m UNIVERSITED SHERBROOKE E
Transcript of 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
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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 4.23: Reinforcement details and stirrup instrumentation of SC-9.5-3 152
Figure 4.24: Reinforcement details and stirrup instrumentation of SC-9.5-4 153
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
Figure 5.30: Stirrup strain distribution along the shear span of
SC-9.5-3 beam (CFRP@<//3) 207
Figure 5.31: Stirrup strain distribution along the shear span of
SC-9.5-4 beam (CFRP@<//4) 208
Figure 5.32: Stirrup strain distribution along the shear span of
SG-9.5-2 beam (GFRP@<//2) 209
Figure 5.33: Stirrup strain distribution along the shear span of
SG-9.5-3 beam (GFRP@J/3) 210
Figure 5.34: Stirrup strain distribution along the shear span of
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
Chapter 1: Introduction
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
Chapter 1: Introduction
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
Chapter 1: Introduction
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
Chapter 1: Introduction
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: Introduction
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
^
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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 of^ithtat 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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
°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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
^>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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
(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.
Minimum shear reinforcement
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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.
Minimum shear reinforcement
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
<^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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
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
Minimum shear reinforcement
The AASHTO LRFD specifications (2004) require a minimum amount of shear reinforcement
vmin for non prestressed concrete members given by:
63
Chapter 2: Shear Behaviour of Concrete Beams Reinforced with Steel: Background and Review
^ 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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
(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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
«> 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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
findings of this study can be summarized as follows:
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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 Ap^E^ , 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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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:
A^E^ ( 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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
where Eji and Es are the modulus of elasticity of the FRP longitudinal reinforcement and steel,
respectively, /T^is 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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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)
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Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
&= (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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
findings of this study can be summarized as follows:
108
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
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Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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:
Kf^ad+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)
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Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
The mode of failure of the reinforced concrete beam varies depending on the rigidity
of longitudinal and shear reinforcements (pflEfl + 10 p^E^). 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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
£„ =
(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)
Minimum shear reinforcement
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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).
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Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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).
Minimum shear reinforcement
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Minimum shear reinforcement
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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.
Minimum shear reinforcement
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.
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Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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).
Minimum shear reinforcement
Where transverse GFRP reinforcement is required, the area of GFRP reinforcing bars, Aj\, m j n ,
shall satisfy:
127
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
_ 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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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
Chapter 3: Shear Behaviour of Concrete Beams Reinforced with FRP Stirrups: Background and Review
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).
Minimum shear reinforcement
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
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
Figure 4.17: Compression test of the standard concrete cylinders.
Figure 4.18: Splitting test of the standard concrete cylinders.
145
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
°p-
o o
1200-
810-
NEBT 1000
f 1200 1
810-
NEBT 1200
-1200
180
<£? rfT
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Y M*i
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+ 180
4>
—810—
NEBT 1600
-1200-
Tp *£,
180
#
-810-
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
Chapter 4: Experimental Program
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
148
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D
Dem
ec g
auge
s
| LV
DTs
Plan
Figu
re 4
.21:
Geo
met
ry a
nd d
imen
sion
of
beam
spe
cim
ens.
149
Cha
pter
4:
Exp
erim
enta
l P
rogr
am
Tab
le 4
.3:
Con
cret
e pr
oper
ties
and
rein
forc
emen
t de
tails
of
test
spe
cim
ens.
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
Con
cret
e1
fc
MPa
40.8
42.2
35.0
35.8
39.5
41.0
33.5
ft
MPa
3.22
3.03
2.94
2.69
3.19
2.91
2.65
Ec
GPa
24.7
25.3
20.6
19.9
23.1
22.3
18.9
Flex
ural
Rei
nf.
9 st
rand
s
of 1
5.4
mm
diam
eter
Shea
r re
info
rcem
ent2
Mat
eria
l
Stee
l
CFR
P
CFR
P
CFR
P
GFR
P
GFR
P
GFR
P
Dia
m.
mm
9.5
9.5
9.5
9.5
9.5
9.5
9.5
Spac
ing
mm
300
300
200
150
300
200
150
Ejv
GPa
£,=
200
130±
6
130±
6
130±
6
45±2
45±2
45±2
Rat
io p
j\,
Afi
/{b w
s)
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0.26
2
0.26
2
0.39
4
0.52
6
0.26
2
0.39
4
0.52
6
ffuv
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6
1538
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1538
±57
1538
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664±
25
664±
25
664±
25
Jben
d
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712±
47
712±
47
712±
47
387±
15
387±
15
387±
15
inde
x
0.26
2
0.17
1
0.25
6
0.34
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0.06
0
0.09
0
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0 1 f c
'. C
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sive
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.22:
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nfor
cem
ent
deta
ils a
nd s
tirru
p in
stru
men
tatio
n of
SC
-9.5
-2.
151
Cha
pter
4:
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re 4
.23:
Rei
nfor
cem
ent
deta
ils a
nd s
tirru
p in
stru
men
tatio
n of
SC
-9.5
-3.
152
Cha
pter
4:
Exp
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Figu
re 4
.24:
Rei
nfor
cem
ent
deta
ils a
nd s
tirru
p in
stru
men
tatio
n of
SC
-9.5
-4.
153
Cha
pter
4: E
xper
imen
tal
Pro
gram
CD
(2)
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rrups
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re 4
.25:
Rei
nfor
cem
ent
deta
ils a
nd s
tirru
p in
stru
men
tatio
n of
SG
-9.5
-2.
154
Cha
pter
4:
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rogr
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.26:
Rei
nfor
cem
ent
deta
ils a
nd s
tirru
p in
stru
men
tatio
n of
SG
-9.5
-3.
155
Cha
pter
4:
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re 4
.27:
Rei
nfor
cem
ent
deta
ils a
nd s
tirru
p in
stru
men
tatio
n of
SG
-9.5
-4.
156
Cha
pter
4:
Exp
erim
enta
l P
rogr
am
n n
n %
%
%
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<2>
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ross
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tion
Figu
re 4
.28:
Rei
nfor
cem
ent
deta
ils a
nd s
tirru
p in
stru
men
tatio
n of
SS-
9.5-
2.
157
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
Figure 4.31: Concrete casting of a beam specimen.
Figure 4.32: A concrete beam specimen just after casting and adjusting the surface.
160
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
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
Cha
pter
4:
Exp
erim
enta
l Pro
gram
2 N
o. 1
5M
o
500
mm
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1000
mm
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10
00 m
m
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1000
mm
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1000
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50
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7000
mm
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750
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t mid
-spa
n A
t loa
d
Figu
re 4
.34:
Loc
atio
ns o
f th
e lo
ngitu
dina
l re
info
rcem
ent
stra
in g
auge
s fo
r th
e te
st s
peci
men
s.
163
Chapter 4: Experimental Program
Figure 4.35: Steel strands after attaching the strain gauges.
Figure 4.36: CFRP stirrups instrumented with strain gauges.
164
Chapter 4: Experimental Program
T
OS
Uf . „
(b) At mid-span (a) At mid-shear span
Figure 4.37: Deflection measurement using LVDTs.
'£ . : • *
D!3
* . BJ1
Wl
DID 0i
Dl.
(a) East shear span (b) West shear span
Figure 4.38: The demec gauges installed in both shear spans of each beam.
165
Chapter 4: Experimental Program
i f^ v? -•• , / / - • •
y
! • ' /
• : • - • • ' - / •
Figure 4.39: Measuring the demec gauges using the digital extensometer.
Figure 4.40: The data acquisition systems utilized in beam testing.
166
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
Steel Frame
Steel Beam
~T Steel Frame
2)0
4000
335 2000
I . . I
4 : ^ i
r — T
335
3270
r i
r—n
•4T
r~~i
.r n
Steel Plate ^
£ *
2000
2)0
500 \ Test Specimen (Beam)
?WfKSOTS5RS55W5?5!W!S!3 Laboratory strong floor
^%V^V^VK»CK%*X»&<KK^WK*KV^^^
2000 2000 2000
Figure 4.41: Schematic for the setup used for testing the beams reinforced with CFRP stirrups.
168
Chapter 4: Experimental Program
500 J,
Steel Frame Steel Frame
Steel Beam
"P
Test Specimen (Beam)
*««««««&$Sw
335 ± 2000 4 !k
& 335
r~~1 r~~i
r-e-T Steel Plate -e-1
2000 w
Tp
210
Laboratory strong floor
500
CHS^^W<^m<m«CW«««W!4^%^^«V««4«i^W^
2000 2000 4
Figure 4.42: Schematic for the setup used for testing the beams reinforced with GFRP and
steel stirrups.
169
Chapter 4: Experimental Program
Figure 4.43: A photograph of the test setup for the beams reinforced with CFRP stirrups.
170
Chapter 4: Experimental Program
Figure 4.44: A photograph of the test setup for the beams reinforced with GFRP stirrups.
171
Chapter 4: Experimental Program
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
Chapter 4: Experimental Program
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
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
600
500
400
300
O
re JZ (0 1 200 "o. Q. <
100
Mid-Shear-Span
~SC-9.5-4 ^___—
y^SC-9.5-3 > ^ Z ' j T ^ SC-9.5-3
> y ^ SC-9.5-2 ^^C ffl "•" " ^ ^ SC-9.5-2
, ^ S S - 9 . 5 - 2 ^ ^ - SS-9.5-2
i»* v i ^ ^
a JZS
r I i i r - • i i
mid-shear span
Mid-Span
SC^5-4
P CL * 1
1 mid-span
k_ - | T
Shear span (a)
20 40 120 140 60 80 100
Deflection (mm)
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
Chapter 5: Experimental Results and Analysis
SC-9.5-4
SC-9.5-3\\
SS-9.5-2 -
Concrete
— e e e -
500 -
400 \SC-9.5-
\ \ r00
\ M O
iol
OH
lied
Sh
ear
Fo
rce
(kN
) A
pp
SC-9.5-2
SS-9.5-2 \ ^
/ ^ S C - 9 . 5 - 4 SC-9.5-3 /
Longitudinal Reinforcement
-4000 -2000 2000 4000 6000
Strain (Microstrain)
8000 10000 12000
Figure 5.3: Flexural strains of beam reinforced with CFRP stirrups.
I 6ee-i
500
SG-9.5-4 V 4 ( ) 0 .
SG-9.5-3 Y 0 0
SG-9.5-2 \ 2*0
SS-9.5-2 |
1 0 *
Concrete \ 1 Q4
I
ear
Fo
rce
Ap
plie
i
/ SG-9.5-4
>/sG-9.5-3
SS-9.5-2 \ / r
^ ^ S G - 9 . 5 - 2
M
f Longitudinal Reinforcement
I I I
-4000 -2000 2000 4000 6000 8000 10000 12000
Strain (Microstrain)
Figure 5.4: Flexural strains of beam reinforced with GFRP stirrups.
177
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
(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
Strain (Microstrain)
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
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
Figure 5.6: Shear failure of beam SC-9.5-2 (CFRP@d/2).
182
Chapter 5: Experimental Results and Analysis
Figure 5.7: Shear failure of beam SC-9.5-3 (CFRP@d/3).
183
Chapter 5: Experimental Results and Analysis
Figure 5.8: Flexure failure of beam SC-9.5-4 (CFRP@d/4).
184
Chapter 5: Experimental Results and Analysis
Figure 5.9: Shear failure of beam SG-9.5-2 (GFRP@o?/2).
185
Chapter 5: Experimental Results and Analysis
Figure 5.10: Shear failure of beam SG-9.5-3 (GFRP@d/3).
186
Chapter 5: Experimental Results and Analysis
Figure 5.11: Shear failure of beam SG-9.5-4 (GFRP@a?/4).
187
Chapter 5: Experimental Results and Analysis
Figure 5.12: Shear failure of control beam SS-9.5-2 (steel@<i/2).
188
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
£ £ o o
o o
6 £
© o r-
Figure 5.16: Crack pattern at failure for beams reinforced with CFRP stirrups.
192
Chapter 5: Experimental Results and Analysis
B
s o o
a B
© o
o o
Figure 5.17: Crack pattern at failure for beams reinforced with GFRP stirrups.
193
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
average stirrup strains in comparison with that reinforced with CFRP stirrups at the same
spacing.
2000 4000 6000 8000 10000
Stirrup Strain (Microstrain)
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
Strain (Microstrain)
8000 10000
Figure 5.21: Typical applied shear force-stirrup strain at the bend of FRP stirrups (SC-9.5-2).
196
Chapter 5: Experimental Results and Analysis
(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
Average Stirrup Strain (microstrain)
10000
SC-9.5-4 CFRP@d/4
Average
2000 4000 6000 8000
Average Stirrup Strain (microstrain)
10000
Figure 5.22: Comparisons between the average stirrup strains calculated from both shear spans
of beams reinforced with CFRP stirrups.
197
Chapter 5: Experimental Results and Analysis
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 (p^E^fE,) for that beam compared to the others
198
Chapter 5: Experimental Results and Analysis
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
Average Stirrup Strain (Microstrain)
8000 9000 10000
Figure 5.24: Applied shear force-average stirrup strain for beams with GFRP stirrups.
199
Chapter 5: Experimental Results and Analysis
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
Average Stirrup Strain (Microstrain)
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
Average Stirrup Strain (Microstrain)
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
Average Stirrup Strain (Microstrain)
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
Chapter 5: Experimental Results and Analysis
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 (p^E^IEs) 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
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
600
500 SC-9.5-4 CFRP @ of/4
SC-9.5-3 CFRP @ d/3
2000 4000 6000 8000
Stirrup Strain (Microstrain)
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
Stirrup Strain (Microstrain)
10000 12000
Figure 5.28: Applied shear force-maximum stirrup strain relationships for GFRP stirrups in
beam specimens comparing to the steel stirrup.
203
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
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
Distance from the Support (mm)
Figure 5.30: Stirrup strain distribution along the shear span of SC-9.5-3 beam (CFRP@d/3).
207
Chapter 5: Experimental Results and Analysis
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
Distance from the Support (mm)
Figure 5.31: Stirrup strain distribution along the shear span of SC-9.5-4 beam (CFRP@d/4).
208
Chapter 5: Experimental Results and Analysis
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
Distance from the Support (mm)
Figure 5.32: Stirrup strain distribution along the shear span of SG-9.5-2 beam (GFRP@J/2).
209
Chapter 5: Experimental Results and Analysis
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
Distance from the Support (mm)
Figure 5.33: Stirrup strain distribution along the shear span of SG-9.5-3 beam (GFRP@J/3).
210
Chapter 5: Experimental Results and Analysis
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
Distance from the Support (mm)
Figure 5.34: Stirrup strain distribution along the shear span of SG-9.5-4 beam (GFRP@J/4).
211
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
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
Applied Shear Force (kN)
500 600
Figure 5.38: Shear resisting components of beams reinforced with GFRP stirrups.
214
Chapter 5: Experimental Results and Analysis
(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
Applied Shear Force (kN)
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
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
(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
Shear Crack Width (mm)
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
Shear Crack Width (mm)
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
Chapter 5: Experimental Results and Analysis
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
Shear Crack Width (mm)
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
Shear Crack Width (mm)
4.5
Figure 5.42: Maximum shear crack width for beams reinforced with GFRP stirrups.
219
Chapter 5: Experimental Results and Analysis
(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
Shear Crack Width (mm)
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
Shear Crack Width (mm)
__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
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
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
Stirrup Strain (Microstrain)
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
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
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
Chapter 5: Experimental Results and Analysis
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
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
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 /
• From Literature A Current Study
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)
• From Literature A Current Study
100 200 300 400
Vpnd. (kN)
500 600
Figure 6.5: Experimental to predicted shear strength using ACI (2006) and CSA (2009).
237
Chapter 6: Analytical Study
£
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
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
(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
Average Stirrup Strain (Microstrain)
10000
(b) SC-9.5-3
(CFRP@<//3)
svu
\ 500
Sh
ear
Forc
e
i i
"S 200 Q.
< 100
0
MCFT . y ^ ^ ^
-^^Exper 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
Average Stirrup Strain (Microstrain)
10000
Experimental
.' MCFT
SC-9.5-4 CFRP@o74
2000 4000 6000 8000
Average Stirrup Strain (Microstrain)
10000
Figure 6.9: Comparison between measured average stirrup strain and the predicted using the
MCFT for beams reinforced with CFRP stirrups.
241
Chapter 6: Analytical Study
(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
Average Stirrup Strain (Microstrain)
10000
SG-9.5-3 GFRP@d73
Experimental MCFT
2000 4000 6000 8000
Average Stirrup Strain (Microstrain)
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
Average Stirrup Strain (Microstrain)
10000
Figure 6.10: Comparison between measured average stirrup strain and the predicted using the
MCFT for beams reinforced with GFRP stirrups.
242
Chapter 6: Analytical Study
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
Shear Crack Width (mm)
Figure 6.11: Measured shear crack width versus predicted using MCFT for the control beam
SS-9.5-2.
243
Chapter 6: Analytical Study
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
Shear Crack Width (mm)
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
Shear Crack Width (mm)
SC-9.5-4 CFRP@d/4
0 1 2 3 4 5
Shear Crack Width (mm)
Figure 6.12: Measured shear crack width versus predicted using MCFT for beams reinforced
with CFRP stirrups.
244
Chapter 6: Analytical Study
600
Z
600
500
£ 400 o u.
S 3 0 0
•o .£ "a. a. <
200
100
Shear Crack Width (mm)
EXP.
. - MCFT
SG-9.5-3 GFRP@d/3
1 2 3 4
Shear Crack Width (mm)
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
Shear Crack Width (mm)
Figure 6.13: Measured shear crack width versus predicted using MCFT for beams reinforced
with GFRP stirrups.
245
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
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 = ^Afv ffv where ^Afv 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
Chapter 6: Analytical Study
^
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
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
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
251
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405.90
712
285.04
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Chapter 6: Analytical Study
1.20
0.00 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 6.17: Measured shear strength versus predicted using SFM.
J2
1 .£.
1
0.8
0.6
0.4
0.2
0
. . . A - - " . ; ; ' .
A'"" *" / Failed in Flexure
i
. - &
- - ' ' " . . - - - •
- -•• - CFRP stirrups - Exp.
- -&• - 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
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
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
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154.
1 20
0 10
00
1000
S-
G3B
0.85
0 36
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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
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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
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42.1
0 14
5.0
0.50
40
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225
250
200
950
BA
4
Raz
aqpu
r et
al.
(200
4)
1.31
6 54
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41.4
2 42
.0
0.72
37
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346
380
0
950
G07
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1.53
8 63
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41.4
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380
0
950
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6 38
0
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G
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1.06
7 45
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42.6
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380
0 ^0
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G
10N
2
1.16
7 48
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34
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15N
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1150
G
15N
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310
380
0
950
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43.8
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0.0
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310
380
0 en
950
C07
N2
1.02
4 47
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46.5
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0.0
1.10
43
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310
380
0 en
1150
C
10N
1
1.13
3 52
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46.5
1 12
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43
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310
380
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1150
C
10N
2
1.22
6 55
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45.6
1 12
0.0
1.54
34
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310
380
0 CO
1150
C
15N
1
1.27
8 58
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45.6
1 12
0.0
1.54
34
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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
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0.96
39
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360
406.
4 45
7 12
19.2
V
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1 T
urey
en a
nd
0 0
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s
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08
37.6
0.
96
39.9
36
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457
1219
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V-G
2-1
0.91
9 11
4.80
12
4.90
47
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0.96
40
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360
406.
4 45
7 12
19.2
V
-A-l
0.89
7 13
7.00
15
2.70
40
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CN ON
42.3
36
0 42
6.7
457
1219
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V-G
l-2
1.08
1 15
2.60
14
1.22
37
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CN ON
42.5
36
0 40
6.4
457
1219
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V-G
2-2
1.17
8 17
7.00
15
0.26
47
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CN ON
42.6
36
0 40
6.4
457
1219
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V-A
-2
Fros
ch
(200
2)
0.96
2 39
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40.6
6 40
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-
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
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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
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44.6
1 40
.3
NO NO
36.3
22
5 28
6 22
9 91
4 3F
RPb
1.00
2 44
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44.6
1 40
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NO NO
36.3
22
5 28
6 22
9 91
4 3F
RPc
0.96
2 43
.80
45.5
1 40
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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
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RP
b
1.01
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1 40
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00
36.3
22
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4
"5T
0.72
7 37
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51.8
8 40
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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
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Pa
0.87
2 41
.80
47.9
5 40
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2.27
36
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224
286
229
914
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Pb
0.86
1 41
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47.9
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.3
2.27
36
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224
f 28
6 22
9 91
4
so
1.16
1 53
.40
45.9
9 40
.0
2.30
24
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279
330
178
750
BM
7
0.96
7 36
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37.3
1 40
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24
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287
330
178
750
BM
8
0.96
8 40
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41.4
5 40
.0
1.34
24
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287
330
178
750
BM
9
Alk
hrda
ji et
al. (
2001
)
0.84
9 26
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31.5
8 40
.0
0.74
28
.6
157.
5
o as
305
710
GF
RP
1
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29.5
1 40
.0
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30
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157.
5
©
305
913
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RP
2
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8 40
.0
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27
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157.
5
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305
as
GF
RP
3
0.99
1 28
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28.7
7 40
.0
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28
.2
157.
5
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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
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100.
62
41.3
0.
96
63.1
10
4
© in
1000
13
00
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41
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154
200
1000
13
00
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Mic
halu
k et
al. (
1995
)
0.99
5 45
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45.2
2 10
5.0
1.51
34
.3
250
300
150
750
No.
l
0.88
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6
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34
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No.
15
Zha
o et
al.
(199
5)
TJ- in Os •>* as ~-H
so
2 Q
3 > o u
o
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
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
Shear Crack Width (mm)
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
Chapter 6: Analytical Study
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
Chapter 6: Analytical Study
(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
Shear Crack Width (mm)
SC-9.5-3
Experimental Proposed
2 3
Shear Crack Width (mm)
600
(c) SC-9.5-4
CFRP@d/4
SC-9.5-4
Experimental Proposed
2 3
Shear Crack Width (mm)
Figure 6.25: Prediction of shear crack width for beams reinforced with CFRP stirrups using
the proposed equation (Equation 6.9).
269
Chapter 6: Analytical Study
(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
Experimental Proposed
2 3
Shear Crack Width (mm)
SG-9.5-3
Experimental Proposed
1 2 3
Shear Crack Width (mm)
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
Experimental Proposed
2 3
Shear Crack Width (mm)
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
Chapter 7: Summary and Conclusions
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
Chapter 7: Summary and Conclusions
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
Chapter 7: Summary and Conclusions
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
Chapter 7: Summary and Conclusions
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, p^E^/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
Chapter 7: Summary and Conclusions
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
Chapter 7: Summary and Conclusions
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
Chapter 7: Summary and Conclusions
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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