-9.5-2\

s<

^S

* — > - t

SC^9.5-3~~ 1

Vrf

Vc

•

100 200 300 400

Applied Shear Force (kN)

500 600

Figure 5.37: Shear resisting components of beams reinforced with CFRP stirrups.

600

100 200 300 400


500 600

Figure 5.38: Shear resisting components of beams reinforced with GFRP stirrups.

214


(a) Stirrups@d/2

(b) Stirrups@d/3

(c) Stirrups@d/4

guu

z" £. 500 *-» c a> c ° 400 E o o o, 300 c

isti

$ 200 S. k.

JB 100 (0

0

/ ^ SG-9.S-2

^S^^^ SC-9.5-2

s^

Vs,

Vc

I I

600

600

100 200 300 400


100 200 300 400 Applied Shear Force (kN)

500 600

500 600

100 200 300 400 Applied Shear Force (kN)

500 600

Figure 5.39: Comparison between the shear resisting components for FRP stirrups in beams

with similar stirrups spacing: (a) spacing=d/2; (b) spacing -dfh; and (c) spacing=i//4.

215


with CFRP stirrups is shown in Figure 5.37 and for the beams reinforced with GFRP stirrups

in Figure 5.38. It can be noticed that the concrete contribution component, Vc, at any load

level was higher than the shear force at the initiation of the first shear crack, Vcr. Thus, it can

be concluded that in addition to the contribution of the FRP stirrups to the shear carrying

capacity, Vsj, it enhances the contribution of the concrete by confining the cross-section and

controlling the shear cracks. A comparison between each two beams reinforced with FRP

stirrups with the same stirrup spacing is shown in Figure 5.39. From this comparison it is clear

that providing close shear reinforcement enhances well the contribution of the concrete after

the appearance of the shear cracks. With very close stirrups, even with low modulus FRP

materials as the case of GFRP stirrups with a spacing of d/4, there was no significant

difference with that beam reinforced with CFRP stirrups spaced at d/4.

5.2.8 Shear crack width

After the appearance of the first shear crack in each beam, the shear crack width was

monitored till the failure of the beam. Three shear cracks in each span were monitored and

their widths were measured. As soon as the three shear cracks appeared in each shear span,

their initial crack widths were measured using a hand held microscope and a high accuracy

LVDT was installed. However, the considered crack is the failure shear crack (the critical

shear crack). Figure 5.40 shows the relationship between the applied shear force and the shear

crack width for the three shear cracks in the failed shear span of the beam specimens

reinforced with GFRP stirrups. The applied shear force versus shear crack width relationships

for the beams reinforced with CFRP stirrups are shown in Figure 5.41, compared with the

beam with steel stirrups. The applied shear force versus shear crack width relationships for the

beams reinforced with GFRP stirrups are shown in Figure 5.42, compared with the beam with

steel stirrups. A comparison between each pair of beams reinforced with FRP stirrups with the

same spacing is presented in Figure 5.43. Generally, as shown in Figure 5.41 and Figure 5.42,

it can be noticed that the closer the FRP stirrups, the smaller the shear crack width at the same

loading level. In other words, the low values of the shear crack width were observed for

beams with a higher shear reinforcement ratio.

For the beams reinforced with CFRP stirrups, the three beams showed smaller shear

crack widths than the control beam reinforced with steel stirrups (SS-9.5-2). Although SC-9.5-

216


3 (CFRP stirrups@flf/3) and SS-9.5-2 (steel stirrups@d/2) had the same shear reinforcement

index (pfr Eft/Es), SS-9.5-2 showed larger shear crack width. This indicates that shear crack

width is not only affected by the shear reinforcement index (presented by shear reinforcement

ratio and modulus of elasticity of shear reinforcement) but also with the bond performance of

the shear reinforcement. Thus, the smaller shear crack width of SC-9.5-3 than that of SS-9.5-2

is attributed to the better bond performance of the sand-coated CFRP stirrups and their closer

spacing.

For the beams reinforced with GFRP stirrups, similar behaviour as the ones reinforced

with CFRP stirrups was observed. The closer the stirrup the smaller the shear crack width. The

applied shear versus shear crack width for the control beam (SS-9.5-2) with a reinforcement

index equals 0.262 falls between the two beams reinforced with GFRP stirrups and had shear

reinforcement indexes equal 0.09 and 0.12. Moreover, SG-9.5-3 with a reinforcement index

of 0.09 showed the same crack width as SS-9.5-2 of a shear reinforcement index of 0.262 till

the yielding of the steel stirrups. This confirms the finding of the smaller shear crack widths

due to effect of the good bond behaviour of the sand-coated FRP materials. The closer stirrups

also provide more enhancement as a direct result of the confinement and more stirrups

intersecting the critical shear plane.

Regarding the comparison between each two beams reinforced with FRP stirrups

spaced at the same distance showed in Figure 5.43, it can be noticed the beams reinforced

with GFRP stirrups spaced at d/2, d/3, and d/A showed larger crack width than those

reinforced with CFRP stirrups spaced at d/2, d/3, and d/A, respectively. Both FRP stirrups

(carbon and glass) had a sand-coated surface to enhance the bond between the FRP stirrups

and the surrounding concrete. Thus, using different FRP materials with the same bond

characteristics minimizes the effect of the bond and leads to the direct proportion between the

measured shear crack width and the shear reinforcement index (or shear reinforcement

stiffness). Besides, it also leads to the direct proportion between the measured average stirrup

strain and the shear reinforcement index as mentioned earlier in the stirrup strains section.

This confirms the effect of the bond characteristics of the FRP stirrups strains and the shear

crack width of the beams reinforced with FRP stirrups.

217


(a) SG-9.5-2

(GFRP@<//2)

SG-9.5-2 GFRP@d/2

Maximum

1.5 2 2.5 3 3.5

Shear Crack Width (mm)

4.5

500

(b) SG-9.5-3

(GFRP@J/3) I

450

400

350

300

250

200

150

100

50

0

Maximum

0.5 1.5 2 2.5 3 3.5


SG-9.5-3 GFRP@d/3

4.5

(C) SG-9.5-4

(GFRP@rf/4)

I

1.5 2 2.5 3 3.5


SG-9.5-4 GFRP@d/4

4.5

Figure 5.40: Applied shear force-shear crack width relationships for beam specimens

reinforced with GFRP stirrups: (a) SG-9.5-2; (b) SG-9.5-3; and (c) SG-9.5-3.

218


z Q)

2 it t

P (0

Ap

plie

d

500

400

300

200

100

0

SC-9.5-4 CFRP@d/4,

' 1 1 1 1 —

^ SC-9.5-3 CFRP@d/3

. SC-9.5-2 ^^s~^ CFRP@d/2

•T 1 1

SS-9.5-2 Steel@d/2

I i

0.5 1.5 2 2.5 3 3.5


4.5

Figure 5.41: Maximum shear crack width for beams reinforced with CFRP stirrups.

600

500

g 400 o u.

3 300 . c OT

•2 200 Q. a. <

100

SG-9.5-4 GFRP@d/4

. ^ ^ S G - 9 . 5 - 3 ^S^S~~Gf=RP@dl3

\ / s r f ^^^~*§G-9.5-2 / / ^ ^ £?*~* GFRP@d/2

1 1 1 1 1 1 1

SS-9.5-2 - Steel@d/2

i i

0.5 1.5 2 2.5 3 3.5


4.5

Figure 5.42: Maximum shear crack width for beams reinforced with GFRP stirrups.

219


(a) Stirrups@J/2

600

_ 500 z

8 400

3 300

V)

| 200 Q. Q. <

100 H

i

« SC-9.5-2 ^^__^-^^CFRP@d/2

^ 5 - r - "

; eS\^ " ^ _

! CjS"^ ^^^-*tG-9.S-2 Jtfr ^^-£-—" GFRP@d/2

SS-9.5-2 Steel@c//2

0.5 1.5 2 2.5 3 3.5

Shear Crack Width (m m)

4.5

(b) Stirrups@d/3

600

500 7. .* 8 i -

o u.

s £ to • o

• Q. Q.

<

400

300

200

100 1

0.5

SC-9.5-3 'CFRP@d/3

G-9.5-3 GFRP@d/3

1.5 2 2.5 3 3.5


SS-9.5-2 Steel@d/2

4.5

600

(c) Stirrups@<i/4

^ 500 \

0) o

400

g 300

V)

1 200 a a

< 100

0.5

SG-9.5-4 GFRPffid/4

1.5 2 2.5 3 3.5


__SS-9.5-2 Steel@d/2

4.5

Figure 5.43: Comparison between the maximum shear crack width for beams reinforced with

FRP stirrups at the same spacing: (a) spacing=J/2; (b) spacing =d/3; and (c) spacing=af/4.

220


From the comparisons shown in Figures 5.43 and 5.44 it can be noticed that SC-9.5-2

and SG-9.5-4 showed almost the same applied shear-crack width relationship. Thus, it can be

concluded that providing very close stirrups even with low modulus FRP materials enhances

the performance and reduces the shear crack width.

5.2.9 Serviceability limits

A flexural crack width limit is specified in most of design codes for steel-reinforced concrete

structures to protect the reinforcing bars and stirrups from corrosion and to maintain the

aesthetical shape of the structure. Unlike steel reinforcement, the FRP is non-corrodible by

nature. Thus, the serviceability limits for crack width of FRP reinforced concrete elements

may be directly related to aesthetic considerations.

For flexure, the FRP design codes and guidelines recommend a greater crack width

limit value for FRP reinforced concrete elements than steel reinforced concrete elements. The

ACI 318-05 (ACI 2005) does not consider a limiting crack width (neither flexural nor shear

crack) value but the commentary recommends a 0.41 mm limit for flexural cracks. The ACI

318-08 (ACI 2008) limits the flexural cracks to a width that is generally acceptable in practice

but may vary widely in a given structure. The JSCE (1997) specified a limiting crack width

for aesthetic consideration nevertheless corrosion of 0.5 mm. The CSA (2002; 2006) specifies

a limiting flexural crack width of 0.5 mm for exterior exposure and 0.7 mm for interior

exposure. However, there is no specified limit for shear crack width.

As there is a direct relationship between the strain in the reinforcing bars and the crack

width, the CHBDC (CSA 2006) specifies a limiting stirrup strain value of 2500 microstrain at

ultimate to keep the shear crack width controlled whereas the ACI (2006) specifies a 4000

microstrain stirrup strain at ultimate and the CSA (2002) limits the maximum design stress of

the FRP stirrups to be 0.4 of its strength parallel to the fibres direction. In lieu of a specific

limit for the shear crack width, the 0.5 mm is used in the current study as an upper limit for

comparison. All the previous limits are at the ultimate state and there is no code or guidelines

requirement for any limits at service load.

A unified strain limit of 2000 microstrain for the strain in the FRP stirrups was

recommended (Shehata 1999) to keep the shear crack width at service less than or equal to

0.5 mm. This value was proposed based on the average stirrup strain-maximum shear crack

221


width relationship and it may be very conservative because it relates the average stirrup strains

to the maximum shear crack width. The stirrup strain at the service load can be calculated

based on the 45° truss model as follows:

' fvser AfiEfid 0.002 (5.2)

where Vser is shear force at service load (N); Vcr is the concrete shear resistance (N); Ap is the

nominal cross-sectional area of FRP stirrups (mm2); d is the effective depth of tensile

reinforcement (mm); Ep modulus of elasticity of FRP stirrup (MPa); and s is the stirrup

spacing.

2000 4000 6000


8000 10000

Figure 5.44: Applied shear force-maximum stirrup strain across the critical shear crack-

serviceability requirements.

The maximum shear crack width is plotted against the maximum strain in the stirrups

crossing the shear plane failure as shown in Figure 5.44 for both beam groups reinforced with

CFRP and GFRP stirrups. The average relationship for the beams reinforced with GFRP

222


stirrups did not include the one with stirrup spacing equal to d/2 because its shear

reinforcement ratio was less than the minimum shear reinforcement specified by the CSA

(2006). At a crack width of 0.50 mm the corresponding stirrup strain was 3208 and 2900

microstrain for the beams reinforced with CFRP and GFRP stirrups, respectively. Thus, a

limit of 2500 microstrains for the FRP stirrup at service is proposed. This value provides an

average factor of safety equal to 1.25 between the measured and the proposed value for the

beams reinforced with carbon and glass FRP stirrups. The proposed limit for Equation (5.3) is

2500 microstrain and the equation can be expressed as follows:

(v -V \s

5.2.10 Effect of bend strength on the design shear capacity

As discussed earlier, providing FRP stirrups with bend strength not less than 60% of the

strength in the fibre's direction will allow achieving the capacity of the FRP stirrups in beams.

The ratios for the bend strength relative to the strength of the straight portions less than 60%

may lead the failure mode of the concrete beams to be governed by the tensile strength of the

straight portions of the FRP stirrups.

To check the effect of the bend strength of the FRP stirrups on the design shear

capacity of concrete beams reinforced with FRP stirrups, the 4000 microstrain limit specified

by the ACI (2006), CSA (2009), and AASHTO LRFD (2009) was considered as a reference.

The strain at the bend locations corresponding to 4000 microstrain average stirrup strain in the

straight portions of the stirrups is listed in Table 5.2. From Table 5.2 it can be noticed that,

when the strain in the straight portion of the FRP stirrups was 4000 microstrain, the strain at

the bend ranged from 613 to 3590 microstrain for beams reinforced with GFRP stirrups and

447 and 1785 for beams reinforced with CFRP stirrups. These values correspond to stresses

ranging from 27.59 to 206.55 MPa and from 58.11 to 161.55 MPa for GFRP and CFRP

stirrups, respectively. The maximum stress induced at the bend in the GFRP and CFRP

represented 41.7 and 32.6% of the bend strength, respectively. Moreover, these values

represent only 24.3 and 15.1 % of the FRP stirrup strength parallel to the fibres. This indicates

that the bend strength of the FRP stirrups did not govern the design strength of the concrete

members reinforced with FRP stirrups.

223


Table 5.2: The stress at the bend zone of FRP stirrups corresponding to an average strain

equals 4000 microstrain in the straight portions

Beam

SG-9.5-2

SG-9.5-3

SG-9.5-4

SC-9.5-2

SC-9.5-3

SC-9.5-4

At 4000 \\,& in straight portion

Applied shear

(kN)

193

225

257

241

309

414

Strain at the

bend (us)

613

1866

3590

447

1785

1016

Stress at the

bend (MPa)1

27.59

83.97

161.55

58.11

232.05

132.08

Stress at the

bend//w2

0.071

0.217

0.417

0.082

0.326

0.186

Stress at the

bend/fjuv

0.042

0.126

0.243

0.038

0.151

0.086

Based on strain gauge reading. 2 Jlend- Bend strength of FRP stirrups. 2 fjUv- Tensile strength of FRP stirrups in fibre's direction.

All the tests conducted on bare FRP bent bars and FRP bent bars embedded in concrete

blocks concluded that the bend strength of the FRP bent bars was lower than the tensile

strength in the fibre's direction and may be the governing parameter that limits the strength of

the FRP stirrups and bent bars. On the other hand, the behaviour of the stirrups in beams

specimens proved that the reduced bend strength of the FRP stirrups did not limit its design

limit as presented in Table 5.2 The maximum measured stress at the bend, corresponding to

the ultimate strain specified by the codes in the straight portions, was only 42% of the bend

strength of the FRP stirrups. Furthermore, the summary of the results listed in Table 5.1

showed that the maximum strain in the straight portions of the CFRP and GFRP stirrups was

very close to its ultimate value when the strain at the bend was equal to less than its ultimate

value. This confirms the independence of the shear failure of concrete beams reinforced with

FRP stirrups on the bend strength provided that the bend strength relative to the strength

parallel to the fibres is greater than or equal to 42%. It should be mentioned that the bend

strength of the single stirrups predicted using the B.5 method was in good agreement with that

predicted from the beams and it may be recommended to use this method rather than B. 12.

224


5.3 Summary

The results of the seven beams reinforced with FRP and steel stirrups tested in this

investigation were presented in this chapter. The shear behaviour of the tested beams in terms

of mode of failure and shear deformations was presented and discussed. Through this

investigation it was observed that:

1. The use of FRP stirrups as shear reinforcement for concrete members did not affect the

carried load at the initiation of the shear cracking of the tested beams. The slight

observed difference occurred due to the difference in the concrete strengths.

2. All the beam specimens failed in shear tension mode, except the beam reinforced with

CFRP stirrups every d/4, due to rupture of FRP stirrup or yielding of steel stirrups. In

the beams reinforced with CFRP stirrups, the failure was initiated by the failure of at

least one CFRP stirrup at the bend zone. The capacity of the GFRP stirrups was

achieved in the beam specimens due to high bend strength.

3. The shear deformation was affected by the shear reinforcement stiffness, stirrup

material and spacing, and the bond characteristics of the stirrups. The average stirrup

strain was directly proportional to the stiffness of the shear reinforcement. However,

the shear crack width was affected not only by the shear reinforcement stiffness but

also with the stirrup spacing and the bond characteristics. Closer spacing even with

low modulus FRP materials controls the shear crack width because the crack width

intersects more stirrups and the closely spaced stirrups provide section confinement.

4. The inclination angle of the shear crack in concrete beams reinforced with FRP

stirrups ranged from 42° to 46° which is in good agreement with the traditional 45°

truss model.

5. The design capacity of the concrete beams reinforced with FRP stirrups is not affected

by the bend strength of FRP stirrups. Corresponding to an average strain value equal to

4000 in the FRP stirrups, the stresses at the bend of FRP stirrups ranged from 7.1 to

41.7% of the bend strength, ftend, (4.2 to 24.3% of the strength if the fibres direction)

which yields a factor of safety greater than 2 between the actual stresses at the bend

and the bend strength of FRP stirrups.

6. As a serviceability requirement to control the shear crack width, the strain of the FRP

stirrups at the service load should be limited to 2500 microstrain. Keeping the stirrup

225


strain less than or equal to this proposed value yields a shear crack width below

0.5 mm which is the limit for the flexural crack width in FRP reinforced concrete

members in severe exposure.

226

Chapter 6: Analytical Study

CHAPTER 6

ANALYTICAL STUDY

6.1 General

There are many analytical models concerning the shear behaviour of reinforced concrete

members. In this study, the most common and the most recently introduced theories were used

to investigate the shear behaviour of the tested beams as well as other beams from literature.

The analysis was initiated by using the simplified shear design equations provided by the

design codes and guidelines for FRP reinforced concrete structures including the CSA (2009)

which was approved considering the experimental resulted presented in Chapter 5. Thereafter,

the analysis was extended to include other shear theories. The code prediction was conducted

to evaluate the accuracy of the current design codes and guidelines shear provisions

considering the tested beams and other 24 beams from literature.

The behaviour of the tested beams was investigated using different theories concerning

the shear behaviour of reinforced concrete members to evaluate the applicability and accuracy

of these theories. The modified compression field theory (MCFT) was employed to predict the

full response of the tested beams including shear strength, stirrup strains, and shear crack

width at different loading levels. The shear friction model (SFM) was used to predict the shear

strength of the tested beam as well. The analytical investigation was extended to include a

recently published unified shear strength model for steel-reinforced concrete beams for

predicting the shear strength of FRP-reinforced concrete beams after modifying its equations

to reflect using FRP materials instead of the steel. The proposed modifications were verified

using the tested beams as well as 73 other beams from literature. Moreover, the shear crack

width of the control beam, reinforced with steel stirrups, was predicted using an equation from

literature and a modified version of this equation was proposed for calculating the shear crack

width in concrete beams reinforced with FRP stirrups.

6.2 Predictions using Design Codes and Guidelines

The experimental results and analysis presented in Chapter 5 contributed to amending the FRP

stirrup contribution incorporated in the Canadian Highway Bridge Design Code (CSA 2006)

227


which yielded the CSA-Addendum (CSA 2009). The shear strengths of the tested beams as

well as other beams from literature were predicted using the shear provisions given by the

following design codes and guidelines which are shown in detail in Chapter 3 to evaluate their

accuracy:

1. The Japanese Society of Civil Engineering recommendations (JSCE 1997).

2. The Japanese Building Research Institute (BRI) recommendations (Sonobe et al.

1997).

3. The American Concrete Institute guidelines for design of FRP reinforced concrete

structures (ACI 2006).

4. The Italian National Research Council (CNR-DT 203) (CNR 2006)

5. The Canadian Highway Bridge Design Code (CSA 2006).

6. The Canadian Highway Bridge Design Code Update - Addendum (CSA 2009).

The predicted nominal shear strength, V„, was determined using a value of 1.0 for all

material and safety factors. As the ACI (2006) equation requires the concrete modulus of

elasticity, the measured modulus was used in the calculation. The strength of the control beam

(SS-9.5-2) was calculated using the original JSCE and BRI equations for steel reinforced

concrete, the ACI (2006) equation, and the CSA (2006) equation of steel reinforced sections.

As the test specimens were reinforced with high strength steel strands with yield strength

greater than 400 MPa, the general method for determining 0 and /? was used in CSA (2006 &

2009) shear strength prediction. The predicted shear strengths for beams reinforced with

CFRP stirrups are presented in Figure 6.1 while the shear strengths for beams reinforced with

GFRP stirrups are presented in Figure 6.2. A comparison between the Vexp/Vpred ratio using

the different design codes and guidelines is shown in Figure 6.3. The numerical values for

both beam groups as well as the control beam are listed in Table 6.1.

From Table 6.1, it is clear that both CSA (2006) and JSCE (1997) shear provisions

greatly underestimate the shear strength of the test specimens. This is due to the common

concept in calculating the FRP stirrup contribution, Vsf. The stirrup strength is limited to the

least of: (i) the bend strength of the FRP stirrups and (ii) the values obtained by Equations

(3.35) and (3.36) CSA (2006), or Equations (3.21b; c) for JSCE (1997). The calculated strains

for the beams reinforced with CFRP stirrups were 1703, 1265 and 1107 microstrain

corresponding to average stresses of 221.5, 164.4 and 143.9 MPa which represent 14.4, 10.7

228


and 9.4% of the CFRP stirrup strength parallel to the fibre direction and 31.1, 23.1 and 20.2%

of the bend strength of the stirrups for SC-9.5-2, SC-9.5-3 and SC-9.5-4, respectively. The

calculated strains for the beams reinforced with GFRP stirrups were 2500 (the code upper

limit), 2104, and 2013 microstrain corresponding to an average stresses of 112.5, 94.7 and

90.6 MPa, respectively. These average stresses represent 17%, 14% and 14% of the GFRP

stirrup strength parallel to the fibre direction and 30%, 24% and 23% of the bend strength of

the stirrups for SG-9.5-2, SG-9.5-3 and SG-9.5-4, respectively. Moreover, when high modulus

FRP materials, as CFRP, is used as shear reinforcement, the 2500 microstrain upper limit for

this equation (CSA 2006) will not be reached at all. From Equation (3.36) output, it can be

noticed that the FRP stirrup strain at ultimate the stress in the FRP stirrups was limited to an

average of 11.5 and 15% of the strength parallel to the fibres or 24.8 and 25.7 % of the bend

strength for CFRP and GFRP stirrups, respectively. The JSCE (1997) relaxed the upper limit

of Equation (3.21b) to the bend strength of the FRP stirrups; however the equation itself still

governs the design. Furthermore, comparing to the experimental results, the corresponding

applied shear force at an average FRP stirrup strain was 56 and 58%) of the shear failure load

for the beams reinforced with CFRP and GFRP stirrups, respectively. This indicates that, even

using the 2500 microstrain value (the upper limit for the stirrup strain) yielded unduly

conservative prediction for the shear capacity of the tested beams.

On contrary, keeping a constant strain value for all types of FRP stirrups as specified

by the ACI (2006) and CSA (2009), yields more reasonable yet conservative results. The

average VexpJVpred. predicted using the ACI (2006) and CSA (2009) was 1.69 and 1.67 with

corresponding standard deviation of 0.27 and 0.14, respectively. The CSA (2009) showed

16.0% COV in comparison to 8.4 % for the ACI (2006). This indicates that the CSA (2009) is

capable of predicting well the FRP stirrup contribution to the shear capacity for RC members

reinforced with FRP stirrups. The applied shear force corresponding to the 4000 microstrain

was 70 and 68% of the failure shear load for the beams reinforce with CFRP and GFRP

stirrups, respectively, which is yet conservative.

Regarding the inclination angle of the shear crack, it can be noticed that the CSA

2006) under-estimates this angle. On the other hand, using the 4000 microstrain stirrup strain

at ultimate as specified in the CSA (2009) resulted in enhancing the predicted inclination

angles as shown in Table 6.1.

229


The BRI (1997) provided also a conservative prediction for the shear strength of the

tested beams. But the conservativeness level was also high. The ratio of VexpJVprec/, was 2.21

with a corresponding standard deviation of 0.27 and COV of 12.2%. The better prediction for

the BRI equations over the JSCE (1997) and CSA (2006) was referred to its dependence on

the experimentally measured bend strength for the used FR stirrups.

The CNR (2006) predicted well the shear strength of the test specimens. This is due to

the reduced tensile strength utilized in evaluating the FRP stirrup contribution, Vrd- It equals

$fdI'"¥f $ w n e r e ffd 1S the design strength of FRP and yflj)=2.Q. Disregarding the material

safety factor ffd will equal to f/uv/2 which means that the stress in the FRP stirrups at ultimate

state equals to 50% their strength in the fibre direction. From the experimental results, the

average stress in the carbon and glass FRP stirrups at failure was about 58% of the strength in

the fibre direction, measured using the strain gauge readings listed in Table 5.1. It is obvious

not that the CNR (2006) limit for the stress in FRP stirrups at ultimate was very close to the

experimentally measured bend strength of the FRP stirrups. Thus, the CNR (2006) predicted

well the shear strength of concrete members reinforced with FRP stirrups.

To further investigate the accuracy of the codes and guidelines shear strength

prediction, a data set includes 24 other beams reinforced with FRP stirrups were analysed in

addition to the six specimens tested in this study. The results are presented in Table 6.2. A

comparison between the predicted and experimental values for the shear strength using JSCE

(1997) and CSA (2006) is shown in Figure 6.4 while a comparison using the ACI (2006) and

CSA (2009) is shown in Figure 6.5. The experimental results to the predicted using CNR

(2006) are shown in Figure 6.6. From Table 6.2 and the previous comparisons the findings

regarding the well predicted shear strength using CSA (2009) as well as the highly

conservative prediction for JSCE (1997) and CSA (2006) are confirmed.

From Figure 6.6 it can be noticed that the CNR (2006) predicted well, on average, the

nominal shear strength of RC members reinforced with FRP stirrups. On the other hand, the

CNR (2006) predictions showed some unconservative points for some beams from literature.

However, this is the nominal shear strength, but slightly higher factor of safety for shear

design would be of interest and may improve the reliability of this equation. Furthermore, to

assure the design shear strength of the test specimens listed in Table 6.2, the material factors

of safety are considered and the data set was re-analysed. The average ratio between the

230


experimental and the predicted values, VexpJVpred, was 1.71 with a standard deviation equal to

0.4 and a relatively high coefficient of variation equal to 23.5%.

600

SC-9.5-2 SC-9.5-3 SC-9.5-4

Figure 6.1: Predicted shear strength of beams reinforced with CFRP stirrup.

600

500

z ^^ >» +^ 'o re Q. (0 O ^ re o

400

300

200 (0

100

SG-9.5-2 SG-9.5-3 SG-9.5-4

Figure 6.2: Predicted shear strength of beams reinforced with GFRP stirrup.

231


4.0

3.5

3.0

2.5

1 ^ 2 . 0

J 1.5

1.0

0.5

0.0

JSCE(1997) Average=2.85±0.48 3,4 3.33-

2.99

2.59 2.63

2.17

SC-9.5-2 SC-9.5-3 SC-9.5-4 SG-9.5-2 SG-9.5-3 SG-9.5-4

4.0

3.5

3.0

2.5

! ^ 2 . 0

J 1.5

1.0

0.5

0.0

BRI (1997) Average=2.21±0.27

2;27 2.24 1.94 ^ • 201 m

_. Pf

I l l

IB

• i up m*

M

2.70

IP

| | - .

SC-9.5-2 SC-9.5-3 SC-9.5-4 SG-9.5-2 SG-9.5-3 SG-9.5-4

(a)JSCE(1997) (b) BRI (1997)

SC-9.5-2 SC-9.5-3 SC-9.5-4 SG-9.5-2 SG-9.5-3 SG-9.5-4 SC-9.5-2 SC-9.5-3 SC-9.5-4 SG-9.5-2 SG-9.5-3 SG-9.5-4

(c) ACI (2006) (d) CNR 203 (2006)

4.0

3.5

3.0

2.5

CSA (2006) Average=2.34±0.33

2.72 2.68

4.0

3.5

3.0

2.5

CSA (2009) Average=1.67±0.14

SC-9.5-2 SC-9.5-3 SC-9.5-4 SG-9.5-2 SG-9.5-3 SG-9.5-4

1 ^ 2 0 f V . 8 4 1 . 6 1 ™ 9 " S

S? 1.5

1.0

0.5

0.0

-1.87.

• I . • • • III II I SC-9.5-2 SC-9.5-3 SC-9.5-4 SG-9.5-2 SG-9.5-3 SG-9.5-4

(e) CSA (2006) (f) CSA (2009)

Figure 6.3: Comparison between measured and predicted shear strength.

232

Cha

pter

6:

Ana

lyti

cal

Stud

y

Tab

le 6

.1: P

redi

cted

she

ar s

tren

gth

of te

st s

peci

men

s.

Bea

m

SS-9

.5-2

SC-9

.5-2

SC-9

.5-3

SC-9

.5-4

SG-9

.5-2

SG-9

.5-3

SG-9

.5-4

Exp

erim

enta

l

'exp

.

(kN

)

272

376

440

536

259

337

416

d

(deg

ree)

44

45

44

~ 46

42

44

Ave

rage

1

SD

CO

V

JSC

E

(199

7)

'exp

/ 'p

red.

1.18

2.59

2.99

>3.

4

2.17

2.63

3.33

2.85

0.48

16.7

BR

I

(199

7)

'exp

/ 'p

red.

1.28

1.94

2.09

>2.2

7

2.01

2.24

2.70

2.21

0.27

12.4

CN

R 2

03

(200

6)

'exp

/ 'p

red.

0.98

1.12

1.03

0.99

1.27

1.32

1.46

1.20

0.18

15.0

AC

I

(200

6)

'exp

.' 'p

red.

1.05

1.58

1.44

>1.4

1

1.74

1.9

2.09

1.69

0.27

16.7

CSA

(20

06)

'exp

.' 'p

red.

1.14

2.32

2.72

>2.

68

1.85

2.12

2.34

2.34

0.33

17.5

6 (d

egre

e)

41.0

37.5

37.5

35.5

36.2

34.2

34.8

CSA

(20

09)

'exp

.' 'p

red.

1.14

1.64

1.61

>1.

44

1.69

1.75

1.87

1.67

0.14

8.3

9 (d

egre

e)

41.0

40.5

42.7

40.9

36.9

35.3

36.2

Ave

rage

for

bea

ms

rein

forc

ed w

ith F

RP

stir

rups

.

233

Cha

pter

6:

Ana

lyti

cal

Stud

y

Tab

le 6

.2:

Shea

r st

reng

th p

redi

ctio

n of

bea

ms

rein

forc

ed w

ith F

RP

stir

rups

.

Ref

eren

ce

Cur

rent

stu

dy

She

hata

(199

9)

Als

ayed

(199

7)

Nak

amur

a et

al. (

1995

)

Dim

ensi

ons

b

(mm

)

180

180

180

180

180

180

135

135

135

135

135

135

200

200

200

d

(mm

)

600

600

600

600

600

600

470

470

470

470

470

470

310

250

250

a/dx

3.30

3.30

3.30

3.30

3.30

3.30

3.72

3.72

3.72

3.72

3.72

3.72

2.36

3.00

3.00

fc

(MPa

)

42.2

35.0

35.8

39.5

41.0

33.5

54.0

54.0

51.0

54.0

33.0

33.0

35.7

34.7

34.4

Flex

ural

Rei

nfor

cem

ent

Psl

(%)

1.17

1.17

1.17

1.17

1.17

1.17

1.32

1.32

1.32

1.32

1.32

1.32

0.99

1.72

1.72

Est

(GPa

)

200

200

200

200

200

200

200

200

200

200

200

200

200

180

180

Shea

r R

einf

orce

men

t

Typ

e2

C

C c G

G

G

C

C

C

G

G

G

G

G

G

Pjv

(%)

0.26

0.39

0.53

0.26

0.39

0.53

0.24

0.36

0.47

0.71

1.05

1.40

0.40

0.23

0.23

fjuv

(MPa

)

1538

1538

1538

664

664

664

1800

1800

1800

713

713

713

565

544

649

(GPa

)

130

130

130

45

45

45

137

137

137

41

41

41

42

31

31

v exp.

(kN

)

376.

0

440.

0

536.

0

259.

0

337.

0

416.

0

277.

5

341.

0

375.

5

292.

0

312.

0

311.

5

144.

4

96.4

106.

3

'exp

/ 'p

red.

JSC

E

1997

2.59

3.00

3.40

2.17

2.63

3.33

2.81

3.18

3.33

3.03

3.50

3.30

1.95

1.46

1.61

CN

R

2006

1.12

1.03

0.99

1.27

1.32

1.46

1.24

1.17

1.07

1.18

1.05

0.83

1.14

1.15

1.19

AC

I

2006

1.54

1.39

1.36

1.74

1.90

2.09

1.94

1.84

1.69

2.18

1.94

1.58

1.65

1.66

1.83

CSA

2006

2.32

2.72

2.68

1.85

2.12

2.34

2.48

2.84

3.03

2.65

3.12

2.97

1.70

1.51

1.66

CSA

2009

1.64

1.61

1.44

1.69

1.75

1.87

1.95

1.98

1.93

2.16

2.03

1.74

1.42

1.40

1.54

234

Cha

pter

6: A

naly

tica

l St

udy

Tottori et al.

(199

3)3

200

200

200

200

200

200

200

200

200

200

200

200

150

150

200

250

250

285

285

285

285

285

285

325

325

325

325

250

260

250

3.00

3.00

2.11

2.11

3.16

3.16

3.16

4.21

3.23

3.23

4.31

4.31

2.50

3.08

3.20

35.6

35.8

37.2

37.2

35.3

35.3

35.3

31.4

42.2

71.6

50.6

65.7

29.4

38.8

40.7

1.72

1.72

4.07

4.07

4.07

4.07

4.07

4.07

0.86

0.86

0.86

0.86

2.06

2.98

4.65

180

180

206

206

206

206

206

206

192

192

192

192

206

206

206

G

G

V

V

V

V

V

V

V

V

V

V c A

A

0.14

0.14

0.54

0.27

0.54

0.27

0.18

0.27

0.41

0.41

0.41

0.41

0.12

0.13

0.38

544

649

602

602

602

602

602

602

602

602

602

602

1283

1766

1278

31

31

36

36

36

36

36

36

36

36

36

36

94

53

64

79.8

79.8

230.5

221.7

169.7

137.3

117.7

115.8

157.9

165.8

150.1

153.0

105.9

84.9

191.8

Average

S.D.

COV %

)

1.25

1.25

1.94

2.07

1.46

1.31

1.21

1.15

2.10

2.02

1.91

1.88

1.92

1.24

1.63

2.19

0.78

35.7

1.10

1.05

1.45

1.96

1.08

1.24

1.24

1.10

1.07

0.90

0.95

0.87

1.61

0.92

1.04

1.16

0.23

19.97

1.51

1.51

1.97

2.33

1.46

1.46

1.36

1.27

1.85

1.78

1.71

1.67

2.03

1.51

1.63

1.71

0.26

15.2

1.31

1.31

1.81

2.02

1.48

1.39

1.25

1.30

2.05

1.88

2.06

1.99

1.86

1.60

2.40

2.06

0.56

27.5

1.25

1.25

1.57

1.85

1.28

1.26

1.18

1.18

1.77

1.69

1.81

1.78

1.65

1.49

2.02

1.64

0.28

16.9

a/d:

she

ar s

pan-

to-d

ept

ratio

. 2 A

=A

FRP;

C=

CFR

P; G

=GFR

P; V

=VFR

P (V

ynyl

on).

3 D

etai

ls o

f te

st s

peci

men

s ob

tain

ed f

rom

She

hata

(19

99).

235


i

ouu.u ~

500.0

400.0

300.0

200.0

100.0

0.0

•

A A

• •

• A

1 A y

• yS

^ 1 1

JSCE (1997) yS

• From Literature • Current Study

I !

100 200 300 400

Vpred. (kN)

500 600

I

600.0

500.0

400.0

300.0

200.0

100.0

0.0

A

A A

• A

• • *

A / • • yS

• /

* i i

CSA (2006) y /

— i

• From Literature A Current Study

100 200 300 400

Vpred. (kN)

500 600

Figure 6.4: Experimental to predicted shear strength using JSCE (1997) and CSA (2006).

236


i

\>\I\J.\I -

500.0

400.0

300.0

200.0

100.0

0.0

*

•

< 4t

i

•

A

• • y

A

•

i

• A

A

i

A C A ( 2 0 0 6 ) y /


i i

100 200 300 400

Vpred. (kN)

500 600

1

600.0

500.0

400.0

300.0

200.0

100.0

0.0

* • •

CSA (2009)


100 200 300 400

Vpnd. (kN)

500 600

Figure 6.5: Experimental to predicted shear strength using ACI (2006) and CSA (2009).

237


£

600.0

500.0

400.0

300.0

200.0

100.0

0.0

CNR (2006)

• From Literature • Current Study

100 200 300 400

Vpred. (kN)

500 600

Figure 6.6: Experimental to predicted shear strength using CNR DT-203 (2006).

6.3 Predictions using MCFT

The Modified Compression Field Theory, MCFT, (Collins and Vecchio 1986) is described in

detail in Section 2.4.6. As described, it is a rational theory to predict the response of any

reinforced concrete element subjected to axial and shear stresses. The MCFT uses equilibrium

and compatibility equations and the stress-strain relationship for concrete and reinforcement to

determine the average stresses, the average strains, and the crack angle at any load level. The

MCFT analysis of the tested beams was conducted using the Response 2000 (R2K) (Bentz

2000). Both member response analysis and sectional analysis were used in Response 2000 to

predict the behaviour of the beams. Unlike steel reinforcement, the FRP stirrups have two

different characteristic values: the tensile strength parallel to the fibre direction (straight

portions) and the bend strength. When the section response analysis was used, the bend

strength was defined as the governing ultimate stress for the GFRP stirrups. This assumption

was based on the experimentally observed strain values. The bend strength of the CFRP

stirrups was achieved while the corresponding stress in the straight portions was not reached

238


while the bend strength of the GFRP stirrups was achieved and the corresponding stress in the

straight portions was very close to its ultimate value. On the other hand, when the full member

response was used, the ultimate strength of the straight portion of the GFRP stirrups was

defined as the governing material strength. A comparison between the predicted and

experimental values using both methods is presented in Figure 6.7. From this figure it can be

seen that both methods are capable of predicting the shear strength of the beams reinforced

with FRP stirrups however, the full member response yielded a conservative shear strength

with an average VexpJVpred. equals 1.10 ± 0.09 and a corresponding coefficient of variation

equals 8%. The average Vexp)Vpred. resulted from the sectional analysis was 0.98 ± 0.06 with a

corresponding coefficient of variation equals 6%. It is worth mentioning that when the

sectional analysis method is used, it is important to select the section at which the calculations

are performed. This is controlled through the Moment/Shear (M/V) ratio because both the

initial values for moment, M, and shear, V, are user input data. Bentz (2000) recommended

using the section located at a distance dv from the loading point, which was used in this study.

1.60

1.40 —

1.20

B Full Member Response Average = 1.10 ± 0.09

0 Sectional Analysis Average = 6.98 ± 6.06 1.27

SC-9.5-2 SC-9.5-3 SC-9.5-4 SG-9.5-2 SG-9.5-3 SG-9.5-4

Figure 6.7: Measured shear strength versus the predicted using the MCFT.

The stresses in the FRP stirrups at failure were verified using the beams reinforced

with GFRP stirrups. When the full member response was employed the limiting stress of the

stirrups was entered as 664 MPa and from the results corresponding to the failure shear load

239


the average stress in the GFRP stirrups was 325 MPa while the stress in the GFRP stirrups at

the intersection with the shear crack was 664 MPa (the stirrup capacity). On contrary, in the

sectional analysis and corresponding to stress equals 387 MPa in the GFRP stirrups, the stress

in the GFRP stirrups exceeded the 664 MPa at the intersection with the shear crack which is

the straight portion strength.

The effect of the FRP stirrup spacing is investigated using the predicted shear strength

of the beams reinforced with FRP as shown in Figure 6.8. From this figure, the previous

finding regarding the FRP stirrup spacing is confirmed. The closer the FRP stirrups, the lower

the effective stirrup stress in the FRP stirrup. Thus, the MCFT is capable of predicting the

effect of the stirrup spacing on the shear strength of the beams reinforced with FRP stirrups.

1.2

0.8

«£ 0.6

0.4

0.2

. - • " * "

• -

A f-"•'

~ Failed in Flexure

" ,f (VtestorVn-tVcr)s

I

. . - - •

- -X- - GFRP stirrups - Exp.

- • • - CFRP stirrups - Exp.

- -•• - GFRP stirrups - MCFT

- -A- - CFRP stirrups-MCFT

i i

0.2 0.3 0.4

s/d

0.5 0.6

Figure 6.8: Effect of stirrup spacing of the effective FRP stirrup capacity using MCFT.

The applied shear force versus the average stirrup strains as predicted by the MCFT in

comparison with the measured values are shown in Figure 6.9 for the beams reinforced with

CFRP stirrups and Figure 6.10 for the beams reinforced with GFRP stirrups. It is evident from

those figures that there is good agreement between the measured average FRP stirrup strains

and the predicted values using the MCFT.

240


(a) SC-9.5-2

(CFRP@J/2)

guu -

S 500 0) o o 400 LL.

| 300 (A

I 200 Q. Q. < 100

0

s ^ -

**

I

MCFT. .

• I

SC-9.5-2 CFRP@d/2

' Experimental

2000 4000 6000 8000


10000

(b) SC-9.5-3

(CFRP@<//3)

svu

\ 500

Sh

ear

Forc

e

i i

"S 200 Q.

< 100

0

MCFT . y ^ ^ ^

-^Êxper imenta l

f*^"

SC-9.5-3 CFRP@d/3

600

500

(c) SC-9.5-4

(CFRP@J/4)

ir F

orce

S

he:

Ap

plie

d

400

300

200

100

2000 4000 6000 8000


10000

Experimental

.' MCFT

SC-9.5-4 CFRP@o74

2000 4000 6000 8000


10000

Figure 6.9: Comparison between measured average stirrup strain and the predicted using the

MCFT for beams reinforced with CFRP stirrups.

241


(c) SG-9.5-4

(GFRP@e?/4)

600

500

(a) SG-9.5-2

(GFRP@c//2) ir

Forc

e Sh

e;

App

lied

400

300

200

100

600

500

(b) SG-9.5-3

(GFRP@d/3)

ir F

orce

Sh

e:

App

lied

400

300

200

100

600

£ 500 o o 400

J 300

| 200 Q. Q. < 100

SG-9.5-2 GFRP@d/2

Experimenta

2000 4000 6000 8000


10000

SG-9.5-3 GFRP@d73

Experimental MCFT

2000 4000 6000 8000


10000

-

-

-

r i

SG-9.5-4 GFRP@d/4

E x p e r i m e n t a l

^ " * \ . - - ' MCFT

1 1 1

2000 4000 6000 8000


10000

Figure 6.10: Comparison between measured average stirrup strain and the predicted using the

MCFT for beams reinforced with GFRP stirrups.

242


The shear crack width can be calculated based on the MCFT using Equations (2.31) to

(2.34). This procedure is implemented in the Response 2000 which was used to analyze the

test specimens. The predicted shear crack width of the control beam reinforced with steel

stirrups using MCFT compared to the measured is shown in Figure 6.11. From this figure it

can be noticed that the shear crack width resulted from the MCFT was in good agreement with

the experimentally measured one. Thus, it can be concluded that the MCFT was capable of

predicting well the response of the steel reinforced concrete beams.

On the other hand, the shear crack width calculated based on the MCFT analysis for

beams reinforced with CFRP stirrups are shown in Figure 6.12 while the calculated shear

crack width for beams reinforced with GFRP stirrups are shown in Figure 6.13. Although the

MCFT predicted well the shear strength of the beams reinforced with FRP beams and the

average stirrup strain, it was not able to accurately predict the shear crack width. It over

estimated the shear crack width for all beams reinforced with FRP stirrups except SG-9.5-2

(GFRP stirrups@t//2) which was provided with very small effective reinforcement ratio

(p., EfvJEs). This may be referred to the crack spacing estimation which is governed by the

crack spacing parameters as illustrated in Equations (2.31) to (2.34).

2 500

a. 400 o li

ra 300

•a 200 a>

a. 100 <

o J t/

MCFT

EXP.

SS-9.5-2 Steel@d/2

1 2 3 4


Figure 6.11: Measured shear crack width versus predicted using MCFT for the control beam

SS-9.5-2.

243


600

z .* *••*

a> y o u. a> £ (0 •o a>

ppl

500

400

300

200

100

EXP.

MCFT

SC-9.5-2 CFRP@d/2

- | 1 1 r~

1 2 3 4


a> o

600

500

400

S 300 H

V) •a 200

a. 100

EXP.^s

J?* ' j r 7 , 'n/ICFT

Jy'' _ Jr

1- 1 1

SC-9.5-3 CFRP@d/3

1 2 3 4


SC-9.5-4 CFRP@d/4

0 1 2 3 4 5


Figure 6.12: Measured shear crack width versus predicted using MCFT for beams reinforced

with CFRP stirrups.

244


600

Z

600

500

£ 400 o u.

S 3 0 0

•o .£ "a. a. <

200

100


EXP.

. - MCFT

SG-9.5-3 GFRP@d/3

1 2 3 4


Z 500

a> a 400 o u. <5 300 V

" 200 0)

S 100 <

o -I

E X P . ^ .

y ^ " ^ , * MCFT

1 1

SG-9.5-4 GFRP@d/4

i 1

0 1 2 3 4 5


Figure 6.13: Measured shear crack width versus predicted using MCFT for beams reinforced

with GFRP stirrups.

245


6.4 Shear Friction Model (SFM)

The detailed shear friction model (SFM) is illustrated in Section 2.4.10. In the SFM model, the

stirrups and the longitudinal reinforcement are assumed to provide a clamping force and

consequently increasing the friction force which can be transferred across the potential failure

crack. To determine the shear strength of a concrete beam all possible failure planes between

the inside edge of the support plate and the inside edge of the loading plate should be checked.

The plane with the lowest calculated shear strength yields the shear strength of the beam.

According to the SFM, the shear resistance associated with a potential failure plane is

calculated as follows:

V ^- = Q.5k2

Cw

where Cw is the force in concrete web considering the total beam depth h (Cw= f'c bwh), T is

the tensile force in the longitudinal reinforcement at a shear force equal to Vn, 6 is the

inclination angle of the potential failure plane, k is the shear friction factor (k = 2.1/c"04), Tp

is the ultimate load carrying capacity of the stirrups crossing the potential failure plane, bw is

the beam web width. A complete illustration of the internal forces at a potential failure plane

is shown in Figure 6.14.

The SFM requires checking all possible failure planes between the inside edge of the

loading plate and the inside edge of the supporting plate. For the test specimens reinforced

with CFRP stirrups the potential failure planes are shown in Figure 6.15 while the potential

failure planes for the test specimens reinforced with GFRP stirrups are shown in Figure 6.16.

The analysis procedure was performed for each potential failure plane using the following

steps:

1. For the selected failure plane, determine its angle, 6.

2. Calculate the characteristic force C, = f' b h considering the area of the web and

neglecting the effect of the flange of the tested T-beams.

3. Determine the shear friction factor k = 2.1/J"04

4. Determine the strength of the stirrups corresponding to the potential failure plane. A

lower limit for the development of the FRP stirrups equal to 5 times the stirrup

diameter is assumed (/</=5 db). Corresponding to this limit, the strength of the FRP

246

10.25k2C • + cor6>-cot<9 (l + cot ' f lJ-^-cotf l + f < ™ (6.1)

C.„ C f w J c


stirrups should be equal to the bend strength of the FRP stirrups. This assumption was

important in lieu of enough data about the strength of the used FRP stirrups with

development lengths less than 5 db. However, if the potential failure plane intersects

with the FRP stirrup at a development length greater than 5 db, the strength of the FRP

stirrups would be considered as the strength in the direction of the fibres.

5. Determine the contribution of the FRP stirrups as Tfv = Âfv ffv where Âfv is the

total area of the FRP stirrups crossing the potential failure plane, andj^, is the strength

of the FRP stirrups determined in step 4.

6. Determine the tensile force in the longitudinal reinforcement, T. The tensile force, T,

can be determined considering the moment equilibrium at the intersection point

between the potential failure plane and mid-height of the beam flange (see Figure

6.14). This would yield the following equation for T:

x (x, + (x, +s) + (x, + 2s)) T = ^Vn-

y ' V ' ; V ' }1A f (6.2) ya y«

where xa,yct, xi, and s are illustrated in Figure 6.14.

7. The previously calculated values in steps 1 to 6 are substituted in Equation (6.1).

Solving the equation yields the shear strength, Vn, corresponding to the considered

potential failure plane.

The results of the SFM for the tested beams reinforced with FRP stirrups are

summarized in Table 6.3. Table 6.3 gives the values for the different parameters

corresponding to each failure plane as well as the predicted shear strength, V„, and predicted

mode of failure. A comparison between the experimentally measured shear strength and

predicted shear strength of the tested beams using SFM is shown in Figure 6.17. The

governing potential failure plane with the lowest Vn is highlighted in Figure 6.15 and Figure

6.16 and marked with bold letter in Table 6.3.

247


^

w&w&K^

Jf——Tf—-—^h

\Afrfjv

Afrffi,

Figure 6.14: Internal forces at a potential failure plane using SFM.

From the comparison shown in Figure 6.17, it can be noticed that the SFM model

predicted the shear strength of beams reinforced with FRP stirrups with a reasonable accuracy.

The average Vexp/Vpred. ratio was 0.9 with a standard deviation of 0.1 and a COV of 11%. The

slightly high predicted shear strength of beam reinforced with FRP stirrups is referred to the

assumed lower limit of 5 db for the development length of the FRP stirrups. As evident from

Table 6.3, the SFM estimated well the shear crack angle and the number of the FRP stirrups

crossing the failure plane.

The failure of the beam specimens as predicted using the SFM was governed by the

bend strength of the FRP stirrups because the potential failure crack intersects the FRP

stirrups at the bend as shown in Figure 6.15 and Figure 6.16. The effect of the FRP stirrup

spacing of the effective stress in the FRP stirrups is investigated using Equation (5.1). The

relationship between the stirrup spacing and the effective stirrup stress predicted using the

SFM for the beams reinforced with CFRP stirrups is shown in Figure 6.18. As observed from

the experimental results, the closer the FRP stirrups the lower the effective stirrup stresses.

Thus, the effect of the FRP stirrup spacing on the shear strength of the beams reinforced with

FRP stirrups can be predicted using the shear friction model (SFM).

248


B B o o r-

CFRP Stirrups @ d/3

SC-9.5-3 Observed Predicted

o o

o o

Figure 6.15: Potential failure planes for beams reinforced with CFRP stirrups for SFM

analysis.

249


Observed Predicted

o © r-

GFRP Stirrups @ d!2>

Observed Predicted

o

GFRP Stirrups @ dIA

SG-9.5-4 Observed Predicted

o o

Figure 6.16: Potential failure planes for beams reinforced with GFRP stirrups for SFM

analysis.

250

Cha

pter

6:

Ana

lyti

cal

Tab

le 6

.3: S

hear

fri

ctio

n an

alys

is o

f te

sted

bea

ms

rein

forc

ed w

ith F

RP

stir

rups

.

Tes

t

Spec

imen

SC-9

.5-2

SC-9

.5-3

r kN

5317

.2

4410

Shea

r

fric

tion

fact

or, k

0.47

0

0.50

7

Failu

re

plan

1 2 3 4 5 6 7 8

Tes

t

1 2 3 4 5 6 7

Ang

le o

f

the

plan

e,

d 73

51

37

41

44

44

44

43

44

61

49

40

45

42

45

45

FRP

stir

rup

cont

ribu

tion

No.

of

stir

rups

1 2 3 2 2 2 2 3 2 2 3 4 3 3 3 3

ZA

jy

mm

2

71.2

6

142.

52

213.

78

142.

52

142.

52

142.

52

142.

52

213.

78

142.

52

213.

78

285.

04

213.

78

213.

78

213.

78

213.

78

ffi

MPa

712

712

712

712

712

712

712

712

712

712

712

712

712

712

712

Tv

kN

101.

47

202.

95

304.

42

202.

95

202.

95

202.

95

202.

95

304.

42

202.

95

304.

42

405.

90

304.

42

304.

42

304.

42

304.

42

Shea

r

stre

ngth

,

F„,

kN

1061

515

451

415

456

477

486

577

376

672

542

516

500

472

539

567

Mod

e of

failu

re

SR

SR

SR

SR

SR

SR

SR

SR

SR

SR

SR

SR

SR

SR

SR

SR

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Figure 6.17: Measured shear strength versus predicted using SFM.

J2

1 .£.

1

0.8

0.6

0.4

0.2

0

. . . A - - " . ; ; ' .

A'"" *" / Failed in Flexure

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- -&• - CFRP stirrups - SFM

0.2 0.3 0.4

s/d

0.5 0.6

Figure 6.18: Effect of stirrup spacing of the effective CFRP stirrup stress using SFM.

254


6.5 Unified Shear Strength Model

A theoretical model was recently developed to predict the shear strength of slender reinforced

concrete beams without web reinforcement by Park et al. (2006). Through this model, the

shear force applied to a cross section of the beam assumed to be resisted primarily by the

compression zone of intact concrete rather than by the tension zone and the shear capacity of

the cross section was defined based on the material failure criteria. Later, Choi et al. (2007)

and Choi and Park (2007) presented a unified shear strength model for reinforced concrete

beams. This model was based on strain-based shear strength for evaluating the concrete

contribution. The assumptions and details of this model were presented in Section 2.4.11.

Due to the relatively low modulus of elasticity of FRP composite materials, concrete

members reinforced with FRP bars will develop wider and deeper cracks than members

reinforced with steel. Deeper cracks decrease the depth of the compression zone, thereby

reducing the contribution of the uncracked concrete to the shear carrying capacity.

Furthermore, wider cracks may result in a reduction in the shear strength contributions from

aggregate interlock as well as from residual tensile stresses across the cracks. Additionally, the

relatively small transverse strength of FRP bars coupled with increased crack widths may

result in neglecting the dowel action (Tureyen and Frosch 2002). Therefore, the shear strength

of FRP-reinforced concrete members without transverse (shear) reinforcement can be

reasonably assumed to be provided by the uncracked concrete above the neutral axis. Thus,

the strain-based calculation of shear strength of such members may provide an appropriate

approach to calculate the shear strength of FRP RC members.

Thus, the first step to evaluate the applicability of this model to FRP reinforced

concrete beams was to determine the concrete contribution for beams longitudinally

reinforced with FRP. In this study, some of the model assumptions are modified to be applied

for the slender beams longitudinally reinforced with FRP bars and without shear

reinforcement. A previous assumption based on the test results of MacGregor et al. (1960)

assumed that an additional applied force of 0.05sjfc bw d (MPa) is required to make a tensile

crack reach the neutral axis. However, for FRP reinforced concrete elements this value will be

255


modified considering the difference in the axial stiffness between the FRP material and steel.

/—7 En

Thus, it will be considered as: 0.05 J f bwd- -J— (6.3) Es

Applying Equation (6.3) in the strain based calculations, the shear strength of 73 FRP

reinforced concrete beams (from literature) without shear reinforcement are calculated and

compared to the experimental ones. Table 6.4 provides the predicted shear strength compared

to the experimentally-obtained shear carrying capacity. A comparison between the current

approach and the design codes and guidelines is shown in Figures 6.19 to 6.22. From this

comparison, it can be seen that the strain-based calculated shear strength was in a good

agreement with the experimentally obtained value. The experimental to predicted ratio of

shear strength, VeXp/Vpred, was 0.994 with a standard deviation of 0.149 and a coefficient of

variation of 14.6 %. On the other hand, this ratio, Vexp/Vpred, obtained by the JSCE (1997),

CSA (2006) and ACI (2006) was 1.40, 1.43 and 2.0 with a corresponding standard deviation

of 0.26, 0.40 and 0.34, respectively.

For evaluating the FRP stirrups contribution to the shear strength, Choi et al. (2007)

and Choi and Park (2007) presented the following equation for steel stirrups:

Vs=Psvfybwd (6.4)

It is evident from Equation (6.4) that the contribution of the steel stirrups is governed

by its yield strength. Thus, replacing this value by the reduced strength of the FRP stirrups to

account for the bend, the previous equation will be in the following format:

Vsf = pfvffvbwd (6.5)

The fjv of the stirrups was suggested to be one of the following values which will be

verified against the results of the tested beam:

.#,=0.004 Ep (6.6)

fjv= the bend strength measured experimentally,^^. (6.7)

The experimental to predicted values for the shear strength considering the previous

two values for the stirrup stress presented in Equations (6.6) and (6.7) are presented in Table

6.5

256

Cha

pter

6:

Ana

lyti

cal

Stud

y

Tab

le 6

.4: S

train

-bas

ed c

alcu

late

d sh

ear

stre

ngth

for

FR

P R

C b

eam

s w

ithou

t stir

rups

in c

ompa

rison

to th

e ex

perim

enta

l res

ults

.

Reference

El-Sayed et

al. (2006a)

El-Sayed et

al. (2006b)

El-Sayed et

al. (2005)

Symbol

CN-1

GN-1

CN-2

GN-2

CN-3

GN-3

CH-1.7

GH-1.7

CH-2.7

GH-2.2

S-Cl

S-C2B

S-C3B

S-Gl

S-G2

S-G2B

S-G3

a

(mm)

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

b w

(mm)

250

250

250

250

250

250

250

250

250

250

1000

1000

1000

1000

1000

1000

1000

h

(mm)

400

400

400

400

400

400

400

400

400

400

200

200

200

200

200

200

200

d

(mm)

326

326

326

326

326

326

326

326

326

326

165.3

165.3

160.5

162.1

159

162.1

159

f'c

(MPa)

50.0

50.0

44.6

44.6

43.6

43.6

63.0

63.0

63.0

63.0

40.0

40.0

40.0

40.0

40.0

40.0

40.0

Pfl

%

0.87

0.87

1.24

1.22

1.72

1.71

1.71

1.71

2.20

2.20

0.39

0.78

1.18

0.86

1.70

1.71

2.44

(GPa)

128.0

39.0

134.0

42.0

134.0

42.0

135.0

42.0

135.0

42.0

114.0

114.0

114.0

40.0

40.0

40.0

40.0

'pre

d.

(kN)

104.95

77.87

109.24

81.15

115.83

86.28

134.95

100.25

142.22

105.72

140.19

166.71

183.70

115.52

136.93

137.69

150.25

' e

xp.

(kN)

77.50

70.50

104.00

60.00

124.50

77.50

130.00

87.00

174.00

115.50

140.00

167.00

190.00

113.00

142.00

163.00

163.00

v exp.

' 'p

red.

0.738

0.905

0.952

0.739

1.075

0.898

0.963

0.868

1.223

1.093

0.999

1.002

1.034

0.978

1.037

1.184

1.085

257

a

"3

a s

!

1.10

4 16

8.00

15

2.11

40

.0

2.63

40

.0

154.

1 20

0 10

00

1000

S-

G3B

0.85

0 36

.10

42.4

7 14

5.0

0.25

40

.5

225

250

200

600

BR

1

0.88

6 47

.00

53.0

2 14

5.0

0.50

49

.0

225

250

200

600

BR

2

0.91

7 47

.20

51.4

6 14

5.0

0.63

40

.5

225

250

200

600

BR

3

0.77

4 42

.70

55.1

8 14

5.0

0.88

40

.5

225

250

200

600

BR

4

1.13

2 49

.70

43.9

0 14

5.0

0.50

40

.5

225

250

200

800

BA

3

0.91

4 38

.50

42.1

0 14

5.0

0.50

40

.5

225

250

200

950

BA

4

Raz

aqpu

r et

al.

(200

4)

1.31

6 54

.50

41.4

2 42

.0

0.72

37

.3

346

380

0

950

G07

N1

1.53

8 63

.70

41.4

2 42

.0

0.72

37

.3

346

380

0

950

G07

N2

0 0

42.7

0 42

.65

42.0

1.

10

43.2

34

6 38

0

0

1150

G

10N

1

1.06

7 45

.50

42.6

5 42

.0

1.10

43

.2

346

380

0 ^0

1150

G

10N

2

1.16

7 48

.70

41.7

4 42

.0

1.54

34

.1

325

380

0 ^0

1150

G

15N

1

1.07

6 44

.90

41.7

4 42

.0

1.54

34

.1

325

380

0

1150

G

15N

2

1.12

2 49

.20

43.8

5 12

0.0

0.72

37

.3

310

380

0

950

C07

N1

1.04

4 45

.80

43.8

5 12

0.0

0.72

37

.3

310

380

0 en

950

C07

N2

1.02

4 47

.60

46.5

1 12

0.0

1.10

43

.2

310

380

0 en

1150

C

10N

1

1.13

3 52

.70

46.5

1 12

0.0

1.10

43

.2

310

380

0 CO

1150

C

10N

2

1.22

6 55

.90

45.6

1 12

0.0

1.54

34

.1

310

380

0 CO

1150

C

15N

1

1.27

8 58

.30

45.6

1 12

0.0

1.54

34

.1

0 co

380

0 co

1150

C

15N

2

Tar

iq a

nd

New

hook

(200

3)

0.90

7 10

8.10

11

9.18

40

.5

0.96

39

.7

360

406.

4 45

7 12

19.2

V

-Gl-

1 T

urey

en a

nd

0 0

3

"5

s

!

0.80

9 94

.70

117.

08

37.6

0.

96

39.9

36

0 40

6.4

457

1219

.2

V-G

2-1

0.91

9 11

4.80

12

4.90

47

.1

0.96

40

.3

360

406.

4 45

7 12

19.2

V

-A-l

0.89

7 13

7.00

15

2.70

40

.5

CN ON

42.3

36

0 42

6.7

457

1219

.2

V-G

l-2

1.08

1 15

2.60

14

1.22

37

.6

CN ON

42.5

36

0 40

6.4

457

1219

.2

V-G

2-2

1.17

8 17

7.00

15

0.26

47

.1

CN ON

42.6

36

0 40

6.4

457

1219

.2

V-A

-2

Fros

ch

(200

2)

0.96

2 39

.10

40.6

6 40

.3

-

36.3

22

5 28

6 22

9 91

4 lF

RP

a

0.94

7 38

.50

40.6

6 40

.3

-

36.3

22

5 28

6 22

9 91

4 lF

RP

b

0.90

5 36

.80

40.6

6 40

.3

~

36.3

22

5 28

6 22

9 91

4 lF

RP

c

0.84

0 28

.10

33.4

5 40

.3

36.3

22

5 28

6 17

8 91

4 2F

RPa

1.04

6 35

.00

33.4

5 40

.3

CN 36

.3

225

286

CO

914

2FR

Pb

0.96

0 32

.10

33.4

5 40

.3

CN

36.3

22

5 28

6 17

8 91

4

CN

0.89

7 40

.00

44.6

1 40

.3

NO NO

36.3

22

5 28

6 22

9 91

4 3F

RPa

1.08

9 48

.60

44.6

1 40

.3

NO NO

36.3

22

5 28

6 22

9 91

4 3F

RPb

1.00

2 44

.70

44.6

1 40

.3

NO NO

36.3

22

5 28

6 22

9 91

4 3F

RPc

0.96

2 43

.80

45.5

1 40

.3

CO

36.3

22

5 28

6 22

9 91

4 4F

RPa

1.00

9 45

.90

45.5

1 40

.3

CO

36.3

22

5 28

6 22

9 91

4 4F

RP

b

1.01

3 46

.10

45.5

1 40

.3

00

36.3

22

5 28

6 22

9 91

4

"5T

0.72

7 37

.70

51.8

8 40

.3

2.04

36

.3

224

286

254

914

5FR

Pa

0.98

3 51

.00

51.8

8 40

.3

2.04

36

.3

224

286

254

914

5FR

Pb

0.89

8 46

.60

51.8

8 40

.3

2.04

36

.3

224

286

254

914

Yos

t et

al.

(200

1)

ON

CN

a

"5

a s

s

0.90

7 43

.50

47.9

5 40

.3

2.27

36

.3

224

286

229

914

6FR

Pa

0.87

2 41

.80

47.9

5 40

.3

2.27

36

.3

224

286

229

914

6FR

Pb

0.86

1 41

.30

47.9

5 40

.3

2.27

36

.3

224

f 28

6 22

9 91

4

so

1.16

1 53

.40

45.9

9 40

.0

2.30

24

.1

279

330

178

750

BM

7

0.96

7 36

.10

37.3

1 40

.0

0.77

24

.1

287

330

178

750

BM

8

0.96

8 40

.10

41.4

5 40

.0

1.34

24

.1

287

330

178

750

BM

9

Alk

hrda

ji et

al. (

2001

)

0.84

9 26

.80

31.5

8 40

.0

0.74

28

.6

157.

5

o as

305

710

GF

RP

1

0.95

9 28

.30

29.5

1 40

.0

0.74

30

.1

157.

5

©

305

913

GF

RP

2

1.03

3 29

.20

28.2

8 40

.0

0.74

27

.0

157.

5

o as

305

as

GF

RP

3

0.99

1 28

.50

28.7

7 40

.0

0.74

28

.2

157.

5

o as

305

as

Hyb

rid

1

0.92

7 27

.60

29.7

8 40

.0

0.74

30

.8

157.

5

o as

305

913

Hyb

rid

2

Dei

tz e

t al

.

(199

9)

0.74

1 74

.60

100.

62

41.3

0.

96

63.1

10

4

© in

1000

13

00

I-15

0-C

1.25

3 15

8.10

12

6.19

41

.3

0.77

63

.1

154

200

1000

13

00

I-20

0-C

Mic

halu

k et

al. (

1995

)

0.99

5 45

.00

45.2

2 10

5.0

1.51

34

.3

250

300

150

750

No.

l

0.88

1 46

.00

52.2

0 10

5.0

3.02

34

.3

250

300

o in

750

No.

6

0.82

3 40

.50

49.2

1 10

5.0

2.27

34

.3

250

300

o l/->

750

No.

15

Zha

o et

al.

(199

5)

TJ- in Os •>* as ~-H

so

2 Q

3 > o u

o


0 500 1000 1500 2000 2500 3000 3500 pf lE/ ; (MPa)

4.0

3.5

3.0

< 2.0

I 5? 1.5

1.0

0.5

0.0

• Strain-Based Analysis

:::£i:£!::|;::;:::

1.0 2.0 3.0 4.0 5.0 6.0 a/d

4.0

3.5

3.0

1" v° S 1.5

1.0

0.5 0.0

• Strain-Based Analysis

- i - i t - f r -** t

20.0 30.0 40.0 50.0 fc (Mpa)

60.0 70.0

Figure 6.19: Predicted shear strength according to the strain-based analysis.

261


4.0

3.5

3.0

i2* .a.

1 ^ 2.0

£ 1-5

1.0

0.5

0.0

JSCE(1997)

• • •

w fe$ ^ • • H ^ v

0 500 1000 1500 2000 2500 3000 3500 ptfEf, (MPa)

20.0 30.0 40.0 50.0 60.0 70.0 fc (Mpa)

Figure 6.20: Predicted shear strength according to the JSCE (1997).

262


4.0

3.5

3.0

| 2.5 a ^ 2.0 d

| 1.5

1.0

0.5

0.0

-

-

-

;

:

•

•

•

• CSA (2002)

•

. . .AMtUl •

1 1

•

• •

500 1000 1500 2000 PflEfl(MPa)

2500 3000 3500

4.0

3.5

3.0

^ 2.0

5* 1.5

1.0

0.5

0.0

.•. i . . t i . ! • . . . * * . • • %

20.0 30.0 40.0 50.0 f'c (Mpa)

CSA (2002)

60.0 70.0

Figure 6.21: Predicted shear strength according to the CSA (2002).

263


4.0

3.5

3.0

< 2.0

I 5 1.5

1.0

0.5

0.0

ACI (2006)

4 *- -••*•*•*• *?

' » * P • A t •

tV.\#.V;../...v.......:....

0 500 1000 1500 2000 2500 3000 3500 pnEf, (MPa)

20.0 30.0 40.0 50.0

fc (Mpa) 60.0 70.0

Figure 6.22: Predicted shear strength according to the ACI (2006).

264


Table 6.5: The predicted shear strength of the beam specimens using the unified shear strength

model.

Beam

SC-9.5-2

SC-9.5-3

SC-9.5-4

SG-9.5-2

SG-9.5-3

SG-9.5-4

Vexp. (kN)

376

440

536

259

337

416

ffi=0.004 Ep

Vexp. (kN)

225

295

372

128

151

177

Average

SD

COV (%)

' expf ' pred.

1.67

1.49

1.44

2.03

2.23

2.34

1.87

0.39

20.65

Jfv J bend

Vexp. (kN)

279

376

482

186

239

296

'expf 'pred.

1.35

1.17

1.11

1.39

1.41

1.41

1.31

0.13

10.10

From Table 6.5 it can be noticed that the unified shear strength model predicted well

the shear strength of beams reinforced with FRP stirrups considering the limit for stirrup stress

to be the bend strength. The average Vexp/ Vpred. was 1.31 with a standard deviation of 0.13

and a corresponding COV equal to 10.10%. However, for design considering the maximum

stirrup strain at ultimate equals to 4000 microstrain, the Vexp./ Vpred. was 1.87 with standard

deviation of 0.39 and a corresponding COV equal to 20.65%. Thus, this model is capable of

predicting the shear strength of the concrete members reinforced longitudinally with steel and

transversally with FRP stirrups.

From the following paragraphs it was concluded that the unified shear strength is

capable of predicting the shear strength of FRP reinforced concrete section with/without

stirrups considering the following:

1. The additional force which is required to force the shear crack to reach the neutral axis

is modified to account for the FRP flexural reinforcement as follows:

2. The stress in the FRP is limited to 0.004 Ep which is the new proposed limit for the

ACI (2006) and CSA (2009).

265


3. The effect of the longitudinal reinforcement is already included in the calculation of

the neutral axis depth.

1.V

3.5

3.0

2.5

!

^•2 .0 -

i 1.5 • 1.U

0.5

0.0

Strain Based: ffv=fbend Average=1.31±0.13

1 35

I

1.17 1.11 1.39 1.41

i i

1.41

SC-9.5-2 SC-9.5-3 SC-9.5-4 SG-9.5-2 SG-9.5-3 SG-9.5-4

(a) Stirrup stress,^,, equals bend strength, fbend-

4.0

3.5

3.0

2.5

£ ^ 2.0

> 1.5

1.0

0.5

0.0

Strain Based: t'^=0.004 Average=1.87±0.39

1.67

i

1.49 1.44

I I

2.03

i

2.23

I

2 34

SC-9.5-2 SC-9.5-3 SC-9.5-4 SG-9.5-2 SG-9.5-3 SG-9.5-4

(b) Stirrup stress, ffi,, equals 0.004 Efi.

Figure 6.23: Predicted shear strength of beam specimens using the unified shear model.

266


6.6 Theoretical Predictions of the Shear Crack Width

The shear crack width in reinforced concrete beams has not been extensively investigated as

the flexural crack width. A few equations are provided to estimate the shear crack width in

beams reinforced with steel stirrups. Placas and Regan (1971) provided the following

expression for estimating the shear crack width in concrete beams reinforced with steel

stirrups:

ssina (V'-Vcr) w = - (lb; in. units) (6.8)

lov.U'r Kd

The shear crack width for the control beam, reinforced with steel stirrup, was

estimated using Equation (6.8) as shown in Figure 6.24. The comparison between the

measured and predicted shear crack width for the control beam showed good agreement and

Equation (6.8) estimated well the shear crack width of the beam reinforced with steel stirrups.

600

SS-9.5-2

Steel@d/2

Experimental

2 3


Figure 6.24: Prediction of shear crack width for the control beam (SS-9.5-2) using Equation

(6.8).

Due to the different modulus of elasticity of the FRP materials comparing to the

conventional steel, this equation can not be applied directly to estimate the shear crack width

of the beams reinforced with FRP stirrups. Thus, a proposed modification to this equation was

provided by multiplying the shear reinforcement ratio by the square root of the FRP modulus

of elasticity divided by the steel modulus of elasticity. The proposed equation for the vertical

stirrups can be expressed as follows:

267


s (V-V ) w = ?7 ^ ^ (lb; in. units) (6.9a)

^Psv(Ep/Es)A(f:)A Kd

27.6055 [V-K) ~T .+ , , , O M

w = r, rr- (N; mm units) (6.9b)

The shear crack widths were predicted using the proposed Equation (6.9) and

compared to the experimentally measured crack widths for the beams reinforced with FRP

stirrups. Figure 6.25 shows the comparison for the beams reinforced with CFRP stirrups while

and Figure 6.26 shows the comparison for the beams reinforced with GFRP stirrups. From

those comparisons it can be concluded that the proposed equation is capable of predicting the

shear crack width for the beams reinforced with FRP stirrups with adequate accuracy.

6.7 Summary

An analytical investigation was conducted to evaluate the accuracy of the current design

provisions of the design codes and the complex shear theories. The behaviour of the beams

tested in this study (presented in Chapter 5) as well as other beams from literature was

predicted using the MCFT, SFM, and the unified shear strength model after modifying its

equations. The shear crack width also was theoretically predicted. Through this investigation

it was observed that:

1. The CSA (2009) provisions which was approved considering the experimental results

presented in Chapter 5 yielded reasonable conservative prediction of the shear strength

of the beam specimens reinforced with FRP stirrups as will as other beams from

literature. Using the 4000 microstrain as stirrup strain at ultimate which is incorporated

in the ACI (2006) and the CSA (2009) enables predicting the shear strength of

concrete beams reinforced with FRP stirrups with adequate factor of safety. Moreover,

using this limit enhances the inclination angle prediction using the CSA (2009).

2. The MCFT and the SFM were capable of predicting the shear strength of concrete

beams reinforced with FRP stirrups. The MCFT also predicted well the stirrup strain

but over estimated the shear crack width due to the crack spacing parameters.

3. The proposed equation predicted the shear crack width in concrete beam reinforced

with FRP stirrups with adequate accuracy.

268


(a) SC-9.5-2

CFRP@J/2

(b) SC-9.5-3

CFRP@d/3

600

— 500 Z

8 400 O u.

S 300 .n w | 200 a a. <

100

SC-9.5-2

600

Experimental Proposed

2 3


SC-9.5-3


2 3


600

(c) SC-9.5-4

CFRP@d/4

SC-9.5-4


2 3


Figure 6.25: Prediction of shear crack width for beams reinforced with CFRP stirrups using

the proposed equation (Equation 6.9).

269


(a) SG-9.5-2

GFRP@J/2

600

~ 500

o 400 o

600

(b) SG-9.5-3

GFRP@d/3

I

r F

orc

e S

hea

i A

pp

lied

500

400

300

200

4M\

SG-9.5-2


2 3


SG-9.5-3


1 2 3


600

(c) SG-9.5-4

GFRP@d/4

z * 0) JJ o LL

!=

She

a A

pp

lied

500

400

300

200

•inn

/ /

/

SG-9.5-4


2 3


Figure 6.26: Prediction of shear crack width for beams reinforced with CFRP stirrups using

the proposed equation (Equation 6.9).

270

Chapter 7: Summary and Conclusions

CHAPTER 7

SUMMARY AND CONCLUSIONS

7.1 Summary

The current study investigates the structural performance of FRP stirrups as shear

reinforcement for concrete beams. The study includes both experimental and analytical

investigations. The different parameters affecting the shear behaviour of FRP-reinforced

concrete beams such as the stirrup material, spacing, and shear reinforcement ratio are

investigated. Based on the findings of this investigation, the Canadian Highway Bridge

Design Code (CAN/CSA-S6) was amended and the updated provisions were approved in the

CSA-S6-Addendum (2009). Besides, the accuracy of the shear design codes and guidelines

for members reinforced with FRP stirrups are evaluated. A limiting strain value for the FRP

stirrup strain at service is introduced to keep the shear crack width controlled. A simple

equation for evaluating the shear crack width for beams reinforced with FRP stirrups is also

proposed.

The experimental program includes seven large-scale concrete T-beams reinforced

with FRP and steel stirrups. Three beams are reinforced using sand-coated CFRP stirrups,

three beams using sand-coated GFRP stirrups, and one beam using steel stirrups. The CFRP

stirrups have tensile strength and modulus of elasticity of 1538±57 MPa and 130±6 GPa,

respectively while the bend strength is 712±46 MPa. The GFRP stirrups have tensile strength

and modulus of elasticity of 664±25 MPa and 45±2 GPa, respectively while the bend strength

is 387±15 MPa. The geometry of the T-beams is selected to simulate the New England Bulb

Tee Beams (NEBT) that are being used by the Ministry of Transportation of Quebec, Canada.

The beams are 7.0 m long with a T-shaped cross section measuring a total height of 700 mm,

web width of 180 mm, flange width of 750 mm, and flange thickness of 85 mm. The large-

scale T-beams are constructed using normal-strength concrete and are tested in four-point

bending over a clear span of 6.0 m till failure to investigate the modes of failure and the

ultimate capacity of the FRP stirrups in beam action. The maximum strains in the FRP stirrup,

average stirrup strains, and the crack width of the major shear cack (failure crack), and the

inclination angle of the failure plane are examined. The test variables considered in this

271


investigation are the material of the stirrups, shear reinforcement ratio, and stirrup spacing.

The specimens are designed to fail in shear to utilize the full capacity of the used FRP stirrup.

As designed, six beams failed in shear due to FRP (carbon and glass) stirrup rupture or steel

stirrup yielding. The seventh beam, reinforced with CFRP stirrups spaced at dIA, failed in

flexure due to yielding of the longitudinal reinforcement. The test results of the experimental

investigation contributed to amending the shear provisions in the Canadian Highway Bridge

Design Code (CAN/CSA-S6).

The analytical investigation includes analysis of the tested beams using different

available codes and guidelines. The shear strength of the tested beams as well as other beams

from literature reinforced with FRP stirrups is predicted using: the Canadian Standard

Association, CSA-S6-06 (CSA 2006), and CSA-S6-06 (CSA 2009) which was approved

considering the results of the experimental investigation conducted herein, the design

recommendations of the Japanese Society of Civil Engineers (JSCE 1997), the Japanese

Building Research Institute (BRI) recommendations (Sonobe et al. 1997), the American

Concrete Institute design guideline (ACI 2006), and the Italian National Research Council

(CNR 2006). The accuracy of the above listed codes and guidelines is verified against the

experimental results. The verification is extended to include additional 24 beams reinforced

with FRP stirrup form literature.

The beams are also analysed using shear theories: the modified compression field

theory (MCFT), the shear friction model (SFM), and the unified shear strength model. The

predicted shear strengths using the aforementioned shear models were compared with the

experimentally measured values. The shear crack width and the stirrups strain are also

predicted using the MCFT and compared with the measured values. Based on the predicted

results, the effect of the stirrup spacing is investigated.

The shear crack width of the beam reinforced with steel stirrups is also calculated

using Placas and Regan (1971) equation. Upon verification of the equation results for the

beam reinforced with steel stirrups, a modified version of the equation is proposed to account

for the difference between the FRP and the steel. The predicted shear crack width for the

beams reinforced with FRP stirrups are verified against the experimentally measured values.

The proposed equation is capable of predicting the shear crack width for the tested beams

reinforced with carbon and glass FRP stirrups.

272


7.2 Conclusions

The current study included experimental and analytical evaluation of the FRP stirrups as shear

reinforcement for concrete beams. The findings of this investigation can be summarized as

follows:

7.2.1 FRP stirrup characterisation

Before using the FRP stirrups as shear reinforcement in concrete beams, their characteristics

were evaluated using the B.5 and B.12 tests specified by the ACI 440.3R-04 (ACI 2004).

Based on the test results the following conclusions were drawn:

1. The B.12 test method underestimated the bend strength of FRP stirrups in comparison

with the B.5 method. The bend strength measured according to B.12 test method was

30 and 40% less than that based on B.5 test method for carbon and glass FRP bent

bars, respectively.

2. Since the bend capacities obtained by B.12 test method are consistently lower than

those obtained by B.5 test method, different limits for the acceptable bend capacity

should be presented for each test method. The ISIS Canada (2006) bend strength limit

of 35% of the strength parallel to the fibres, resulted from both of B.5 and B.12 test

methods, seems to be more conservative when B.5 method is used. The set limit may

be kept for B.12 method and a revised value ranging from 40 to 45% of the strength

parallel to the fibres may be used for B.5 method.

7.2.2 FRP stirrup in beam specimens

Through testing the concrete beams reinforced with carbon and glass FRP stirrups and

comparing their results with those of the one reinforced with steel stirrups, when applicable,

the following conclusions were drawn:

3. Two beams reinforced with CFRP stirrups (CFRP stirrups @ d/2 and CFRP stirrups @

d/3) failed in shear due to rupture of CFRP stirrups. The failure of CFRP stirrups was

governed by the bend strength of the CFRP stirrups. As soon as, at least, one CFRP

stirrup failed at the bend, the shear resisting mechanism did not resist the applied shear

force and the beam failed. The third beam reinforced with CFRP stirrups failed in

273


flexure because the shear reinforcement (CFRP stirrups @ dIA) was enough to provide

shear strength higher than flexural one.

4. Like the beams reinforced with CFRP stirrups, the three beams reinforced with GFRP

stirrups failed due to rupture of GFRP stirrups. However, the capacity of bend portion

and the straight portion of the GFRP stirrups were achieved at the failure. This is

referred to higher bend strength to the strength in the fibres direction ratio for GFRP

stirrups in comparison with CFRP stirrups.

5. Using FRP stirrups with a ratio of bend-to-straight portion strength, fbend I ffuv, not less

than 0.6 enables utilizing the capacity of the straight portions of the FRP stirrups in

beam specimens. Lower ratios will cause the bend strength to govern the strength of

the beam whatever the tensile strength of the straight portion is.

6. Generally, the response of concrete members reinforced with FRP stirrups is directly

proportional to the stiffness of the shear reinforcement provided. The higher the shear

stiffness, the higher the capacity and the lower the average stirrup strain.

7. The inclination angle of the shear crack in concrete beams reinforced with FRP

stirrups ranged from 42° to 46° which is in good agreement with the traditional 45°

truss model.

8. Both of SS-9.5-2 (steel stirrups @ dll) and SC-9.5-3 (CFRP stirrups @ d!3) beams,

with the same shear reinforcement index, pfi EfvjEs, showed almost the same average

strains values at different loading levels till yielding of the steel stirrups. However, due

to the difference in bond characteristics and the spacing of stirrups, the shear crack

width was not the same.

9. Both of SC-9.5-2 (CFRP stirrups @ dll) and SG-9.5-4 (GFRP stirrups @ d/4) showed

the same applied shear force-shear crack width relationship. Using closely spaced

stirrups even with low elastic FRP materials enhances and controls the crack width

rather than high modulus FRP stirrups with larger stirrup spacing.

10. The beam reinforced with steel stirrups showed the least strain at the same loading

level in comparison with its counterparts reinforced with GFRP stirrups. This may be

due to the high shear reinforcement index {pfiE^/Es) for steel stirrups. However,

this beam with steel stirrups did not show the smallest shear crack width. This is

274


referred to the difference in bond characteristics between steel and FRP and the stirrup

spacing.

11. The closer the FRP spacing the smaller the effective stirrup stress (fj\, I fj^). The lower

limit resulted form CFRP stirrups and it was about 53%. Thus, the FRP stirrups may

be designed for 50% of its strength in the fibres direction.

12. The design capacity of the concrete beams reinforced with FRP stirrups is not affected

by the bend strength of FRP stirrups. Corresponding to an average strain value equals

4000 in the FRP stirrups, the stresses at the bend of FRP stirrups ranged from 7.1 to

41.7% of the bend strength, fbend, (4.2 to 24.3% of the strength if the fibres direction)

which yields a factor of safety greater than 2 between the actual stresses at the bend

and the bend strength of FRP stirrups.

13. The average stirrup strain, in the straight portion, at ultimate for the beam specimens

failed in shear was 7198 and 8500 microstrain for the CFRP and GFRP stirrups,

respectively. These values represent almost double the limit for the strain in the FRP

stirrups at ultimate specified by the ACI (2006) and CSA (2009). However, these

values correspond to about 0.6 of the tensile strength of FRP stirrups parallel to the

fibres.

14. Providing effective shear reinforcement, pÊ^/E^., for SC-9.5-3 beam (CFRP

stirrups @ d/3) equals to that of SS-9.5-2 beam (steel stirrups @ d/2) increased the

shear capacity by 62% due to higher strength of CFRP relative to steel.

15. The beam specimens reinforced with GFRP stirrups showed lower shear crack spacing

in comparison with those reinforced with CFRP stirrup based on average or maximum

crack spacing criteria. However, both group showed average crack spacing less than

300 mm, except SC-9.5-2 (CFRP stirrups @ d/2). This indicates that the 300 mm

specified by the CHBDC S6-06 for the sze parameter in Equations (2.129) and (2.130)

leads to conservative predictions.

16. The tested carbon and glass FRP stirrups provide alternative shear reinforcement for

reinforced concrete structures subjected to severe environmental conditions.

275


1.2.3 Code predictions

The amended shear provisions of the CS A (2009) was approved considering the experimental

results of the current investigation. The shear strength of the tested beams as well as other

beams reinforced with FRP stirrups was predicted using different design codes and guidelines.

Based on the analysis of the predicted results the following conclusions were drawn:

17. The JSCE (1997) and the CAN/CSA S6-06 (2006) yielded very conservative

prediction for the shear strength of concrete beams reinforced with FRP stirrups. The

stirrup strain equations and limits implemented in both provisions (which are basically

the same) were the main reason for limiting the FRP stirrups contribution to the shear

strength. However, JSCE (1997) relaxed the upper limit of Equation (3.52d) to the

bend strength of the FRP stirrups, the equation itself governed the FRP stirrup strain

and, in turn, the FRP stirrups contribution.

18. Using the 4000 microstrain as FRP stirrup strain at the ultimate limit state as specified

by the ACI 440.1R-06 (2006) and the updated CAN/CSA S6-09 (2009), was approved

considering the experimental results of the current investigation, provides better

predictions for the shear strength of concrete members reinforced with FRP stirrups,

yet conservative. The CSA (2009) showed an average VexpJVpred. for the tested beam

specimens equals 1.67±0.14 with a corresponding COV equals 8.3%.

19. The CAN/CSA S6-09 (2009) provides better estimation for the shear crack inclination

angle, 8, in comparison with the CAN/CSA S6-06 (2006) due to the relaxed strain

value for the maximum stirrup strain at ultimate.

20. The CNR-DT 203 (2006) predicted very well the shear strength of the tested beams

reinforced with FRP stirrups obtaining an average VexpJVpre^ equals 1.2±0.18 and a

corresponding COV equals 15%. This good agreement is due to the reduced FRP

stirrup strength utilized in the stirrup contribution equation. The CNR (2006) considers

a reduced strength equals 50% of the tensile strength in the fibres direction, which

coincided with the experimentally measured bend strength for the FRP stirrups tested

in the current study.

21. As a serviceability requirement to control the shear crack width, it is recommended

that the strain of the FRP stirrups at the service load should be limited to 2500

microstrain. Keeping the stirrup strain less than or equal to this proposed value yields a

276


shear crack width below 0.5 mm, which is the limit for the flexural crack width in

FRP reinforced concrete members in severe exposure; set by several codes.

7.2.4 Analytical investigation

22. The modified compression field theory (MCFT) is capable of predicting the response

of concrete beams reinforced with FRP stirrups in terms of shear capacity, mode of

failure and average stirrup strain.

23. Although, the MCFT predicted well the average stirrups strain of the test specimens, it

over estimated the shear crack width for the beams reinforced with carbon and glass

FRP stirrups. This is referred to the crack spacing parameters implemented in the

calculation procedure.

24. Employing the MCFT for predicting the shear strength of beams reinforced with FRP

stirrups, considering the bend strength of the FRP stirrups as failure criteria, yielded

good predictions.

25. The shear friction method (SFM) was able to predict the shear failure of the concrete

beams reinforced with FRP stirrups with reasonable accuracy. However, the main

reason for the non-conservative prediction for some specimens is referred to the

assumption of maintaining the development length equals at least 5 db (5 times the

stirrup diameter).

26. The unified shear strength model, modified to consider the different FRP material

properties, was capable of predicting well the shear strength of FRP reinforced

concrete beams. Reasonably conservative predictions were achieved when the stress in

the FRP stirrups is taken equal to the bend strength for the FRP stirrups.

27. The proposed equation to estimate the shear crack width for concrete beams reinforced

with FRP stirrups was capable of predicting the applied shear-shear crack width

relationship of the tested beams with reasonable accuracy. For concrete beams with

high shear reinforcement ratio, slightly underestimation of the shear crack width was

observed.

277


7.3 Recommendations for Future Work

Based on the conducted experimental and analytical investigations and their findings, the

following recommendations for future work are proposed:

1. The behaviour of concrete beams reinforced with very high FRP shear reinforcement

ratio should be investigated to evaluate the shear compression failure.

2. The effects of bond characteristics on the average stirrups strains and shear crack

width in concrete beams reinforced with FRP stirrups are important issues to

investigate.

3. More experimental work is needed to refine the shear crack width predictions and

develop a rational model.

4. The shear behaviour of prestressed concrete beams reinforced with FRP stirrups needs

to be investigated.

5. Testing of beams reinforced with both FRP stirrups and FRP longitudinal

reinforcement is recommended.

278

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