1 UNIVERSITY OF CALGARY Long-Term Flexural Performance of Prestressed-NSM-CFRP
Transcript of 1 UNIVERSITY OF CALGARY Long-Term Flexural Performance of Prestressed-NSM-CFRP
University of Calgary
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2013-11-07
Long-Term Flexural Performance of
Prestressed-NSM-CFRP Strengthened RC Beams
Yadollahi Omran, Hamid
Yadollahi Omran, H. (2013). Long-Term Flexural Performance of Prestressed-NSM-CFRP
Strengthened RC Beams (Unpublished doctoral thesis). University of Calgary, Calgary, AB.
doi:10.11575/PRISM/26783
http://hdl.handle.net/11023/1159
doctoral thesis
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1
UNIVERSITY OF CALGARY
Long-Term Flexural Performance of Prestressed-NSM-CFRP Strengthened RC Beams
by
Hamid Yadollahi Omran
A THESIS
SUBMITTED TO THE FACULTY OF GRADUATE STUDIES
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
DEPARTMENT OF CIVIL ENGINEERING
CALGARY, ALBERTA
November, 2013
© Hamid Yadollahi Omran 2013
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Abstract
The use of prestressed Fibre Reinforced Polymer (FRP) for strengthening
structural members requires gaining further knowledge about the long-term behaviour of
these members. In this research, the long-term flexural performance of the prestressed
Near-Surface Mounted (NSM) Carbon Fibre Reinforced Polymer (CFRP) strengthened
Reinforced Concrete (RC) beams subjected to accelerated environmental exposure and
sustained load condition was studied. The static behaviour of the exposed and unexposed
beams was predicted numerically and analytically, and the predicted results were
compared with the experimental ones. The prestressing system used for tensioning the
NSM CFRP reinforcements was modified. The prestress loss in the NSM CFRP
reinforcements was studied. Deformability and ductility of the prestressed NSM CFRP
strengthened RC beams were studied in detail. Furthermore, the effects of the different
parameters on the flexural behaviour of the NSM CFRP strengthened RC beams and on
the pullout capacity of the anchorage system used for prestressing were investigated
numerically. The findings showed the significant effect of the applied exposure on the
flexural performance of the beams, and furthermore, the high reliability of the developed
numerical and analytical models for simulation of the static flexural behaviour of the
exposed and unexposed beams. The results of this research lead to an understanding of
the long-term flexural behave iour of the RC beams strengthened using prestressed NSM
CFRP reinforcements and pursue the evolution of this strengthening system to be used in
practical projects with sufficient confidence.
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Preface
In a country like Canada, deterioration of reinforced concrete (RC) bridges and
buildings due to severe weather conditions combined with aging and overloading causes
significant economical and social problems. Repairing damaged structures using proper
technique is vital to halt the losses of cost and time. The main advantages of FRP
materials such as excellent corrosion resistance, low density, and high tensile strength in
comparison with the conventional strengthening materials made FRP one of the most
commonly applied strengthening materials within past fifteen years. Among different
types of the strengthening systems developed for RC beams, prestressed Near-Surface-
Mounted (NSM) Carbon Fibre Reinforced Polymer (CFRP) is one of the latest techniques
for strengthening of concrete members.
This thesis consists of three parts: experimental study, finite element (FE)
analysis, and analytical investigation in which the long-term flexural performance of the
NSM CFRP strengthened RC beams was investigated. The experimental study consisted
of two phases and an additional investigation for the modification of the prestressing
system. The flexural performance of the prestressed NSM CFRP strengthened RC beams
subjected to freeze-thaw cycles was investigated in phase I, which consisted of nine
large-scale (5.15 m long with rectangular section 200×400 mm) beams: one un-
strengthened control RC beam, four strengthened RC beams using CFRP strips, and four
strengthened beams using CFRP rebars. CFRP rebar and strips with similar axial stiffness
were used for strengthening. The strengthened beams were prestressed to 0, 20, 40, and
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60% of the ultimate CFRP tensile strain reported by the manufacturer. After
strengthening, all nine beams were initially loaded up to 1.2 times the analytical cracking
load for each beam, and then placed inside an environmental testing facility chamber,
exposed to 500 freeze-thaw cycles where each cycle was programmed between -34oC to
+34oC with period of 8 hrs and a relative humidity of 75% for temperatures above +20
oC.
The flexural performance of the prestressed NSM CFRP strengthened RC beams
subjected to combined freeze-thaw cycles and sustained load was investigated in phase II,
which consisted of five RC beams: one un-strengthened control beam and four beams
similar to the beams strengthened with CFRP strips in phase I. The beams in phase II
were subjected to the exposure similar to that of phase I (except that the relative humidity
of 75% for temperatures above +20oC was replaced with water spray, 18 L/min for a time
period of 10 min, at temperature +20oC, to increase the severity of the applied exposure)
while each beam was being subjected to a sustained load equal to 62 kN (47% of
analytical ultimate load of the non-prestressed NSM-CFRP strengthened RC beam). After
being subjected to exposure and loading, all beams in phases I and II were tested to
failure under four-point bending configuration and static monotonic loading. The tests
results revealed that the flexural performance of the beams tested in phase II was
significantly affected by the applied exposure and sustained loading while the exposure
had insignificant effects on the flexural performance of the beams tested in phase I.
Furthermore, an experimental investigation was performed on the modification of the
prestressing system used for NSM CFRP strengthening in phases I and II, to avoid
cracking at the location of the brackets during prestressing. The temporary steel brackets
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were modified to be capable of changing the eccentricity for prestressing (the location of
the jacks). To investigate the performance of the modified prestressing system, the
prestressing using the modified system was applied to three concrete specimens
(200×400×1500 mm) to a load equivalent to 93% of the CFRP ultimate strength reported
by the manufacturer, for three different eccentricities. The results showed the modified
system performed appropriately so that the cracking at location of the brackets can be
avoided during prestressing.
The FE analysis consisted of four parts performed using finite element software,
ANSYS. In part I, a nonlinear 3D FE model was developed to simulate the behaviour of
RC beams strengthened with prestressed NSM-CFRP strips. The model considered the
debonding at the concrete-epoxy interface. The FE model was compared and validated
with experimental test results reported by Gaafar (2007). In part II, a parametric study
was performed on the RC beams strengthened with prestressed NSM-CFRP strips by
developing a simplified 3D nonlinear FE model to decrease the solution time for doing
the parametric study. Then, the model was used to analyze twenty-three beams to assess
the effects of the prestressing level in NSM-CFRP strips, the tensile steel reinforcement
ratio, and the concrete compressive strength. In part III, a 3D FE model was developed to
simulate the behaviour of the end-steel anchor used for the prestressed NSM-CFRP
reinforcement. The CFRP-epoxy and epoxy-anchor interfaces were modeled by assigning
Coulomb friction model. Then, fourteen models were analyzed to investigate the effects
of bond cohesion, anchor length, anchor width, and anchor height on the interfacial stress
distributions and anchorage capacity. In part IV, the post-exposure load-deflection
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responses of the five beams tested in phase II of the experimental program were predicted
by developing a nonlinear 3D FE model similar to part I (FE modeling of unexposed
beams).
The analytical investigation consisted of two sections. In section I, after a brief
review on the available deformability or ductility indices, three deformability indices
were modified to be applicable for NSM-CFRP strengthened RC beams. Afterwards,
results of eighteen large-scale RC beams strengthened with prestressed and non-
prestressed NSM-CFRP strips and rebars were employed to evaluate their ductility and
deformability based on the modified models and the conventional indices. Furthermore,
the limits of the design Code (CAN/CSA-S6-06, 2011) for ductility and deformability of
the beams were used and new limits were proposed and validated for different models. In
section II, the load-deflection responses of the nine tested beams in phase I of the
experimental program were predicted analytically by developing a code in Mathematica
software. The code has the capabilities of assigning the actual concrete stress-strain curve
based on Loov's equation, elasto-plastic behaviour for compression and tension steel,
linear behaviour for FRP, and different prestressed CFRP length along the length of the
beam. Perfect bond is assumed in the analytical model. The mid-span deflection at each
applied load (moment) is calculated using integration of curvatures along the length of
the beam.
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Acknowledgements
I would like to express my greatest gratitude to the supervisor of this research, Dr.
Raafat El-Hacha who offered invaluable assistance, support, and guidance during this
PhD journey.
Thanks to the Intelligent Sensing for Innovative Structures Network (ISIS
Canada) and the University of Calgary through the URGC for partially financially
supporting this research. The in-kind support from Lafarge Canada for supplying the
Concrete, Sika Canada for providing the epoxy materials, and Hughes Brothers for
providing the CFRP reinforcements used in this project. Thanks to civil engineering lab
technicians at the University of Calgary: Terry Quinn, Dan Tilleman, Don Anson, Mirsad
Berbic, and Daniel Larson for endless help in progress of this project, and making
friendly environment in the lab. Many thanks to my friends and fellow graduate students,
in particular, Fadi Oudah, Khaled Abdelrahman, Donna Chen, Pouya Zangeneh, Khoa
Tran, Rashid Popal, Mohamadreza Seraji, Maryam Taghbostani, and Mona Amiri for
sharing thoughts, their supports, and all loving memories. Special thanks to Dr. Gerd
Birkle who provided me the opportunity to work during last two years of my education
that without his support it could have been tough. At the end, I would like to express my
gratitude and love to my beloved family and relatives for their support and endless love
during my studies.
To each one of you who has helped me on this journey:
“May the wind always be on your back and the sun upon your face”
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Dedication
With respect and love to:
My parents, Eyni & Leili, my brother, Saeid, and my sisters, Sara & Fariba, who have
made the happiest moments of my life whenever I have passed at home in the bosom of
my family
My uncle Ebrahim, who bravely fought against liver cancer for two years just after I
embarked upon this PhD journey and finally…, with all loving memories
My dearest grandparents
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Table of Contents
Approval Page ..................................................................................................................... ii
Abstract .............................................................................................................................. iii Preface................................................................................................................................ iv Acknowledgements .......................................................................................................... viii Dedication .......................................................................................................................... ix Table of Contents .................................................................................................................x
List of Tables ................................................................................................................. xviii List of Figures and Illustrations ...................................................................................... xxii
List of Nomenclature and Symbols................................................................................xxxv
List of Abbreviations ......................................................................................................... xl
CHAPTER ONE: GENERAL INTRODUCTION ..............................................................1 1.1 Introduction ................................................................................................................1
1.2 The Most Important Reasons for Strengthening of Structures ..................................2 1.3 Methods for Upgrading the RC Members .................................................................3
1.4 Statement of the Problem ...........................................................................................3 1.4.1 Performance of Strengthened Beam with Prestressed NSM-FRP .....................3 1.4.2 Effects of Freeze-Thaw Exposure .....................................................................4
1.4.3 Effects of Sustained Load Combined with Freeze-Thaw Exposure ..................5
1.4.4 FE Analysis of the Prestressed NSM-FRP Strengthened RC Beams ................5 1.4.5 Analytical Model of the Exposed Prestressed NSM-FRP Strengthened RC
Beams .................................................................................................................6
1.4.6 Anchorage for Prestressed NSM-FRP Strengthening Method ..........................7 1.4.7 Modification of NSM-FRP Prestressing System ...............................................7
1.4.8 Deformability and Ductility of the Prestressed FRP Strengthened RC
Beams .................................................................................................................8
1.5 Research Objectives ...................................................................................................9 1.5.1 Principal Objectives ...........................................................................................9 1.5.2 Secondary Objectives ......................................................................................10
1.6 Scope of Work .........................................................................................................10 1.7 Thesis Layout ...........................................................................................................14
CHAPTER TWO: LITERATURE REVIEW ....................................................................15 2.1 Introduction ..............................................................................................................15
2.2 History of Engineering Materials ............................................................................15 2.3 Fibre Reinforced Polymer ........................................................................................16
2.3.1 Fibres ...............................................................................................................18 2.3.1.1 Carbon ....................................................................................................19 2.3.1.2 Glass .......................................................................................................20 2.3.1.3 Aramid ...................................................................................................21
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2.3.2 Matrices ...........................................................................................................21 2.3.3 FRP Composite ................................................................................................24
2.4 Strengthening Concrete Structures Using FRP Materials ........................................26 2.4.1 Externally Bonded Strengthening Method ......................................................27
2.4.2 Near-Surface Mounted Strengthening Method ...............................................27 2.5 History of NSM Method ..........................................................................................30 2.6 Material Used for NSM ...........................................................................................31
2.6.1 Reinforcements ................................................................................................31 2.6.2 Groove Filler ...................................................................................................32
2.7 Comparison between NSM-FRP and EB-FRP Technique ......................................33 2.8 Background of the Topic .........................................................................................34
2.9 Prestressed NSM-FRP Strengthened RC Beam .......................................................35
2.10 Environmental Exposure ........................................................................................47 2.10.1 Effect of Freeze-Thaw Exposure on Concrete ..............................................47 2.10.2 Effect of Freeze-Thaw Exposure on Steel Rebar ..........................................49
2.10.3 Effect of Freeze-Thaw Exposure on CFRP Reinforcement ..........................50 2.10.4 Effect of Freeze-Thaw Exposure on Epoxy Adhesive ..................................52
2.10.5 Effect of Sustained Loading on Concrete ......................................................53 2.10.6 Effect of Sustained Loading on FRP and Adhesive ......................................54 2.10.7 Synergistic Effect of Sustained Load and Freeze-Thaw Exposure ...............55
2.10.8 Effect of Environmental Exposure on FRP-Strengthened RC Beam ............56
2.11 FE Modeling of FRP-Strengthened RC Beams .....................................................64 2.12 Research Gaps ........................................................................................................73 2.13 Summary ................................................................................................................76
CHAPTER THREE: EXPERIMENTAL PROGRAM ......................................................77 3.1 Introduction ..............................................................................................................77
3.2 Test Matrix ...............................................................................................................77 3.3 RC Beam Specimens ...............................................................................................81
3.3.1 Design ..............................................................................................................81 3.3.2 Details of Beams ..............................................................................................84 3.3.3 Manufacturer Material Properties ....................................................................87
3.3.3.1 Steel Reinforcements .............................................................................87 3.3.3.2 Concrete .................................................................................................87
3.3.3.3 CFRP Reinforcements ...........................................................................87 3.3.3.4 Epoxy Adhesives ...................................................................................87
3.3.3.5 Anchor Bolts ..........................................................................................88 3.3.4 Fabrication .......................................................................................................88 3.3.5 Instrumentation ................................................................................................89
3.4 Prestressed NSM FRP Strengthening System .........................................................91 3.5 Initial Loading after Strengthening ..........................................................................91 3.6 Freeze-Thaw Cycling Exposure ...............................................................................92 3.7 Sustained Loading ....................................................................................................97
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3.8 Testing Procedure ..................................................................................................107 3.9 Summary ................................................................................................................108
CHAPTER FOUR: EXPERIMENTAL RESULTS AND DISCUSSION ......................109 4.1 Introduction ............................................................................................................109
4.2 Phase I: Prestressed NSM-CFRP Strengthened RC Beams under Freeze-Thaw
Exposure ..............................................................................................................110 4.2.1 Test Beams and Material Properties ..............................................................110
4.2.1.1 Steel Reinforcements ...........................................................................110
4.2.1.2 Concrete ...............................................................................................111 4.2.1.3 CFRP Reinforcements .........................................................................112
4.2.1.4 Epoxy Adhesives .................................................................................112 4.2.1.5 Anchor Bolts ........................................................................................112
4.2.2 Load-Deflection Response ............................................................................112 4.2.2.1 Pre-Cracking Behaviour ......................................................................116 4.2.2.2 Post-Cracking Behaviour .....................................................................118
4.2.2.3 Failure Mode and Cracking Pattern .....................................................120 4.2.3 Load-Strain Response ....................................................................................131
4.2.4 Strain Profile along the CFRP Strips or Rebar ..............................................140 4.2.5 Strain Distribution at Mid-span .....................................................................144
4.3 Effects of CFRP Geometry: Rebar versus Strips ...................................................149
4.4 Calculation of Optimum and Beneficial Prestressing Levels ................................152
4.5 Effects of Freeze-Thaw Cycling Exposure ............................................................156 4.5.1 Material Properties of the Unexposed Beams ...............................................156
4.5.1.1 Steel Reinforcements ...........................................................................156
4.5.1.2 CFRP Reinforcements .........................................................................156 4.5.1.3 Concrete ...............................................................................................157
4.5.1.4 Epoxy Adhesives .................................................................................157 4.5.1.5 Anchor Bolts ........................................................................................157
4.5.2 Error Analysis ................................................................................................157 4.5.3 Load-Deflection Response ............................................................................161
4.5.3.1 Beams Strengthened with CFRP Strips ...............................................161 4.5.3.2 Beams Strengthened with CFRP Rebar ...............................................165 4.5.3.3 Beams Strengthened with CFRP Rebar versus Strips .........................170
4.5.4 Effects of Prestressing ...................................................................................173 4.6 Deformability and Ductility of NSM CFRP Strengthened RC Beams ..................178
4.6.1 Existing Ductility and Deformability Models ...............................................181 4.6.1.1 Displacement Ductility Index ..............................................................181 4.6.1.2 Curvature Ductility Index ....................................................................182 4.6.1.3 Rotational Ductility Index ...................................................................182 4.6.1.4 Deformability Factor ............................................................................183 4.6.1.5 Naaman and Jeong (1995) Index .........................................................183 4.6.1.6 Abdelrahman Index ..............................................................................184
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4.6.1.7 CHBDC Deformability Factor .............................................................185 4.6.1.8 Zou Index .............................................................................................186 4.6.1.9 Rashid Index ........................................................................................187
4.6.2 Modification of the Deformability Models for FRP Strengthened RC
Beams .............................................................................................................189 4.6.2.1 Modified Deformability Factor ............................................................189 4.6.2.2 Modified CHBDC Deformability Index ..............................................190 4.6.2.3 Modified Zou Index .............................................................................191
4.6.3 Deformability of NSM-CFRP Strengthened RC Beam .................................192
4.6.3.1 Considered Beams ...............................................................................192 4.6.3.2 Deformability Analysis and Discussions .............................................194
4.7 Phase II: Prestressed NSM-CFRP Strengthened RC Beams under Combined
Sustained Load and Freeze-Thaw Exposure ........................................................206 4.7.1 Test Beams and Material Properties ..............................................................206
4.7.1.1 Steel Reinforcements ...........................................................................207
4.7.1.2 Concrete ...............................................................................................207 4.7.1.3 CFRP Strips .........................................................................................208
4.7.1.4 Epoxy Adhesives .................................................................................208 4.7.1.5 Anchor Bolts ........................................................................................208
4.7.2 Results from Sustained Load and Freeze-Thaw Exposure ............................208
4.7.3 Load-Deflection Response ............................................................................223
4.7.4 Load-Strain Response ....................................................................................236 4.7.5 Strain Profile along the CFRP Strips .............................................................243 4.7.6 Strain Distribution at Mid-span .....................................................................246
4.8 Combined Effects of Freeze-Thaw Cycling Exposure and Sustained Load ..........248 4.8.1 Material Properties of the Compared Beams .................................................249
4.8.2 Error Analysis ................................................................................................249 4.8.3 Load-Deflection Response ............................................................................250
4.9 Prestress Losses in Phases I & II ...........................................................................256 4.10 Modification of Temporary and Fixed Brackets of the Anchorage System for
Prestressing ..........................................................................................................265 4.10.1 Modified Prestressing System and Material Properties ...............................269
4.10.1.1 Concrete .............................................................................................271
4.10.1.2 Steel Reinforcements .........................................................................271
4.10.1.3 Dywidag Thread-Bar and Nuts ..........................................................271
4.10.1.4 Steel Bolts ..........................................................................................271 4.10.2 Testing Procedure ........................................................................................272 4.10.3 Results and Discussion ................................................................................273
4.11 Summary ..............................................................................................................277
CHAPTER FIVE: NUMERICAL AND ANALYTICAL SIMULATIONS ...................279 5.1 Introduction ............................................................................................................279
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5.2 Finite Element Modeling of RC Beams Strengthened with Prestressed NSM-
FRP ......................................................................................................................280 5.2.1 Experimental Program Overview and Material Properties ...........................280
5.2.1.1 Steel Reinforcements ...........................................................................282
5.2.1.2 Concrete ...............................................................................................283 5.2.1.3 CFRP Strips .........................................................................................283 5.2.1.4 Epoxy Adhesives .................................................................................283 5.2.1.5 Anchor Bolts ........................................................................................283
5.2.2 Description of Finite Element Model ............................................................284
5.2.3 Modeling of Materials ...................................................................................285 5.2.3.1 Concrete ...............................................................................................285
5.2.3.2 Steel Reinforcements ...........................................................................292
5.2.3.3 CFRP Strips .........................................................................................295 5.2.3.4 Epoxy Adhesives .................................................................................296 5.2.3.5 End Anchor and Loading and Supporting Steel Plates ........................298
5.2.3.6 Bolts at End Anchors ...........................................................................298 5.2.4 Debonding Model ..........................................................................................299
5.2.4.1 Identification of Shear Stress-Slip Model ............................................304 5.2.4.2 Identification of Normal Tension Stress-Gap Model ..........................306
5.2.5 Modeling of Prestressing ...............................................................................307
5.2.6 Mesh Sensitivity Analysis .............................................................................308
5.2.7 Nonlinear Analysis ........................................................................................316 5.2.8 FE Results, Validation, and Discussion ........................................................318
5.2.8.1 Load-Deflection Curve ........................................................................318
5.2.8.2 Strain Profiles and Distributions ..........................................................324 5.2.8.3 Debonding aspects ...............................................................................329
5.3 Parametric Study on RC Beams Strengthened with Prestressed NSM-FRP .........332 5.3.1 Modeled Beams .............................................................................................332
5.3.2 Description of FE Model ...............................................................................334 5.3.3 Modeling of Materials ...................................................................................335
5.3.3.1 Concrete ...............................................................................................335 5.3.3.2 Steel Reinforcements ...........................................................................337 5.3.3.3 CFRP Strips .........................................................................................337
5.3.3.4 Epoxy Adhesive ...................................................................................337
5.3.3.5 Bolts at Steel End Anchor ....................................................................338
5.3.3.6 Steel End Anchor and Loading and Supporting Steel Plates ...............338 5.3.3.7 Bond at Concrete-Epoxy Interface ......................................................338 5.3.3.8 Modeling of Prestressing .....................................................................339
5.3.4 Nonlinear Solution .........................................................................................339 5.3.5 Validation of the Model .................................................................................340
5.3.6 Parametric Study ...........................................................................................343 5.3.6.1 Effects of Prestressing Level in the NSM CFRP .................................343 5.3.6.2 Effects of Tension Steel Reinforcement ..............................................357
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5.3.6.3 Effects of Concrete Compressive Strength ..........................................363 5.4 FE Modeling of Steel End Anchor and Parametric Study .....................................364
5.4.1 Description of the FE Model .........................................................................365 5.4.2 Modeling of Materials ...................................................................................367
5.4.2.1 Steel End Anchor .................................................................................367 5.4.2.2 CFRP Strip ...........................................................................................368 5.4.2.3 Epoxy Adhesive ...................................................................................368 5.4.2.4 Anchor Bolt ..........................................................................................369 5.4.2.5 Bond .....................................................................................................369
5.4.3 Mesh Sensitivity Analysis .............................................................................370 5.4.4 Nonlinear Analysis ........................................................................................374
5.4.5 Numerical Results and Discussion ................................................................378
5.4.5.1 Effects of Bond Cohesion ....................................................................378 5.4.5.2 Effects of Anchorage Length ...............................................................381 5.4.5.3 Effects of Adhesive Width ...................................................................385
5.4.5.4 Effects of Adhesive Height ..................................................................390 5.5 Analytical Modeling of RC Beams Strengthened With Prestressed NSM-CFRP
Reinforcements Subjected to Freeze-Thaw Exposure .........................................395 5.5.1 Experimental Program Overview ..................................................................396 5.5.2 Description of Algorithm ..............................................................................397
5.5.2.1 Concepts for Calculation of Deflection at an Arbitrary Load Level ...397
5.5.3 Modeling of Materials ...................................................................................402 5.5.3.1 Concrete of Exposed Beam ..................................................................402 5.5.3.2 Steel Reinforcement .............................................................................403
5.5.3.3 CFRP Strip or Rebar ............................................................................404 5.5.4 Nonlinear Analysis ........................................................................................404
5.5.5 Analytical Results and Discussion ................................................................406 5.5.5.1 Load-Deflection Curve ........................................................................406
5.6 FE Modeling of RC Beams Strengthened with Prestressed NSM-CFRP
Reinforcement Subjected to Freeze-Thaw Exposure and Sustained Load ..........413 5.6.1 Experimental Program Overview ..................................................................413 5.6.2 Description of finite element model ..............................................................413 5.6.3 Debonding Model of Exposed Beams ...........................................................414
5.6.3.1 Bond-Slip Model for Exposed Beams .................................................414
5.6.3.2 Normal Tension Stress-Gap Model for Exposed Beams .....................415
5.6.4 Modeling of Prestressing ...............................................................................415 5.6.5 Modeling of Materials ...................................................................................416
5.6.5.1 Concrete of Exposed Beams ................................................................416 5.6.5.2 Steel Reinforcement .............................................................................418 5.6.5.3 CFRP Strip ...........................................................................................419
5.6.5.4 Epoxy Adhesive, Loading Plate, Steel Anchors, and Steel Bolts ........420 5.6.6 Nonlinear Analysis ........................................................................................420 5.6.7 Numerical Results and Discussion ................................................................421
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5.7 Summary ................................................................................................................425
CHAPTER SIX: CONCLUSIONS AND RECOMMENDATIONS ..............................427 6.1 Introduction ............................................................................................................427 6.2 Conclusions ............................................................................................................428
6.2.1 Experimental Test Results .............................................................................428 6.2.1.1 Phase I: Experimental Study on RC Beams Strengthened with
Prestressed NSM-CFRP Strips and Rebar Subjected to Freeze-Thaw
Exposure................................................................................................428
6.2.1.2 Deformability and Ductility of NSM CFRP Strengthened RC Beams 431 6.2.1.3 Phase II: Prestressed NSM-CFRP Strengthened RC Beams under
Combined Sustained Load and Freeze-Thaw Exposure .......................432 6.2.1.4 Prestress Losses in Prestressed NSM CFRP Strips and Rebar ............435
6.2.1.5 Modification of the NSM CFRP Prestressing System .........................435 6.2.2 Numerical and Analytical Simulations ..........................................................436
6.2.2.1 Finite Element Modeling of RC Beams Strengthened with
Prestressed NSM-FRP...........................................................................436 6.2.2.2 Parametric Study on RC Beams Strengthened with Prestressed
NSM-FRP..............................................................................................437 6.2.2.3 FE Modeling of Steel End Anchor and Parametric Study ...................438 6.2.2.4 Analytical Modeling of RC Beams Strengthened With Prestressed
NSM-CFRP Reinforcements Subjected to Freeze-Thaw Exposure .....439
6.2.2.5 FE Modeling of RC Beams Strengthened with Prestressed NSM-
CFRP Reinforcement Subjected to Freeze-Thaw Exposure and
Sustained Load ......................................................................................440
6.3 Recommendations ..................................................................................................441
REFERENCES ................................................................................................................443
LIST OF TO DATE PUBLICATIONS FROM THE RESEARCH PRESENTED IN
THIS PHD THESIS ................................................................................................467
APPENDIX A: BEAM DESIGN.....................................................................................470 A.1 Introduction ...........................................................................................................470
A.2 Design Concepts, Source Code, and Results ........................................................470
APPENDIX B: FABRICATION OF BEAMS ................................................................477 B.1 Introduction ...........................................................................................................477 B.2 Fabrication of Formwork ......................................................................................477 B.3 Steel Cage ..............................................................................................................478
B.4 Casting Concrete ...................................................................................................479 B.5 Strengthening Procedure .......................................................................................480
B.5.1 General Steps ................................................................................................480
B.5.2 Preparation of CFRP Strips or Rebar ............................................................483
xvii
B.5.3 Steel Bolts for End Anchors and Temporary Brackets .................................484 B.5.4 Mechanical Anchors .....................................................................................485 B.5.5 Temporary Brackets ......................................................................................486 B.5.6 Cutting Grooves ............................................................................................487
B.5.7 Drilling Holes for Bolts ................................................................................488 B.5.8 Prestressing System for NSM CFRP ............................................................489
APPENDIX C: ANCILLARY TEST RESULTS ............................................................491 C.1 Introduction ...........................................................................................................491
C.2 Concrete ................................................................................................................491 C.3 CFRP Strip and Rebar ...........................................................................................495
C.4 Steel Reinforcements ............................................................................................498
APPENDIX D: ANSYS LOGS .......................................................................................501
D.1 Introduction ...........................................................................................................501 D.2 ANSYS Logs for BS-P2-R ...................................................................................501
D.2.1 BS-P2-R.mntr ...............................................................................................501
D.2.2 BS-P2-R.BSC ...............................................................................................505 D.2.3 BS-P2-R.stat .................................................................................................505
D.2.4 BS-P2-R.s01 .................................................................................................506 D.2.5 BS-P2-R.s02 .................................................................................................507 D.2.6 BS-P2-R.s03 .................................................................................................508
D.2.7 BS-P2-R.s04 .................................................................................................509
D.2.8 BS-P2-R.s05 .................................................................................................511 D.2.9 BS-P2-R.s06 .................................................................................................512 D.2.10 BS-P2-R.s07 ...............................................................................................513
APPENDIX E: DEVELOPED COMPUTATIONAL SOURCE CODE IN
MATHEMATICA...................................................................................................516
E.1 Introduction ...........................................................................................................516 E.2 Calculation of the Exposed Concrete Stress-Strain Curve ....................................516
E.3 Computational Source Code ..................................................................................517
xviii
List of Tables
Table 2-1: Some application of polymer composites (Sheikh-Ahmad, 2008). ................. 18
Table 2-2: Tensile properties of typical carbon fibres (Akovali, 2001). .......................... 20
Table 2-3: Typical properties of different glass fibres (Akovali, 2001). .......................... 20
Table 2-4: Properties of some aramid fibres (Akovali, 2001). ......................................... 21
Table 2-5: Mechanical and thermal properties of matrix materials at room
temperature (Sheikh-Ahmad, 2008). ......................................................................... 23
Table 2-6: Some aspects of epoxy and polyester thermosets (Akovali, 2001). ................ 24
Table 2-7: Environmental considerations for different FRP materials (NCHRP, 2004). . 25
Table 2-8: Typical properties of FRP bars (ISIS Design Manual No.3, 2007). ............... 26
Table 2-9: Aspects of EB and NSM strengthening methods (Täljsten et al., 2003). ........ 34
Table 2-10: Summary of existing experimental work on flexural strengthening using
NSM-FRP reinforcements. ....................................................................................... 39
Table 2-10: Summary of existing experimental work on flexural strengthening using
NSM-FRP reinforcements (Cont’d). ......................................................................... 40
Table 2-10: Summary of existing experimental work on flexural strengthening using
NSM-FRP reinforcements (Cont’d). ......................................................................... 41
Table 2-10: Summary of existing experimental work on flexural strengthening using
NSM-FRP reinforcements (Cont’d). ......................................................................... 42
Table 2-10: Summary of existing experimental work on flexural strengthening using
NSM-FRP reinforcements (Cont’d). ......................................................................... 43
Table 2-10: Summary of existing experimental work on flexural strengthening using
NSM-FRP reinforcements (Cont’d). ......................................................................... 44
Table 2-10: Summary of existing experimental work on flexural strengthening using
NSM-FRP reinforcements (Cont’d). ......................................................................... 45
Table 2-10: Summary of existing experimental work on flexural strengthening using
NSM-FRP reinforcements (Cont’d). ......................................................................... 46
xix
Table 2-11: Thermal expansion coefficient of concrete in different temperature
(Oldershaw, 2008). .................................................................................................... 49
Table 2-12: Summary of some existing research on freeze-thaw exposure (study of
the considered cycles). .............................................................................................. 62
Table 2-12: Summary of some existing research on freeze-thaw exposure (study of
the considered cycles) (Cont’d). ............................................................................... 63
Table 3-1: Test matrix. ...................................................................................................... 79
Table 3-2: Summary of the specimens used for modification of the brackets.................. 81
Table 3-3: Summary of designed specimens. ................................................................... 83
Table 3-4: Properties of CFRP strip and rebar recommended by the manufacturer
(Hughes Brothers, 2010a and b). .............................................................................. 87
Table 3-5: Properties of epoxy adhesives reported by the manufacturer (Sika, 2010a
and b). ....................................................................................................................... 88
Table 3-6: Summary of initial loading and obtained experimental and theoretical
cracking loads. .......................................................................................................... 92
Table 3-7: Environmental chamber schedule for one freeze-thaw cycle. ......................... 96
Table 4-1: CFRP material properties obtained from tension tests. ................................. 112
Table 4-2: Summary of the test results of the beams subjected to freeze-thaw
exposure (phase I). .................................................................................................. 115
Table 4-3: Strain in CFRP strips or rebar, extreme compression fibre of concrete,
compression steel, and tension steel at mid-span at different stages. ..................... 139
Table 4-4: Strain in extreme compression fibre of concrete, compression steel, tension
steel, and CFRP strips or rebar at mid-span. ........................................................... 149
Table 4-5: CFRP material properties for unexposed beams. .......................................... 156
Table 4-6: Uncertainty in comparison of the exposed and unexposed beams based on
material properties. ................................................................................................. 160
Table 4-7: Summary of the test results for strengthened beam using CFRP strips. ....... 163
Table 4-8: Summary of the test results for strengthened beam using CFRP rebars. ...... 169
xx
Table 4-9: Summary of existing ductility and deformability indices. ............................ 188
Table 4-10: Results of the beams (load-deflection). ....................................................... 193
Table 4-11: Results of the beams (moment-curvature). .................................................. 194
Table 4-12: Ductility or deformability indices of beams. ............................................... 196
Table 4-13: CFRP material properties obtained from tension tests. ............................... 208
Table 4-14: Debonded length of the beams shown in Figure 4-67. ................................ 217
Table 4-15: Summary of the test results for phase II (beams subjected to combined
sustained load and freeze-thaw exposure). ............................................................. 227
Table 4-16: Strain in CFRP strips or rebar, extreme compression fibre of concrete,
compression steel, and tension steel at mid-span at different stages. ..................... 243
Table 4-17: Strain in extreme compression fibre of concrete, compression steel,
tension steel, and CFRP strip or rebar at mid-span section. ................................... 248
Table 4-18: Uncertainty in comparison of sets BS-FS and BS-F based on material
properties. ................................................................................................................ 250
Table 4-19: Summary of the test results for strengthened beam using CFRP strips
(phases I & II). ........................................................................................................ 253
Table 4-20: Modification of the prestressing system test results. ................................... 274
Table 5-1: Mesh sensitivity models. ............................................................................... 311
Table 5-2: Summary of load-steps assigned for nonlinear analysis. .............................. 317
Table 5-3: Summary of the results. ................................................................................. 323
Table 5-4: Properties of the modeled beams. .................................................................. 333
Table 5-5: Summary of load-steps assigned for nonlinear analysis. .............................. 339
Table 5-6: Comparison between numerical and experimental results of beam BS-58-
0.75-40. ................................................................................................................... 343
Table 5-7: Summary of the results for the effects of prestressing. ................................. 346
Table 5-8: Summary of the results for the effects of tension steel ratio. ........................ 357
xxi
Table 5-9: Summary of the results for the effects of concrete compressive strength. .... 364
Table 5-10: Summary of the modeled steel end anchors. ............................................... 366
Table 5-11: Summary of FE results, cohesion effects. ................................................... 380
Table 5-12: Summary of FE results, anchor length effects. ........................................... 384
Table 5-13: Summary of FE results, adhesive width effects. ......................................... 387
Table 5-14: Summary of FE results, adhesive height effects. ........................................ 392
Table 5-15: Summary of the results for BS-F set. .......................................................... 410
Table 5-16: Summary of the results for BR-F set. .......................................................... 412
Table 5-17: Summary of load-steps assigned for nonlinear analysis. ............................ 421
Table 5-18: Summary of the results. ............................................................................... 423
Table A-1: Summary of designed specimens. ................................................................ 476
Table B-1: Groove and CFRP strips/rebar lengths. ........................................................ 484
Table C-1: Concrete compression test results. ................................................................ 494
Table C-2: Properties of the CFRP materials obtained from tension tests. .................... 497
xxii
List of Figures and Illustrations
Figure 2-1: The evolution of materials for civil engineering (Ashby, 1987). ................... 16
Figure 2-2: Typical stress-strain curves of the different fibres and common steel
reinforcements (ACI 440R, 2007). ........................................................................... 19
Figure 2-3: Different types of FRP composites (Sireg, 2011). ......................................... 25
Figure 2-4: Typical stress-strain curves for matrix, fibres, and resulted FRP composite
(ISIS Design Manual No.3, 2007). ........................................................................... 26
Figure 2-5: Schematic of flexural strengthening using FRP: (a) EB FRP, (b) NSM-
FRP strips, and (c) NSM-FRP rebars. ....................................................................... 28
Figure 2-6: Some field applications of NSM-FRP based strengthening........................... 29
Figure 2-7: Different shapes of FRP reinforcements for NSM strengthening (De
Lorenzis and Teng, 2007). ........................................................................................ 32
Figure 2-8: Damage done to the concrete cylinder after 500 cycles of freeze-thaw
(tested in this research). ............................................................................................ 48
Figure 2-9: Concept of residual stresses in composite at high and low temperatures
(Dutta, 1989). ............................................................................................................ 51
Figure 2-10: Applied exposure on the FRP specimens (Micelli, 2004). .......................... 52
Figure 2-11: Creep strain-time relationship for concrete under uni-axial stress (Bisby,
2006). ........................................................................................................................ 54
Figure 3-1: Geometry of the beams and test setup. .......................................................... 85
Figure 3-2: Details of the beams. ...................................................................................... 86
Figure 3-3: Beams instrumentation: (a) elevation and (b) cross-section at mid-span
location. ..................................................................................................................... 90
Figure 3-4: Maximum mean daily temperature (CAN/CSA-S6-06, 2011). ..................... 93
Figure 3-5: Minimum mean daily temperature (CAN/CSA-S6-06, 2011). ...................... 93
Figure 3-6: Annual mean relative humidity (CAN/CSA-S6-06, 2011). ........................... 94
Figure 3-7: Three typical freeze-thaw cycles.................................................................... 96
xxiii
Figure 3-8: Plan view of chamber floor equipped for sustained loading. ......................... 99
Figure 3-9: Plan view of sustained loading..................................................................... 100
Figure 3-10: Side view of sustained loading. .................................................................. 101
Figure 3-11: Cross view of sustained loading. ................................................................ 102
Figure 3-12: Sustained load setup in the environmental chamber. ................................. 103
Figure 3-13: Applying Sustained load in the chamber. .................................................. 104
Figure 3-14: Beams under sustained load and after 500 freeze-thaw cycles. ................. 105
Figure 3-15: Beams under sustained load and after 500 freeze-thaw cycles. ................. 106
Figure 3-16: Test setup. .................................................................................................. 107
Figure 4-1: Load-deflection curves of the beams subjected to freeze-thaw exposure
(phase I). ................................................................................................................. 114
Figure 4-2: Interaction between temporary brackets and beam due to prestressing. ...... 117
Figure 4-3: Photos of beam B0-F at failure. ................................................................... 123
Figure 4-4: Photos of beam BS-NP-F at failure.............................................................. 124
Figure 4-5: Photos of beam BR-NP-F at failure. ............................................................ 125
Figure 4-6: Photos of beam BS-P1-F at failure. ............................................................. 126
Figure 4-7: Photos of beam BR-P1-F at failure. ............................................................. 127
Figure 4-8: Photos of beam BS-P2-F at failure. ............................................................. 128
Figure 4-9: Photos of beam BR-P2-F at failure. ............................................................. 129
Figure 4-10: Photos of beam BS-P3-F at failure. ........................................................... 130
Figure 4-11: Photos of beam BR-P3-F at failure. ........................................................... 131
Figure 4-12: Load-strain curves: BS-NP-F vs BR-NP-F. ............................................... 135
Figure 4-13: Load-strain curves: BS-P1-F vs BR-P1-F. ................................................. 135
Figure 4-14: Load-strain curves: BS-P2-F vs BR-P2-F. ................................................. 136
xxiv
Figure 4-15: Load-strain curves: BS-P3-F vs BR-P3-F. ................................................. 136
Figure 4-16: Load-CFRP strain curves for all beams. .................................................... 137
Figure 4-17: Load-concrete strain curves for all beams. ................................................ 137
Figure 4-18: Load-tension steel strain curves for all beams. .......................................... 138
Figure 4-19: Load-compression steel strain curves for all beams. ................................. 138
Figure 4-20: Local buckling of compression steel bars at mid-span of beam B0-F. ...... 139
Figure 4-21: Strain profile along the length of the CFRP strips or rebar at cracking. .... 142
Figure 4-22: Strain profile along the length of the CFRP strips or rebar at yielding. .... 143
Figure 4-23: Strain profile along the length of the CFRP strips or rebar at ultimate. .... 143
Figure 4-24: Strain distribution at mid-span at cracking. ............................................... 146
Figure 4-25: Strain distribution at mid-span at yielding. ................................................ 147
Figure 4-26: Strain distribution at mid-span at ultimate. ................................................ 148
Figure 4-27: Damage done to the prestressed NSM CFRP strengthened beams at
failure (bottom view) (Cont’d). ............................................................................... 151
Figure 4-28: Effects of prestressing on energy absorption and calculation of optimum
prestressing level ..................................................................................................... 153
Figure 4-29: Schematic for the concept of improvement in energy absorption. ............ 155
Figure 4-30: Calculation of the beneficial prestressing level. ........................................ 155
Figure 4-31: Comparison between exposed and unexposed RC beams strengthened
using CFRP strips. .................................................................................................. 162
Figure 4-32: Comparison between exposed and unexposed beams strengthened with
CFRP rebars. ........................................................................................................... 168
Figure 4-33: Comparison between exposed and unexposed beams. ............................... 172
Figure 4-34: Effects of prestressing on cracking load w.r.t non-prestressed NSM
CFRP strengthened beam in each set. ..................................................................... 173
xxv
Figure 4-35: Effects of prestressing on yield load w.r.t non-prestressed NSM CFRP
strengthened beam in each set. ................................................................................ 174
Figure 4-36: Effects of prestressing on ultimate load w.r.t non-prestressed
strengthened beam in each set. ................................................................................ 175
Figure 4-37: Effects of prestressing on deflection at ultimate load w.r.t non-
prestressed NSM CFRP strengthened beam in each set. ........................................ 177
Figure 4-38: Effects of prestressing on the energy absorption of the exposed and
unexposed NSM CFRP strengthened RC beams. ................................................... 178
Figure 4-39: Total, elastic, and inelastic energies (Retrieved from Naaman and Jeong,
1995). ...................................................................................................................... 184
Figure 4-40: Equivalent deflection, Δ1, and failure deflection, Δu (Retrieved from
Abdelrahman et al., 1995). ...................................................................................... 185
Figure 4-41: Idealized tri-linear slope load-deflection response. ................................... 190
Figure 4-42: Idealized tri-linear slope moment-curvature response. .............................. 191
Figure 4-43: Deformability and ductility models applied to the unexposed beams. ...... 197
Figure 4-44: Deformability and ductility models applied to the exposed beams. .......... 198
Figure 4-45: Comparison between the original and the modified deformability models
applied to the unexposed beams.............................................................................. 200
Figure 4-46: Comparison between the original and the modified deformability models
applied to the exposed beams.................................................................................. 201
Figure 4-47: Verification of proposed limit for curvature ductility index (µ). ............. 203
Figure 4-48: Verification of proposed limit for displacement ductility index (µD). ....... 203
Figure 4-49: Verification of proposed limit for modified J factor (Jm). ......................... 204
Figure 4-50: Verification of proposed limit for modified Zou index (Zm). .................... 204
Figure 4-51: Verification of proposed limit for modified deformability factor (µEm). ... 205
Figure 4-52: Load-deflection history for beam B0-FS. .................................................. 210
Figure 4-53: Load-deflection history for beam BS-NP-FS. ............................................ 211
xxvi
Figure 4-54: Load-deflection history for beam BS-P1-FS. ............................................ 211
Figure 4-55: Load-deflection history for beam BS-P2-FS. ............................................ 212
Figure 4-56: Load-deflection history for beam BS-P3-FS. ............................................ 212
Figure 4-57: Sustained load history for beam B0-F........................................................ 213
Figure 4-58: Sustained load history for beam BS-NP-FS. .............................................. 213
Figure 4-59: Sustained load history for beam BS-P1-FS. .............................................. 213
Figure 4-60: Sustained load history for beam BS-P2-FS. .............................................. 214
Figure 4-61: Sustained load history for beam BS-P3-FS. .............................................. 214
Figure 4-62: Deflection history for beam B0-FS. ........................................................... 214
Figure 4-63: Deflection history for beam BS-NP-FS. .................................................... 215
Figure 4-64: Deflection history for beam BS-P1-FS. ..................................................... 215
Figure 4-65: Deflection history for beam BS-P2-FS. ..................................................... 215
Figure 4-66: Deflection history for beam BS-P3-FS. ..................................................... 216
Figure 4-67: Debonding occurred at concrete-epoxy interface due to freeze-thaw
exposure and sustained load. ................................................................................... 217
Figure 4-68: Images of beam B0-FS after exposure. ...................................................... 218
Figure 4-69: Images of beam BS-NP-FS after exposure. ............................................... 219
Figure 4-70: images of beam BS-P1-FS after exposure. ................................................ 220
Figure 4-71: Images of beam BS-P2-FS after exposure. ................................................ 221
Figure 4-72: Images of beam BS-P3-FS after exposure. ................................................ 222
Figure 4-73: Load-deflection curves of the beams subjected to combined sustained
load and freeze-thaw exposure (phase II, set BS-FS, including permanent
deflection after sustained load and freeze-thaw exposure). .................................... 225
Figure 4-74: Load-deflection curves of the beams subjected to combined sustained
load and freeze-thaw exposure (phase II, set BS-FS). ............................................ 226
xxvii
Figure 4-75: Photos of beam B0-FS at failure. ............................................................... 228
Figure 4-76: Photos of beam BS-NP-FS at failure. ........................................................ 229
Figure 4-77: Photos of beam BS-P1-FS at failure. ......................................................... 230
Figure 4-78: Photos of beam BS-P2-FS at failure. ......................................................... 231
Figure 4-79: Photos of beam BS-P3-FS at failure. ......................................................... 232
Figure 4-80: Load-strain curves for BS-NP-FS. ............................................................. 239
Figure 4-81: Load-strain curves for BS-P1-FS. .............................................................. 239
Figure 4-82: Load-strain curves for BS-P2-FS. .............................................................. 240
Figure 4-83: Load-strain curves for BS-P3-FS. .............................................................. 240
Figure 4-84: Load-CFRP strain for all beams................................................................. 241
Figure 4-85: Load-concrete strain in extreme compression fibre for all beams. ............ 241
Figure 4-86: Load-tension steel strain curves for all beams. .......................................... 242
Figure 4-87: Load-compression steel strain curves for all beams. ................................. 242
Figure 4-88: Gap between bolt and jacking end anchor causing future prestress loss. .. 244
Figure 4-89: Strain profile along the length of the NSM CFRP strip at yielding. .......... 245
Figure 4-90: Strain profile along the length of the NSM CFRP strip at ultimate. .......... 246
Figure 4-91: Strain distribution at mid-span at yielding. ................................................ 247
Figure 4-92: Strain distribution at mid-span at ultimate. ................................................ 248
Figure 4-93: Comparison between exposed beams tested in phase I and II (freeze-
thaw exposure versus combined sustained load and freeze-thaw exposure). ......... 252
Figure 4-94: Effects of exposure on the energy absorption of the prestressed NSM
CFRP strengthened RC beams. ............................................................................... 255
Figure 4-95: Losses in prestressed NSM CFRP strip or rebar: BS-P1-F and BR-P1-F. 258
Figure 4-96: Losses in prestressed NSM CFRP strip or rebar: BS-P2-F and BR-P2-F. 258
xxviii
Figure 4-97: Losses in prestressed NSM CFRP strip or rebar: BS-P3-F and BR-P3-F. 259
Figure 4-98: Losses in NSM CFRP strip (BS sets) at room temperature. ...................... 259
Figure 4-99: CFRP Strain fluctuation in beam BS-NP-F under freeze-thaw exposure. . 262
Figure 4-100: CFRP Strain fluctuation in beam BS-P1-F under freeze-thaw exposure. 262
Figure 4-101: CFRP Strain fluctuation in beam BS-P2-F under freeze-thaw exposure. 263
Figure 4-102: CFRP Strain fluctuation in beam BS-P3-F under freeze-thaw exposure. 263
Figure 4-103: CFRP Strain fluctuation in beam BR-NP-F under freeze-thaw
exposure. ................................................................................................................. 264
Figure 4-104: CFRP Strain fluctuation in beam BR-P1-F under freeze-thaw exposure. 264
Figure 4-105: CFRP Strain fluctuation in beam BR-P2-F under freeze-thaw exposure. 265
Figure 4-106: Prestressing system developed by Gaafar (2007). ................................... 266
Figure 4-108: Cracks at the locations of steel brackets at high prestress level. .............. 267
Figure 4-109: Interaction between temporary steel brackets and beam. ........................ 268
Figure 4-110: Modified prestressing system applied to the specimens. ......................... 270
Figure 4-111: Applied test steps: low, medium, and high eccentricities. ....................... 273
Figure 4-112: Damage done to the specimens after three steps of test. .......................... 275
Figure 5-1: Details of the modeled beams. ..................................................................... 281
Figure 5-2: Stress-strain curves of steel bars. ................................................................. 282
Figure 5-3: Quarter of the beam to be modeled. ............................................................. 284
Figure 5-4: Geometry of Solid65 element (SAS, 2009). ................................................ 286
Figure 5-5: Concrete constitutive model in compression under flexural loading. .......... 289
Figure 5-6: Concrete constitutive model in tension (Retrieved from SAS, 2009).......... 292
Figure 5-7: Different approaches for modeling of reinforcement (Tavarez, 2001). ....... 293
Figure 5-8: Geometry of Link8 element (SAS, 2009). ................................................... 295
xxix
Figure 5-9: Geometry of Solid45 element (SAS, 2009). ................................................ 296
Figure 5-10: Strain-strain curve assigned to CFRP strip elements. ................................ 296
Figure 5-11: Strain-strain curve assigned to epoxy elements, Sikadur® 330. ................. 297
Figure 5-12: Strain-strain curve assigned to epoxy elements, Sikadur® 30. ................... 297
Figure 5-13: Geometry of Beam4 element (SAS, 2009). ............................................... 299
Figure 5-14: Geometry of elements for concrete-epoxy interface (SAS, 2009). ............ 301
Figure 5-15: Bilinear shear stress-slip model. ................................................................ 302
Figure 5-16: Bilinear normal tension stress-gap model. ................................................. 302
Figure 5-17: Mesh sensitivity models. ............................................................................ 312
Figure 5-18: Mesh sensitivity at 20 kN........................................................................... 313
Figure 5-19: The meshed beam (quarter of the tested beam). ........................................ 314
Figure 5-20: Cross-section of the beam. ......................................................................... 314
Figure 5-21: Steel reinforcements. .................................................................................. 315
Figure 5-22: Mesh at the end groove. ............................................................................. 315
Figure 5-23: Contact around the groove. ........................................................................ 315
Figure 5-24: End-steel anchor. ........................................................................................ 316
Figure 5-25: Comparison between FE and experimental results for B0-R and BS-NP-
R. ............................................................................................................................. 321
Figure 5-26: Comparison between FE and experimental results for BS-P1-R. .............. 321
Figure 5-27: Comparison between FE and experimental results for BS-P2-R. .............. 322
Figure 5-28: Comparison between FE and experimental results for BS-P3-R. .............. 322
Figure 5-29: Comparison between experimental and numerical strain profile along the
CFRP strip for beam BS-NP-R. .............................................................................. 325
Figure 5-30: Comparison between experimental and numerical strain profile along the
CFRP strip for beam BS-P1-R. ............................................................................... 325
xxx
Figure 5-31: Comparison between experimental and numerical strain profile along the
CFRP strip for beam BS-P2-R. ............................................................................... 326
Figure 5-32: Comparison between experimental and numerical strain profile along the
CFRP strip for beam BS-P3-R. ............................................................................... 326
Figure 5-33: Comparison between experimental and numerical strain distribution
across the depth at mid-span for beam BS-NP-R. .................................................. 327
Figure 5-34: Comparison between experimental and numerical strain distribution
across the depth at mid-span for beam BS-P1-R. ................................................... 327
Figure 5-35: Comparison between experimental and numerical strain distribution
across the depth at mid-span for beam BS-P2-R. ................................................... 328
Figure 5-36: Comparison between experimental and numerical strain distribution
across the depth at mid-span for beam BS-P3-R. ................................................... 328
Figure 5-37: Debonding Parameter (dm) contour at the concrete-epoxy interface in the
model: (a) BS-NP-R at initiation of debonding (load = 130.4 kN, deflection =
80.14 mm) and (b) BS-NP-R at ultimate. ............................................................... 330
Figure 5-38: Debonding Parameter (dm) contour at the concrete-epoxy interface in the
model: (a) BS-P2-R at initiation of debonding (load = 140.4 kN, deflection =
68.32 mm) and (b) BS-P2-R at ultimate. ................................................................ 331
Figure 5-39: Simplified concrete compressive stress-strain curves. ............................... 336
Figure 5-40: Meshed beam. ............................................................................................ 340
Figure 5-41: Comparison between experimental and numerical load-deflection curves
of beam BS-58-0.75-40. .......................................................................................... 341
Figure 5-42: Comparison between experimental and numerical strain profile along the
length of CFRP strips of beam BS-58-0.75-40. ...................................................... 342
Figure 5-43: Load-deflection curves of the modeled beams-effects of prestressing
level on set BS-0.75-40. .......................................................................................... 344
Figure 5-44: Load-deflection curves of the modeled beams-effects of prestressing
level on set BS-1.25-40. .......................................................................................... 344
Figure 5-45: Load-deflection curves of the modeled beams-effects of prestressing
level on set BS-1.75-40. .......................................................................................... 345
xxxi
Figure 5-46: Load-deflection curves of the modeled beams-effects of prestressing
level on set BS-2.25-40. .......................................................................................... 345
Figure 5-47: Effects of prestressing on negative camber. ............................................... 347
Figure 5-48: Effects of prestressing on cracking load. ................................................... 348
Figure 5-49: Effects of prestressing on yield load. ......................................................... 349
Figure 5-50: Effects of prestressing on ultimate load. .................................................... 350
Figure 5-51: Effects of prestressing on ultimate deflection. ........................................... 351
Figure 5-52: Effects of prestressing on ductility index. .................................................. 353
Figure 5-53: Effects of prestressing on energy absorption. ............................................ 353
Figure 5-54: Determination of optimum prestressing level for set BS-0.75................... 355
Figure 5-55: Determination of optimum prestressing level for set BS-1.25................... 355
Figure 5-56: Determination of optimum prestressing level for set BS-1.75................... 356
Figure 5-57: Determination of optimum prestressing level for set BS-2.25................... 356
Figure 5-58: Effects of tension steel ratio on negative camber. ..................................... 359
Figure 5-59: Effects of tension steel ratio on cracking load. .......................................... 360
Figure 5-60: Effects of tension steel ratio on yield load. ................................................ 360
Figure 5-61: Effects of tension steel ratio on ultimate load. ........................................... 361
Figure 5-62: Effects of tension steel ratio on ultimate deflection. .................................. 361
Figure 5-63: Effects of tension steel ratio on ductility index.......................................... 362
Figure 5-64: Effects of tension steel ratio on energy absorption. ................................... 362
Figure 5-65: Effects of concrete compressive strength on the load-deflection curve. .... 363
Figure 5-66: Anchorage system for prestressed NSM-CFRP strengthening. ................. 365
Figure 5-67: Details of the modeled end anchors and abbreviation of dimensions. ....... 367
Figure 5-68: Stress-strain curve of anchor steel (Emam, 2007). .................................... 368
xxxii
Figure 5-69: Stress-strain curve for anchor bolts (Hilti Inc)........................................... 369
Figure 5-70: Anchorage model with 1509 elements developed for sensitivity analysis. 372
Figure 5-71: Anchorage model with 2813 elements developed for sensitivity analysis. 372
Figure 5-72: Anchorage model with 5077 elements developed for sensitivity analysis. 373
Figure 5-73: Anchorage model with 8309 elements developed for sensitivity analysis. 373
Figure 5-74: Mesh sensitivity (at 100 kN). ..................................................................... 374
Figure 5-75: Meshed anchor (steel tube length = 250 mm). ........................................... 376
Figure 5-76: Assigned constraints to the anchor model.................................................. 377
Figure 5-77: Effects of cohesion value (5-20 MPa) on load-displacement curves. ........ 378
Figure 5-78: Effects of cohesion value (5-20 MPa) on shear stress at CFRP-epoxy
vertical interface at 50 kN. ...................................................................................... 379
Figure 5-79: Effects of cohesion value (5-20 MPa) on shear stress at steel-epoxy
vertical interface at 50 kN. ...................................................................................... 379
Figure 5-80: Developed FE models for the effects of anchorage length. ....................... 382
Figure 5-81: Effects of bond length (150-450 mm) on load-displacement curves. ........ 383
Figure 5-82: Effects of bond length (150-450 mm) on shear stress at CFRP-epoxy
vertical interface at 50 kN. ...................................................................................... 383
Figure 5-83: Effects of bond length (150-450 mm) on shear stress at steel-epoxy
vertical interface at 50 kN. ...................................................................................... 384
Figure 5-84: Developed FE models for the effects of adhesive width. .......................... 386
Figure 5-85: Effects of adhesive width (Wa=3.5-10.5 mm) on load-displacement
curves. ..................................................................................................................... 387
Figure 5-86: Effects of adhesive width (Wa=3.5-10.5 mm) on shear stress at steel-
epoxy horizontal interface at 50 kN. ....................................................................... 388
Figure 5-87: Effects of adhesive width (Wa=3.5-10.5 mm) on shear stress at steel-
epoxy vertical interface at 50 kN. ........................................................................... 388
xxxiii
Figure 5-88: Effects of adhesive width (Wa=3.5-10.5 mm) on shear stress at CFRP-
epoxy horizontal interface at 50 kN. ....................................................................... 389
Figure 5-89: Effects of adhesive width (Wa=3.5-10.5 mm) on shear stress at CFRP-
epoxy vertical interface at 50 kN. ........................................................................... 389
Figure 5-90: Developed FE models for the effects of adhesive height. .......................... 391
Figure 5-91: Effects of adhesive height (Ha=1.5-7.5 mm) on load-displacement
curves. ..................................................................................................................... 392
Figure 5-92: Effects of adhesive height (Ha=1.5-7.5 mm) on shear stress at steel-
epoxy horizontal interface at 50 kN. ....................................................................... 393
Figure 5-93: Effects of adhesive height (Ha=1.5-7.5 mm) on shear stress at steel-
epoxy vertical interface at 50 kN. ........................................................................... 393
Figure 5-94: Effects of adhesive height (Ha=1.5-7.5 mm) on shear stress at CFRP-
epoxy horizontal interface at 50 kN. ....................................................................... 394
Figure 5-95: Effects of adhesive height (Ha=1.5-7.5 mm) on shear stress at CFRP-
epoxy vertical interface at 50 kN. ........................................................................... 394
Figure 5-96: Finding the integration limits for Equation 5-29 using moment diagram. 400
Figure 5-97: Strain and stress distribution on a prestressed NSM-CFRP strengthened
section. .................................................................................................................... 406
Figure 5-98: Comparison between experimental and analytical load-deflection
responses for BS-F set. ........................................................................................... 409
Figure 5-99: Comparison between experimental and analytical load-deflection
responses for BR-F set. ........................................................................................... 411
Figure 5-100: Simulation of the beams with exposed concrete materials. ..................... 417
Figure 5-101: Stress-strain curves of the steel bars for exposed beams in phase II. ...... 419
Figure 5-102: Stress-strain curves assigned to the CFRP strip elements........................ 420
Figure 5-103: Comparison between experimental and numerical load-deflection
curves. ..................................................................................................................... 422
Figure B-1: Fabrication of formwork. ............................................................................ 477
xxxiv
Figure B-2: Fabrication of the steel cage and placement in the formwork. .................... 479
Figure B-3: Fabrication of RC beams. ............................................................................ 480
Figure B-4: Attaching the CFRP reinforcements to the end anchors. ............................ 485
Figure B-5: Prestressing system developed by Gaafar (2007). ....................................... 486
Figure B-7: Cutting the groove. ...................................................................................... 488
Figure B-8: Groove preparation. ..................................................................................... 488
Figure B-9: Prestessed NSM strengthening. ................................................................... 490
Figure C-1: Concrete compression test and type of failure ............................................ 493
Figure C-2: Typical stress-strain curves of concrete (from batch#1 at 28 days) ............ 493
Figure C-2: Tension tests on CFRP strips and rebars. .................................................... 495
Figure C-3: Stress-strain relation of CFRP strip from batch #1. .................................... 496
Figure C-4: Stress-strain relation of CFRP rebar from batch #2. ................................... 496
Figure C-5: Stress-strain relation of CFRP strip from batch #3. .................................... 497
Figure C-6: Stress-strain curve of 15M steel bars in batch #1. ....................................... 499
Figure C-7: Stress-strain curve of 10M steel bars in batch #2. ....................................... 499
Figure C-8: Stress-strain curve of 15M steel bars in batch #3. ....................................... 500
xxxv
List of Nomenclature and Symbols
Symbol Definition
Ab
Abdelrahman deformability index
Ac area of concrete, mm2
Afrp area of FRP, mm2
Asc area of compression steel reinforcement, mm2
Ash area of one leg of the stirrup, mm2
Ast area of tension steel reinforcement, mm2
b width of RC beam, mm
b′ width of the stirrup (between centre lines of the bar), mm
b″ width of confined core measured to outside of the stirrup, mm
c depth of the neutral axis, mm
C cohesion, MPa
Cc compressive force carried by concrete, kN
Cs force in compression steel rebars, kN
d′ depth of the stirrup (between centre lines of the bar), mm
d″ depth of confined core measured to outside of the stirrup, mm
db bar diameter, mm
df depth to the centroid of the CFRP strips or rebars, mm
dm debonding parameter
dsc depth to the centroid of the top steel rebars, mm
dst depth to the centroid of the bottom steel rebars, mm
db bolt diameter, mm
dh hole diameter, mm
Ec modulus of elasticity of concrete, MPa
Ec exposed modulus of elasticity of concrete after exposure, MPa
Ec unexposed modulus of elasticity of concrete before exposure, MPa
Eel elastic part of the total energy, kN.mm
Efrp modulus of elasticity of FRP, GPa
Es area under load-deflection curve at service, kN.mm
Esc modulus of elasticity of compression steel reinforcement, GPa
Est modulus of elasticity of tension steel reinforcement, GPa
Etot total energy absorption, kN.mm
Eu area under load-deflection curve up to peak load, kN.mm
EI(x) flexural stiffness as a function of distance x, N.mm2
f′c concrete compressive strength, MPa
fc28 concrete compressive strength at 28 days, MPa
fc concrete compressive stress, MPa
fc exposed concrete compressive strength after exposure, MPa
xxxvi
fc unexposed concrete compressive strength before exposure, MPa
ffrpu ultimate tensile strength of FRP, MPa
fr tensile strength of concrete, MPa
fyc yield stress of compression steel, MPa
fyt yield stress of tension steel, MPa
Gcn total values of normal fracture energies, N/mm
Gct total values of shear fracture energies, N/mm
Gfo the base value of fracture energy, N/mm
h height of RC beam, mm
hf height of the CFRP strip, mm
Ha height of adhesive, mm
Ht height of anchor tube, mm
Igt moment of inertia of the gross transformed section, mm4
Igt-st the moment of inertia of the gross transformed strengthened section, mm4
Igt-un moment of inertia of the gross transformed un-strengthened section, mm4
J J deformability factor
Jm modified J factor
Kn contact normal stiffness, N/mm3
Kt contact shear stiffness, N/mm3
Lp distance from the support to the point load, mm
Lf length of CFRP strips, mm
Lo un-strengthened length of the beam at one side, mm
Lp length of anchor plate, mm
Lt length of anchor tube, mm
M moment, kN.m
Mapplied applied moment on the beam, kN.m
Mc moment corresponding to maximum concrete compressive strain of 0.001,
kN.m
Mcr moment at cracking, kN.m
Mu moment at ultimate state, kN.m
M(x) applied moment as a function of distance x, kN.m
Mp(x) moment due to prestressing as a function of distance x, kN.m
N number of freeze-thaw cycles
p contact pressure, MPa
Papplied applied load to each beam after strengthening for cracking, kN
Pcn cracking load of non-prestressed strengthened beam, kN
Pcr cracking load, kN
Pcr-exp. experimental cracking load, kN
Pcr-theo. theoretical cracking load, kN
Pcr-theo. sw. theoretical cracking load by considering the effect of self-weight, kN
Pu0 ultimate load of un-strengthened control beam, kN
xxxvii
Pu ultimate load, kN
Pun ultimate load of non-prestressed strengthened beam, kN
Py0 yielding load of un-strengthened control beam, kN
Py yielding load, kN
Pyn yielding load of non-prestressed strengthened beam, kN
R Rashid index
s percentage of uncertainty
sc uncertainty due to axial stiffness of the concrete material
scu uncertainty due to strength of the concrete material
sfrp uncertainty due to axial stiffness of the CFRP material
sfrpu uncertainty due to strength of the CFRP material
ssc uncertainty due to axial stiffness of the compression steel
sst uncertainty due to axial stiffness of the tension steel reinforcements
ssty uncertainty due to strength of the tension steel reinforcements
Ssh spacing of stirrups, mm
tf thickness of CFRP strip, mm
Tf force in CFRP strip or rebar, kN
Ts force in bottom steel rebars, kN
Tf thickness of CFRP strips, mm
Tt thickness of anchor tube, mm
un contact gap, mm
ūn contact gap at the maximum contact normal tension stress, mm
unc contact gap at the completion of debonding, mm
ut contact slip, mm
ūt contact slip at the maximum contact shear stress, mm
utc
contact slip at the completion of debonding, mm
Wa adhesive width, mm
Wf width of CFRP strips, mm
Wp width of anchor plate, mm
Wt width of anchor tube, mm
x distance from the support, mm
xcr distance from the support to a point where the applied moment is equal to
the cracking moment of the section, mm
xcr-st distance from the support to a point where the applied moment is equal to
the cracking moment capacity of the strengthened section, mm
xcr-un distance from the support to a point where the applied moment is equal to
the cracking moment capacity of the un-strengthened section, mm
y vertical distance from the neutral axis, mm
ӯCc distance between neutral axis and point of action of the resultant
compressive force on concrete, mm
Z Zou index
xxxviii
Zm modified Zou index
αfrp coefficient of thermal expansion of the CFRP, 1/oC
γ aspect ratio of the interface failure plane
Δ deflection, mm
Δcr deflection at cracking load, mm
Δcrush deflection at the initiation of concrete cover crushing, mm
Δl equivalent uncracked deflection at peak load, mm
Δo initial camber due to prestressing, mm
Δoe effective camber at seven days after prestressing, mm
Δop permanent deflection after initial loading, or sustained loading, mm
Δu deflection at ultimate load, mm
Δy deflection at yielding load, mm
ɛ Strain
ɛ0 strain at maximum concrete compressive strength
0 exposed concrete strain at peak stress after exposure
0 unexposed concrete strain at peak stress before exposure
ɛ50c confined concrete strain on the descending branch at 0.5f′c
ɛ50u unconfined concrete strain on the descending branch at 0.5f′c ɛc concrete strain
ɛc@u concrete strain at extreme compression fibre at ultimate load
cc concrete strain at extreme compression fibre
f strain in CFRP rebar or strip
ɛfrp@u maximum CFRP strain at ultimate load
ɛfrpu ultimate tensile strain of CFRP reinforcement
ɛl strain at the end of the linear part up to 0.3f′c
ɛp target prestrain value in CFRP reinforcement
pe effective prestrain in CFRP rebar or strips at seven days after prestressing
ɛsc strain in compression steel
ɛst strain in tension steel
yc yield strain of compression steel
yt yield strain of tension steel
u rotation at peak load, rad
y rotation at yielding, rad
μ friction coefficient
µD displacement ductility index
µE deformability factor
µEm modified deformability factor
µN-J Naaman and Jeong index
µ rotation ductility index
µ curvature ductility index
xxxix
oC degree Celcius
σ axial stress, MPa
σmax maximum normal tensile stress of contact, MPa
σn contact normal stress, MPa
τ shear strength, MPa
τt contact shear stress, MPa
τmax maximum shear stress of contact, MPa
Φ area under P-Δ curve, kN.mm
φ curvature, rad/mm
c curvature corresponding to maximum concrete compressive strain of 0.001,
rad/mm
cr mid-span curvature at cracking, rad/mm
o curvature due to prestressing, rad/mm
oe effective curvature seven days after prestressing, rad/mm
u mid-span curvature at peak load, rad/mm
y mid-span curvature at yielding, rad/mm
(x) curvature at distance x, rad/mm
xl
List of Abbreviations
Abbreviation Definition
AFRP
aramid fibre reinforced polymer
CC concrete crushing
CCS concrete cover spalling
CFRP carbon fibre reinforced polymer
DB debonding
EB
FE
externally bonded
finite element
FM failure mode
FR FRP rupture
FRP fibre reinforced polymer
GFRP glass fibre reinforced polymer
HSS hollow structural steel,
LSC linear strain conversion
NSM near-surface mounted
RC reinforced concrete
SG strain gauge
SRLS self-reacting loading system
TC thermocouple
UV ultra-violet
1
Chapter One: General Introduction
1.1 Introduction
In a country like Canada which experiences an annual mean relative humidity of
50-90% (CAN/CSA–S6–06, 2011) and an average freeze-thaw frequency of 39 cycles
per year (Fraser, 1959), deterioration of reinforced concrete (RC) members of bridges and
buildings due to severe weather conditions is a common problem. In most cases, this
deterioration is accompanied by aging, cyclic/fatigue loads, and overloading causing
serious economic and social problems. Canada has over 80,000 bridges of which about
50% are over 35 years old and close to their 50 years design life (Ramcharitar, 2004). In
the United States, the Federal Highway Administration (FHWA) data in the National
Bridge Inventory (NBI) show almost 40% of the 650,000 highway bridges are
structurally deficient or functionally obsolete (Yanev, 2005). The annual rehabilitation
and replacement cost of bridges in Canada is $0.7 billion (Mirza and Haider, 2003) while
this value is $7 billion in the United States (Yanev, 2005). Just in the province of Alberta,
Canada, there are over 1500 reinforced concrete bridges built during mid-part of the 20th
century (Sayed-Ahmed et al., 2004). Most of them are short span (8-12 m) and simply
supported. Over the years, many of these bridges have shown signs of degradation due to
severe environmental conditions. Identification of proper upgrading methods for
damaged structures is vital to overcome the problems. Among the different types of
strengthening techniques developed for RC girders/beams, the prestressed Near-Surface
Mounted (NSM) Carbon Fibre Reinforced Polymer (CFRP) method is one of the latest.
The CFRP material has the advantages of excellent corrosion resistance, high tensile
2
strength, and low density in comparison with conventional steel reinforcement, which is
being replaced in some cases by FRP within past fifteen years. In the NSM method, the
strengthening reinforcement is mounted in a groove made in the concrete cover and is
bonded with epoxy adhesive/cement mortar. These main advantages of the NSM-CFRP
method include reduced debonding possibility and better resistance against fire in
comparison with Externally Bonded (EB)-FRP method. The effectiveness of the
prestressed NSM strengthening technique has been proved through conducting laboratory
projects (Nordin and Täljsten, 2006; De Lorenzis and Teng, 2007; Badawi and Soudki,
2009); However, in these researches, prestressing of the NSM-CFRP reinforcements was
performed against both ends of the RC beam or against an independent steel reaction
frame that made the proposed prestressed NSM method unsuitable for field application.
In the research described here, the CFRP strips/rebars were prestressed using an
innovative anchorage system, developed by Gaafar (2007), that consists of two steel
anchors bonded to the end of the CFRP strips/rebar using epoxy and a movable bracket
temporarily mounted on the beam. Overall, this project mainly focuses on the effects of
prestressing level, freeze-thaw exposure, and sustained and static loading to cover the
gaps in this field and to provide a better understanding of the effectiveness of the NSM
strengthening technique to be employed in practical projects with confidence.
1.2 The Most Important Reasons for Strengthening of Structures
Strengthening of damaged/deficient structures is categorized based on the
following main reasons:
Respond to change in performance level or increase in applied load
3
Upgrade to meet new Standards and Codes criteria
Correct an error in design and construction
Repair environmental damages due to severe weather condition, earthquake,
corrosion etc
Correct architectural difficulties and practical problems
1.3 Methods for Upgrading the RC Members
To satisfy the demands mentioned above, upgrading a structure or a member of a
structure can be performed according to one of the following methods:
Steel jacketing
Concrete covering with reinforcement
Post-tensioned cables
Fibre Reinforcement Polymer (FRP) strengthening
1.4 Statement of the Problem
The research significance of the study reported in this thesis is built upon on the
gaps that exisist in the filed of understanding the long-term performamnce of RC
structures strengthened using FRP materials.
1.4.1 Performance of Strengthened Beam with Prestressed NSM-FRP
Recently application of prestressed NSM-FRP has become an interesting topic for
researchers (Nordin and Täljsten, 2006; De Lorenzis and Teng, 2007; Gaafar, 2007;
Badawi and Soudki, 2009). In fact, strengthening using prestressed NSM-FRP can
4
improve the performance of a beam with respect to a non-prestressed strengthened beam
in terms of serviceability, crack development propagation and load-carrying capacity.
Different issues including applying the prestressing; instantaneous and long-term
prestressing losses, effect of prestressing on the bond behaviour; energy absorption;
ductility; deformability; cracking, yielding, and ultimate loads; CFRP geometry for
strengthening need to be addressed in detail to enhance the understanding of prestressed
NSM-FRP strengthened beam to be confidently implemented in practical projects.
1.4.2 Effects of Freeze-Thaw Exposure
Deterioration of concrete/strengthened concrete members due to long-term
exposure including freeze-thaw cycling exposure is well documented (Toutanji and
Gómez, 1997; Frigione et al., 2006; Tan et al., 2009; El-Hacha et al., 2010) but, the long-
term performance of the NSM-FRP strengthened RC beams is rarely studied (Derias,
2008; Mitchell, 2010). In this context, the long-term behaviour of the prestressed NSM-
FRP strengthened RC beams subjected to freeze-thaw cycling exposure has never been
examined. The freeze-thaw exposure probably has its major effect on the concrete and
bond of the strengthened RC beams resulting in a reduced load-carrying capacity. These
issues need to be studied in detail by experimental investigations of prestressed NSM-
FRP strengthened RC beams subjected to freeze-thaw cycling exposure and comparing
the results with those from similar beams without any environmental exposure.
5
1.4.3 Effects of Sustained Load Combined with Freeze-Thaw Exposure
To pursue the study on the long-term performance of the prestressed NSM-CFRP
strengthened beams, the combined effects of freeze-thaw cycling exposure and sustained
load, which have never been examined on these types of strengthened RC beams, are
investigated. Sustained load causes creep and cracks in the beams and under freeze-thaw
exposure along with humidity or moisture may cause major damage to the strengthened
beams. In this context, the performance of the prestressed NSM-FRP strengthened RC
beams under the combined effects of sustained load and freeze-thaw exposure are studied
in detail in terms of damage due to exposure, load-deflection response, ductility, energy
absorption, and mode of failure in comparison with the results of the similar beams
subjected to the freeze-thaw cycles.
1.4.4 FE Analysis of the Prestressed NSM-FRP Strengthened RC Beams
Numerical and analytical investigations of FRP strengthening methods have been
pursued parallel to the experiments and practical applications. Many researchers
simulated the behaviour of Externally Bonded (EB) FRP strengthened RC flexural
members using 2D or 3D FE models, considering perfect bond between interfaces due to
the fact that debonding failure was not observed in tests (Kachlakev et al., 2001;
Chansawat, 2003; Jia, 2003; Supaviriyakit et al., 2004; Chansawat et al., 2006; Camata
et al., 2007; Nour et al., 2007; Rafi et al., 2007); however, a few researchers considered
debonding effects in the FE modeling of EB strengthened RC beams of which most are in
2D (Buyle-Bodin et al., 2002; Kishi et al., 2005; Pham and Al-Mahaidi, 2005; Coronado
and Lopez, 2006). On the other hand, FE modeling of NSM-FRP strengthened RC beams
6
is rarely carried out (Kang et al., 2005; Omran and El-Hacha, 2010a; Soliman et al.,
2010). In the NSM strengthened RC beam, the debonding occurs at the concrete-epoxy
interface which is the weakest interface, and the main reason for a/the shortage of
research in this field is identification of appropriate bond behaviour that can be
reasonably applicable to the NSM technique. Therefore, developing a 3D FE model of
NSM strengthened RC beams considering the effects of debonding, prestressing, freeze-
thaw exposure and sustained load seems necessary in this field to be used as a predictive
tools in future researches and designs. In this context, a parametric study was conducted
on the flexural behaviour of the prestressed NSM-CFRP strengthened RC beam
considering the effects of the prestressing level, tension steel ratio, and concrete
compressive strength that leads to a better understanding of this strengthening system.
1.4.5 Analytical Model of the Exposed Prestressed NSM-FRP Strengthened RC Beams
The analytical studies on the NSM-CFRP strengthened concrete members need to
be pursued in the evolution of this strengthening system parallel to the experimental
investigations. Therefore, an analytical model is developed to simulate the load-
deflection response of the prestressed or non-prestressed NSM-CFRP strengthened beams
subjected to freeze-thaw cycling exposure. The model needs to be capable of assigning
the exposed freeze-thaw concrete material, the compression and tension steel
reinforcements, the partial prestressing length of the NSM-CFRP reinforcement along the
length of the beam (since the beams might not be strengthened for entire length with
NSM-CFRP), and the type of loading. Also, the developed model was verified with the
7
experimental test results to be confidently used as an analytical predictive tool for the
load-deflection response of the prestressed NSM-FRP strengthened RC beams.
1.4.6 Anchorage for Prestressed NSM-FRP Strengthening Method
One of the challenges for using the prestressed NSM-FRP method is developing a
practical method for prestressing. Most research in this area was performed while the
NSM-FRP was prestressed for the entire length of the beam against both ends of the
beam or against an external independent steel reaction frame from the beam itself
(Nordin and Täljsten, 2006; De Lorenzis and Teng, 2007; Badawi and Soudki, 2009).
Moreover, in the research performed by Gaafar (2007) the advantage is the NSM-FRP
was prestressed against the bottom/side of the beam itself. Gaafar (2007) applied
prestressing using an innovative mechanical anchorage system that consists of two steel
anchors bonded to the ends of the CFRP rebar or strips and movable brackets temporarily
mounted on the beam. In this research, the performance of this anchorage system is
addressed more in detail and required modifications were performed by conducting
experimental and analytical investigations. Furthermore, a 3D FE model of the end
anchor was developed along with a parametric study considering the effects of bond
strength, length, and section dimensions on the anchorage capacity and interfacial stress
distribution. The findings lead to better understanding of the anchorage performance.
1.4.7 Modification of NSM-FRP Prestressing System
In earlier research (Nordin and Täljsten, 2006; De Lorenzis and Teng, 2007;
Badawi and Soudki, 2009), prestressing of the NSM-CFRP reinforcements was
8
performed against both ends of the RC beam or against an independent steel reaction
frame that made the prestressed NSM method unsuitable for field applications. The
practical issue of the prestressed NSM-FRP method was solved with the development of
an innovative prestressing and anchorage system enabling prestressing the NSM-CFRP
strips or rebars against the bottom/side of the concrete beam itself (Gaafar, 2007; El-
Hacha and Gaafar, 2011). An issue related to the developed prestressing system, reported
by Gaafar (2007) and also Oudah (2011), is that cracks occur at the location of the
brackets at high prestress levels (above about 40% of the CFRP ultimate tensile strength).
Therefore, the prestressing system requires modification to avoid these types of cracks
during prestrtessing.
1.4.8 Deformability and Ductility of the Prestressed FRP Strengthened RC Beams
In spite of the conventional ductility factors (displacement or curvature ductility)
which are appropriate for steel reinforced concrete members, a variety of deformability
indices have been proposed for concrete members reinforced with prestressed and non-
prestressed FRP (Naaman and Jeong, 1995; Abdelrahman et al., 1995; Zou, 2003; Rashid
et al., 2005; ACI 440.1R, 2006; CAN/CSA–S6–06, 2011). In this context, there is a gap
for the appropriate deformability or ductility models that need to be developed for the RC
members strengthened with prestressed and non-prestressed FRP; furthermore,
reasonable limits for the developed deformability or ductility models need to be proposed
to be used in design.
9
1.5 Research Objectives
The author mainly focuses on the issues mentioned earlier; therefore, the
following principal and secondary objectives are outlined for this research.
1.5.1 Principal Objectives
To study the long-term performance of RC beams strengthened in flexure using
prestressed NSM-CFRP strips/rebars subjected to freeze-thaw cycling exposure
and tested under quasi-static monotonic loading in terms of damage due to
exposure, load-deflection response, energy absorption and ductility
performance, and CFRP geometry (strip versus rebar)
To investigate the long-term performance of RC beams strengthened in flexure
with prestressed NSM-CFRP strips subjected to combined freeze-thaw cycling
exposure and sustained load and tested under static monotonic loading in terms
of damage due to exposure, load-deflection response, energy absorption and
ductility performance
To propose appropriate deformability or ductility models for RC beams
strengthened with the non-prestressed and prestressed FRP, and to propose the
reasonable limits for the developed deformability or ductility models
To develop nonlinear 3D FE models that can simulate the exact behaviour of
prestressed NSM-CFRP strengthened RC beams without any environmental
exposure and validate the model with experimental data from beams tested by
Gaafar (2007)
10
To develop nonlinear 3D FE models of the tested beams subjected to combined
freeze-thaw exposure and sustained load conditions
To develop an analytical model that can produce the load-deflection responses
of the tested beams exposed to freeze-thaw cycles
1.5.2 Secondary Objectives
To study the instantaneous and long-term prestress losses in the NSM-CFRP
To propose and analyze the practical concepts of optimum prestressing level
and beneficial prestressing level for tested beams
To conduct a paramedic study using the developed 3D FE models and
investigate the effects of the prestressing level, tension steel reinforcement
ratio, and concrete compressive strength on the flexural performance of the
prestressed NSM-CFRP strengthened RC beams
To develop 3D FE models of the end anchors and to conduct a parametric
study considering the effects of adhesive thickness, bond characteristics, and
anchor length on the anchorage capacity and interfacial shear stress distribution
To modify the prestressing system used for NSM-FRP strengthening
1.6 Scope of Work
The thesis consists of three parts: experimental study, finite element (FE)
analysis, and analytical investigation.
The experimental part of the project consists of two phases and an additional
investigation for the modification of the prestressing system. Phase I consists of nine
11
large-scale (5.15 m long with rectangular section 200×400 mm) beams: one un-
strengthened control RC beam, four strengthened RC beams using CFRP strips, and four
strengthened beams using CFRP rebars. The CFRP rebar and strips with similar axial
stiffness are used for strengthening. The strengthened beams are prestressed to 0, 20, 40,
and 60% of the ultimate CFRP tensile strain reported by manufacturer. The beams in
phase I are initially loaded up to 1.2 times the analytical cracking load for each beam
after strengthening, and then, placed inside an environmental testing facility chamber,
subjected to 500 freeze-thaw cycling exposure where each cycle is programmed between
-34oC to +34
oC with period of 8 hr and a relative humidity of 75% for temperatures
above +20oC. Phase II consists of five beams: one un-strengthened control RC beam and
four beams similar to the strengthened RC beams with CFRP strips in phase I. The beams
in phase II are subjected to the exposure conditions similar to that of phase I (except that
the relative humidity of 75% for temperatures above +20oC was replaced with water
spray, 18 L/min for a time period of 10 min, at temperature +20oC, to increase the
severity of the applied exposure) while each beam is being subjected to a sustained load
equal to 62 kN representing 47% of analytical ultimate load of the non-prestressed NSM-
CFRP strengthened RC beam. After being subjected to exposure and loading, all beams
in phases I and II were tested to failure under a four-point bending configuration and
static monotonic loading.
An experimental investigation is performed on the modification of the
prestressing system used for NSM CFRP strengthening in phases I and II. The temporary
steel brackets were modified by welding two steel plates to the sides to be capable of
changing the eccentricity (the location of the jacks). To investigate the performance of
12
the modified prestressing system, three concrete specimens are fabricated with identical
cross-section with the RC beams tested in phases I and II (200×400 mm) and having a
length of 1500 mm. A dywidag bar with two adjustable nuts at the ends is used instead of
the CFRP reinforcements to facilitate the execution of the experiment. The end anchors
are made to have enough bolts to carry the applied load up to ultimate capacity of the
dywidag bar. Then, the prestressing using the modified system is applied to the dywidag
bar up to a load equivalent to 93% of the CFRP ultimate tensile strength reported by the
manufacturer, for three different eccentricities (distance between the locations of the
jacks and centre of bolt groups at temporary fixed bracket).
The FE analysis consists of four sections performed using finite element software,
ANSYS. In section I, a nonlinear 3D FE model is developed to simulate the behaviour of
the RC beams strengthened with prestressed NSM-CFRP strips. The model considers the
debonding at the concrete-epoxy interface by assigning fracture energies including a
bilinear shear stress-slip model and a bilinear normal tension stress-gap model.
Furthermore, the prestressing is applied to the CFRP strip elements using the equivalent
temperature method. The FE model is compared and validated with experimental test
results reported by Gaafar (2007). In section II, a parametric study is conducted on the
RC beams strengthened with prestressed NSM-CFRP strips. A simplified 3D nonlinear
FE model similar to section I is developed but with a simplified material properties to
facilitate the trend of the parametric study. The model is validated with the experimental
data. Then, it is employed to analyze twenty-three beams to assess the effects of the
prestressing level in NSM-CFRP strips, the tensile steel reinforcement ratio, and the
concrete compressive strength. In section III, a 3D FE model is developed to simulate the
13
behaviour of the end-steel anchor used for the prestressed NSM-CFRP strengthening. The
CFRP-epoxy and epoxy-anchor interfaces are modeled by assigning Coulomb friction
model. Since the analysis is a pure FE one, the accuracy of the model is confirmed by
conducting a sensitivity analysis on the results. Then, fourteen models are analyzed to
investigate the effects of bond cohesion, anchor length, anchor width, and anchor height
on the interfacial stress distributions and anchorage capacity. In section IV, the post-
exposure load-deflection responses of the five beams tested in phase II of the
experimental program are predicted by developing a nonlinear 3D FE model similar to
the section I (FE modeling of unexposed beams) except that in the analysis the material
properties are different since the beams are exposed to environmental effects.
The analytical investigation consists of two sections. In section I, a brief review
was performed on the deformability or ductility indices available in the literature. Then,
three deformability indices are modified to be applicable for NSM-CFRP strengthened
RC beams. Afterwards, results of eighteen large-scale RC beams strengthened with
prestressed and non-prestressed NSM-CFRP strips and rebars are employed to evaluate
their ductility and deformability based on the modified models and conventional indices.
Furthermore, the limits of the design Codes for ductility and deformability of the beams
are checked and new limits are proposed and validated for different models to be used in
practice. In section II, the load-deflection responses of the nine tested beams in phase I of
the experimental program are predicted analytically by developing a code in Mathematica
software. The code has the capabilities of assigning the actual concrete stress-strain curve
based on Loov's equation, elasto-plastic behaviour for compression and tension steel,
linear behaviour for FRP, and different prestressed CFRP length along the length of the
14
beam. Perfect bond is assumed in the analytical model. The mid-span deflection at each
applied moment is calculated using integration of curvatures along the length of the beam
(from support to mid-span).
1.7 Thesis Layout
A summary of the research performed on the performance of RC beams
strengthened using FRP, the effects of environmental exposure, and FE modeling of
strengthened RC beams with more focus on the NSM method is provided in Chapter
Two. The experimental program and the developed testing matrix in this research are
presented in Chapter Three. Chapter Four provides the experimental test results of the
fourteen beams, relevant discussion, and comparison with similar beams tested under
static loading without any environmental exposure found elsewhere in literature. The
development of the finite element and also analytical models of the tested beams are
presented in Chapter Five, and finally, the conclusions and the recommendations are
presented in Chapter Six. Appendices A and B include the beam design and fabrication,
respectively, the ancillary test results are included in Appendix C, the ANSYS files
generated for FE model of the beams are presented in Appendix D, and the source code
developed for the analytical model is included in Appendix E.
15
Chapter Two: Literature Review
2.1 Introduction
This chapter is categorized to five sections based on the topics to be covered in
the research. The first two sections include a summary about Fibre Reinforced Polymer
materials and NSM strengthening methods, then, a brief review of the research conducted
on prestressed FRP-strengthened RC beams, long-term behaviour of FRP-strengthened
RC beams and components mainly subjected to freeze-thaw exposure and sustained load,
and FE modeling of FRP strengthened RC beams. At the end of this chapter, the
identified research gaps are outlined which were studied and summarized in the following
chapters (these gaps are considered in the objectives listed in Chapter One).
2.2 History of Engineering Materials
Ashby (1987) presented the evolution of conventional and advanced engineering
materials (comprising four classes: ceramics, composites, polymers, and metals) for
mechanical and civil engineering from 10000 BC to 2020. The relative importance for
each class of material in life as a function of time is presented in Figure 2-1. The diagram
is schematic and does not describe any value or tonnage. Before 2000 BC metals played
almost no role and engineering structures (houses, boats, weapons etc) were made of
ceramics (stone, pottery, and glass), composite (straw bricks), and polymers (wood,
straw, and skins). After finding the ways to make metals (around 1500 BC for bronze and
1850 for steel), they dominated the engineering design. After 1960, the rate of metal
development started to decrease and the new materials in the other three classes started to
16
be widely produced. For instance, the production of carbon based composites is rising
about 30% per year. The diagram shows the world is experiencing a revolution and a
transition from the steel age to an age consisting of more advanced materials which
demonstrates the importance of the research in this field.
Figure 2-1: The evolution of materials for civil engineering (Ashby, 1987).
2.3 Fibre Reinforced Polymer
FRP is a composite material. In general, a composite material signifies two or
more materials, which are combined on a macroscopic scale to form a useful third
material (Jones, 1999). Some of the properties, which can be enhanced or affected by
forming a composite material, are listed below:
Strength
Stiffness
17
Corrosion resistance
Weight
Fatigue life
Wear resistance
Attractiveness
Temperature-dependent behaviour
Thermal insulation
Thermal conductivity
Acoustical insulation
Not all of these properties are simultaneously improved by forming a composite
material. The composite is produced based on the design task and demand. FRP is made
of two components: fibre and matrix; to make FRP it is known that long fibres of a
material are much stronger than the same material in bulk form (strength of ordinary
glass=20 MPa while strength of glass fibres=2800 MPa to 4800 MPa). The fibres need to
be bonded together to behave as an efficient structural element. The binder material
usually has lower stiffness and strength and is called a matrix. Some applications of the
polymer composites materials are presented in Table 2-1.
18
Table 2-1: Some application of polymer composites (Sheikh-Ahmad, 2008).
Application area Examples
Aerospace Space structures, satellite antenna, rocket motor cases, high pressure fuel
tanks, nose cones, launch tubes
Aircraft
Fairings, access doors, stiffeners, floor beams, entire wings, wing skins, wing
spars, fuselage, radomes, vertical and horizontal stabilizers, helicopter
blades, landing gear doors, seats, interior panels
Chemical Pipes, tanks, pressure vessels, hoppers, valves, pumps, impellers
Construction Bridges and walkways including decks, handrails, cables, frames, grating
Domestic Interior and exterior panels, chairs, tables, baths, shower units, ladders
Electrical Panels, housing, switchgear, insulators, connectors
Leisure Tennis racquets, ski poles, skis, golf clubs, protective helmets, fishing rods,
playground equipment, bicycle frames
Marine Hulls, decks, masts, engine shrouds, interior panels
Medical Prostheses, wheel chairs, orthofies, medical equipment
Transportation Body panels, dashboards, frames, cabs, spoilers, front end, bumpers, leaf
springs, drive shafts
2.3.1 Fibres
Fibres are the main components of the FRP materials. The diameter of a fibre is
varied from 1-100 µm (Jones, 1999). Three types of fibres are mostly used in civil
engineering domain: Carbon, Glass, and Aramid; the composite is called by its
reinforcing fibre, e.g. Glass Fibre Reinforced Polymer (GFRP). Each type of fibre has
different mechanical properties as plotted in Figure 2-2 along with conventional steel bars
and steel tendons. Carbon fibre has been employed extensively in civil engineering
applications in comparison with the other fibre types. For the purpose of comparison,
properties of a few fibre materials and common structural materials are presented in
Table 2-2 to Table 2-6.
19
Figure 2-2: Typical stress-strain curves of the different fibres and common steel
reinforcements (ACI 440R, 2007).
2.3.1.1 Carbon
Carbon fibres possess a high modulus of elasticity, 200-800 GPa, and their
ultimate elongation varies from 0.3-2.5 %. As an advantage when compared to Aramid
and glass, carbon fibres do not absorb water and are resistant to most chemical solutions,
withstand fatigue excellently, do not stress corrode, show insignificant creep or
relaxation, have less relaxation compared to low relaxation high tensile prestressing steel
strands. The main disadvantage of the carbon fibre is being electrically conductive and,
therefore, might initiate galvanic corrosion when in direct contact with steel (Carolin,
2003). The carbon fibres are categorized based on their modulus or strength as presented
in Table 2-2.
20
Table 2-2: Tensile properties of typical carbon fibres (Akovali, 2001).
Fibre type Young’s modulus
(GPa)
Tensile strength
(GPa)
Strain to failure
(%)
Polyacrylonitrile (PAN)-
based high modulus 350-550 1.9-3.7 0.4-0.7
PAN-based intermediate
modulus 230-300 3.1-4.4 1.3-1.6
PAN-based high strength 240-300 4.3-7.1 1.7-2.4
2.3.1.2 Glass
Glass fibres are significantly cheaper than carbon fibres and aramid fibres.
Therefore, glass fibre composites have become popular in many applications outside the
civil engineering domain, e.g. the boat industry. The modulus of elasticity of the glass
fibres varies from 70-85 GPa with ultimate elongation of 2-5% based on type and quality.
Glass fibres are: sensitive to moisture, stress corrosion at high stress levels, and also may
have problems with relaxation; these drawbacks can be overcome with the correct choice
of matrix which protects the fibres (Carolin, 2003). Typical properties of different glass
fibres are presented in Table 2-3.
Table 2-3: Typical properties of different glass fibres (Akovali, 2001).
Material Density
(kg/m3)
Tensile
strength (MPa)
Young’s
modulus (GPa)
Coefficient of
thermal expansion
(10-6
/oC)
Strain to
failure (%)
Electrical
(E)-glass 2620 3450 81 5 4.9
High strength
(S)-glass 2500 4590 89 5.6 5.7
High alkali
(A)-glass 2500 3050 69 8.6 5
21
2.3.1.3 Aramid
Aramid is the abbreviation for aromatic polyamide. A well-known trademark of
aramid fibres is Kevlar. The modulus of elasticity of the aramid fibres varies from 70-200
GPa with ultimate elongation of 1.5-5%. Aramid has a high fracture energy and therefore
is used for helmets and bullet-proof garments. Aramid fibres are sensitive to elevated
temperatures, moisture and ultra-violet radiation and have problems with relaxation and
stress; therefore, they are not widely employed in civil engineering applications (Carolin,
2003). Properties of some aramid fibres are listed in Table 2-4.
Table 2-4: Properties of some aramid fibres (Akovali, 2001).
Fibre type Density
(kg/m3)
Young’s modulus
(GPa)
Tensile strength
(MPa)
Strain to failure
(%)
Kevlar 29
(High toughness) 1440 85 3000-3600 4
Kevlar 49
(High modulus) 1440 131 3600-4100 2.8
Kevlar 149
(Ultra-high modulus) 1470 186 3500 2
2.3.2 Matrices
The matrix performances comprise: durability, inter-laminar toughness,
shear/compressive/transverse strengths by binding the components together, and thermo-
mechanical stability of the composite, protecting the fibres from environmental damages,
transferring the forces to the fibres, maintaining the desired fibre orientations and
spacing. Thermosetting resins (thermosets) are almost exclusively employed in civil
engineering. Epoxy and vinylester are the most common thermoset matrices. Epoxy is
extensively used in comparison with vinylester but is also more costly. Epoxy has a pot
22
life around 30 minutes at 20oC but can be changed with different formulations. The
curing rate increases with increased temperature. Table 2-5 and Table 2-6 present the
mechanical and thermal properties of matrix materials and some applications of the
conventional matrix materials, epoxy and polyester.
23
Table 2-5: Mechanical and thermal properties of matrix materials at room temperature (Sheikh-Ahmad, 2008).
Type of matrix Density
(kg/m3)
Young’s
modulus
(GPa)
Tensile
strength
(MPa)
Strain to
failure
(%)
K
(W/m oC)
Cp
(kJ/kg oC)
α
(10-6
/oC)
Tg
(oC)
Tm
(oC)
Poly
mer
s-T
her
mose
ts
Unsaturated polyester 1.1-1.23 3.1-4.6 50-75 1-6.5 0.17-0.22 1.3-2.3 55-100 70 -
Epoxy 1.1-1.2 2.6-3.8 60-85 1.5-8 0.17-0.2 1.05 45-65 65-175 -
Phenolics (Bakelite) 1-1.25 3-4 60-80 1.8 0.12-0.24 1.4-1.8 25-60 300 -
Bismaleimide 1.2-1.32 3.2-5 48-110 1.5-3.3 - - - 230-345 -
Vinylesters 1.12-1.13 3.1-3.3 70-81 3-8 - - - 70 -
Po
lym
ers-
Ther
mopla
stic
s Polypropylene 0.9 1.1-1.6 31-42 100-600 0.11-0.17 1.8-2.4 80-100 -20-5 165-175
Polyamide (nylons) 1.1 2 70-84 150-300 0.24 1.67 80 55-80 265
Poly (phenylene sulfide) 1.36 3.3 84 4 0.29 1.09 49 85 285
Poly (ether ether ketone) 1.26-1.32 3.2 93 50 0.25 1.34 40-47 145 345
Poly (ether sulfone) 1.37 3.2 84 40-80 0.26 1 55 225 -
Poly (ether imide) 1.27 3 105 60 0.07 47-56 - 215 -
Poly (amide imide) 1.4 3.7-4.8 93-147 12-17 - - 245-275 - -
Cer
amic
s Alumina Al2O3 (99.9% pure) 3.98 380 282-551 - 39 0.775 7.4 - -
Silicon nitride Si3N4 (sintered) 3.3 304 414-650 - 33 1.1 3.1 - -
Silicon carbide SiC (sintered) 3.2 207-483 96-520 - 71 0.59 4.1 - -
Met
als Aluminum alloys (7075 T6) 2.8 71 572 11 1.3 0.96 23.4 - -
Steel alloy (1020 Cold drawn) 7.85 207 420 15 51.9 0.486 11.7 - -
K= thermal conductivity, Cp= specific heat, α= coefficient of thermal expansion, Tg= glass transition temperature, Tm= melting temperature
23
24
Table 2-6: Some aspects of epoxy and polyester thermosets (Akovali, 2001).
Thermoset Some characteristics Main uses Limitations
Epoxy
Good electrical properties
Chemical resistance
High strength
Filament winding
Printed circuit-board
tooling
Required heat curing
for maximum
performance
Cost
Polyester
Good all-around properties
Ease of fabrication
Low cost
Versatile
Corrugated
Sheeting
Boats, piping, tanks
Ease of degradation
2.3.3 FRP Composite
In a FRP composite, the fibres may be placed in one direction (unidirectional) or
may be woven or bonded in many directions (bi-or multi-directional). Unidirectional
composites are commonly employed for strengthening purposes. FRP composites can be
produced by different methods: hand lay-up, pultrusion, filament winding, and moulding;
and also, in different shapes such as rebar, strip, plate, and section as shown in Figure
2-3. The composites’ mechanical properties are based on the fibres, matrix, fibre content,
and fibre direction. Also, the volume or size of the composite will affect the mechanical
properties. The fibre content by volume, (volume of fibre to volume of the composite)
varies from 30-70%, but in most cases about 30-40% of composite volume is made of
matrix (fibre content of 60-70%). In order to provide the reinforcing function, the fibre-
volume fraction should be more than 55% for FRP bars and rods and 35% for FRP grids
(ISIS Design Manual No.3, 2007). Normally, the volume fraction of fibres in FRP
strips/plates is about 50-70% and that in FRP sheets is about 25-35% (Setunge et al.,
2002). Typical stress-strain relationships for matrix, fibres, and produced FRP composite
are shown Figure 2-4. FRP materials react differently in miscellaneous environmental
25
conditions as presented in Table 2-7. Mechanical properties of some commercially
available FRP bars are listed in Table 2-8.
Figure 2-3: Different types of FRP composites (Sireg, 2011).
Table 2-7: Environmental considerations for different FRP materials (NCHRP,
2004).
Consideration Carbon Glass Not tolerant
Alkalinity/acidity
exposure Highly resistant Not tolerant Not tolerant
Thermal expansion Near zero, may cause
high bond stress Similar to concrete
Near zero, may cause
high bond stress
Electrical conductivity High Excellent insulator Excellent insulator
Impact tolerance Low High High
Creep rupture and fatigue High resistance Low resistance Low resistance
FRP strips/plates FRP rebars
Fabric/sheets FRP sections
26
Str
es
s (
MP
a)
Strain (%)
Fibres
FRP
Matrix
0.4 - 4.8 > 10
1800 - 4900
34 - 130
600 - 3000
Figure 2-4: Typical stress-strain curves for matrix, fibres, and resulted FRP
composite (ISIS Design Manual No.3, 2007).
Table 2-8: Typical properties of FRP bars (ISIS Design Manual No.3, 2007).
Trade name Tensile strength
(MPa)
Modulus of elasticity
(GPa) Ultimate tensile strain
Carbon fibre
V-rod 1596 120 0.013
Aslan 2068 124 0.017
Leadline 2250 147 0.015
NEFMAC 1200 100 0.012
Glass fibre
V-rod 710 46.4 0.015
Aslan 690 40.8 0.017
NEFMAC 600 30 0.02
2.4 Strengthening Concrete Structures Using FRP Materials
Generally, concrete members are strengthened with FRP in two methods:
Externally Bonded (EB) and Near-Surface Mounted (NSM) which are briefly explained
within this section.
27
2.4.1 Externally Bonded Strengthening Method
In EB method, the FRP fabrics, sheets or plates are bonded on the tension face of
the concrete members using epoxy adhesive. The concrete surface should be cleaned and
concrete cover should be in reasonable condition to be able to transfer the loads to the
installed FRP sheets/plates. The concrete surface could be ground or sand blasted to the
level of aggregate to ensure the appropriate performance of the bond between concrete-
epoxy interface. EB strengthening can be performed in two methods: hand-applied wet
lay-up system and pre-cured system. To implement hand-applied wet lay-up
strengthening, first, where required, primer and putty should be applied to the surface,
then, dry or pre-impregnated fibre sheets and fabrics are installed on the surface using a
saturating resin. The FRP ply orientation and the ply stacking sequence needs to be
specified and performed in the exact manner. If multiple layers of FRP materials are
used, all layers must be fully impregnated within the appropriate resin to be able to
transfer the shearing load between layers and FRP-concrete. To implement pre-cured
system, the FRP plates are installed using paste epoxy-based adhesive which is uniformly
applied to the prepared surface. In both EB methods, entrapping the air under the
laminates should be avoided. A schematic of the EB strengthening method is shown in
Figure 2-5a.
2.4.2 Near-Surface Mounted Strengthening Method
NSM strengthening is a method classified as pre-cured strengthening system. To
implement this method, the FRP strip/rebar, is bonded into the groove cut in concrete as
shown in Figure 2-5b and c. The cross-section of the bar can be round, oval, square or
28
rectangular with a sand-coated, ribbed or plain surface. The depth of the groove and
dimensions of the reinforcements are limited by the depth of the concrete cover. The
groove filler can be epoxy adhesive or cement mortar. A few field applications of NSM-
FRP based strengthening are presented in Figure 2-6. The NSM strengthening should be
implemented based on the following steps:
Sawing groove in concrete cover
Cleaning the groove carefully with air pressure or water pressure (100-150 bar)
Filling the groove using epoxy or cement grout, the groove should be dry when
the epoxy is employed as a filler and should be wet when cement grout is
employed as a filler
Cleaning the FRP rebar/strip using acetone and mounting the reinforcement in
the groove
Removing the extra epoxy using spatula
(a) (b) (c)
Figure 2-5: Schematic of flexural strengthening using FRP: (a) EB FRP, (b) NSM-
FRP strips, and (c) NSM-FRP rebars.
29
(a) Trenchard Street eleven-storey parking strengthened with NSM-CFRP rebar
(DTI MMS 6, 2005)
(b) Strengthening of parking garage decks using NSM-CFRP bars (Tumialan et al.,
2007)
(c) Strengthening of bridge in Switzerland in 1999 using NSM-CFRP laminate
(Carolin, 2003)
Figure 2-6: Some field applications of NSM-FRP based strengthening.
30
(d) Strengthening a bridge deck using NSM-CFRP strip (Casadei et al., 2003)
(e) Cement silo repair and upgrade using NSM-CFRP bar (Concrete repair
bulletin, 2001)
Figure 2-6: Some field applications of NSM-FRP based strengthening (Cont’d).
2.5 History of NSM Method
NSM-FRP method is one of the latest techniques for strengthening of concrete
members, however, the NSM is not a new method. The use of NSM reinforcement was
developed in Europe for strengthening of RC structures in the early 1950s. In 1948 an RC
bridge deck in Sweden, which needed to be upgraded in its negative moment region due
to an excessive settlement of the steel cage during construction, was strengthened by
31
inserting steel reinforcement bars in grooves made in the concrete surface and filling it
with cement mortar (Asplund, 1949). At the onset of development, the black steel was
replaced using stainless steel. In 1960s, development of high strength adhesive such as
epoxy encouraged the use of epoxy instead of cement grout. Developing the FRP
materials led to use them instead of steel reinforcements for strengthening. In comparison
to FRP, the steel reinforcements are heavy, rigid, difficult to install, highly susceptible to
corrosion, and cheaper. Also, they need bigger grooves. Three shapes of FRP
reinforcement have been used in NSM method: round bars, rectangular/square bars, and
strips. Recently‚ prestressed FRP has been used for strengthening of RC members due to
better utilization of the strengthening material, smaller and better distributed cracks in
concrete, taking a large portion of the tension force from steel reinforcement and higher
steel yielding loads. The significant drawback of strengthening with prestressed FRP is
the design requirement of an anchorage device for end zones that should be practical in
implementation (Nordin and Täljsten, 2006).
2.6 Material Used for NSM
2.6.1 Reinforcements
Three kinds of FRP reinforcements have been used in NSM strengthening. In
most cases, CFRP reinforcements have been used. After CFRP, GFRPs have been used
for most application in timber and masonry. The application of AFRP is very rare. The
CFRP reinforcements have higher modulus of elasticity and tensile strength than those of
GFRP and AFRP, which leads to use of smaller CFRP section for the same tensile
strength, furthermore, this leads to making smaller grooves in the concrete and easer
32
installation. For these reasons, the CFRP is used in most applications. The NSM-FRP
reinforcements are produced in different shapes: round, square, rectangular, and oval.
The surface of a bar can be in different styles: smooth, sand-blasted, sand-coated, spirally
wound with a fibre tow, ribbed, and roughened with a peel-ply surface treatment.
Different shapes of the FRP reinforcements practiced in NSM strengthening are shown in
Figure 2-7.
Figure 2-7: Different shapes of FRP reinforcements for NSM strengthening (De
Lorenzis and Teng, 2007).
2.6.2 Groove Filler
The groove filler transfers the stresses between FRP reinforcement and substrate
concrete. The shear and tensile strengths of the groove filler are important in structural
behaviour of the member; the shear strength is important to avoid cohesive shear failure
of the bonded reinforcement, on the other hand, tensile strength is important when
deformed rebar is used to resist against high circumferential tensile stress in groove filler.
Two-component epoxy is the most common groove filler used in NSM method. High-
33
viscosity epoxy is used for strengthening in positive moment regions (upper hand
applications) and low-viscosity epoxy is used for strengthening in the negative moment
regions. In some applications cement mortar has been used as groove filler (Täljsten et
al., 2003). The use of cement mortar decreases the cost, reduces the hazard to workers,
allows effective bonding to wet surfaces, causes better resistance in high temperature, and
leads to better thermal compatibility with surrounding concrete, but the main drawback of
the cement mortar is having inferior mechanical properties when compared to common
epoxies.
2.7 Comparison between NSM-FRP and EB-FRP Technique
In comparison to EB, the NSM method provides better protection against
mechanical damages and accidental impacts, better resistance against debonding, the
concrete surface is not completely covered which can lead to less freeze and thaw
problems in future, no surface preparation after sawing the grooves and cleaning, the
ability to replace the epoxy with cement grout due to the harmful effects of it, and the
increase in force transfer and durability. On the other hand, the NSM method requires
more extensive labour, equipment, time, and sufficient clear concrete cover but both of
the strengthening methods are less costly than replacing a structure or structural member
(Quattlebaum et al., 2005; De Lorenzis and Teng, 2007). Different aspects of EB and
NSM are listed in Table 2-9.
34
Table 2-9: Aspects of EB and NSM strengthening methods (Täljsten et al., 2003).
Plates Sheets NSM
Shape Rectangular strips Thin unidirectional or
bidirectional fabrics
Rectangular strips or
laminates
Dimension:
Thickness
width
1-2 mm
50-150 mm
0.1-0.5 mm
200-600 mm
1-10 mm
10-30 mm
Use Simply bonding of
factory-made profiles
with adhesives
Bonding and impregnation
of the dry fibre with resin
and curing at site
Simple bonding of factory
made profiles with
adhesive or cement mortar
in pre-sawed slots in the
concrete cover
Application
aspects
For flat surfaces
Thixotropic adhesive
for bonding
Not more than one
layer recommended
Stiffness of laminate
and use of thixotropic
adhesive allow for
certain surface
unevenness
Simple in use
Quality guaranteed
from factory
Suitable for
strengthening in
bending
Needs to be protected
against fire
Easy to apply on curved
surface
Low viscosity resin from
bonding and impregnation
Multiple layers can be
used, more than 10
possible
Unevenness needs to be
levelled out
Needs well documented
quality systems
Can easily be combined
with finishing systems,
such as plaster and paint
Suitable for shear and
bending strengthening
Needs to be protected
against fire
For flat surfaces
Depends on the distance to
steel reinforcement
A slot needs to be sawn up
in the concrete cover
The slots needs careful
cleaning before bonding
Bonded with a thixotropic
adhesive
Possible to use cement
mortar for bonding
Protected against impact
and vandalism
Suitable for strengthening
in bending
Minor protection against
fire
2.8 Background of the Topic
Performance of the NSM strengthening method under environmental exposure
and sustained load is an important issue for future applications of this technique in
practical projects. In this context, the performed experimental, numerical, and analytical
studies mainly on the prestressed NSM-FRP method are briefly reviewed to identify the
possible gaps in this field. In each section the most related researches are cited and the
35
rest are presented in a table format at the end. Finally, the existing research gaps are
summarized.
2.9 Prestressed NSM-FRP Strengthened RC Beam
In this context, Täljsten and Nordin (2005) studied the effect of strengthening
with prestressed external steel and NSM-CFRP reinforcement. Eight beams were tested:
one as un-strengthened control beam, two beams strengthened with non-prestressed
NSM-CFRP square bar, three beams strengthened using prestressed external steel tendon
(with 34% prestressing level of the yielding strength of the tendon), one beam
strengthened using external prestressed CFRP square bars anchored at the ends (with
14% prestressing level of the tensile strength of the CFRP bar), and one beam
strengthened with prestressed NSM-CFRP rods (with 19% prestressing level of the
tensile strength of the CFRP rod). The results showed that beams strengthened with
external prestressed steel tendons failed by steel yielding while the beam strengthened
with prestressed CFRP rods failed due to anchorage fracture. The beams strengthened
with non-prestressed NSM-CFRP failed due to anchorage and debonding failure while
the beam with prestressed NSM-CFRP rod failed due to concrete spalling. An increase of
100% at yielding load and 181% at ultimate load was observed for the beam prestressed
with NSM-CFRP rod.
Wu et al. (2005) studied the effectiveness of RC beams strengthened with
prestressed NSM-CFRP tendons (rods) tested under four-point bending configuration and
static monotonic loading. Seven beams (150 × 200 × 2000 mm; width × height × length)
were tested: one reference beam, one strengthened with non-prestressed NSM-CFRP, and
36
five strengthened with prestressed NSM-CFRP tendons (with 14.5% and 30%
prestressing levels of the ultimate tensile strength of the CFRP tendon). Different groove
filers were used, epoxy putty and cement mortar in addition to adding extra layer of both
after curing the filler. Test results revealed the beams with cement mortar failed due to
concrete crushing. Enhancements of 200%, 50%, and 93% were observed at cracking,
yielding and ultimate loads, respectively.
Nordin and Täljsten (2006) tested fifteen beams (200 × 300 × 4000 mm; width ×
height × length) strengthened with prestressed NSM-CFRP quadratic rods under static
loading. The test results showed a significant enhancement in the cracking and yielding
loads. The developed prestressing method by these researchers is not practical because it
needs access to the entire length of the beam. Furthermore, these researchers found that it
is necessary to use a mechanical anchoring device. Lack of the mechanical anchorage
caused a large difference between prestressing losses in CFRP reinforcements at the end-
point and mid-span.
Casadei et al. (2006) tested three full-scale Prestressed Concrete (PC) I-girders
(11 m long); one un-strengthened beam, one impact damaged PC beam strengthened with
prestressed NSM-CFRP bars and one impact damaged PC beam strengthened with EB-
CFRP laminate along the length accompanied by U-wrap. The impact damage was
enforced by cutting two of seven low-relaxation tendon wires prestressed to 75% of
yielding strength. The prestressing force of CFRP bar was calculated to restore the same
level of prestressing prior to damage (33% of ultimate tensile strength of CFRP bar). The
bars were prestressed against both ends of the beam using hydraulic jack. This method is
not practical in implementation. The results revealed that all beams almost had the same
37
stiffness and cracking load as well as the same ultimate load. The EB strengthened beam
failed in a brittle mode by debonding the laminate followed by rupture of the U-warp
sheet. The beam strengthened with the NSM method failed due to splitting of the
concrete cover which caused debonding failure of one of the CFRP bars at the bottom
and slowly led to progressive failure in the system.
Jung et al. (2007) studied the strengthening performance and flexural behaviour of
RC beams strengthened with prestressed CFRP strips using an EB system and CFRP rods
with mechanical interlocking (MI) and prestressed NSM. Eight beams were tested (200 ×
300 × 3000 mm; width × height × length): one as un-strengthened control beam; another
strengthened with EB-CFRP plates; and other six beams strengthened using different
NSM techniques: NSM, NSM+MI, and prestressed NSM (with 20% prestressing level of
the ultimate tensile strength of the CFRP strip/bar) using strips and bars. The EB-CFRP
strengthened beam failed due to debonding at 30% of the ultimate tensile strain of the
CFRP plate. The beams strengthened with NSM-CFRP rods and strips failed due to
separation of CFRP and epoxy from the concrete substrate at 82-87% of the ultimate
tensile strain of the CFRP strip/rebar. The beams strengthened with MI failed due to
CFRP rupture. However, the beam strengthened with prestressed NSM-CFRP strip failed
due to separation of CFRP and epoxy from concrete substrate while the beam
strengthened with prestressed NSM-CFRP rod failed due to CFRP rupture.
Gaafar (2007) developed an innovative anchorage system for prestressed NSM
technique to overcome the practical issue of the earlier studies on the prestressed NSM-
FRP strengthening. Nine large-scale beams (200 × 400 × 5150 mm; width × height ×
length) were tested: one un-strengthened control beam, four beams strengthened with
38
prestressed NSM-CFRP strips (with 0, 20, 40, and 60% prestressing levels of ultimate
tensile strength of CFRP strips), and another four beams strengthened with prestressed
NSM-CFRP rebars (with 0, 20, 40, and 60% prestressing levels of ultimate tensile
strength of CFRP rebars). All strengthened beams failed due to FRP rupture without any
premature failure while up to 68% enhancement in ultimate capacity was achieved in
comparison with un-strengthened control beam. Furthermore, the prestressing enhanced
the cracking and yielding loads, significantly, and leads to delay in crack formation while
the ultimate load almost stayed constant and ductility decreased.
Badawi and Soudki (2009) investigated the effectiveness of strengthening RC
beams using prestressed NSM CFRP rods. Four beams (152 × 254 × 3500 mm; width ×
height × length) were tested: one un-strengthened control beam and three beams
strengthened with prestressed NSM-CFRP rods (with 0, 40, and 60% prestressing levels
of ultimate tensile strength of CFRP rods). The non-prestressed beams failed due to
concrete crushing while the prestressed beams failed due to CFRP rupture and up to 79%
improvement in ultimate capacity was achieved. Also, the load-deflection responses of
the tested beams were predicted by developing an analytical model. The main issue in
this study was using the external seats for prestressing requiring access to both ends of
the beam which is not practical, and furthermore, a significant amount of the prestress
loss was observed at the beam ends while the prestress loss was insiginifacnt at the mid-
span.
The most related researches in the area are reviewed above and the rest are
presented in Table 2-10.
39
Table 2-10: Summary of existing experimental work on flexural strengthening using
NSM-FRP reinforcements.
Reference Crasto et al. (1999) De Lorenzis et al. (2000) Blaschko (2001)
Test method and type of NSM
strengthening
Static
Four-point bending
Non-prestressed
Static
Four-point bending
Non-prestressed
Static
Four-point bending
Non-prestressed
Number of specimens N.A.
Four: one control, two strengthened
with NSM CFRP rods, one strengthened
with NSM GFRP rods
N.A.
Bea
m g
eom
etry
Cross section (mm) 152×457
356×914
T shape, total height = 406, web height
= 305, flange width = 381, web width =
152
200×500
600×500
Net span (mm) 2400
7500 3900
2800
7500
Shear span (mm) 800
2500 1830
1150
3250
f'c (MPa) NA 36 44
Bottom
steel
Amount 1.14%
1.19% 2#7 (0.89%)
0.63%
0.84%
fyt (MPa) N.A. 494 N.A.
Top
steel
Amount N.A. 2#4 N.A.
fyc (MPa) N.A. 494 N.A.
Str
eng
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eria
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Groove
filler
Type Epoxy Epoxy Epoxy
Tensile strength
[Modulus of
elasticity] (MPa)
30
[N.A.]
13.8
[N.A.]
33.3
[N.A.]
FRP
Type CFRP bar GFRP bar
CFRP bar CFRP strip
shape/surface Round, smooth Round/ribbed
Round/sand-coated Roughened
Dimension
db or tf×hf (mm)
4.75
6.35
12.7
9.5, 12.7 2×20
Number of FRP
reinforcements 4, 11 2 3, 11
Efrp (GPa) 122 GFRP:41.3
CFRP:164.7 156
Tensile strength
(MPa) 1326
GFRP:800
CFRP:1550 1813
Groove dimensions
(mm) 10.2×varying h
19×19
25×25 3.3×23
Cut-off distance
from the support (mm) N.A. Extended over supports 150, 300
Test variables Beam size, steel ratio,
groove size Type of FRP bar, bar diameter
End anchorage, type
of loading
Observed failure modes
Concrete crushing,
secondary debonding
and partial bar rupture
debonding of NSM SB bar, concrete
cover separation
concrete cover
separation, bar
rupture
Increase in capacity (%) 20-50 26-44 67-82
40
Table 2-10: Summary of existing experimental work on flexural strengthening using
NSM-FRP reinforcements (Cont’d).
Reference De Lorenzis (2002) Taljsten et al. (2003) Hassan and Rizkalla (2003)
Test method and type of NSM
strengthening
Static
Four-point bending
Non-prestressed
Static
Four-point bending
Prestressed and non-prestressed
Static
Three-point bending
Non-prestressed
Number of specimens N.A.
Eight: two controls, four
strengthened with non-
prestressed NSM CFRP rods,
two strengthened with
prestressed NSM CFRP rods
Nine: one control, eight
strengthened with NSM CFRP
strips
Bea
m g
eom
etry
Cross section (mm) 200×400 200×300
T shape, total height = 300,
web height = 250,
flange width = 300,
web width = 150
Net span (mm) 4000 3600 2500
Shear span (mm) 1750 1300 1250
f'c (MPa) 15 60.7-68 48
Bottom
steel
Amount 0.38-0.64% 2-Ø16 (0.67%) 2-10M
fyt (MPa) N.A. 490 400
Top
steel
Amount N.A. 2-Ø16 2-10M
WWF 51×51 MW5.6×MW5.6
fyc (MPa) N.A. 490 400
Str
eng
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eria
ls
Groove
filler
Type Epoxy Epoxy and cement grout Epoxy
Tensile strength
[Modulus of
elasticity] (MPa)
27.4
[N.A.]
31 [7000] for epoxy
N.A. [N.A.] for cement grout
N.A.
[N.A.]
FRP
Type CFRP bar CFRP rod CFRP strip
shape/surface Round, spirally wound
and sand-coated Square, smooth N.A.
Dimension
db or tf×hf (mm) 7.5 10×10 1.2×25
Number of FRP
reinforcements 1, 2 1, 2 1
Efrp (GPa) 175 230, 160 150
Tensile strength
(MPa) 2214 4140, 2800 2000
Groove dimensions
(mm) 16×16
15×15 (for epoxy bonded)
20×20 (for cement grout
bonded)
5×25
Cut-off distance
from the support (mm) Extended over supports 300 or extended over supports 1100-50
Test variables Steel ratio, number of
FRP bars NSM bar length, groove filler Bar anchorage length
Observed failure modes
Concrete crushing,
concrete cover
separation, edge failure
Debonding, bar rupture Debonding, bar rupture
Increase in capacity (%) 21-61 56-92 0–54
41
Table 2-10: Summary of existing experimental work on flexural strengthening using
NSM-FRP reinforcements (Cont’d).
Reference Hassan and Rizkalla (2004) El-Hacha and Rizkalla (2004) Yost et al. (2004)
Test method and type of NSM
strengthening
Static
Three-point bending
Non-prestressed
Static
Three-point bending
Non-prestressed
Static
Four-point bending
Non-prestressed
Number of specimens
Eight: one control, seven
strengthened with NSM CFRP
bars
Eight: one control, two strengthened
with NSM CFRP strips, two
strengthened with EB CFRP strips,
one strengthened with NSM CFRP
bar, one strengthened with NSM
GFRP strips, one strengthened with
EB GFRP strips
N.A.
Bea
m g
eom
etry
Cross section (mm)
T shape, total height = 300,
web height = 250,
flange width = 300,
web width = 150
T shape, total height = 300,
web height = 250,
flange width=300,
web width=150
152-304×188
Net span (mm) 2500 2500 1750
Shear span (mm) 1250 1250 500
f'c (MPa) 48 48 37
Bottom
steel
Amount 2-10M 2#13 (0.48%) 0.83–1.74%
fyt (MPa) 400 400 N.A.
Top
steel
Amount 2-10M
WWF 51×51 MW5.6×MW5.6
2#13
WWF 51×51 MW5.6×MW5.6 N.A.
fyc (MPa) 400 400 N.A.
Str
eng
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Groove
filler
Type Gel epoxy, Epoxy Epoxy Epoxy
Tensile strength
[Modulus of
elasticity] (MPa)
48 [1200] for gel epoxy
62 [3000] for epoxy
48 [1200] (for bars)
70 [3500] (for strips) N.A.
FRP
Type CFRP rod CFRP and GFRP CFRP strip
shape/surface Round-ribbed
CFRP/round/spirally wound
CFRP/strip/ N.A.
CFRP/strip/ N.A.
GFRP/strip/ N.A.
Roughened
Dimension
db or tf×hf (mm) 9.5 9.5, 2×16, 1.2×25, 2×20 0.25×15.5
Number of FRP
reinforcements 1 1, 2 (CFRP), 5 (GFRP) 1, 2
Efrp (GPa) 111 122.5, 140, 150, 45 136.6
Tensile strength
(MPa) 1918 1408, 1525, 2000, 1000 1656
Groove dimensions
(mm) 18×30 18×30, 6.4×19, 6.4×25, 6.4×25 6.4×19
Cut-off distance
from the support (mm) 1100-50 50
Extended over
supports
Test variables Bar anchorage length,
different epoxy Type of FRP bar
Section width,
steel ratio, number
of FRP bars
Observed failure modes Concrete splitting
concrete cover separation (CFRP
round bars and GFRP strips), bar
rupture (CFRP strips)
Concrete crushing, bar
rupture
Increase in capacity (%) 0–41 69-99 15–55
42
Table 2-10: Summary of existing experimental work on flexural strengthening using
NSM-FRP reinforcements (Cont’d).
Reference Arduini et al. (2004) Kishi et al (2005) Barros and Fortes (2005)
Test method and type of NSM
strengthening
Static
Four-point bending
Non-prestressed
Static
Four-point bending
Non-prestressed
Static
Four-point bending
Non-prestressed
Number of specimens N.A. Three: strengthened with
NSM AFRP rods
Eight: four series of two beams
(one control, one strengthened
with NSM CFRP strips)
Bea
m g
eom
etry
Cross section (mm) 200×120 150×250 100×170-180
Net span (mm) 1100 2600 1500
Shear span (mm) 500 1050 500
f'c (MPa) 20-63 34.3 46.1
Bottom
steel
Amount 0.28, 0.57% 2-D13 0.33–0.84%
fyt (MPa) N.A. 362 730-524.2
Top
steel
Amount N.A. 2-D19 2-Ø8
fyc (MPa) N.A. 362 524.2
Str
eng
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Groove
filler
Type Epoxy Epoxy Epoxy
Tensile strength
[Modulus of
elasticity] (MPa)
N.A.
[N.A.]
N.A.
[N.A.]
16–22
[5000]
FRP
Type CFRP bar AFRP rod CFRP strip
shape/surface Round-N.A. N.A. N.A.
Dimension
db or tf×hf (mm) 7 (net), 8 (external) 5, 7.3, 9 1.45×9.59
Number of FRP
reinforcements 1, 3 2 1-3
Efrp (GPa) 201 62.5 158.8
Tensile strength
(MPa) 1940 1450 2739.5
Groove dimensions
(mm) N.A. N.A. 4×12
Cut-off distance
from the support (mm) 50 100 50
Test variables
Number of FRP
bars, concrete
strength
Axial stiffness Steel ratio,
number of NSM FRP strips
Observed failure modes Concrete crushing,
debonding Debonding Concrete cover separation
Increase in capacity (%) 140–430 1.51-1.86 (Pu/Py) 78–98
43
Table 2-10: Summary of existing experimental work on flexural strengthening using
NSM-FRP reinforcements (Cont’d).
Reference Quattlebaum et al. (2005) Nordin and Täljsten (2006) Teng et al. (2006)
Test method and type of NSM
strengthening
Static
Fatigue
Three-point bending
Non-prestressed
Static
Four-point bending
Prestressed and non-prestressed
Static
Four-point bending
Non-prestressed
Number of specimens
Four: one control, one
strengthened under static, one
under low-stress fatigue, one
under high-stress fatigue
Fifteen: one control, four
strengthened with non-
prestressed NSM CFRP rods,
and ten strengthened with
prestressed NSM CFRP rods
Five: one control, four
strengthened with NSM
CFRP strips
Bea
m g
eom
etry
Cross section (mm) 152×254 200×300 150×300
Net span (mm) 4572 3600 3000
Shear span (mm) 2286 1300 1200
f'c (MPa) 29.5 61-68 44
Bottom
steel
Amount 3-Ø13 2-Ø16 2-Ø12
fyt (MPa) 446 496 532
Top
steel
Amount N.A. 2-Ø16 2-Ø8
fyc (MPa) N.A. 496 375
Str
eng
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eria
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Groove
filler
Type Epoxy Epoxy, BPE Lim 456/564 Epoxy
Tensile strength
[Modulus of
elasticity] (MPa)
72.4
[3200]
31
[7000]
42.6
[2620]
FRP
Type CFRP strip CFRP rods: S, M CFRP strip
shape/surface Rectangular, smooth Quadratic, smooth Roughened with peel-ply
surface treatment
Dimension
db or tf×hf (mm) 1.4×25 10×10 2-2×16
Number of FRP
reinforcements 2 1 1
Efrp (GPa) 154.29 S: 160
M: 250 151
Tensile strength
(MPa) 2785.7
S: 2800
M: 2000 2068
Groove dimensions
(mm) 6.4×32 15×15 8×22
Cut-off distance
from the support (mm) 152.5 200 or extended over supports 1250-50
Test variables
Type of loading (static and
fatigue), different types of
strengthening
Prestressing level (0-0.27fu), the
bond length, and the modulus of
elasticity of CFRP
Bar anchorage length
Observed failure modes
Concrete crushing followed
concrete cover splitting,
fatigue fracture of tension
reinforcements
FRP rupture, Concrete crushing
+ FRP rupture Concrete cover separation
Increase in capacity (%)
Static:33.2
LS Fatigue: failed after 2×106
cycles,
HS Fatigue: failed around
829423 cycles
S: 56-97.3
M: 62.7-76 0–106
44
Table 2-10: Summary of existing experimental work on flexural strengthening using
NSM-FRP reinforcements (Cont’d).
Reference Aidoo et al. (2006) Tang et al. (2006) Barros et al. (2007)
Test method and type of NSM
strengthening
Static
Fatigue
Three-point bending
Non-prestressed
Static
Four-point bending
Non-prestressed
Static
Four-point bending
Non-prestressed
Number of specimens
Four: two controls, two
strengthened with NSM CFRP
laminates
Eight: three controls, four
strengthened with NSM
GFRP#5, one strengthened with
NSM GFRP#3
Twelve: six controls, six
strengthened with NSM
CFRP laminates
Bea
m g
eom
etry
Cross section (mm)
T shape, total height = 825,
web height = 660,
flange width = 927,
web width = 343
180×250 120×170
Net span (mm) 8025 1200 900
Shear span (mm) 4012.5 500 300
f'c (MPa) 45 58, 37, 21 52.2
Bottom
steel
Amount 3#11+3#10+2#8 2- Ø16 2-Ø5, 2-Ø6.5, 3-Ø6.5
fyt (MPa) 364 398, 512 788, 627, 627
Top
steel
Amount N.A. N.A. 2-Ø6.5
fyc (MPa) N.A. N.A. 627
Str
eng
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Groove
filler
Type Epoxy+Silica fume Epoxy, XH-111, XH-130 Epoxy, CFK 150/2000
Tensile strength
[Modulus of
elasticity] (MPa)
N.A.
[N.A.]
27, 49
[N.A.]
16-22
[5000]
FRP
Type CFRP laminate GFRP bar CFRP laminate
shape/surface Rectangular, smooth Round, sand coated Rectangular, smooth
Dimension
db or tf×hf (mm) 1.4×25 9.5, 16 1.4×9.6
Number of FRP
reinforcements 4 2 1, 2, 3
Efrp (GPa) 154.29 68, 64 158.8
Tensile strength
(MPa) 2785.7 650, 512 2740
Groove dimensions
(mm) N.A.×32
15×15
20×20 (4-5)×(12-15)
Cut-off distance
from the support (mm) Extended over supports Extended over supports N.A.
Test variables
Strengthening of aged
member (42 years old), type
of loading, different types of
retrofitting
Type of concrete, type of epoxy,
area of GFRP bar Axial stiffness
Observed failure modes Concrete crushing+concrete
cover splitting
Shear failure+GFRP rupture,
shear failure+GFRP debonding,
Concrete crushing+epoxy paste
splitting
Delamination of concrete
cover at cut-off location
Increase in capacity (%) 6-10 23.7-51.6 35-118
45
Table 2-10: Summary of existing experimental work on flexural strengthening using
NSM-FRP reinforcements (Cont’d).
Reference Gaafar (2007) Al-Mahmoud et al. (2009) Badawi and Soudki (2009)
Test method and type of NSM
strengthening
Static
Four-point bending
Prestressed and non-
prestressed
Static
Four-point bending
Non-prestressed
Static
Four-point bending
Prestressed and non-prestressed
Number of specimens
Nine: one control, two
strengthened with non-
prestressed NSM CFRP
rebars/strips, six strengthened
with prestressed NSM CFRP rebars/strips
Eight: one control, seven
strengthened with NSM
CFRP bars
Four: one control, one
strengthened with non-
prestressed NSM CFRP rod,
two strengthened with
prestressed NSM CFRP rods
Bea
m g
eom
etry
Cross section (mm) 200×400 150×280 152×254
Net span (mm) 5000 2800 3500
Shear span (mm) 2000 800 1100
f'c (MPa) 40 35.1-38.1
66.5-67.2 45
Bottom
steel
Amount 3-15M 2-12mm 2-15M
fyt (MPa) 475 600
E=210GPa 440
Top
steel
Amount 2-10M 2-6mm 2-10M
fyc (MPa) 500 600 440
Str
eng
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eria
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Groove
filler
Type Epoxy Epoxy
Mortar Epoxy
Tensile strength
[Modulus of
elasticity] (MPa)
24
[4500]
29.5 [4940] for epoxy
6.2 [31400] for mortar
N.A.
[N.A.]
FRP
Type CFRP strip and rebar CFRP rod CFRP rod
shape/surface
Strip: rectangular, rough
textured
Rebar: round, sand coated
Round, sand coated Round-N.A.
Dimension
db or tf×hf (mm) Strip:2-2×16, rebar: 9 6,12 9.5
Number of FRP
reinforcements 1
1 (for 12mm)
2 (for 6mm) 1
Efrp (GPa) Strip:124, rebar:124 146 136
Tensile strength
(MPa) 2610 1875 1970
Groove dimensions
(mm)
Strips: 16×25
Rebar: 20×25
12×12
24×24 15×25
Cut-off distance
from the support (mm) 310, mechanical anchor used
350, 50, or extended over
supports Extended over supports
Test variables Prestressing level (0-60% fu),
type of CFRP material
Strengthening length,
concrete strength, groove
filler, area of CFRP rod
Prestressing level (0-60% fu)
Observed failure modes
Concrete crushing, CFRP
rupture, concrete cover
spalling
CFRP rod pull-out,
concrete peeling-off at
cut-off point, concrete
crushing, debonding at
mortar-concrete interface
Concrete crushing, CFRP rod
rupture
Increase in capacity (%) Strip: 60.7-77.3
Rebar: 60.71-66.67
2-Ø6: 48.8-100.7
Ø12: 121.7-148.1 50-79
46
Table 2-10: Summary of existing experimental work on flexural strengthening using
NSM-FRP reinforcements (Cont’d).
Reference Rasheed et al. (2010) Oudah (2011)
Test method and type of NSM
strengthening
Static
Three-point bending
Non-prestressed
Static
Fatigue
Four-point bending
Prestressed and non-prestressed
Number of specimens
Four: two controls, one
strengthened with NSM CFRP
strips, one strengthened with
NSM stainless steel (both
strengthened in shear too)
Nine: one control, two
strengthened with non-
prestressed NSM CFRP
rebars/strips, six strengthened
with prestressed NSM CFRP rebars/strips
Bea
m g
eom
etry
Cross section (mm) 254×457 200×400
Net span (mm) 4720 5000
Shear span (mm) 2360 2000
f'c (MPa) 34.5 40
Bottom
steel
Amount 4#6 3-15M
fyt (MPa) 576 (beam with NSM CFRP)
477 (beam with NSM steel) 440
Top
steel
Amount 2#3 2-10M
fyc (MPa) 576 (beam with NSM CFRP)
477 (beam with NSM steel) 440
Str
eng
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mat
eria
ls
Groove
filler
Type Epoxy Epoxy
Tensile strength
[Modulus of
elasticity] (MPa)
N.A.
[N.A.]
24.8
[4500]
FRP
Type CFRP strip
Stainless steel bar CFRP strip and rebar
shape/surface Rectangular, smooth
Round, deformed bar
Strip: rectangular, rough
textured
Rebar: round, sand coated
Dimension
db or tf×hf (mm)
2-2×16
#4 Strip:2-2×16, rebar: 9.5
Number of FRP
reinforcements
4
3 1
Efrp (GPa) 131
200 Strip:124, rebar:124
Tensile strength
(MPa)
2068
883 (fy=683)
Strip: 2610
Rebar: 1896
Groove dimensions
(mm)
6×19
19.1×19.1
Strips:16×25
Rebar:20×25
Cut-off distance
from the support (mm) Extended over supports 310, mechanical anchor used
Test variables
Type of strengthening
materials, type of
strengthening
Prestressing level (0-60% fu),
type of CFRP material
Observed failure modes Concrete crushing Concrete crushing, CFRP
rupture
Increase in capacity (%) NSM CFRP: 46.4
NSM Steel: 46.1
Strip: 58-63
Rebar: 58-75
47
2.10 Environmental Exposure
To use NSM-FRP system confidently in practice, the performance of this system
under different environmental conditions should be studied. Durability is defined by
Karbhari et al. (2003) as “the ability to resist cracking, oxidation, chemical degradation,
delaminating, wear, and/or the effects of foreign object damage for a specified period of
time, under appropriate load conditions and specified environmental conditions”. Several
environmental factors causes deterioration including (the last four factors are considered
in this research):
Chemical solution (salt, alkaline, and acid)
Oxidation
UV radiation
Fatigue
Fresh water/ sea water
Thermal cycling
Humidity
Freeze-thaw
Creep and relaxation
2.10.1 Effect of Freeze-Thaw Exposure on Concrete
When concrete freezes, the volume of the water in the pores increases due to
freezing (approximately by 9%) and this behaviour produces high energy/pressure in a
small volume that can causes severe damage to the structure of the concrete. If thawing
and freezing take place, additional expansion of concrete will occur; This damage
48
appears as the cracks on the surface of the concrete and can cause a decrease of about
75% in strength of the plain concrete (observed by the author based on testing the
concrete cylinder specimens exposed to 500 freeze-thaw cycles) while increase the
ductility due to presence of the cracks. Entraining air to the concrete mix provides closely
spaced micro voids which decrease the pressure and avoid severe damage and
breakdown. An air entrainment of 5-8% provides sufficient protection for normal and
high-strength concrete exposed to thermal cycling (Neville, 2011). Also, the following
conditions need to be met to avoid possible damage to the concrete due to freeze-thaw
cycling exposure: the specimen should be fully cured, a water-cement ratio less than 0.45,
a minimum cement content of 335 kg/m3, adequate drainage, a minimum of seven days
of moist curing above 10°C, a minimum 30 day drying period after curing, and a
minimum compressive strength of 24 MPa at the time of first frost exposure (Neville,
2011; Kosmatka, 1998). If these conditions are taken into account, no adverse effects to
concrete from freeze-thaw cycling exposure will be observed. Figure 2-8 shows the
damage on concrete cylinder specimen after 500 cycles of freeze-thaw from +34oC to -
34oC and relative humidity of 75% for temperatures above +20
oC.
Figure 2-8: Damage done to the concrete cylinder after 500 cycles of freeze-thaw
(tested in this research).
49
The typical signs of freeze-thaw exposure are classified as:
Spalling and scaling of the surface
Large pieces (cm size) are spalled
Exposing of aggregate
Usually exposed aggregate are un-cracked
Surface parallel cracking
Gaps around aggregate
Furthermore, the thermal expansion coefficient of concrete is affected due to
temperature changes. Table 2-11 represents the thermal expansion coefficient of partially
dried concrete at different temperature; the changes are negligible when temperature
change from +20oC to -70
oC.
Table 2-11: Thermal expansion coefficient of concrete in different temperature
(Oldershaw, 2008).
Study Temperature
(oC)
Coefficient of thermal expansion
(10-6
/oC)
Browne and Bamforth (1981) 20 10 to 12
-165 5 to 6
Yamane et al. (1978) 20 12
-70 10
2.10.2 Effect of Freeze-Thaw Exposure on Steel Rebar
In RC members the steel is covered by the concrete and is not exposed to severe
environmental condition directly; this fact decreases the concern about the damage on
steel in RC member subjected to freeze-thaw. However, when the section is cracked there
will be a concern about the corrosion and possible damage to the steel rebar. Browne and
50
Bamforth (1981) performed tests on a wide range of the steel rebar with different strength
when the temperature was changed from 20oC to -140
oC. These researchers concluded
that the regular steel rebar strength enhances in a rate of 1 MPa/oC when temperature
decreases. However, the thermal expansion coefficient of steel remains constant 11.3×10-
6/oC from 20
oC to -165
oC.
2.10.3 Effect of Freeze-Thaw Exposure on CFRP Reinforcement
FRPs subjected to freeze-thaw cycling exposure are affected by thermal
incompatibility and polymer embrittlement (Green, 2007). Thermal incompatibility
which is a result of different thermal expansion coefficients of fibres and matrix produces
residual stresses in the FRP at low and high temperatures. The coefficients of thermal
expansion for most epoxies, glass fibres, and carbon fibres are about 45 to 65×10-6
/oC,
5×10-6
/oC, and -0.2 to 0.6×10
-6/oC, respectively (Mufti et al., 1991). The simple concept
of the residual stress in a composite at low and high temperatures is illustrated in Figure
2-9. The high enough residual tensile stress in matrix may lead to formation of micro
cracking, furthermore, thermal cycling can increase the size of these cracks or propagate
them which can result in strength degradation or failure (Dutta, 1989). The polymer
embrittlement is the increase in brittleness of polymer due to low temperature. Green et
al. (2006) concluded that polymer embrittlement may reduce the ability of the matrix in
transferring the stress to the individual fibres, or between the composite and substrate
concrete.
51
Figure 2-9: Concept of residual stresses in composite at high and low temperatures
(Dutta, 1989).
Among the studies performed on the freeze-thaw exposure effects on FRP
materials, Bisby and Green (2002) reported that for uniaxial CFRP and GFRP material
subjected to 300 freeze-thaw cycles, there is insignificant effect on the strength and
stiffness. Dutta (1989) concluded that tensile strength and stiffness of glass and carbon
fibres are not affected by thermal cycling. Micelli (2004) studied the effects of
accelerated aging on CFRP and GFRP bars subjected to accumulative 200 freeze-thaw
cycling exposure (-18oC to 4
oC), 480 high humidity cycles (in constant temperature), 600
high temperature cycles (16oC to 49
oC), and ultraviolent radiation (during the high
temperature and high humidity cycles as shown in Figure 2-10. Tensile test results
indicated that the longitudinal mechanical properties of the CFRP bars were not affected
by the applied environmental exposure, however, a slight reduction in average strength of
GFRP bars was observed after exposure. Furthermore, the transverse material properties
which are most influenced by resin properties did not significantly alter. On the other
hand, the freeze-thaw effect can also be beneficial. Karbhari et al. (2003) reported that
52
temperature below zero can result in matrix hardening which can lead to enhancements in
modulus, tensile and flexural capacity, creep and fatigue resistance (GangaRao et al.,
2007).
Figure 2-10: Applied exposure on the FRP specimens (Micelli, 2004).
2.10.4 Effect of Freeze-Thaw Exposure on Epoxy Adhesive
The effect of freeze-thaw exposure combined with humidity or moisture on epoxy
is important in two aspects: the effect on the matrix properties, and the effect on the bond
behaviour. Moisture affects matrix mechanical properties such as shear strength. There is
always a potential for possible air voids in the epoxy or between FRP and concrete. The
water can penetrate to these voids and by subsequent freezing and thawing gradually the
voids will grow and causes a weakness in the interface. Colombi et al. (2010) concluded
that the bond of CFRP plates to concrete attached with Sikadur 30 is not affected by 200
freeze-thaw cycles.
53
2.10.5 Effect of Sustained Loading on Concrete
Sustained loading on a structural member produces time dependant increases in
strain known as creep and time dependant decreases in stress known as relaxation. The
instant deformation when a load is applied to concrete member enhances under sustained
load due to creep (Neville, 2011). Creep in concrete occurs at a microscopic level due to
the meta-stability of the concrete, which is related to the pore structure and the amount
and type of water in the pores (Bisby, 2006). On the other hand, creep is a function of the
volumetric content of the cement paste in the concrete and only the hydrated cement in
concrete undergoes creep while the aggregate acts as a resistant (Neville, 2011).
Therefore, concrete with higher modulus aggregates undergoes smaller creep deformation
under load. The magnitude of the sustained load plays a significant role in creep so that
the creep strain can be several times larger than the strain generated during the instant
loading. After removing the sustained load, some a large amount of creep strain is not
recoverable, the amount of irrecoverable strain/deformation known as residual
strain/deformation (Neville, 2011). The subsequent gradual decrease in strain is known as
creep recovery. The residual deflection is a result of the re-orientation of particles with
the diffusion of water, as the microstructure attempts to achieve a more stable state
(Bisby, 2006). Overall, the creep amount in concrete is affected by the moisture content,
the degree of hydration, the aggregate properties, the volume to surface ratio, the relative
humidity, the temperature, the concrete strength, and the existence of admixture.
Concepts of elastic strain, creep strain, elastic recovery, creep recovery, and residual
deformation are illustrated by Figure 2-11.
54
Figure 2-11: Creep strain-time relationship for concrete under uni-axial stress
(Bisby, 2006).
2.10.6 Effect of Sustained Loading on FRP and Adhesive
Creep is not only related to concrete, it also occurs in FRP composite and
adhesives. The creep strain-time relationship for FRPs subjected to uni-axial stress is
similar to concrete creep strain-time relationship (Oldershaw, 2008), as shown in Figure
2-11. GangaRao et al. (2007) illustrated the sustained stress damage on the FRP
composites using three stages: (1) random fibres rupture and the matrix around those
ruptured fibres relaxed which results in stiffness reduction; (2) more cracking occurs,
fibre/matrix interface debonds, and more fibre ruptures which leads to rapid drop in
stiffness; (3) total failure due to stress rupture. Karbhari et al. (2003) reported stress
levels of 50% and 75% for glass and carbon fibres, respectively, under ambient
conditions with 10% failure possibility. On the other hand, polymer matrix is visco-
elastic and can undergo higher amount of the creep than fibres (Bisby, 2006). In
comparison with other materials in the case of creep, Hollaway and Leeming (1999)
55
found that CFRPs are better than standard steels and comparable with low relaxation
steels. The creep response of FRPs is related to (Hollaway and Leeming, 1999):
The type of polymer matrix and its stress history
The direction, type, and volume fraction of the fibre reinforcement
The nature of the applied loading
The temperature and moisture conditions
GFRPs are more vulnerable to creep than CFRPs and AFRPs. Canadian Highway
Bridge Design Code (CAN/CSA-S6-06, 2011) limits the allowable stress (creep rupture
stress) in the CFRP, AFRP, and GFRP to 65%, 35%, and 25% of the ultimate tensile
strength of the corresponding reinforcements, respectively. On the other hand, for the
FRP loaded axially in the direction of the fibres, ACI 440.1R (2006) limits the permanent
stresses in the CFRP, AFRP, and GFRP to 50%, 30%, and 20% of the their capacity.
Furthermore, Ceroni et al. (2006) indicated the 50 year period creep rupture failure
strengths of 79-93% for CFRP, 47-66% for AFRP, and 29-55% for GFRP.
2.10.7 Synergistic Effect of Sustained Load and Freeze-Thaw Exposure
A major research gap exists in combination of freeze-thaw cycling exposure and
sustained loading for prestressed NSM-FRP strengthened RC beams. Combining
environmental factors might rapidly increase or decrease the amount of degradation
which occurs on the components of a structural member. For example, low temperature
might decrease the amount of creep due to improvement in modulus of elasticity while
high temperature might accelerate the amount of creep.
56
Vijay and GangaRao (1999) studied the combined and separate effects of salt/
alkaline exposure and sustained stress on GFRP rebars. Results revealed decreases of
24.5% and 30% in ultimate tensile strength at room temperature, after 30 months of
exposure to salt and alkali respectively. On the other hand, a decrease of 25.2% in
ultimate strength was observed after 10 months of exposure to sustained load (32% of
ultimate tensile strength) and salt exposure. Similarly, a decrease of 14.2% in capacity
was reached after 8 months of exposure to sustained load (25% of ultimate tensile
strength) and alkaline exposure. It is estimated by Turner (1979), that at temperatures
between -10oC to -30
oC the value of the concrete creep is about half of that at 20
oC. The
reason is increasing the modulus of elasticity with decreasing the temperature below the
freezing point of capillary water (about -2oC). Oldershaw (2008) reported that beams
subject to a period of sustained load prior to testing displayed greater stiffness than
control beams, likely a result of the stiffening effect on concrete which experiences creep.
2.10.8 Effect of Environmental Exposure on FRP-Strengthened RC Beam
The effects of environmental exposure (including sustained load and freeze-thaw
exposure) on the RC beams strengthened with prestressed NSM-CFRP reinforcements
have not been addressed by the researchers. Therefore, in this section, the researches that
have been performed on the beams strengthened with non-prestressed NSM-CFRP and
also related subjects are briefly reviewed. In this context, Toutanji and Gómez (1997)
investigated the performance of the small-scale EB-FRP strengthened RC beams (300 ×
50 × 50 mm) subjected to wet/dry cycling exposure. 56 RC beams were fabricated: half
were exposed to 300 wet/dry cycles including salt water for the wet cycles (4 hr-35g of
57
salt per 1 litre of water) and hot air at 35oC and 90% humidity for dry cycles (2 hr); the
other half were kept in room temperature (20oC). The beams were strengthened with
different types of Carbon and Glass fibre sheets while 8 beams considered as un-
strengthened control beams. Three different types of the epoxy were implemented in
strengthening. All beams which were tested under the four-point bending configuration
failed due to FRP debonding. The results revealed that epoxy with higher elongation and
higher modulus has a better performance in strength increase for the beams.
Lopez-Anido et al. (2004) evaluated the freeze-thaw resistance of fibre-reinforced
polymer composites (E-glass/vinyl ester) adhesive bonds with underwater curing epoxy
to repair wood piles in the field. These researchers discriminated the effect of freeze-thaw
cycling exposure on the performance of the adhesive bond and compared the lap shear
strength and the mode of failure of the control and exposed samples. Twenty cycles were
adopted for the freeze-thaw exposure: 8 hr in the freezer (-18oC) and 16 hr in the hot-
water immersion bath (+38oC). The authors concluded that the shear strength of the
underwater curing epoxy is sensitive to freezing and thawing cycles where the mean
shear strength decreased to 57% of the control value. Furthermore, the exposure to
freeze-thaw cycles leads to a change in the mode of failure from predominantly adhesive
type to combined adhesive/cohesive type.
El-Hacha et al. (2004) studied the performance of RC beams strengthened with
non-prestressed and prestressed EB-CFRP sheets exposed to room and low temperatures.
The beams were also subjected to both short and long-term loading. Low temperature can
induce micro-cracks in matrix or resin-fibre interface due to large differences in
coefficients of thermal expansions (in order of magnitudes). Eight large scale T-beams
58
were tested: Four beams at room temperature and four at -28°C. At each temperature, one
beam was considered as un-strengthened control, one tested for short-term behaviour, one
tested for long-term behaviour under self-weight and one tested for long-term behaviour
under sustained load (50% of the strengthened beam capacity). At room temperature,
results revealed a significant prestress loss (12% after 7 days) in short-term test with 50%
prestressing level of the CFRP capacity. The loss increased to 18% after 13 months.
However, sustained load did not cause significant additional losses (the prestress loss
measured was 22%). In spite of the losses in both short and long-term beam tests, the
ultimate load almost remained unchanged with 1% difference. At -28°C, 19%
prestressing loss after 7 days of strengthening was reported for the short-term test while
long-term test had a 22% loss. The same results were observed in the specimens
subjected to sustained load. The difference between beams’ capacities in short-term and
long-term tests was insignificant. However, strengthened beam subjected to long-term
sustained load showed slight degradation (8% reduction) in ultimate strength when tested
at -28 °C. The authors concluded that strengthened beams were enhanced considerably in
strength and stiffness compared to the un-strengthened beams. The long-term behaviour
with or without sustained load had no effect on the beam capacity, but the combined
effects of sustained load and low temperature reduced the ultimate strength of beam
slightly (8%).
Frigione et al. (2006) studied the water effects on the bond strength of the
concrete-epoxy joints by performing experimental tests on the immersed samples. The
specimens were made by cutting the concrete cylinder in inclined surface at 30o from
bottom surface. Then, two surfaces were glued together. The authors examined three
59
parameters including properties of adhesive and concrete, thickness of the adhesive layer
(0.5, 2, 5 mm), and presence of the water (0, 2, 7, 14, 28 days). It was concluded that the
performance of the concrete-resin is influenced by the mechanical properties of the
concrete and the epoxy, the joint effectiveness gradually decreases by increasing the
thickness of the adhesive layer, a maximum decrease of 40% in bond strength is possible
after 28 days of immersion.
Derias (2008) studied the long-term flexural performance of concrete beams (150
× 300 × 300 × 50 × 2500; web width × height × flange width × flange thickness × length)
strengthened with NSM-FRP reinforcements subjected to combined accelerated synthetic
weathering conditions including saline solutions with high concentration (15%) and
elevated temperature (+55oC). Eight beams with different type of FRP materials and
shapes were tested. Four beams were subjected to sustained load (40% of ultimate
capacity of the beams) and other beams were unloaded and tested at room temperature
(+22oC). A significant degradation in the epoxy-concrete interface was observed due to
harsh environmental conditions which caused change in failure mode in comparison with
the similar beams at room temperature.
Subramaniam et al. (2008) investigated the effects of freeze-thaw exposure on
interface fracture energy of EB-FRP-concrete using a direct shear test. The shear stress-
slip relations of the interface were developed for damage associated with freezing and
thawing action. The concrete specimens (125 × 125 × 330 mm, width × height × length)
were placed inside an environmental chamber for 100, 200, and 300 cycles. Each cycle
was accomplished in 12 hr where the temperature changed from +5oC to -18
oC (4.2 hr at
+5oC, 2.4 hr from +5
oC to -18
oC, 2.4 hr at -18
oC, and 3 hr from -18
oC to +5
oC). One day
60
before being subjected to exposure, the specimens were placed in the chamber at 99%
RH and 23oC. Then, each two days after starting the cycling exposure, water was sprayed
in the middle of the thawing part. The chamber was kept sealed and a pool of water was
placed below the specimens to maintain the moisture constant. The results revealed that:
there was no decrease in the elastic modulus of the FRP sheet under freeze-thaw cycling
exposure (up to 300 cycles), furthermore, there was a consistent decrease in load-carrying
capacity of the specimens subjected to freeze-thaw exposure, there was a significant
decrease in the length of the cohesive stress transfer zone with increasing the number of
freeze-thaw cycles (78 and 68mm, 82 mm, and 92 mm for 300, 200, and 100 freeze-thaw
cycles, respectively), the maximum interface shear stress at debonding decreases from
5.97 MPa to 4.85 MPa after 300 freeze-thaw cycles, and the fracture energy decreases
from 0.65 N.mm to 0.42 N.mm after 300 freeze-thaw cycles.
Tan et al. (2009) examined the effects of sustained load and tropical weathering
on the EB-GFRP strengthened RC beam experimentally and analytically. In the analytical
part, flexural strength was calculated based on the modulus of elasticity of concrete and
FRP which were modified due to effect of creep and creep plus tropical weathering,
respectively. The experimental was performed on the small-scale (100 × 100 × 700 mm)
and large-scale (100 × 100 × 2100 mm) specimens strengthened with different GFRP
configuration. The large-scale and small-scale specimens were subjected to 59% and 53%
of the calculated capacity of the un-strengthened beams, respectively. The sustained load
was applied up to 1 and 2.75 years. The authors applied tropical weathering as a hot and
humid condition (temperature between 23oC to 33
oC, relative humidity between 80-90%
at night and 50-60% during the day, and monthly rainfall of 100-180 mm). The deflection
61
and crack width were measured at different time intervals (1-30 days) using gauges and a
hand-held microscope, respectively. The results showed 16% increase in deflection and
18% increase in crack width of the specimens under sustained load after 1 year and 2.75
years outdoor weathering, respectively. Also the beams were tested and a reduction of
15-50% was observed in ductility (ratio of deflection at ultimate to deflection at yielding)
and the failure mode changed from concrete crushing or FRP debonding to FRP rupture.
Mitchell (2010) investigated the combined effects of freeze-thaw exposure and
sustained load (125% of un-strengthened control specimen) on flexural performance of
strengthened RC slab strips using non-prestressed NSM-CFRP tape (Aslan 500).
Furthermore, pull-out bond tests were carried out. 21small-scale slabs (254 × 102 × 1524
mm) were tested, as presented in Table 2-12, to study the effects of adhesive type (grout
or epoxy) and exposure condition (room temperature, freeze-thaw, sustained load, or
freeze-thaw under sustained load). The results revealed insignificant effects on the
performance of the grout strengthened members after exposure to freeze-thaw cycles or
sustained load. The slabs strengthened with epoxy adhesive and exposed to freeze-thaw
cycle or sustained load showed negligible changes in ultimate load (less than three
percent). The combined effect of freeze-thaw cycles and sustained load caused an
average reduction of eight percent in ultimate capacity. The epoxy adhesive strengthened
pull-out bond tests experienced a 27% average drop in ultimate load after 150 freeze-
thaw cycles.
The most related researches in the area are reviewed above and the rest are
presented in Table 2-12.
62
Table 2-12: Summary of some existing research on freeze-thaw exposure (study of the considered cycles).
Reference Test method Number of specimens
Beam geometry Freeze thaw exposure
Geometry Guideline
Temperature
Period of each cycles No of cycles Min
oC Max oC
Santofimio
(1997)
Confined cylinders
with FRP composite 6 confined cylinders expose to freeze-thaw 36×305 mm
ASTM
C-666-97 -17.8 4.4 4 hr
300- in a salt water
solution
Bisby and
Green (2002)
EB bonded FRP
sheets, freeze-thaw cycles
39 small-scale flexural beams reinforced
in tension with externally bonded FRP sheets
102×152×1220 mm ASTM
C-666-97 -18 18
24 hr ( 16 hr at -18oC,
thawing in a water bath for 8 hrs)
0-300
El-Hacha et
al. (2004)
Prestressed EB-CFRP
sheets, sustained load plus low temperature
8 T-beams: 4 at room temperature, 4 at -28oC (one control, one strengthened, one
strengthened under self-wight., one under
sustained load +low tem.)
T shape, total height
= 375,
web height = 300, flange width = 535,
web width = 60
N.A. -28 N.A. 13 months N.A.
Dent (2005)
Small scale flexural test,
EB strengthened, 0 or
200 freeze-thaw cycles 0-2×106 fatigue cycles
45 RC beams EB strengthened
15 under fatigue loading, 15 under freeze-
thaw and fatigue loading, 15 at room temperature
102×152×1220 mm ASTM
C-666-97 -18 20
24 hr ( 16 hr at -18oC,
thawing in a water bath
for 8 hrs)
200
Wu et al. (2006)
GFRP composite bridge deck
N.A. N.A. ASTM
C-666-97 -17.8 4.4 2hr and 5 hr
625 salt water,
distilled water, and dry air, prestrained
specimens subjected
to 250 cycles (16,40,100,250,625)
Laoubi et al.
(2006)
Concrete beams reinforced with GFRP
bars under freeze-thaw
and sustained load
21 130×180×1800 mm N.A. -20 20
12 hr (6 hr to -20oC and 6 hr to 20oC), Humidity
50% during all freeze-
thaw exposure
100,200,360
62
63
Table 2-12: Summary of some existing research on freeze-thaw exposure (study of the considered cycles) (Cont’d).
Reference Test method Number of specimens
Beam geometry Freeze thaw exposure
Geometry Guideline
Temperature
Period of each cycles No of cycles Min
oC Max oC
Tam (2007)
Bond test, FRP to
concrete prisms,
single-lap bond test,
48 CFRP and GFRP coupons, 48 sngle lap specimens, 48 FRP-to-concrete prisms
N.A. N.A. 20 -20
6 hr (2 hr from 20oC to -
20oC, 1 hr at -20oC, 2 hr from -20oC to 20oC, 1 hr
at 20oC)
300
Oldershaw (2008)
EB strengthened small
scale concrete beam,
freeze-thaw, freeze-
thaw and sustained loading
48:3 control, 45 strengthened, groups of 3 as control, and groups of 4 as exposed
102×152×1220 mm ASTM
C-666-97
-30
(-18 in
core)
20
(5 in
core)
5 hr: 25 min (30 min from 10oC to 1oC, 1 hr
from 1 to -30oC, 2 hr at -
30oC, 45 min from -30oC to 1oC, 40 min from 1oC
to 10oC use a water bath
for thawing, 30 min from10oC to 20oC)
300, (10-20 yrs for
exterior application
in Toronto)
Saiedi (2009)
CFRP-prestressed
comvrete beams,
sustained load and fatigue loading at low
temperature
7 : five CFRP-prestressed and two steel-
prestressed concrete beams
T shape, total height
= 300,
web height = 250, flange width = 500,
web width = 130
N.A. -27
-28 N.A. 163 days N.A.
Mitchell
(2010)
Non-prestressed NSM
FRP strips,
strengthened slab specimens
21:5 bond test (3 with grout, 2 with epoxy), 5 under freeze-thaw(3 with grout,
2 with epoxy), 6 under sustained load(3
with grout, 3 with epoxy), 5 under sustained load and freeze-thaw(3 with
grout, 2 with epoxy)
254×102×1524 mm N.A
-30
(-13 in
core)
20
(8 in
core)
6 hr: 10 min (5 hr from
0oC to -30oC, and 70
min thawing using a water bath)
300, (10-20 yrs for
exterior application
in Toronto)
Abdelrahman
(2011)
EB Strengthened RC
columns, freeze-thaw 38: wrapped with CFRP and SRP sheets
1200×300 mm
900×150 mm 600×150 mm
300×150 mm
CAN/CSA-
S6-06 -34 34
8 hr (20 min at 20oC, 2 hr: 40 min at -34oC, 5
min at 20oC, 2 hr: 20
min at 34oC having 75% humidity, 10 min at
20oC)
500
63
64
2.11 FE Modeling of FRP-Strengthened RC Beams
In this section a brief review of the performed researches on the FE modeling of
FRP strengthened RC beams is presented with more focus on the modeling procedure. In
this context, Vecchio and Bucci (1999) presented a finite element algorithm to analyze
rehabilitated concrete structures using EB-FRP method. To consider the damage effects,
the authors defined appropriate plastic offset strains for concrete and reinforcement.
These offsets were assigned to the model by prestrain nodal forces. The FE model was
formulated to consider both the initial beam and the plate added beam. After enforcing
the damage on the initial beam the bonded plate was engaged and became active. The
authors validated the 2D FE model with glass and carbon FRP-strengthened RC beams
under monotonic loading and shear wall under cyclic loading.
Kachlakev et al. (2001) developed finite element models for reinforced concrete
beams and bridge that had been strengthened with EB-FRP (Unidirectional Carbon and
Glass) composites under static loading. The models were 3D performed in ANSYS
software validated with the results from laboratory tests, (McCurry, 2000), and the actual
bridge measurements. Four strengthened RC beams were modeled similar to (Chansawat,
2003). The authors assumed perfectly plastic behaviour for concrete material after
ultimate compressive strength (f′c) and complete bond between FRP layers and adjacent
concrete elements. Comparison between FE and experimental results showed a relatively
good agreement. In general, load-strain curves for CFRP, steel rebar and concrete were
softer than those from experimental curves. Comparison between Load-deflection curves
showed that FE load-deflection curves were stiffer than those experimental curves by 12-
66% in linear range and by 14-28% after cracking. a 5-24% difference at ultimate loads
65
(FE was smaller) and 6-34% difference at cracking loads (FE was bigger) was observed.
FE crack pattern at failure for the flexural strengthened beam confirmed that the beam
failing in flexure. In addition, the author modeled the Horsetail Creek Bridge before and
after strengthening under static loading, and concluded that the FE results on strain and
trends of strain versus truck location have a reasonable agreement with the field data. In
comparison with parallel research Chansawat (2003), the results of this research showed
slightly more difference with the experiments, due to difference in mesh, material data,
load-step size, and type of analysis.
Buyle-Bodin et al. (2002) proposed a non-linear 2D finite element model to
analyze the flexural behaviour of EB-CFRP strengthened RC beams under four-point
bending configuration. The FE model was intended to investigate effects of initial
damage and the number of CFRP layers. The experimental tested beams (150 × 300 ×
3000 mm) were modeled using French Code Castem 2000 program. The authors
assumed: concrete behaves as an elasto-plastic material, and interface elements for steel-
concrete and CFRP-concrete interfaces. A load-unload cycle was applied to the FE model
to implement the precracking effects. The precracking load was applied to result in a 3%
strain in tension steel reinforcement. Comparison between FE and experimental load-
deflection curves showed that the FE curve is stiffer than experimental curve at high load
level. A maximum difference of 12% was observed between FE and experimental mid-
span deflection.
Jia (2003) simulated RC beams strengthened with EB CFRP sheets using 3D FE
model in ANSYS program. Nine RC beams (110 × 160 × 1800 mm) were modeled under
four-point bending configuration: one un-strengthened control beam, four beams
66
strengthened with organic epoxy, and four beams strengthened with inorganic epoxy. The
number of CFRP layers was varied from 2-4. The author assumed complete bond
between different materials and perfect plastic behaviour for concrete curve after ultimate
compressive strength. The same procedure as Kachlakev et al. (2001) was employed for
FE modeling. Comparison between FE and experimental results was carried out in terms
of load-deflection curve, load-strain plots for CFRP sheets, cracking, yielding, and failure
loads. After cracking, the FE load-deflection curves were stiffer than those of
experimental results. Results of strain plots for CFRP sheets showed the same trend as
the load-deflection curve. The FE model overestimates the cracking load, yielding load,
and failure load by 6.5-15.8%, 1.1-9.5%, and 2.1-8.6%, respectively. In general the
author achieved a good correlation between FE and experimental results.
Chansawat (2003) performed nonlinear finite element analysis of full-scale
strengthened reinforced concrete beams and bridge strengthened with EB FRP sheets and
beams and bridge using 3D models in ANSYS. Four RC beams (305 × 770 × 6095 mm)
tested by (McCurry, 2000) were modeled: one un-strengthened control beams, one
flexural-strengthened beam using unidirectional CFRP sheets, one shear-strengthened
beam using unidirectional GFRP sheets and one flexural/shear-strengthened beam using
combination of unidirectional CFRP and GFRP sheets tested under four-point bending
configuration. In the FE models, the author considered a confined concrete constitutive
model where the GFRP sheets or loading plates were located. The model for the GFRP-
confined concrete was assigned similar to a model for stirrup-confined concrete.
Complete bonding was assumed between different materials at interfaces. Furthermore,
FRP rehabilitated Horsetail Creek Bridge was modeled before and after strengthening
67
under static and dynamic loading. The existing damage of the bridge and soil interaction
effects were considered in the bridge FE models and a realistic concrete strength based on
in-situ test was employed. A sensitivity analysis was performed by comparing the results
with field data at service stage to find the best model. Comparison showed that the FE
models are in a very good agreement with the experiments in terms of load-deflection
curve and load-tension steel strain plot, and are in a reasonable agreement in terms of
load-FRP strain plot, crack pattern, and load-compressive strain at extreme fibre of the
section. The FE load-deflection curves are stiffer than those from experimental curves.
Comparison between FE and experimental ultimate loads showed 6% to 18% difference
(under estimation). The flexural/shear strengthened beam was tested up to the capacity of
the testing machine and did not fail. The FE results showed that strengthening of the
bridge with FRP could increase the capacity of the bridge by 37% based on mass-
proportional loading and by 28% based on scaled truck loading. Dynamic response of the
bridge showed that the bridge may fail due to collapse in columns.
Supaviriyakit et al. (2004) presented 2D finite element analysis of reinforced
concrete beams strengthened with EB FRP plates and compared the results to the
experiment. The concrete model considered the effect of cracks and steel reinforcement
was smeared over the entire concrete elements at specified locations. Perfect bond was
considered between FRP and substrate concrete and nonlinear FE models was employed
to predict the end and shear-flexural peeling failure load base on strain concentration at
the plate end and along the length of the FRP plate . The authors modeled two FRP-
strengthened beams: one under four-point and another under three-point bending
configuration, and also one un-strengthened control beam (120 × 220 × 2200 mm) under
68
three-point bending configuration. The FE results showed a good agreement with
experimental results in terms of load-deflection curve, ultimate load, failure mode, and
crack propagation.
Kang et al. (2005) examined the flexural behaviour of RC beams strengthened
with non-prestressed CFRP strips using NSM method, experimentally and analytically.
Five beams (200 × 300 × 3400 mm), one un-strengthened control beam, two beams with
different groove depths as well as CFRP strip widths (15 mm and 25 mm), and two
beams with two CFRP strips (2 - 1.2 × 25 mm) disposed at different groove spacing (60
mm and 120 mm) were tested experimentally under four-point bending configuration and
static monotonic loading. Also, the authors performed parametric study on the area and
spacing of CFRP strips. In developed 3D FE models in ABAQUS software, perfect
bonded interfaces were considered while CFRP widths/groove depths were variable from
5-35 mm and groove spacing was variable from 20-180 mm. Through experimental
investigations, the authors concluded that: strengthening efficiency is not only related to
the amount of CFRP strips and also depends on the arrangement of them in the beam;
NSM strengthening method can cause an increase in the ultimate load of un-strengthened
control beam from 40-95%; and there exists a critical groove depth beyond which the
increase of the ultimate load of strengthened beam becomes very slight. Through
parametric study the following were concluded: there exists a minimum spacing (40 mm)
between adjacent CFRP strips to avoid mutual interference; there exists a minimum
distance (40 mm) from CFRP strip to the concrete edge to prevent the influence of the
concrete cover in the vicinity of the edge; there exists an optimum groove spacing of
80mm which causes the highest ultimate load; the ultimate load versus the CFRP ratio
69
curve is a downward-facing parabola; and for a specific amount of CFRP reinforcement,
strengthening efficiency could be enhanced using several reinforcements at regular
spacing near the surface instead of a single reinforcement but decision should be made
after consideration of the workability and economical efficiency (cutting of the grooves
or the epoxy filling).
Pham and Al-Mahaidi (2005) studied the nonlinear finite element modeling of
reinforced concrete beams strengthened with EB CFRP fabrics followed by a parametric
study considering the effects of CFRP thickness, steel reinforcement ratio, and CFRP
bond length. These authors noticed that all finite element analysis using smeared crack
cannot capture debonding failure modes. The developed FE model was 2D considering
debonding failure of the strengthened beams. The modeled beams were simply supported
under four-point bending with a cross section of 140×260 mm and span length of 2300
mm. A bond-slip relationship obtained from lap-test was assigned to the CFRP-concrete
interface. Eighteen beams were modeled, and it was confirmed that the proposed FE
model can simulate the crack pattern, load-deflection curve, mode of failure, and strain in
CFRP reinforcement. A difference at ultimate load up to 18% was observed between FE
and test results. The main flexural debonding modes were identified as: end-plate
debonding and intermediate debonding. When the number of FRP layer increased from 1
to 3, the ultimate capacity increased by maximum 16%. As the amount of CFRP
reinforcement increased further, the failure mode changed to end-plate debonding and the
load capacity reduced relatively. By increasing the amount of steel, the failure mode
shifted from intermediate debonding to end-plate debonding. Changing the amount of
Steel reinforcement had the most effect in increasing the ultimate load. Furthermore, the
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debonding capacity reduced slightly with decreasing the bond length, an increase of 28%
at ultimate load was observed by extending the bond length from half shear-span to
whole shear-span length.
Kishi et al. (2005) performed 3D elasto-plastic FE analysis of RC beams
reinforced with CFRP and AFRP sheets considering FRP sheet peel-off mode using
DIANA program. Geometrical discontinuities were considered in FE model by applying
stress-relative displacement model to the interface element. Three stress-relative
displacement models consist of: discrete cracking, steel rebar bond-slip, and FRP sheet
debonding models were considered in the FE model. Smeared crack approach was
assigned to the concrete elements. The model was validated and comparison between FE
and experimental results was performed in terms of load-deflection curve, strain profile
along the length of CFRP sheet at yield and ultimate loads, and failure mode showing
very good agreement between FE and experiment results.
Coronado and Lopez (2006) performed 2D finite element modeling and
sensitivity analysis of the RC beams strengthened with EB CFRP and GFRP sheets on
tensile strength, fracture energy, tension softening, compression model, and angle of
dilatancy in ABAQUS software. The FE models were validated by comparing the FE
results in terms of load-deflection curve and failure mode with the results of 19 beams,
which failed either due to concrete crushing or FRP debonding. Up to 10% difference in
ultimate load was observed between FE and experimental results. A damage mechanism
based on the crack propagation was used to consider the plate debonding mode. The
sensitivity analysis revealed that change in concrete tensile strength value from 0.5ft to
2ft, where ft is the tensile strength of the control specimen, has a slight effect on
71
increasing the stiffness; change in fracture energy from 0.5Gf to 2Gf, where Gf is the
fracture energy of the control specimen, has a significant effect on delaying the FRP
debonding failure mode but has an insignificant effect on the behaviour of the beam
failed by concrete crushing; type of softening model (linear, bilinear, and exponential)
has a slight effect on the load-deflection curve; type of concrete stress-strain curve in
compression has a very slight effect on the load-deflection curve; and change in angle of
dilatancy from 20o to 40
o has no effect on the beam failed by concrete crushing but
increase the peak load of the beam failed by FRP debonding. Also, the authors concluded
that modeling of epoxy has a minor effect on the flexural behaviour of the strengthened
beams.
Nour et al. (2007) developed 3D FE models of concrete beams externally
strengthened with CFRP laminates, concrete beams internally reinforced with GFRP bars,
one-way concrete slabs reinforced with GFRP bars, damaged concrete beams externally
strengthened with CFRP laminates, and concrete columns confined with FRP sheets
using a user-defined subroutine at Gauss integration point level for concrete material in
ABAQUS software. Perfect bond was assumed between different materials in FE models.
The authors showed that the numerical responses including load-displacement curves and
failure mechanisms agreed very well with experimental results.
Camata et al. (2007) performed nonlinear FE and experimental analysis of RC
beams strengthened with EB-FRP plates. Four beams (200 × 300 × 3250 mm) (one un-
strengthened and the rest strengthened with one 1.2 × 50 mm CFRP strip) and four one-
way slabs (800 × 120 × 3250 mm) (one un-strengthened and the rest strengthened with
two CFRP strips) were tested monotonically up to failure under four-point bending
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configuration. An increase of 72% and 35% at ultimate load of beam and slab was
observed due to strengthening in comparison with the un-strengthened specimens. The
FE analysis was performed using Merlin program considering smeared crack model for
concrete material and applied discrete cracks for two sets (set A: under the load and at
concrete-epoxy interface, set B: at the level of reinforcing steel and concrete epoxy
interface). Both models were validated well with the experimental results in terms of
load-deflection curve and mode of failure. The authors compared the strengthening using
CFRP versus GFRP and concluded that using bigger contact area of FRP reinforcement
(width) with the same axial stiffness increases the value of ultimate deflection
significantly; the lower ratio of FRP plate width to RC member width decreases the
probability of concrete splitting failure.
Aram et al. (2008) studied debonding failure modes of EB-FRP-strengthened RC
beams analytically and numerically and also compared the results with international
codes and guidelines. Four beams were tested (2400 × 250 × 150 mm): three beams
strengthened with different CFRP plates and one un-strengthened control beam. The
analytical solution was performed based on the section analysis considering complete
bond. To consider the plate end debonding, Kupfer-Gerstle and Mohr-Coulomb failure
criterion were applied. The proposed FE model was 2D developed using ATENA
software. Smeared crack and bilinear bond-slip model of Ulaga et al. (2003) were
implemented. One FE model with nonlinear adhesive behaviour was developed to predict
the debonding failure at the plate end regions. Also debonding criteria of the codes were
classified and compared with the FE and analytical results. Comparison showed that the
FE load-deflection curves are stiffer than experimental ones while the analytical load-
73
deflection curves are softer than the experimental ones. Up to 250% difference was
observed between the predicted debonding failure loads and calculated value from
different codes. It was concluded that assuming the linear properties for adhesive does
not have a significant effect on interfacial stresses. The authors recommended a strain
limitation of 0.008 in CFRP plate to avoid debonding in flexural cracks and a shear stress
limitation equal to concrete tensile strength in high shear stress regions.
Barbato (2009) developed a simple 2D frame FE model to investigate the load-
deflection curve and failure mode of the EB CFRP and GFRP strengthened RC beams
including concrete crushing, CFRP/GFRP rupture, and CFRP/GFRP debonding.
Debonding criteria was employed in the model based on the maximum allowable stress in
EB-FRP sheet and corresponding effective bond length proposed by Monti-Renzelli
(Monti et al., 2003). The FE analysis was implemented using a MATLAB toolbox
considering static, dynamic, linear, and nonlinear features. The model was validated with
many experimental results reported in literature. A maximum difference of 39% between
numerical and experimental ultimate loads was observed. The numerical load-deflection
curve is softer than the experimental one.
2.12 Research Gaps
Based on the performed literature review in this chapter, the following research
gaps related to NSM-FRP strengthening method are identified by the author. In this
context, the existing gaps are classified in different major aspects such as
implementation, performance, type of loading, environmental exposure, FE analysis and
74
analytical investigation. Some of these major gaps are outlined as the research objectives
in Chapter One to be covered in this research.
Implementing a practical prestressed NSM-FRP strengthening system. In this
context, modification of the anchorage system proposed by Gaafar (2007)
needs to be performed. Also, the effect of FRP reinforcement geometry needs
to be addressed.
Studying the long-term performance of the prestressed NSM-FRP strengthened
RC beams under different types of environmental exposure. In this context,
behaviour of the prestressed NSM-FRP strengthened RC beams subjected to
freeze-thaw exposure and sustained load has never been examined. Most
studies applied 300 freeze-thaw cycles and the effects of higher number of
freeze-thaw cycles have not been investigated.
The long-term prestressing loss in NSM-FRP reinforcement needs to be
addressed.
Developing a comprehensive FE model to simulate the behaviour of the NSM-
CFRP strengthened RC beam considering prestressing and debonding aspects.
Furthermore, developing a FE model that predicts the static behaviour of the
prestressed/non-prestressed NSM-FRP strengthened RC beams subjected to
freeze-thaw exposure and also combined freeze-thaw exposure and sustained
load.
Analyzing the effects of concrete, steel and prestressing level in prestressed
NSM-CFRP strengthened RC beams. In this context, a parametric study needs
to be done on strengthened RC beams using FE model.
75
Performing a parametric study on the FRP anchorage system considering the
effects of bond capacity, dimensions etc.
Performing an analytical study to derive the load-deflection response of the
prestressed/non-prestressed NSM-FRP strengthened RC beams subjected to
environmental exposure.
Performing an analytical study on the practical anchorage system for
prestressing the NSM-FRP that needs to address the distribution of interfacial
stresses.
Studying the performance of pre-damaged/deteriorated beams/slabs
strengthened using prestressed NSM-FRP method. In this context, cracking
and damage to the concrete cover of the steel reinforcement may have a
significant effect on the failure process and performance.
Investigating the fatigue, seismic, and dynamic loading on the prestressed
NSM-FRP strengthened beams. Also, the effects of environmental exposure
factors such as Chemical solution (salt, alkaline, and acid), Oxidation, UV
radiation have never been examined on prestressed NSM-FRP strengthened
members.
Studying the deformability and ductility of the prestressed NSM-FRP
strengthened RC beams and proposing appropriate deformability models and
limits.
Studying the application of the prestressed NSM-FRP on the timber structure
and long-term performance of that.
76
2.13 Summary
A comprehensive literature review on the behaviour of RC beams strengthened
using NSM system was presented in this chapter. First, a brief review about the evolution
of the engineering material, different types of the FRP products, and strengthening
methods using FRP materials was provided. Then, the history of the NSM method,
materials used for this type of strengthening, and a comparison between EB-FRP and
NSM-FRP strengthening methods were presented. Afterwards, the recent development
and research progress on the prestressed FRP-strengthened RC beam, long-term
behaviour of FRP-strengthened RC beam and components mainly subjected to freeze-
thaw exposure and sustained load, and FE modeling of FRP strengthened RC beams were
summarized. Finally, the identified research gaps in the area of the NSM-FRP
strengthening method were categorized. In the following chapter, the experimental test
program is presented.
77
Chapter Three: Experimental Program
3.1 Introduction
A survey on the body of literature performed in Chapter Two indicated
insufficient experimental investigation on a practical prestressed NSM-FRP strengthening
system to strengthen RC beams in flexure and also the long-term performance of the
system under the freeze-thaw exposure and sustained loading when combined with
humidity. Furthermore, the effects of prestressing level and shape of FRP reinforcement
(rebar and strip) required investigation. Details of the experimental program conducted in
this research are presented in this chapter. First, the testing matrix of the specimens is
provided followed by a description of the beams’ details, manufacturer material
properties, design, fabrication, and instrumentation. Then, the considered freeze-thaw
cycling exposure and application of the sustained load are illustrated in detail. At the end,
the static testing procedure and configuration are described. It should be noted that the
design and fabrication of the beams, and results of the ancillary tests of the steel,
concrete, and FRP materials are presented in Appendices A, B, and C, respectively.
3.2 Test Matrix
The main experimental part of the project consists of two phases to examine the
long-term performance and effects of different types of loading on the prestressed NSM-
CFRP strengthened RC beams.
During the first phase, the effects of severe environmental conditions on the
flexural behaviour of prestressed NSM-CFRP strengthened beams were studied under
78
static loading. Nine large-scale simply supported RC beams (5.15 m long with
rectangular section 200×400 mm) were tested under four-point bending configuration:
one un-strengthened beam, four strengthened beams using Aslan 500 CFRP strips (2-
2×16 mm, 62.4 mm2), and four strengthened beams using Aslan 200 CFRP rebars (Φ9.5
mm, 71.3 mm2). The CFRP strips/rebar were mounted in one groove made in the
concrete cover on the tension face (named as NSM method). The target prestressing
levels were 0, 20, 40, and 60% based on the ultimate tensile strength of the CFRP
reinforcement reported by the manufacturer. The CFRP strips/rebar were prestressed
using an innovative anchorage system that consisted of two steel anchors bonded to the
ends of the CFRP strips/rebar and using movable and fixed brackets and a hydraulic jack
temporarily mounted on the beam. After strengthening, the beams were precracked
(loaded up to 1.2 times the analytical cracking load for each beam) and placed inside a
testing facility chamber exposed to 500 freeze-thaw cycles (-34oC to +34
oC in 8 hrs) and
average humidity of 75% for temperatures above +20oC.
In the second phase, the focus was on the type of loading where the combined
effects of the sustained load and freeze-thaw exposure were investigated. Five large-scale
RC beams (similar to the beams of phase one strengthened with CFRP strips) were
fabricated and subjected to sustained service load (47% of the analytical ultimate load of
the non-prestressed strengthened beam), 500 freeze-thaw cycles, and fresh water spray
(18 L/min for a time period of 10 min) at a temperature of +20oC. After being exposed to
500 freeze-thaw cycles, the beams were tested under static monotonic loading up to
failure. A summary of the test matrix is presented in Table 3-1.
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Table 3-1: Test matrix.
Phase # Beam ID
Description
NSM
strengthening
material
Target prestressing
level %ffrpu
(prestrain)
Freeze-thaw
exposure
Sustained
load
I
B0-F N.A. N.A. 500 cycles N.A.
BS-NP-F Two CFRP strips
(2-2×16 mm)
0
(0) 500 cycles N.A.
BS-P1-F Two CFRP strips
(2-2×16 mm)
20
(0.0034) 500 cycles N.A.
BS-P2-F Two CFRP strips
(2-2×16 mm)
40
(0.0068) 500 cycles N.A.
BS-P3-F Two CFRP strips
(2-2×16 mm)
60
(0.0102) 500 cycles N.A.
BR-NP-F One CFRP rebar
(9.5 mm)
0
(0) 500 cycles N.A.
BR-P1-F One CFRP rebar
(9.5 mm)
20
(0.0034) 500 cycles N.A.
BR-P2-F One CFRP rebar
(9.5 mm)
40
(0.0068) 500 cycles N.A.
BR-P3-F One CFRP rebar
(9.5 mm)
60
(0.0102) 500 cycles N.A.
II
B0-FS N.A. N.A. 500 cycles 62 kN
BS-NP-FS Two CFRP strips
(2-2×16 mm)
0
(0) 500 cycles 62 kN
BS-P1-FS Two CFRP strips
(2-2×16 mm)
20
(0.0034) 500 cycles 62 kN
BS-P2-FS Two CFRP strips
(2-2×16 mm)
40
(0.0068) 500 cycles 62 kN
BS-P3-FS Two CFRP strips
(2-2×16 mm)
60
(0.0102) 500 cycles 62 kN
It should be mentioned that, in the initial project plan, phase II consisted of nine
beams (one un-strengthened control beam, four strengthened beams using CFRP strips,
and four strengthened beams using CFRP rebars) to be subjected to the same freeze-thaw
exposure as applied in phase I plus sustained load. However, after testing the beams in
phase I and analyzing the results, it was concluded that there is no significant difference
between the overall flexural behaviour of the beams strengthened with CFRP strips and
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the ones strengthened with CFRP rebars. Furthermore, the applied exposure had
insignificant effects on the flexural performance of the beams. Therefore, in phase II,
only the beams strengthened with CFRP strips were fabricated and tested, and the
considered 75% relative humidity was replaced with fresh water spray to increase the
severity of the applied freeze-thaw exposure.
In addition to the main experimental part of the research, a small experimental
program was defined after completion of the tests in phases I and II on the modification
of the temporary movable and fixed steel brackets used for prestressing the NSM CFRP.
This part was done to avoid the occurrence of cracks during prestressing process (jacking
stage) at the locations of the temporary brackets in the RC beams strengthened using
NSM CFRP strips and rebar with high prestress level of 60% (presented in Table 3-1).
Therefore, the temporary steel brackets were modified by adding steel plates to the side
to be capable of changing the location of the jacks, and to test the efficiency of the
modified brackets, three small concrete specimens (1500 mm long with rectangular
section 200×400 mm) were fabricated and very high prestress level (93% based on the
ultimate tensile strength of the CFRP reinforcements reported by the manufacturer) was
applied to them. The concrete specimens had similar cross-sections and target material
properties to the RC beams in phases I and II. To facilitate the execution of the
experiment, the concrete specimens had pre-formed grooves and a dywidag thread steel
bar with two adjustable nuts at the ends was used instead of CFRP reinforcements. A
summary of the specimens are presented in Table 3-2.
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Table 3-2: Summary of the specimens used for modification of the brackets.
Specimen ID Length
(mm)
Cross-section
(mm×mm)
Target prestressing level
%ffrpu (prestrain)
Target prestressing force
in the dywidag bar (kN)
SP-1 1500 200×400 93 (0.0158) 122.8
SP-2 1500 200×400 93 (0.0158) 122.8
SP-3 1500 200×400 93 (0.0158) 122.8
3.3 RC Beam Specimens
The geometry of the RC beams were selected based on prior research performed
by Gaafar (2007) who examined the flexural behaviour of the prestressed and non-
prestressed NSM-CFRP strengthened RC beams at room temperature.
3.3.1 Design
The dimensions of the RC beams were selected to be similar to those from prior
research on the flexural behaviour of the prestressed and non-prestressed NSM-CFRP
strengthened RC beams at room temperature performed by Gaafar (2007), in order to
provide the opportunity for future comparison between the results. Since flexural
strengthening in practice is usually done on the beams with insufficient steel ratios, the
RC beams had small reinforcement ratios: 0.87% for tension steel reinforcements and
0.29% for compression steel reinforcements, which are within the maximum and
minimum reinforcement ratios. To avoid shear failure in the strengthened beams, a shear
span to effective depth ratio of 5.8 with sufficient stirrups along the length was
considered. The beams were considered to be strengthened using one CFRP rebar or two
glued CFRP strips mounted in one groove, and therefore, were designed to provide
sufficient concrete cover at the soffit for cutting the groove and implementing the NSM
strengthening. The groove dimensions were selected to be greater than the minimum
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ratios recommended by ACI 440.2R (2008) to decrease the possibility of premature
failure due to NSM CFRP debonding; These ratios are 3.2 for width of the groove-to-
width of strips, 1.6 for height of the groove-to-height of the strips, 2.1 for width of the
groove-to-width of rebar, and 2.6 for height of the groove-to-height of the rebar versus
the minimum limits of 3, 1.5, 1.5, and 1.5, respectively. The maximum initial prestress
level was selected to be 60% of the tensile strength of the CFRP reinforcements reported
by the manufacturer, which is recommended by CAN/CSA-S806-12 (2012) and
considers creep rupture stress of the CFRP reinforcements and reserve strain capacity
(required deformability limits) for the strengthened beam. The dimensions of the end
anchors and the number of the bolts were designed to avoid any issues such as shear
failure of the bolts, bearing failure of the anchor plate, and failure of the anchor tube/pipe
to anchor plate weld during the prestressing.
Capacity of the designed beam and type of failure based on manufacturer material
properties and target prestressing length of 4320 mm (centre-to-centre of the exterior end
anchor bolts) are presented in Table 3-3. The key points of the load-deflection curves are
calculated by developing a code in Mathematica software that can account for negative
camber due to prestressing, concrete cracking, steel yielding, CFRP rupture, and concrete
crushing of the prestressed and non-prestressed NSM-CFRP strengthened RC beams.
More details regarding the design of the un-strengthened and strengthened beams are
provided in Appendix A. Furthermore, more details on geometry, manufacturer material
properties, fabrication, and instrumentation of the test beams are provided in the
following sections.
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Table 3-3: Summary of designed specimens.
Beam ID ɛp Δo
(mm)
Δcr*
(mm)
Pcr*
(kN)
Δy*
(mm)
Py*
(kN)
Δu*
(mm)
Pu*
(kN) ɛc@u ɛfrp@u
Failure
Mode
B0 N.A. 0 1.70 22.70 21.85 82 121.47 85.73 0.0035 N.A. CC
BS-NP 0 0 1.71 22.91 22.16 88.88 96.92 131.78 0.00302 0.017 FR
BS-P1 0.0034 0.45 1.76 29.60 21.58 97.83 75.74 131.65 0.00259 0.017 FR
BS-P2 0.0068 0.90 1.81 36.28 21.03 106.73 56.36 131.26 0.00217 0.017 FR
BS-P3 0.0102 1.35 1.86 42.97 20.53 115.58 38.85 130.31 0.00173 0.017 FR
BR-NP 0 0 1.71 22.94 22.21 89.86 93.06 135.17 0.00295 0.016 FR
BR-P1 0.0034 0.51 1.77 30.58 21.55 100.08 71.47 134.99 0.00251 0.016 FR
BR-P2 0.0068 1.02 1.82 38.22 20.94 110.24 51.87 134.48 0.00208 0.016 FR
BR-P3 0.0102 1.54 1.88 45.85 20.37 120.33 34.34 133.20 0.00162 0.016 FR
ɛp = target prestrain value in CFRP reinforcement ɛc@u = concrete strain at extreme compression fibre at ultimate load
Δo = initial camber due to prestressing ɛfrp@u = maximum CFRP strain at ultimate load
Pcr and Δcr = load and deflection at cracking CC = concrete crushing
Py and Δy = load and deflection at yielding FR = CFRP rupture
Pu and Δu = load and deflection at ultimate
* self-weight is ignored in calculations (to consider the self-weight effects, values of 6 kN and 0.47 mm should be deducted from the loads and deflections,
respectively)
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84
3.3.2 Details of Beams
The beams were 5150 mm long with 5000 mm span length (centre-to-centre of
the supports) and a rectangular cross-section of 200×400 mm. All beams were simply
supported and tested under four-point bending quasi-static monotonic loading. Geometry
of the beams and the test setup are presented in Figure 3-1. The compression steel
reinforcement consisted of 2-10M deformed steel bars (nominal diameter of 11.3 mm)
with a total area of 200 mm2 and the tension steel reinforcement consisted of 3-15M
deformed steel bars (nominal diameter of 16 mm) with a total area of 600 mm2. The shear
reinforcement consisted of double leg closed 10M deformed steel bars. The beams were
strengthened with either one 9.5 mm sand coated CFRP rebar or two 2×16 mm rough
textured CFRP strips, which were glued together, mounted in one groove on the tension
face of the beam as plotted in Figure 3-2a. The CFRP strips/rebar was prestressed against
the beam itself using the anchorage system developed by Gaafar (2007). The CFRP
rebars and strips were connected to the proper end anchors, as plotted in Figure 3-2b, to
be capable of enforcing the desired prestressing for each beam without any issues.
85
Figure 3-1: Geometry of the beams and test setup.
85
86
(a) Cross-section of the beams and details of the grooves
(b) End anchor details
Figure 3-2: Details of the beams.
87
3.3.3 Manufacturer Material Properties
3.3.3.1 Steel Reinforcements
The tension, compression, and shear reinforcements possessed a specified yield
strength of 440 MPa and a modulus of elasticity of 200 GPa.
3.3.3.2 Concrete
The designed target 28 days concrete compressive strength was 40 MPa having a
maximum aggregate size of 20 mm, an air content of 1%, and a slump value of 80 mm.
3.3.3.3 CFRP Reinforcements
The CFRP materials used for strengthening consisted of Aslan 500 Tape and
Aslan 200 Rebar produced by Hughes Brothers Inc. with the specified properties
presented in Table 3-4.
Table 3-4: Properties of CFRP strip and rebar recommended by the manufacturer
(Hughes Brothers, 2010a and b).
CFRP product Surface
treatment
Dimensions
(mm)
Afrp
(mm2)
ffrpu
(MPa)
Efrp
(GPa) ɛfrpu
Aslan 500 CFRP Tape Rough textured 2×16 31.2 2068 124 0.017
Aslan 200 CFRP Rebar Sand coated Ф9.5 71.26 1896 124 0.016
3.3.3.4 Epoxy Adhesives
Two types of epoxy adhesives, produced by Sika Inc., were employed for NSM
strengthening. Sikadur® 330 was used to connect the CFRP strips and rebars into the steel
88
anchors, and Sikadur® 30 was used to fill in the groove in concrete. The material
properties of these adhesives are presented in Table 3-5.
Table 3-5: Properties of epoxy adhesives reported by the manufacturer (Sika, 2010a
and b).
Epoxy product
(Type)
Mix Ratio
(Mix Method)
Tensile
strength
(MPa)
Elongation
at break
Tensile modulus
of elasticity
(GPa)
Sikadur® 30
(Two-component)
3:1
(by weight) 24.8 0.01 4.5
Sikadur® 330
(Two-component)
4:1
(by weight) 30 0.015 N.A. (3.8
*)
* Flexural modulus of elasticity
3.3.3.5 Anchor Bolts
Carbon Steel Kwik Bolt 3 Expansion Anchor produced by Hilti Inc. was used to
connect the steel anchor to the substrate concrete having a nominal bolt diameter of 15.9
mm and a steel material factored strength of 54.4 kN in shear (Hilti, 2008). This bolt had
a nominal ultimate shear capacity of 65 kN by providing an embedment depth of 70 mm
and enough edge distance in normal weight concrete with compressive strength of 40
MPa (Hilti, 2008).
3.3.4 Fabrication
Fabrication of the RC beam specimens including building of formwork and steel
cage, casting, and implementation of prestressed NSM strengthening are presented in
Appendix B in detail.
89
3.3.5 Instrumentation
The beams were instrumented as shown in Figure 3-3a and b. Six horizontal
Linear Strain Conversions (LSCs) were installed on the beams at mid-span to measure
the strains at the extreme concrete compression fibre, the compression steel level, and the
tension steel level as shown in Figure 3-3. Two laser displacement sensors were used to
measure the vertical deflection at mid-span as shown in Figure 3-3b. Aluminium angles
were attached to both sides of the beams as laser reflectors and the laser sensors, having a
working range of 50 to 250 mm, were connected to the steel stands. For prestressing
application, four horizontal LSCs were installed on the beam at mid-span: two on one
side and two on top face of the beam. In addition, four vertical LSCs were used to
monitor the vertical deflection, two at the mid-span and one at each point load location.
Four Strain Gauges (SGs) were installed on the steel reinforcement at mid-span of
each beam: two on the tension steel bars and two on the compression steel bars. To
measure the strain along the length of the CFRP strips/rebar, eight SGs were installed on
each CFRP strips/rebar according to the spacing and configuration shown in Figure 3-3a.
To monitor the temperature in the concrete core of the beam during freeze-thaw
exposure, one Thermo-Couple (TC) sensor was placed inside each beam at location
shown in Figure 3-3a. These TCs were connected to the environmental chamber data
acquisition system to record the temperature in concrete beams during exposure.
90
(a)
(b)
Figure 3-3: Beams instrumentation: (a) elevation and (b) cross-section at mid-span location.
90
91
3.4 Prestressed NSM FRP Strengthening System
One of the challenges for using prestressed NSM-FRP method is developing a
practical method for prestressing and anchoring the CFRP reinforcement. Most research
in this area was performed while the beam was prestressed by jacking against both ends
of the beam requiring access to entire length. This procedure is very difficult to be
implemented in the field. The anchorage system used to prestress the NSM CFRP
reinforcement used in this research was developed by Gaafar (2007), which overcomes
the practicality drawbacks of previous research as mentioned in Sections 1.4.6 and 2.9. A
brief description of the anchorage system and the prestressing procedure is presented in
Appendix B, and more details can be found in (Gaafar, 2007; El-Hacha and Gaafar,
2011).
3.5 Initial Loading after Strengthening
To increase the effect of freeze-thaw exposure on the beams, each beam in phase I
was loaded after strengthening up to 1.2 times its theoretical cracking load and the
occurrence of flexural cracks was confirmed by visual inspections. The test setup for
initial loading was according to Figure 3-1 where the loading and unloading rates were
0.1mm/min and 0.5 mm/min, respectively. The corresponding deflections and strains
were monitored and the permanent deflection of each beam was recorded for 30 min after
unloading. A summary of initial loading after strengthening and obtained experimental
and theoretical cracking loads for each beam are presented in Table 3-6.
92
Table 3-6: Summary of initial loading and obtained experimental and theoretical
cracking loads.
Beam ID Papplied
(kN)
Pcr-exp.
(kN)
Pcr-theo.
(kN)
Pcr-theo. sw.
(kN)
B0-F 18.34 10.40 22.66 16.06
BS-NP-F 19.09 14.02 22.85 16.25
BS-P1-F 27.2 21.63 29.53 22.93
BS-P2-F 35.34 27.30 36.22 29.62
BS-P3-F 43.34 35.51 42.90 36.30
BR-NP-F 17.73 13.12 22.88 16.28
BR-P1-F 25.69 18.00 30.51 23.91
BR-P2-F 33.57 26.00 38.14 31.54
BR-P3-F 44.07 36.28 45.78 39.18 Papplied = applied load to each beam for cracking after strengthening
Pcr-exp. = experimental cracking load
Pcr-theo. = theoretical cracking load
Pcr-theo. sw. = theoretical cracking load by considering the effect of self-weight
3.6 Freeze-Thaw Cycling Exposure
Freeze-thaw exposure was performed using the environmental chamber in the
University of Calgary’s Civil Engineering Lab. All fourteen beams, phase I and phase II,
were subjected to freeze-thaw cycling exposure applied based on CHBDC (CAN/CSA-
S6-06, 2011) requirements as shown in Figure 3-4 to Figure 3-6. According to Figure 3-4
and Figure 3-5, the average maximum and minimum mean daily temperatures in Canada
are -34oC and +34
oC, respectively, which are selected to simulate the freeze-thaw
exposure inside the environmental chamber. Also according to Figure 3-6, the average
annual mean relative humidity in Canada is 75%, which is selected to simulate the
humidity exposure inside the environmental chamber (Abdelrahman, 2011).
93
Figure 3-4: Maximum mean daily temperature (CAN/CSA-S6-06, 2011).
Figure 3-5: Minimum mean daily temperature (CAN/CSA-S6-06, 2011).
94
Figure 3-6: Annual mean relative humidity (CAN/CSA-S6-06, 2011).
In phase I, nine beams were subjected to 500 freeze-thaw cycles, and in phase II,
five beams were subjected to combined effects of sustained load and 500 freeze-thaw
cycles. Each freeze-thaw cycle in phase I consisted of eight intervals that was
programmed to be accomplished in 8 hrs, including the lower temperature bound of -
34oC and the upper temperature bound of +34
oC with a relative humidity of 75% for
temperatures above +20oC. A similar freeze-thaw cycle to phase I was used in phase II
except that the 75% relative humidity at temperature above +20oC was replaced with
fresh water spray (18 L/min for a time period of 10 min) at a temperature of +20oC to
increase the severity of the applied exposure. Details of the intervals and trend of three
freeze-thaw cycles are presented in Table 3-7 and Figure 3-7 including programmed and
measured temperature in the environmental chamber, temperature in concrete core of the
95
beam, and programmed humidity. The intervals were selected somehow to have
sufficient freezing temperatures at the concrete core. The recorded temperature in the
concrete core shown in Figure 3-7 confirms the occurrence of freezing and thawing
throughout the beam in each cycle. It should be mentioned that due to using the water
spray in phase II, it took longer for the chamber to reach to the programmed temperature
and each cycle was accomplished in an average of 9.5 hr.
Most researchers have considered 300 freeze-thaw cycles as presented in Table 2-
12 while in this research 500 freeze-thaw cycles were applied to investigate the effects of
long-term severe exposure and high number of the cycles. Bisby and Green (2002)
estimated that 300 freeze-thaw cycles, with the details presented in Table 2-12,
correspond to somewhere between 10 to 20 years for an exterior application in Toronto;
Laoubi et al. (2006) estimated that freeze-thaw cycles ranging from 100 to 360, with the
details presented in Table 2-12, conservatively covers the lifetime of a structure in North
America. What is obvious is that the selected number of cycles by the researchers is
arbitrary and depends on the location of the structure and many environmental factors,
which almost make it impossible to have an exact estimation for the corresponding
lifetime. However, the author believes that the nature of the cycles is more severe than
what would be typically encountered in reality and it is possible to have an estimation of
the minimum corresponding lifetime having the annual freeze-thaw frequency of the
relevant geographic location. Therefore, considering an average freeze-thaw frequency of
39 cycles per year for Canada (Fraser, 1959), the accelerated 500 cycles used in this
study (500×8 hr = 4000 hr = 166.7 day), that is equivalent to 0.457 year of exposure
inside the chamber, corresponds to a minimum lifetime of 12.8 years.
96
Table 3-7: Environmental chamber schedule for one freeze-thaw cycle.
Intervals Air temperature
oC Time
(hr:min) Humidity (for phase I)
Water spray (for phase II)
Loop
from Set point
0 Room
temperature +20 00:05 Off Off
1 +20 +20 00:05 Off On
2 +20 +20 00:05 Off Off
3 +20 +20 00:05 Off On
4 +20 +20 00:05 Off Off
5 +20 -34 2:40 Off Off
6 -34 +20 00:05 Off Off
7 +20 +34 02:20 On Off
8 +34 +20 00:10 On Off
-100
-80
-60
-40
-20
0
20
40
60
80
100
-50
-40
-30
-20
-10
0
10
20
30
40
50
0:00 4:00 8:00 12:00 16:00 20:00 24:00 28:00
Hu
mid
ity (
%)
Te
mp
era
ture
(oC
)
Time (hr:min)
Programmed temperature Actual measured air temperature
Temperature in concrete core Programmed humidity @ phase I
Fresh water spary @ phase II
Figure 3-7: Three typical freeze-thaw cycles.
97
3.7 Sustained Loading
Five RC beams in phase II were loaded inside the environmental chamber using a
Self-Reacting Loading System (SRLS) designed for this part of the project. Details of the
SRLS are shown in Figure 3-8 to Figure 3-11. Using the SRLS, the load was applied
downwards from the top using two hydraulic jacks connected to the system shown in
Figure 3-10. The Hollow Structural Steel (HSS) (203×102×13) sections (HSS beam #1
and 2) acted on the five RC beams at the point load locations and pushed the beams
downwards while the Dywidag steel bars (Dywidag bar #1) attached to the HSS sections
(HSS beam #3) moved upward. To have the system locked, the Dywidag bars (Dywidag
bar #1) were connected to two HSS steel beams (HSS beam #3), which were attached to
the strong floor using four Dywidag bars (Dywidag bar #2) as shown in Figure 3-10 and
Figure 3-11. The applied load to the RC beams was measured through the two load cells
placed between hydraulic jacks and the nuts on the Dywidag bars (Dywidag bar #1).
Then, the permanent nuts were tightened and the jacks and load cells were removed. The
setup and application of the sustained load inside the environmental chamber are
presented in Figure 3-12 and Figure 3-13, while Figure 3-14 and Figure 3-15 show the
RC beams under sustained load after 500 freeze-thaw cycles. In this research, to monitor
the value of sustained load in regular time periods during exposure, two strain gauges
were installed on each Dywidag bar (Dywidag bar #1), as shown in Figure 3-13a.
Furthermore, the mid-span deflection was monitored for each beam using LSCs shown in
Figure 3-13b. The applied load on each beam was 62 kN, which is 47% of the theoretical
ultimate load of the non-prestresesd strengthened beam, BS-NP. The value of sustained
load was selected satisfying a creep-rupture stress limit of 65% of ultimate tensile
98
strength of CFRP strips and a tension steel stress limit of 240 MPa recommended by
CAN/CSA-S6-06 (2011), and also an allowable concrete compressive stress under
service and prestress of 0.45f′c recommended by CAN/CSA-A23.3-04 (2004). The
system was monitored for three days and the loss in load was measured, then the applied
load was modified, by unloading and applying the load again, and checked at regular
intervals of one week to keep the value of the load as constant as possible.
99
Figure 3-8: Plan view of chamber floor equipped for sustained loading.
99
100
Figure 3-9: Plan view of sustained loading.
100
101
Figure 3-10: Side view of sustained loading.
101
102
Figure 3-11: Cross view of sustained loading.
103
Figure 3-12: Sustained load setup in the environmental chamber.
103
104
(a) Top view of the beams
(b) Bottom view of the beams
Figure 3-13: Applying Sustained load in the chamber.
Nut
Load cell
Hydraulic jack
Steel chair HSS beam #1
Alignment bar
HSS beam #2
Dywidag bar #1
Permanent nut
Loading plate
& rubber pad
Strain gauge
Dywidag bar #2
HSS beam #3
HSS beam #4 Vertical LSC
Dywidag bar #1
Chamber sealed duct
105
Figure 3-14: Beams under sustained load and after 500 freeze-thaw cycles.
106
(a) Top view of the beams
(b) Bottom view of the beams
Figure 3-15: Beams under sustained load and after 500 freeze-thaw cycles.
107
3.8 Testing Procedure
Following the freeze-thaw exposure for beams from phase I and combined freeze-
thaw and sustained load exposures for beams from phase II, the beams were removed
from the chamber, kept for at least three days at room temperature and then, instrumented
and tested to failure under four-point bending configuration. The test was performed by
monotonically increasing two point loads using displacement control at a rate of
1mm/min using a 500 kN MTS hydraulic actuator mounted to a steel frame at mid-span.
The test setup is shown in Figure 3-16. After failure, the unloading was performed using
displacement control at a rate of 20 mm/min and the test was terminated. The values of
load, strains, and deflections were recorded using a data acquisition system at a rate of 1
reading/sec.
Figure 3-16: Test setup.
108
3.9 Summary
Details of the experimental program were presented in this chapter. First, the test
matrix was presented followed by explaining the design, geometry, material properties,
fabrication, and instrumentation of the beams. Then, the adopted strengthening system,
initial loading after strengthening, freeze-thaw cycling exposure, and sustained loading
were explained in detail. Finally, the testing procedure including details of the applied
monotonic loadings to failure was explained. The experimental test results of the beams
in phase I and II are presented and discussed in the next chapter followed a study of the
prestress losses, deformability and ductility, optimum and beneficial prestressing levels,
effects of CFRP geometry: strips versus rebar, effects of freeze-thaw exposure, and
effects of sustained loading combined with freeze-thaw exposure.
109
Chapter Four: Experimental Results and Discussion
4.1 Introduction
Results of the fourteen tested beams (classified in two phases) and corresponding
ancillary tests are presented in this chapter. Nine RC beams exposed to 500 freeze-thaw
cycles (three cycles per day with temperature ranging between +34oC to −34
oC with a
relative humidity of 75% for temperatures above +20oC) were tested in phase I: one un-
strengthened control beam, four beams strengthened using NSM CFRP rebar with target
prestressing levels of 0%, 20%, 40%, and 60% of the ultimate tensile strength of the
CFRP rebar reported by the manufacturer and four beams strengthened using NSM CFRP
strips with target prestressing level of 0%, 20%, 40%, and 60% of the ultimate tensile
strength of the CFRP strips reported by manufacturer. Five beams were tested in phase II
(one un-strengthened control beam and four beams strengthened using NSM CFRP strips
with target prestressing levels of 0%, 20%, 40%, and 60% of the ultimate tensile strength
of the CFRP strips reported by manufacturer) subjected to 500 freeze-thaw exposure
cycles similar to that of phase I while being subjected to a sustained load equal to 47% of
the analytical ultimate load of the non-prestressed NSM CFRP strengthened RC beam.
Geometry of the beams and details of the experimental program were presented in
Chapter Three. The beams were simply supported and were tested under quasi-static
monotonic loading in four-point bending configuration. In this chapter, the effects of
sustained load and freeze-thaw exposure are shown on the load-deflection response, type
of failure, ductility, energy absorption, and strain in the CFRP by comparing the test
results with the results of similar beams tested without any sustained loading and
110
environmental exposure. Furthermore, the effects of CFRP geometry: rebar versus strip,
the concepts of beneficial and optimum prestressing levels, and the topics of
deformability of NSM CFRP strengthened RC beams are studied in detail. At the end of
this chapter, an experimental investigation was performed by modification of the
prestressing system to avoid the cracking issues observed at the location of the temporary
brackets during prestressing in phases I and II.
The results presented in this chapter were published in refereed conference papers
(Omran and El-Hacha, 2012a, c, and d, and 2013b).
4.2 Phase I: Prestressed NSM-CFRP Strengthened RC Beams under Freeze-Thaw
Exposure
4.2.1 Test Beams and Material Properties
Nine beams exposed to 500 freeze-thaw cycles (based on the test matrix presented
in Chapter Three and Table 3-1) were tested in phase I. Details of the beams including
the geometry, test setup, and used end anchors were presented in Section 3.3.3.2.
Material properties of the beams including steel reinforcements, concrete, and CFRP
rebar and strip obtained from ancillary test results performed according to the specific
ASTM standards are presented in Appendix C in detail. A concise description is provided
in this section.
4.2.1.1 Steel Reinforcements
The tension and compression steel bars (3-15M and 2-10M) possessed yield
strengths of 4929 MPa and 48816 MPa, and yield strains of 0.002460.00017 and
111
0.002440.00027, respectively, obtained from tension tests (see Appendix C) having a
modulus of elasticity of 200 GPa. Also, the stirrups (25-10M) had the same properties as
the compression steel bars.
4.2.1.2 Concrete
Two concrete batches were used to cast the beams. Beams B0-F, BS-NP-F, BS-
P1-F, BS-P2-F, and BS-P3-F were cast from batch #1 with an average concrete
compressive strength of 41.56.2 MPa at the time of testing to failure. Beams BR-NP-F,
BR-P1-F, BR-P2-F, and BR-P3-F were cast from batch #2 with an average concrete
compressive strength of 39.44.2 MPa at the time of testing to failure. The average
concrete compressive strength of the freeze-thaw exposed cylinders from batch #1 and
batch #2 were 32.110.8 MPa and 286.8 MPa, respectively, at the time of testing the
beams to failure; the high standard deviation in the concrete strength is a results of the
severe environmental exposure on the specimens which results in a greater variability. It
should be mentioned that the beams strengthened with NSM CFRP strips and the un-
strengthened control beam were about 21-months old, and the beams strengthened with
NSM CFRP rebars were about 11-months old at the time of testing to failure. Also, the
static testing for each set was performed within two weeks. More details about the
compressive strengths of the concrete cylinders representing each beam at 28 days and at
times of strengthening, preloading (for initial cracking), and testing the beams to failure
are provided in Appendix C, including the date and the number of the tested cylinders.
112
4.2.1.3 CFRP Reinforcements
The material properties of the CFRP reinforcements obtained from tension tests
are presented in Table 4-1.
Table 4-1: CFRP material properties obtained from tension tests.
CFRP product
(Manufacturer)
Dimension
(mm)
Afrp
(mm2)
ffrpu
(MPa)
Efrp
(GPa) ɛfrpu
Aslan 500 CFRP tape
(Hughes Brothers Inc) 2×16 31.2 2624±28 124.4±6.7 0.021±0.0009
Aslan 200 CFRP rebar
(Hughes Brothers Inc) Ф9.5 71.3 2896
* 115.9±1.5 0.025
*
* Only one specimen reached CFRP rupture
4.2.1.4 Epoxy Adhesives
Two types of epoxy adhesives were used as groove filler for NSM strengthening:
Sikadur® 330 was used in the end groove regions (around and inside the end anchors) and
Sikadur® 30 was used to fill in the intermediate concrete groove regions between the end
anchors. Properties of these epoxy adhesives are presented in Section 3.3.3.4.
4.2.1.5 Anchor Bolts
Carbon Steel Kwik Bolt 3 Expansion Anchors were used to connect the end
anchor to the substrate concrete. Properties of these bolts are presented in Section 3.3.3.5.
4.2.2 Load-Deflection Response
The load-deflection curves of the tested beams in phase I are presented in Figure
4-1. The permanent deflections due to initial loading after strengthening (presented in
113
Section 3.5) that caused cracking after strengthening, are considered in the plotted curves.
The load-deflection responses of the prestressed NSM CFRP strengthened RC beams can
be considered as a tri-linear slope curve until failure that include the negative camber due
to prestressing, initiation of flexural cracks, yielding of tensile steel rebar, failure due to
CFRP rupture or concrete crushing which causes a drop in total load at ultimate stage,
and post failure behaviour. All of tested beams showed a typical failure mode, i.e.,
tension steel reinforcements yielding followed by CFRP rupture or concrete crushing.
The failure mode of each beam is marked on Figure 4-1. A summary of the results are
presented in Table 4-2.
114
0
20
40
60
80
100
120
140
160
-5 15 35 55 75 95 115 135 155 175
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-NP-F BS-P1-F BS-P2-F BS-P3-F B0-F
BR-NP-F BR-P1-F BR-P2-F BR-P3-F
: Concrete crushing : FRP rupture
Figure 4-1: Load-deflection curves of the beams subjected to freeze-thaw exposure (phase I).
114
115
Table 4-2: Summary of the test results of the beams subjected to freeze-thaw exposure (phase I).
Beam ID ɛp
(µɛ)
Δo
(mm)
ɛpe
(µɛ)
Δoe
(mm)
Pcr
(kN)
Δcr
(mm) Pcr/Pcn
Δop
(mm)
Py
(kN)
Δy
(mm) Py/Py0 Py/Pyn
Pu
(kN)
Δu
(mm) Pu/Pu0 Pu/Pun FM
B0-F N.A. N.A. N.A. N.A. 10.4 2.22 N.A. 0.65 75.5 18.78 1.00 N.A. 97.8 142.88 1.00 N.A. CC
BS-NP-F 0 0 0 0 14.0 1.36 1.00 0.61 92.4 22.53 1.22 1.00 132.2 104.26 1.35 1.00 CC
BS-P1-F 3574 -0.42 3463 -0.49 21.6 1.43 1.54 0.13 104.1 23.99 1.38 1.13 134.7 82.9 1.38 1.02 CC
BS-P2-F 6900 -0.93 6723 -1.09 27.3 1.24 1.95 -0.81 114.8 25.56 1.52 1.24 149.5 87.85 1.53 1.13 FR
BS-P3-F 10112 -1.39 9884 -1.70 35.5 1.45 2.53 -1.43 124.3 25.91 1.64 1.34 141.7 58.55 1.45 1.07 FR
BR-NP-F 0 0 0 0 13.1 1.23 1.00 0.6 91.6 23.78 1.21 1.00 132.3 102.71 1.35 1.00 CC
BR-P1-F 3801 -0.46 3662 -0.48 18.0 1 1.37 -0.07 105.1 24.98 1.39 1.15 147.5 107.62 1.51 1.11 CC
BR-P2-F 6585 -0.67 6548 -0.92 26.0 1.2 1.98 -0.52 113.4 25.86 1.50 1.24 157.5 98.05 1.61 1.19 CC
BR-P3-F 10272 -1.25 9950 -1.71 36.3 1.21 2.77 -1.4 125.2 25.36 1.66 1.37 157.5 71.28 1.61 1.19 FR
ɛp and Δo = initial prestrain and initial camber due to prestressing Pcr and Δcr = load and deflection at cracking
ɛpe and Δoe = effective prestrain and camber at 7 days after prestressing Py and Δy = load and deflection at yielding
Δop = permanent deflection after initial cracking Pu and Δu = load and deflection at ultimate
Pcr/Pcn = ratio of the cracking load of each beam to that of the corresponding non-prestressed strengthened beam FM = failure mode
Py/Py0 and Pu/Pu0 = ratios of the yielding and ultimate loads of each beam to those from B0-F FR and CC= CFRP rupture and concrete crushing
Py/Pyn and Pu/Pun = ratios of the yielding and ultimate load of each beam to those from corresponding non-prestressed strengthened beam
Note: The quantities for the deflections, loads, and strains are the recorded values from the corresponding instruments and can be round to the nearest number.
115
116
4.2.2.1 Pre-Cracking Behaviour
At jacking stage, an upward initial camber (Δo) ranging from 0.42-1.39 mm for
strengthened beams with CFRP strips and 0.46-1.25 mm for strengthened beams with
CFRP rebar was observed; seven days after prestressing, the camber increased and these
ranges reached to 0.49-1.70 mm and 0.48-1.71 mm, respectively, as presented in Table
4-2 as the effective negative camber (Δoe). Although, the creep after one week is a reason
for the increase in the upwards deflection, but the main reason for the increase in negative
camber is removing the temporary bracket. The mechanism of this behaviour is
illustrated in Figure 4-2. The enforced prestressing force is transferred to the beams
through the bolts which connect the temporary brackets to the side of the beam. At
jacking stage, this eccentricity results in an axial load and an additional positive moment
on the beam length between the movable and fixed brackets while the rest of the beam is
under negative curvature. When the temporary brackets are removed from the side of the
beam these transferred loads are eliminated which results in an increase in negative
camber. If the value of the tensile stress produced by the additional loads (moment and
axial) is greater than the tensile strength of the concrete, then inclined tension cracks
form in concrete between the two brackets during prestressing. Consideration should be
given to avoid cracking during prestressing. In this research, the section between two
brackets was strengthened using externally bonded CFRP sheet for the beams BR-P3-F,
BS-P3-F, and BS-P3-FS with high prestressing levels of 41%, 48%, and 49% of the
CFRP tensile strength, respectively. A modification in the location of the applied
prestressing force on the temporary brackets (hydraulic jacks) in a way that minimizes
the produced additional moment during prestressing can solve the cracking issue. This
117
system is demonstrated in Section 4.10 where the modification on the prestressing system
is performed.
Figure 4-2: Interaction between temporary brackets and beam due to prestressing.
The values of the initial and effective prestrain calculated from the three strain
gauges installed at constant moment region of the beams are presented in Table 4-2. The
effective prestrains are provided for seven days after prestressing and show an average
loss of 2.5 ±1.1%. The beams were initially loaded and cracked after strengthening; the
118
obtained cracking loads show significant enhancement in cracking strength (up to 153%
for the beams strengthened with prestressed NSM CFRP strips and up to 177% for the
beams strengthened with prestressed NSM CFRP rebars) due to prestressing with respect
to the non-prestressed strengthened beam of each group. The un-strengthened control
beams showed a low cracking load which is due to presence of the micro-cracks in the
large-scale beams before testing, mainly caused from moving the beams during the
testing process. In fact, the cracking load of the un-strengthened control beam should
have been close to that of the non-prestressed strengthened beam. The beams
strengthened with CFRP strips (BS-NP-F, BS-P1-F, and BS-P2-F) showed higher value
of cracking loads (ranging from 5-16%) than the corresponding beams strengthened with
CFRP rebars while beam BS-P3-F showed smaller value of cracking loads than beam
BR-P3-F by 2%. This behaviour is mainly due to difference in concrete compressive
strength of the two sets of the beams (the average of the concrete cylinder compressive
strengths for the beams strengthened with CFRP strip and the beams strengthened with
CFRP rebars at the time of initial cracking are presented in Table C-1).
The permanent deflections in the beams dafter initial loading, as described in
Section 3.5, recorded at 0.5 hr after termination of each test for initial cracking, are
presented in Table 4-2, which are the start points of the load-deflection curves plotted in
Figure 4-1.
4.2.2.2 Post-Cracking Behaviour
Comparing the un-strengthened control RC beam B0-F with the non-prestressed
strengthened RC beams, BS-NP-F and BR-NP-F, shows that the flexural performance of
119
these beams is similar before yielding of the un-strengthened control RC beam. The
results reveals that although strengthening the RC beams using non-prestressed NSM
CFRP rebars or strips enhances the flexural performance by improving the yield and
ultimate loads, and stiffness of the beam in the plastic domain (after yielding of tension
steel bars), but has insignificant effects on the flexural performance in the elastic domain
(before yielding of the tension steel bars). Besides, comparing the results of beams
strengthened with prestressed NSM CFRP strips and rebars (BS-P1-F, BR-P1-F, BS-P2-
F, BR-P2-F, BS-P3-F, and BR-P3-F) with beams strengthened with non-prestressed NSM
CFRP strips and rebar (BS-NP-F and BR-NP-F) shows that strengthening using
prestressed NSM CFRP rebars or strips enhances the flexural performance at every
domain. In fact, strengthening RC beams using prestressed NSM CFRP reinforcement
enhanced the serviceability performance of the RC beam by postponing the formation of
flexural cracks, decreasing the crack width, delaying yielding, and increasing further the
ultimate strength of the beam through changing the mode of failure from concrete
crushing to CFRP rupture.
Analyzing the results reveals that up to 64% and 66% increase in yielding load of
the strengthened beam with CFRP strips and rebar, respectively, were achieved with
respect to the un-strengthened control RC beam, as presented in Table 4-2; in which 22%
out of 64% and 21% out of 66% are related to increase due to strengthening and the rest
(which are 42% and 45%) are due to prestressing effect. Besides, up to 53% and 61%
increase in ultimate load of the strengthened beam with CFRP strips and rebar were
recorded; in which 35% out of 61% and 53% are reached by strengthening with non-
prestressed CFRP reinforcement and the remaining is due to prestressing effect. As
120
expected, this behaviour shows more contribution of the prestressing in enhancing of the
yielding load than the ultimate load.
4.2.2.3 Failure Mode and Cracking Pattern
The failure mode of each beam is marked on the curves in Figure 4-1 and shown
in Figure 4-3 to Figure 4-11. The un-strengthened control RC beam (B0-F) failed due to
concrete crushing that occurred between two point loads after steel yielding, as shown in
Figure 4-3. The fluctuations in the load-deflection curve after yielding are due to
occurrence of major flexural cracks in the beam. These cracks got wider as the load
increased further and lead to a large ultimate deflection at mid-span of the beam.
The non-prestressed strengthened RC beams (BS-NP-F and BR-NP-F)
experienced similar behaviour. Debonding at the concrete-epoxy interface initiated from
the point load locations at the deflections and corresponding loads of 71 mm and 121 kN
for beam BS-NP-F and 76 mm and 124 kN for beam BR-NP-F, and propagated towards
the supports as the load applied further before reaching the peak load. These longitudinal
debonding cracks at the concrete-epoxy interface caused a slight decrease in the load-
deflection slopes. The fluctuations in the load-deflection curves are the result of large
flexural cracks’ openings and debonding cracks. For these two beams (BS-NP-F and BR-
NP-F), the failure happened due to concrete crushing between one of the point loads and
mid-span. No further increase in the load was observed while the test continued, and
complete debonding of the NSM-CFRP rebar and strips from concrete substrate occurred.
At this point, the force in the CFRP reinforcement was completely transferred to the end
anchors and complete failure (the last drop in the load-deflection curves) occurred due to
121
end anchor separation from the concrete. Images of the beams BS-NP-F and BR-NP-F at
failure are presented in Figure 4-4 and Figure 4-5, respectively.
Beams BS-P1-F and BR-P1-F, strengthened using prestressed NSM CFRP strips
and rebar with prestress levels of 17% and 15%, respectively, failed due to concrete
crushing but a difference was observed at the ultimate stage of the two load-deflection
curves, as shown in Figure 4-1, mainly caused by the difference in the ultimate tensile
strain of the CFRP rebar and strip presented in Table 4-1. Photos of beams BS-P1-F and
BR-P1-F at failure are presented in Figure 4-6 and Figure 4-7, respectively. For beam
BS-P1-F, concrete crushing started between one of the point load and mid-span at a
deflection and corresponding load of 70.6 mm and 130.6 kN that caused a small drop in
the load-deflection curve. As the load increased further, longitudinal debonding cracks
formed at the concrete-epoxy interface at location of the point load at a deflection and
corresponding load of 79 mm and 133 kN. The test continued and the failure occurred
due to concrete crushing at mid-span region between the two point loads as shown in
Figure 4-6. Afterwards, no future increase in the load was recorded, and finally the CFRP
strips ruptured causing a large drop in the load value. For beam BR-P1-F, debonding
cracks started at concrete-epoxy interface at the point load location at deflection and
corresponding load of 78 mm and 138.8 kN. The concrete crushing occurred between the
point load and mid-span at a load and corresponding deflection of 147.4 kN and 95.9 mm
and then the load dropped to 141.4 kN. The test continued and an increase in the load was
observed; thereafter, the beam failed due to concrete crushing between two point loads at
a load of 147.5 kN and a corresponding deflection of 107.6 mm. No more increase in the
load was recorded after this point and by continuing the test, the CFRP rebar ruptured.
122
Beam BS-P2-F, strengthened using prestressed NSM CFRP strips with prestress
level of 33%, failed due to rupture of the CFRP strips as shown in Figure 4-8; and beam
BR-P2-F, strengthened using prestressed NSM CFRP rebar with prestress level of 26%),
failed due to concrete crushing followed by rupture of the CFRP rebar as shown in Figure
4-9. The failure of beam BR-P2-F was very close to balanced failure condition, since the
CFRP rebar almost ruptured simultaneously with concrete crushing. The differences at
ultimate deflection, ultimate load, and type of failure of beams BR-P2-F and BS-P2-F are
due to the difference between material properties of the CFRP rebar and strip at ultimate
as presented in Table 4-1. Longitudinal debonding cracks at the concrete-epoxy interface
were observed during the test at the point load locations initiated from the deflections and
corresponding loads of 70 mm and 141.6 kN and 82 mm and 149.8 kN for beams BS-P2-
F and BR-P2-F, respectively.
Beams BS-P3-F and BR-P3-F, strengthened using prestressed NSM CFRP strips
and rebar with high prestress levels of 48% and 41%, respectively, failed due to CFRP
rupture at mid-span after tension steel yielding as shown in Figure 4-10 and Figure 4-11,
respectively. The small fluctuations in the load-deflection curves after yielding are due to
formation of flexural cracks at mid-span. No sign of debonding was observed up to CFRP
rupture. After rupture, the load dropped and the behaviour was similar to that of the un-
strengthened control beam.
Comparison between the initiation of debonding cracks at concrete-epoxy
interface for RC beams strengthened with non-prestressed and prestressed NSM-CFRP
strips or rebar, as presented in earlier discussion in this section, demonstrates that these
cracks are almost initiated simultaneously. Therefore, it can be concluded from the results
123
that at a constant beam’s deflection, a combination of interfacial stresses, interfacial slip,
and interfacial gap leads to total dissipation of the fracture energy of the interface, and the
value of this deflection is independent from induced prestressing level in the CFRP rebar
or strips.
(a) Side view of the beam
(b) The other side view of the beam
(c) Bottom view of the beam
Figure 4-3: Photos of beam B0-F at failure.
Concrete crushing
Concrete crushing
124
(a) Side view of the beam
(b) The other side view of the beam
(c) Bottom view of the beam
(d) End of the beam close to the support (e) Bottom view at the end of the beam
Figure 4-4: Photos of beam BS-NP-F at failure.
End anchor separation: secondary failure
Concrete crushing
Concrete crushing
125
(a) Side view of the beam
(b) The other side view of the beam
(c) Bottom view of the beam
(d) Side view at end anchor (e) Bottom view at end anchor (f) Anchor seperation
Figure 4-5: Photos of beam BR-NP-F at failure.
End anchor separation: secondary failure
Concrete crushing
Concrete crushing
126
(a) Bottom view showing debonding cracks at concrete-epoxy interface
(b) Side view of the beam
(c) The other side view of the beam
(d) Bottom view of the beam
Figure 4-6: Photos of beam BS-P1-F at failure.
Concrete crushing
Concrete crushing
127
(a) Side view of the beam
(b) The other side view of the beam
(c) Bottom view of the beam
(d) Bottom view of the beam showing debonding cracks at concrete-epoxy interface
Figure 4-7: Photos of beam BR-P1-F at failure.
Concrete crushing
Concrete crushing
128
(a) Side view of the beam
(b) The other side view of the beam
(c) Bottom view of the beam
(d) Bottom view showing debonding cracks (e) Bottom view at CFRP rupture
Figure 4-8: Photos of beam BS-P2-F at failure.
CFRP rupture
129
(a) Side view of the beam
(b) The other side view of the beam
(c) Bottom view of the beam
(d) Top view of the beam showing concrete crushing
Figure 4-9: Photos of beam BR-P2-F at failure.
Concrete crushing
Concrete crushing
130
(a) Side view of the beam
(b) The other side view of the beam
(c) Bottom view of the beam
(d) Bottom view of the beam showing the CFRP rupture
Figure 4-10: Photos of beam BS-P3-F at failure.
Location of the CFRP rupture
131
(a) Side view of the beam
(b) The other side view of the beam
(c) Bottom view of the beam
Figure 4-11: Photos of beam BR-P3-F at failure.
4.2.3 Load-Strain Response
In this section, a comparison is performed between the load-strain relations of the
beams strengthened with CFRP rebar versus similar beams strengthened with CFRP
strips. The relation between the load and strains in the CFRP strips or rebar, tension steel,
compression steel, and the extreme compression fibre of concrete at mid-span location
Location of the CFRP rupture
132
are presented in Figure 4-12 to Figure 4-15. For all tested beams, the compression steel
strain almost showed linear elastic behaviour up to failure. The load-strain relation for the
concrete at extreme compression fibre, tension steel, and CFRP strips or rebar consists of
three stages: from start of the test to concrete cracking in tension, from concrete cracking
to yielding of tension steel, and from yielding of tension steel to failure by either concrete
or CFRP rupture. From start of the test up to the concrete cracking in tension, the load-
strain relation is linear, the flexural stiffness of the beam decreases after cracking causing
a reduction in the load-strain slope, however, the relation remains linear up to yielding of
the tension steel. Yielding of the tension steel causes a significant reduction in flexural
stiffness of the beam leading to a decrease in the slope of the load-strain curves.
Afterwards, the curve reaches a point in which CFRP rupture or concrete crushing
occurs. It should be mentioned that the load-steel strain curves were calculated based on
the LSCs installed on the side of the concrete beam at the level of the longitudinal tension
steel because the strain gauges on the steel reinforcements were damaged after yielding,
and therefore, no yielding plateau is observed in the plotted curves.
Strain values in the concrete, top steel, bottom steel, and CFRP at different stages
are presented in Table 4-3. Due to prestressing, top steel and top concrete goes to tension
while the bottom steel goes to compression means the neutral axis is somewhere between
top and bottom steel; these strain values are very small and cannot be visible in the
curves.
Comparison between the strain values of the strengthened RC beams using NSM
CFRP rebar versus strengthened beams using NSM CFRP strips shows similar behaviour
of these two sets at different stages, it should be mentioned that the difference at ultimate
133
stage in Figure 4-13 to Figure 4-15 is due to different ultimate tensile strain of the CFRP
rebar and strip, as presented in Table 4-1. However, the difference at ultimate stage does
not exist in Figure 4-12 because both beams, BS-NP-F and BR-NP-F, failed due to
concrete crushing and are not affected by the difference of the CFRP ultimate tensile
strain. The loads versus strain values in the CFRP rebars and strips are compared in
Figure 4-16 for all strengthened beams; the strains are plotted including permanent values
after initial loading described in Section 3.5, showing a minor difference at zero loads
which is caused by: the losses, the initial loading, and the applied strain at prestressing.
The load-strain relation for the CFRP rebar shows stiffer behaviour than that for CFRP
strips. The sudden increase in strain at constant load, which is observed for CFRP strain
of beams BS-P2-F and BS-P3-F is most likely a local effect caused by the major cracks
close to the mid-span or less likely detachment of the two bonded CFRP strips from each
other. This behaviour was not observed in beams BS-P1-F and BS-P2-F (strengthened
using NSM CFRP strips with low prestress level of 17% and 33%, respectively), and also
in the beams strengthened with NSM CFRP rebar. The curves show the same stiffness
after yielding at the plastic range. The concrete strains at top extreme fibre and the strains
in tension steel reinforcements are compared in Figure 4-17 and Figure 4-21,
respectively, for all beams. The results show that the load-strain behaviour of the beams
strengthened using NSM CFRP strips is similar to the corresponding beams strengthened
using NSM CFRP rebars except at ultimate state. In this regards, the difference at
ultimate is mainly due to different mode of failure. On the other hand, although the
instrumentation was performed at mid-span but the location of the concrete crushing
might not be the same to capture the maximum strain reached at failure; this fact results
134
in underestimation of the actual concrete compressive strain and tension steel strain at
failure. The strains in the compression steel reinforcements are compared in Figure 4-19
for all beams. In this figure, the load-strain curve for beam BS-P1-F is calculated based
on the LSCs installed at the compression steel levels since the strain gauges installed on
the compression steel were damaged for this beam, however, the rest of the curves are
plotted based on the reading from strain gauges installed on the compression steel at mid-
span. It can be seen in Figure 4-19 that the load-strain is not perfectly linear. For beams
B0-F, BS-NP-F, BR-NP-F, BS-P1-F, and BS-P2-F, the strain in compression steel
decreases prior to failure; this is due to local buckling of the compression steel at mid-
span location after start of the concrete crushing as shown in Figure 4-20. The occurrence
of the slip between the epoxy and concrete can be identified by changing the slope of the
load-strain curve for bottom steel and CFRP. Comparison between the slope of the curves
related to bottom steel and CFRP at elastic and plastic ranges shows that slip between
concrete and CFRP rebar or strip is insignificant.
135
0
20
40
60
80
100
120
140
160
-0.005 0 0.005 0.01 0.015 0.02 0.025
Lo
ad
(k
N)
Strain at mid-span
BS-NP-F, Concrete Strain
BS-NP-F, Top Steel Strain
BS-NP-F, Bottom Steel Strain
BS-NP-F, CFRP Strain
BR-NP-F, Concrete Strain
BR-NP-F, Top Steel Strain
BR-NP-F, Bottom Steel Strain
BR-NP-F, CFRP StrainTensionCompression
Ultimate load of BR-NP-F= 132.3 kNUltimate load of BS-NP-F= 132.2 kN
Figure 4-12: Load-strain curves: BS-NP-F vs BR-NP-F.
0
20
40
60
80
100
120
140
160
-0.005 0 0.005 0.01 0.015 0.02 0.025
Lo
ad
(k
N)
Strain at mid-span
BS-P1-F, Concrete Strain
BS-P1-F, Top Steel Strain
BS-P1-F, Bottom Steel Strain
BS-P1-F, CFRP Strain
BR-P1-F, Concrete Strain
BR-P1-F, Top Steel Strain
BR-P1-F, Bottom Steel Strain
BR-P1-F, CFRP Strain
TensionCompression
Ultimate load of BS-P1-F= 134.7 kN
Ultimate load of BR-P1-F= 147.5 kN
Figure 4-13: Load-strain curves: BS-P1-F vs BR-P1-F.
136
0
20
40
60
80
100
120
140
160
-0.005 0 0.005 0.01 0.015 0.02 0.025
Lo
ad
(k
N)
Strain at mid-span
BS-P2-F, Concrete Strain
BS-P2-F, Top Steel Strain
BS-P2-F, Bottom Steel Strain
BS-P2-F, CFRP Strain
BR-P2-F, Concrete Strain
BR-P2-F, Top Steel Strain
BR-P2-F, Bottom Steel Strain
BR-P2-F, CFRP Strain
TensionCompression
Ultimate load of BS-P2-F= 149.5 kN
Ultimate load of BR-P2-F= 157.5 kN
Figure 4-14: Load-strain curves: BS-P2-F vs BR-P2-F.
0
20
40
60
80
100
120
140
160
-0.005 0 0.005 0.01 0.015 0.02 0.025
Lo
ad
(k
N)
Strain at mid-span
BS-P3-F, Concrete Strain
BS-P3-F, Top Steel Strain
BS-P3-F, Bottom Steel Strain
BS-P3-F, CFRP Strain
BR-P3-F, Concrete Strain
BR-P3-F, Top Steel Strain
BR-P3-F, Bottom Steel Strain
BR-P3-F, CFRP StrainTensionCompression
Ultimate load of BS-P3-F= 141.7 kN
Ultimate load of BR-P3-F= 157.5 kN
Figure 4-15: Load-strain curves: BS-P3-F vs BR-P3-F.
137
0
20
40
60
80
100
120
140
160
0 0.005 0.01 0.015 0.02 0.025
Lo
ad
(k
N)
Strain in CFRP strip or rebar at mid-span
BS-NP-F BS-P1-F BS-P2-F BS-P3-F
BR-NP-F BR-P1-F BR-P2-F BR-P3-F
Figure 4-16: Load-CFRP strain curves for all beams.
0
20
40
60
80
100
120
140
160
-0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0
Lo
ad
(k
N)
Concrete strain in extreme compression fiber at mid-span
BS-NP-F BS-P1-F BS-P2-F BS-P3-F B0-F
BR-NP-F BR-P1-F BR-P2-F BR-P3-F
Figure 4-17: Load-concrete strain curves for all beams.
138
0
20
40
60
80
100
120
140
160
-0.0005 0.003 0.0065 0.01 0.0135 0.017 0.0205 0.024
Lo
ad
(k
N)
Strain in tension steel at mid-span (mm)
BS-NP-F BS-P1-F BS-P2-F BS-P3-F B0-F
BR-NP-F BR-P1-F BR-P2-F BR-P3-F
Figure 4-18: Load-tension steel strain curves for all beams.
0
20
40
60
80
100
120
140
160
-0.0014 -0.001 -0.0006 -0.0002 0.0002
Lo
ad
(k
N)
Strain in compression steel at mid-span (mm)
BS-NP-F BS-P1-F BS-P2-F BS-P3-F B0-F
BR-NP-F BR-P1-F BR-P2-F BR-P3-F
Figure 4-19: Load-compression steel strain curves for all beams.
139
Figure 4-20: Local buckling of compression steel bars at mid-span of beam B0-F.
Table 4-3: Strain in CFRP strips or rebar, extreme compression fibre of concrete,
compression steel, and tension steel at mid-span at different stages.
Beam ID ɛf-i
(µɛ)
ɛf-7days
(µɛ)
ɛf-cr
(µɛ)
ɛc-i
(µɛ)
ɛc-7days
(µɛ)
ɛc-cr
(µɛ)
ɛsc-i
(µɛ)
ɛsc-7days
(µɛ)
ɛsc-cr
(µɛ)
ɛst-i
(µɛ)
ɛst-7days
(µɛ)
ɛst-cr
(µɛ)
B0-F N.A. N.A. N.A. N.A. N.A. -100 N.A. N.A. -54 N.A. N.A. 23
BS-NP-F 0 0 110 N.A. N.A. -50 N.A. N.A. -26 N.A. N.A. 103
BS-P1-F 3574 3463 3522 0 0 -25 15 16 -10 -39 -46 59
BS-P2-F 6900 6723 6749 50 125 100 33 32 16 -79 -97 -64
BS-P3-F 10112 9884 9968 75 100 125 53 62 46 -118 -129 -108
BR-NP-F 0 0 76 N.A. N.A. 0 N.A. N.A. -24 N.A. N.A. 91
BR-P1-F 3801 3662 3234 25 50 0 15 67 50 -39 -87 6
BR-P2-F 6585 6548 6521 50 75 25 30 37 13 -66 -117 -60
BR-P3-F 10272 9950 9971 100 125 75 50 28 6 -124 -183 -162
ɛf-i, ɛc-i, ɛsc-i, and ɛst-i = initial prestrain in CFRP strips or rebar, extreme concrete fibre at top, top steel and
bottom steel due to prestressing
ɛf-7days, ɛc-7days, ɛsc-7days, and ɛst-7days = strain in CFRP strips or rebar, extreme concrete fibre at top, top steel and
bottom steel at 7 days after prestressing
ɛf-cr, ɛc-cr, ɛsc-cr, and ɛst-cr = strain in CFRP strips or rebar, extreme concrete fibre at top, top steel, and bottom
steel after cracking (initial loading presented in Section 3.5)
Strain gauges on compression steel bars at mid-span
Buckled compression steel bars
140
4.2.4 Strain Profile along the CFRP Strips or Rebar
The strain profiles along the length of the NSM CFRP strip versus the NSM
CFRP rebar at cracking, yielding, and ultimate loads are presented in Figure 4-21 to
Figure 4-23, respectively. The profiles are plotted based on the reading of strains from the
installed strain gauges at specified locations on the CFRP reinforcements. For beam BS-
NP-F and BR-NP-F the strains are close to zero at the ends of the CFRP strip or rebar at
different load levels (as shown in Figure 4-21 to Figure 4-23). This implies the presence
of the full bonding at the end and also complete contribution of the epoxy adhesive in
transferring the forces between the CFRP rebar or strip and the surrounding concrete. On
the other hand, the presence of the end anchors bolted to the concrete at both ends of the
CFRP strips/rebar helps in transferring the load to the beam after occurrence of
debonding at the concrete-epoxy interfaces, which results in a more effective
strengthening method. Furthermore, these anchors avoid initiation of the debonding
cracks at concrete-epoxy interface at the end portions of the NSM CFRP rebar or strip
where highly affected by interfacial stress concentration. In fact, the end anchors have
partial contribution in transferring the load from the NSM CFRP to the concrete before
occurrence of debonding and complete contribution in transferring the load from the
NSM CFRP to the concrete after occurrence of debonding. Therefore, it is very important
that during the prestressing process, i.e., after removing the temporary brackets, that the
end anchors are in contact with the bolts and there is no gap between them.
In Figure 4-21, except for beam BR-P1-F, the drop in strain at length 4350 mm is
a result of small slippage after removing the brackets and transferring the prestressing
force to the steel end anchor; this value of loss at the end location increases when
141
prestressing level increases, but it affects a very short length (100-200 mm) and can be
avoided by making sure that the anchor is in complete contact with bolts before removing
the brackets. In cases where there is a gap, it can be filled with epoxy to minimize the
possible slippage. A very good correlation at cracking is observed between CFRP strip
profiles in comparison with CFRP rebar profiles. The sudden increase in strain level that
can be seen in Figure 4-21 at location 2000 mm (point load location of the beams) for
beams BR-P1-F and BR-P2-F is most likely a local effect caused by formation of the
cracks under the point load. As can be seen in Figure 4-22 as well as Figure 4-23, these
sudden increases get larger as the load applied further up to yielding and the cracks under
the point load get wider.
Comparison between Figure 4-21, Figure 4-22, and Figure 4-23 reveals that as the
load increases further, more fluctuations occur in the strain profile since new cracks form
in the beams. In Figure 4-22, ignoring the sudden increase in the profiles, the strain
profile values for CFRP rebar are smaller than the corresponding profile values for CFRP
strips while, as presented in Table 4-2, the corresponding beams have similar yielding
load. This is most likely due to the reason that the axial stiffness (EfAf where Ef is the
modulus of elasticity and Af is the total cross-sectional area) of the CFRP rebar, based on
Table 4-1, is 6.5% larger than the axial stiffness of the CFRP strips, which leads to
smaller strain in CFRP rebar versus the CFRP strips for the corresponding beams under
similar load. In Figure 4-23, at ultimate load, the strain values of CFRP strips at constant
moment regions are smaller than those from CFRP rebars due to higher strain capacity of
the CFRP rebars versus CFRP strips. For all beams, the highest strain in CFRP strip or
rebar is observed at constant moment region of the beams (location 2000-3000 mm).
142
Comparison between Figure 4-21, Figure 4-22, and Figure 4-23 at locations 650
mm and 4350 mm for each beam reveals that the strain at both ends near the end anchors
remained almost constant during the static test showing no slippage at the ends of the
CFRP rebar/strips and appropriate performance of the epoxy in transferring the forces.
0
0.003
0.006
0.009
0.012
0 1000 2000 3000 4000 5000Str
ain
in
CF
RP
str
ips
or
reb
ar
at
cra
ck
ing
Distance from the support (mm)
BS-NP-F BS-P1-F BS-P2-F BS-P3-F
BR-NP-F BR-P1-F BR-P2-F BR-P3-F
Figure 4-21: Strain profile along the length of the CFRP strips or rebar at cracking.
143
0
0.003
0.006
0.009
0.012
0.015
0 1000 2000 3000 4000 5000Str
ain
in
CF
RP
str
ips
or
reb
ar
at
yie
ldin
g
Distance from the support (mm)
BS-NP-F BS-P1-F BS-P2-F BS-P3-F
BR-NP-F BR-P1-F BR-P2-F BR-P3-F
Figure 4-22: Strain profile along the length of the CFRP strips or rebar at yielding.
0
0.005
0.01
0.015
0.02
0.025
0.03
0 1000 2000 3000 4000 5000Str
ain
in
CF
RP
str
ips
or
reb
ar
at
ult
ima
te
Distance from the support (mm)
BS-NP-F BS-P1-F BS-P2-F BS-P3-F
BR-NP-F BR-P1-F BR-P2-F BR-P3-F
Figure 4-23: Strain profile along the length of the CFRP strips or rebar at ultimate.
144
4.2.5 Strain Distribution at Mid-span
The strain distributions at mid-span section along the depth of the beams at
cracking, yielding, and ultimate loads are presented in Figure 4-24 to Figure 4-26 and
Table 4-4. Each strain distribution is plotted using the strain values in concrete,
compression steel, tension steel, and CFRP rebar or strip including the strain due to
prestressing.
The strain distribution from the extreme concrete compression fibre to the
centroid of the bottom steel (along effective depth of the beam) is linear at cracking, as
shown in Figure 4-24(a) and (b). The increases in the CFRP strains are due to
prestressing. At cracking stage, the curvature at mid-span (which is defined as the slope
of the strain distribution along the effective depth) is the highest for the un-strengthened
control RC beam and as the prestressing level increases the curvature decreases. Similar
behaviour is observed for the RC beams strengthened with NSM CFRP rebar and NSM
CFRP strip.
At yielding, strain distributions are nonlinear. The nonlinearity is caused by
concrete material behaviour and can be observed in top portion of the plots in Figure
4-25(a) and (b). In tension zone, the distribution excluding the prestrain in the CFRP
reinforcements is almost linear as can be seen for beams BS-NP-F and BR-NP-F, which
don’t have the increase in the CFRP strain due to prestressing.
At ultimate, the strain distribution is nonlinear. The un-strengthened control RC
beam, B0-F, showed a very high curvature in comparison with the other beams. By
comparing the slope of the strain distribution between steel level and the CFRP level at
yielding and ultimate loads the occurrence of debonding at mid-span can be identified.
145
During the test, debonding was observed at mid-span regions at concrete-epoxy interface.
The occurrence of the slip between the epoxy and concrete at mid-span can be identified
if there is any difference in the slope of the strain distribution from tension steel level to
CFRP level at yielding stage in comparison with the one at ultimate stage. Therefore,
analyzing the results reveal that beams BS-NP-F, BS-P1-F, BR-NP-F, and BR-P1-F
showed debonding signs at mid-span. These outcomes from the strain distributions are in
accordance with the observations during the test.
146
-400
-350
-300
-250
-200
-150
-100
-50
0
-0.0005 0.002 0.0045 0.007 0.0095 0.012
Se
cti
on
de
pth
(m
m)
Strain at cracking
B0-F BS-NP-F BS-P1-F BS-P2-F BS-P3-F
Bottom steel centroid @ 343 mm
NSM CFRP strips centroid @ 387.5 mm
Top steel centroid @ 35 mm
Top fibres of the beam
(a) Un-strengthened beam and strengthened beams using NSM CFRP strips
-400
-350
-300
-250
-200
-150
-100
-50
0
-0.0005 0.002 0.0045 0.007 0.0095 0.012
Se
cti
on
de
pth
(m
m)
Strain at cracking
B0-F BR-NP-F BR-P1-F BR-P2-F BR-P3-F
Bottom steel centroid @ 343 mm
NSM CFRP rebar centroid @ 387.5 mm
Top steel centroid @ 35 mm
Top fibres of the beam
(b) Un-strengthened beam and strengthened beams using NSM CFRP rebar
Figure 4-24: Strain distribution at mid-span at cracking.
36
36
147
-400
-350
-300
-250
-200
-150
-100
-50
0
-0.002 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
Se
cti
on
de
pth
(m
m)
Strain at yielding
B0-F BS-NP-F BS-P1-F BS-P2-F BS-P3-F
Bottom steel centroid @ 343 mm
NSM CFRP strips centroid @ 387.5 mm
Top steel centroid @ 35 mm
Top fibres of the beam
(a) Un-strengthened beam and strengthened beams using NSM CFRP strips
-400
-350
-300
-250
-200
-150
-100
-50
0
-0.002 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
Se
cti
on
de
pth
(m
m)
Strain at yielding
B0-F BR-NP-F BR-P1-F BR-P2-F BR-P3-F
Bottom steel centroid @ 343 mm
NSM CFRP rebar centroid @ 387.5 mm
Top steel centroid @ 35 mm
Top fibres of the beam
(b) Un-strengthened beam and strengthened beams using NSM CFRP rebar
Figure 4-25: Strain distribution at mid-span at yielding.
36
36
148
-400
-350
-300
-250
-200
-150
-100
-50
0
-0.006 0 0.006 0.012 0.018 0.024 0.03
Se
cti
on
de
pth
(m
m)
Strain at ultimate
B0-F BS-NP-F BS-P1-F BS-P2-F BS-P3-F
Bottom steel centroid @ 343 mm
NSM CFRP strips centroid @ 387.5 mm
Top steel centroid @ 35 mm
Top fibres of the beam
(a) Un-strengthened beam and strengthened beams using NSM CFRP strips
-400
-350
-300
-250
-200
-150
-100
-50
0
-0.006 0 0.006 0.012 0.018 0.024 0.03
Se
cti
on
de
pth
(m
m)
Strain at ultimate
B0-F BR-NP-F BR-P1-F BR-P2-F BR-P3-F
Bottom steel centroid @ 343 mm
NSM CFRP rebar centroid @ 387.5 mm
Top steel centroid @ 35 mm
Top fibres of the beam
(b) Un-strengthened beam and strengthened beams using NSM CFRP rebar
Figure 4-26: Strain distribution at mid-span at ultimate.
36
36
149
Table 4-4: Strain in extreme compression fibre of concrete, compression steel,
tension steel, and CFRP strips or rebar at mid-span.
Beam ID ɛc-cr
(µɛ)
ɛsc-cr
(µɛ)
ɛst-cr
(µɛ)
ɛf-cr
(µɛ)
ɛc-y
(µɛ)
ɛsc-y
(µɛ)
ɛst-y
(µɛ)
ɛf-y
(µɛ)
ɛc-u
(µɛ)
ɛsc-u
(µɛ)
ɛst-u
(µɛ)
ɛf-u
(µɛ)
B0-F -250 -147 261 N.A. -1200 -696 1951 N.A. -5625 -250 22650 N.A.
BS-NP-F -150 -92 106 133 -1150 -563 2428 3131 -3325 -370 14475 14899
BS-P1-F -175 -116 121 3504 -1125 -600 2549 7002 -2475 -675 12161 16592
BS-P2-F -100 -130 34 6889 -1175 -745 2678 10332 -3050 -762 13325 21464
BS-P3-F -100 -161 53 10175 -1425 -808 2620 14246 -2750 -886 10300 21118
BR-NP-F -100 -86 87 48 -1050 -583 2465 2719 -3425 -301 11650 14599
BR-P1-F -75 -27 32 3297 -1275 -700 2500 6014 -4125 -1350 9875 22067
BR-P2-F -125 -117 5 6631 -1150 -787 2496 9212 -3250 -987 10500 23879
BR-P3-F -150 -173 -20 10156 -1350 -535 2231 13010 -3450 -598 12400 24247
ɛc = strain in extreme compression fibre of concrete (compression is negative value) cr = at cracking
ɛst = strain in tension steel y = at yielding
ɛsc = strain in compression steel u = at ultimate
ɛf = strain in CFRP rebar or strips
4.3 Effects of CFRP Geometry: Rebar versus Strips
Comparison between the results of the beams strengthened using NSM method
with sand coated CFRP rebar versus rough textured CFRP strips shows that the flexural
behaviour (load-deflection curve) is similar prior to the ultimate stage. At the ultimate
stage the behaviour depends on three items: concrete material property, CFRP ultimate
strain, and debonding. Two types of failure modes were observed in the experiments:
concrete crushing and CFRP rupture. Beams BS-NP-F and BR-NP-F showed similar
behaviour that confirms there is almost no difference at the load-deflection curves of the
beams strengthened with non-prestressed NSM CFRP rebar versus strips. The other
beams did not show such similar behaviour at ultimate stage due to difference in the
material properties of exposed concrete and CFRP reinforcement in the BS-F set versus
the BR-F set in phase I. The difference between the NSM strengthened beam using CFRP
strip and rebar is more obvious in bond performance and crack pattern than the overall
150
flexural performance. Due to the difference in geometry of the CFRP (rebars versus
strips), groove width (20 mm for the rebar and 16 mm for the strips), and therefore,
distribution of stresses in the groove, the crack pattern in the beams strengthened using
CFRP rebar is different than the beam with CFRP strips as shown in Figure 4-27 for all
strengthened beams at failure. The beams strengthened with sand coated CFRP rebar
showed less damage to bond than the beams strengthened with rough textured CFRP
strips at any specified deflection and at failure as well based on observation during the
tests, e.g., see BR-P2-F and BS-P2-F in Figure 4-27. Furthermore, the CFRP strip or
rebar rupture is accompanied by a loud sound during the test. In the case of the CFRP
rebar, the location of rupture is not visible and the epoxy should be removed to see the
CFRP rebar rupture; this behaviour does not occur in the case of CFRP strip rupture.
BS-NP-F
BR-NP-F
Figure 4-27: Damage done to the non-prestressed NSM CFRP strengthened beams
at failure (bottom view).
151
BS-P1-F
BR-P1-F
BS-P2-F
BR-P2-F
BS-P3-F
BR-P3-F
Figure 4-27: Damage done to the prestressed NSM CFRP strengthened beams at
failure (bottom view) (Cont’d).
152
4.4 Calculation of Optimum and Beneficial Prestressing Levels
In this section, two practical concepts are defined and analyzed, the optimum
prestressing level and the beneficial prestressing level. A procedure is illustrated to
achieve an optimum prestressing level in the NSM CFRP reinforcements (taken as a
percentage of the ultimate tensile strength of the CFRP reinforcements) which enhances
the beam performance under service and ultimate states by maintaining the amount of
energy absorption (area under the load-deflection curve up to the peak load) in the
strengthened beam equal to the un-strengthened control beam. A procedure to determine
the optimum prestressing level (intersection of the energy absorption curve of the
strengthened beams with the un-strengthened beam) is plotted in Figure 4-28. The energy
absorption is calculated up to different load levels: (a) up to the peak load, (b) up to 75%
of the post-peak load, and (c) up to the point that load-deflection curve of the
strengthened beam intersects with the un-strengthened one (B0-F). When the beam fails
due to concrete crushing, the amounts of energy absorption calculated by methods (a),
(b), and (c) result in different values. In this case, methods (b) and (c) are more
appropriate, which avoid underestimation of the energy absorption of the beam. Method
(c) is slightly less conservative than (b). When the beam fails due to CFRP rupture, the
energy values achieved by the different methods are almost the same; this behaviour is
observed in Figure 4-28 by comparing the last two prestressing levels (33 and 48%)
versus the first two (0 and 17%) for beams strengthened with CFRP strips (in BS set),
and furthermore, by comparing the last prestressing level (41%) with the first three
prestressing levels (0, 15, and 26%) for beams strengthened with CFRP rebars (in BR
set).
153
0
3000
6000
9000
12000
15000
18000
0 10 20 30 40 50Are
a u
nd
er
loa
d-d
efl
ec
tio
n c
urv
e (
kN
.mm
)
Prestressing level (% of CFRP tensile strength)
Energy up to intersection with B0-F, BS-F set Energy up to intersection with B0-F, BR-F set
Energy up to 75% of post-peak load, BS-F set Energy up to 75% of post-peak load, BR-F set
Energy up to peak load, BS-F set Energy up to peak load, BR-F set
B0-F energy up to peak load
Figure 4-28: Effects of prestressing on energy absorption and calculation of
optimum prestressing level
Considering the case (b) or (c), and energy absorption of the un-strengthened
beam up to the peak load, the experimental results yield an optimum prestressing level of
27.5% (corresponding to strain value 0.005775 in CFRP strips) for beam strengthened
with CFRP strips versus 31.5% (corresponding to strain value 0.007875 in CFRP rebar)
for beam strengthened with CFRP rebar. These obtained optimum prestressing levels are
less than the maximum prestressing level allowed by the design codes; generally, if the
obtained optimum prestressing level is higher than the maximum prestressing level
allowed by the design codes, then the latter should be used in design. It should be
154
mentioned that the CFRP material creep-rupture stress limit should be considered as the
maximum prestressing level, which can be enforced for design purposes. A creep-rupture
stress limit of 65% of the ultimate tensile strength of the CFRP reinforcement is
recommended by CHBDC (CAN/CSA-S6-06, 2011).
The beneficial prestressing level is defined as a prestressing level which produces
the maximum improvement in energy absorption of the strengthened RC beam with
respect to the un-strengthened control RC beam. The concept of the improvement in
energy absorption with respect to the un-strengthened beam is demonstrated in Figure
4-29; which is the difference between the energy absorption of the strengthened and un-
strengthened beam calculated up to ultimate deflection of the strengthened beam. The
values of improvement in energy values for the beams in phase I are presented in Figure
4-30; by interpolating a polynomial curve for the three highest points corresponding to
each set of the beams (BS-F or BR-F as presented in Figure 4-30) a beneficial CFRP
prestrain values of 0.006603 (corresponding to prestressing level of 31.4% in CFRP
strips) for RC beams strengthened with CFRP strips and 0.006029 (corresponding to
prestressing level of 24.1% in CFRP rebar) for RC beams strengthened with CFRP rebar
are achieved.
155
Figure 4-29: Schematic for the concept of improvement in energy absorption.
y = -5.703796E+7(-0.014792+x)(0.002734+x)
y = -1.125482E+8(-0.012329+x)(-0.000878+x)
2000
3000
4000
5000
0 0.002 0.004 0.006 0.008 0.01
Imp
rove
me
nt
in e
ne
ry a
bs
orp
tio
n w
.r.t
B
0-F
(k
N.m
m)
Prestressing level (CFRP strain)
Energy additional to B0-F, BR-F set Energy additional to B0-F, BS-F set
Poly. (Energy additional to B0-F, BR-F set) Poly. (Energy additional to B0-F, BS-F set)
Figure 4-30: Calculation of the beneficial prestressing level.
156
4.5 Effects of Freeze-Thaw Cycling Exposure
In this section, the flexural behaviour of RC beams strengthened with non-
prestressed and prestressed NSM CFRP rebar and strips subjected to freeze-thaw cycling
exposure are compared to similar beams without any environmental exposure tested by
Gaafar (2007).
4.5.1 Material Properties of the Unexposed Beams
A summary of material properties of the unexposed beams are presented in this
section. More details can be found in Gaafar (2007) and El-Hacha and Gaafar (2011).
4.5.1.1 Steel Reinforcements
The tension and compression steel bars (3-15M and 2-10M) possessed yield
strengths of 475 MPa and 500 MPa, respectively, obtained from tension test.
4.5.1.2 CFRP Reinforcements
The material properties of the CFRP reinforcements are presented in Table 4-5.
Table 4-5: CFRP material properties for unexposed beams.
CFRP product
(surface treatment)
Dimension
(mm)
Afrp
(mm2)
Manufacturer Tension test
ffrpu
(MPa)
Efrp
(GPa) ɛfrpu
ffrpu
(MPa)
Efrp
(GPa) ɛfrpu
Aslan 500 CFRP tape
(Rough textured) 2×16 31.2 2068 124 0.017 2610
† 130.5
† 0.02
†
Aslan 200 CFRP rebar
(Sand coated) Ф9 65.2 2068 124 0.017 2167
†† 130
†† 0.0167
††
† Gaafar (2007)
†† El-Hacha and Gaafar (2011)
157
4.5.1.3 Concrete
Two concrete batches were used to cast the beams. The average compressive
strength of the concrete cylinders from both batches was 40±4.4 MPa.
4.5.1.4 Epoxy Adhesives
Two types of epoxy adhesives were used: Sikadur® 330 was used in the end
groove regions (around and inside the end anchors) which has an ultimate tensile strength
of 30 MPa and Sikadur®
30 was used to fill in the intermediate concrete groove regions
between the end anchors which has an ultimate tensile strength of 24.8 MPa (Sika, 2007a
and b).
4.5.1.5 Anchor Bolts
The anchor bolts were “carbon steel kwik bolt 3 expansion anchor” made of
carbon steel with nominal bolt diameter of 15.9 mm and steel shear strength of 54.4 kN
(Hilti, 2008). This bolt had a nominal ultimate shear capacity of 65 kN by providing an
embedment depth of 70 mm and enough edge distance in normal weight concrete with
compressive strength of 40 MPa (Hilti, 2008).
4.5.2 Error Analysis
An error analysis is performed based on the material properties of the exposed
and unexposed beams to measure the uncertainty of the comparison. The uncertainty in
this section is defined to find the relative difference produced by the axial stiffness and
strength of the components between two sets of the beams. It simply shows the validity of
158
the comparison and is not an exact amount of the difference between two sets for a
particular response. Finding the exact amount of the difference between two
corresponding beams for a particular type of the response, e.g. load-deflection curve,
requires calculation of the load-deflection curve for each beam analytically, and then,
obtaining the exact known difference between two beams at each level of the curve,
which is not the aim of this section. Therefore, four percentages of uncertainty are
obtained: up to yielding that considers the axial stiffness of the components of the beam,
from yielding up to failure, and at failure for concrete crushing and CFRP rupture, which
consider the strength and axial stiffness of the components. Since the load and deflection
can be derived using multiplication and division operations, therefore, the following
equations are employed to calculate uncertainty in comparison. The uncertainty up
yielding of the beam is calculated using Equation 4-1. Due to minor contribution of the
compression steel up to yielding of the beam, it is ignored in calculation of uncertainty up
to yielding. The uncertainty from yielding up to failure, and for CFRP rupture and
concrete crushing failure modes are calculated using Equation 4-2 to Equation 4-4,
respectively, with respect to the unexposed beams. The components of Equations 4-1 to
4-4 are calculated using Equations 4-5 to 4-11.
222100 cstfrp ssss Equation 4-1
2222100 cscstyfrp sssss Equation 4-2
2222100 cscstyfrpu sssss Equation 4-3
159
2222100 cuscstyfrpu sssss Equation 4-4
expunfrpfrp
expunfrpfrpexpfrpfrp
frpEA
EAEAs
Equation 4-5
expunstst
expunststexpstst
stEA
EAEAs
Equation 4-6
expuncc
expunccexpcc
cEA
EAEAs
Equation 4-7
expunytst
expunytstexpytst
styfA
fAfAs
Equation 4-8
expunfrpufrp
expunfrpffrpexpfrpufrp
frpufA
fAfAs
Equation 4-9
expunscsc
expunscscexpscsc
scEA
EAEAs
Equation 4-10
expuncc
expunccexpcc
cufA
fAfAs
Equation 4-11
where s is the percentage of uncertainty, sfrp the uncertainty due to axial stiffness of the
CFRP material, sst the uncertainty due to axial stiffness of the tension steel
reinforcements, sc the uncertainty due to axial stiffness of the concrete material, ssty the
uncertainty due to strength of the tension steel reinforcements, sfrpu the uncertainty due to
strength of the CFRP material, ssc the uncertainty due to axial stiffness of the
160
compression steel reinforcements, and scu is the uncertainty due to strength of the
concrete material. Also, AfrpEfrp is the axial stiffness of the CFRP material, AstEst the axial
stiffness of the tension steel reinforcements, AcEc the axial stiffness of the concrete
material, Astfyt the axial tensile strength of the tension steel reinforcements, Afrpffrpu the
axial tensile strength of the CFRP material, AscEsc the axial stiffness of compression steel
reinforcements, and Acf′c is the axial compressive strength of the concrete material. The
subscripts “exp” and “unexp” refer to the properties of the beams from exposed and
unexposed sets, respectively.
The results of the error analysis for different sets of the exposed beams with
respect to the corresponding set of the unexposed beams are presented in Table 4-6,
which confirms the validity of the comparisons (to be performed in the next sections)
between the exposed beams tested in this research and the unexposed beams tested by
Gaafar (2007) in most cases. For the beams in set BR-F, the high uncertainty of 46.3% at
failure stage is due to difference at ultimate strain of the CFRP from two sets. In other
cases, a maximum uncertainty of 6.7% is probable due to the difference in material
properties of the exposed and unexposed sets of the beams.
Table 4-6: Uncertainty in comparison of the exposed and unexposed beams based on
material properties.
Set
Uncertainty (%)
Up to
yielding (Eq. 4-1)
Yielding up
to failure (Eq. 4-2)
At failure
CFRP rupture (Eq. 4-3)
Concrete crushing (Eq. 4-4)
BS-F w.r.t. BS-R 4.6 5.9 4.1 6.7
BR-F w.r.t. BR-R 2.5 4.4 46.3 4.6
161
4.5.3 Load-Deflection Response
4.5.3.1 Beams Strengthened with CFRP Strips
The results of the exposed and unexposed beams strengthened with CFRP strips
are presented in Figure 4-31 and Table 4-7. The beams (as presented in Table 4-7) were
categorized into two sets: set BS-R were unexposed and tested by Gaafar (2007) while set
BS-F were exposed and tested in this research. The curves of the exposed beams are
plotted with considering the permanent deflections due to initial cracking of the beams
after strengthening. The load-deflection curves include the negative camber due to
prestressing, initiation of flexural cracks, yielding of tensile steel rebar, CFRP rupture or
concrete crushing which causes a large drop in the load at ultimate stage, and post failure
behaviour.
One week after prestressing, an upward camber ranging between 0.49-1.7 mm for
beams from set BS-F and between 0.47-1.6 mm for beams from set BS-R were recorded.
The values of the initial and effective pre-strain in the CFRP strip, computed by taking
the average of the strain values at the constant moment region of the beams, are presented
in Table 4-7 showing an average prestressing loss of 1.7±1.1% one week after
prestressing that is mainly due to combination of the anchorage seating loss, the elastic
shortening, and less likely the creep of the concrete beam within a week.
162
0
20
40
60
80
100
120
140
160
-5 15 35 55 75 95 115 135 155 175
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-NP-F BS-P1-F BS-P2-F BS-P3-F B0-F
BS-NP-R BS-P1-R BS-P2-R BS-P3-R B0-R
: Concrete crushing : FRP rupture : Concrete cover spallingR: Room temperature (unexposed beam)F: Freeze-thaw (exposed beam)
Figure 4-31: Comparison between exposed and unexposed RC beams strengthened using CFRP strips.
162
163
Table 4-7: Summary of the test results for strengthened beam using CFRP strips. S
et
Beam ID ɛp
(µɛ)
ɛpe
(µɛ)
Δoe
(mm)
Pcr
(kN)
Δcr
(mm)
Δop
(mm)
Py
(kN)
Δy
(mm)
Pu
(kN)
Δu
(mm) μD
Φ
(kN. mm)
ɛfrp@u
(µɛ) FM
BS
-R,
un
exp
ose
d*
B0-R N.A. N.A. N.A. 12.5 1.25 N.A. 78.9 25.13 83.8 109.89 4.37 8050 N.A. CC
BS-NP-R 0 0 0 16.8 1.55 N.A. 90.8 25.83 135.1 118.79 4.60 12357 14190 CCS
BS-P1-R 3474 3454 -0.47 22.1 1.24 N.A. 103 24.12 148 103.65 4.30 11829 19405 FR
BS-P2-R 5868 5805 -0.93 30.1 1.69 N.A. 105.8 23.62 148.2 77.96 3.30 8711 17978 FR
BS-P3-R 10287 10237 -1.60 42.1 2.64 N.A. 122.8 25.77 149.2 58.13 2.26 6529 20000 FR
BS
-F,
exp
ose
d B0-F N.A. N.A. N.A. 10.4 2.22 0.65 75.5 18.78 97.8 142.88 7.61 7052
† N.A. CC
BS-NP-F 0 0 0 14 1.36 0.61 92.4 22.53 132.2 104.26 4.63 10649 14900 CC
BS-P1-F 3574 3463 -0.49 21.6 1.43 0.13 104.1 23.99 134.7 82.9 3.46 8667 16592 CC
BS-P2-F 6900 6723 -1.09 27.3 1.24 -0.81 114.8 25.56 149.5 87.85 3.44 10214 21464 FR
BS-P3-F 10112 9884 -1.70 35.5 1.45 -1.43 124.3 25.91 141.7 58.55 2.26 6510 21118 FR
F = the beam under freeze-thaw exposure ɛp = initial prestrain due to prestressing
R = the beam under room temperature ɛpe and Δoe = effective prestrain and camber at 7 days after prestressing
Pcr and Δcr = load and deflection at cracking Δop = camber after initial loading (cracking)
Py and Δy = load and deflection at yielding ɛfrp@u = maximum CFRP strain at failure
Pu and Δu = load and deflection at ultimate Φ = area under P-Δ curve
μD = ductility index = Δu /Δy FM = failure mode
CC = concrete crushing CCS = concrete cover spalling FR = CFRP rupture † calculated based on concrete strain 0.004125 to be consistent with the other beams failed by crushing
* (Gaafar, 2007)
163
164
The beams were cracked after strengthening; the obtained cracking loads show
significant increase due to prestressing (up to 153% for set BS-F and up to 151% for set
BS-R) with respect to the non-prestressed strengthened beam of each set. The un-
strengthened control beams, B0-F and B0-R, showed a low cracking load, which is due to
presence of the micro-cracks in the beams before testing, mainly caused from moving the
beams after casting and during the testing process. In fact, the cracking load of the un-
strengthened control beams should have been close to that of the beams strengthened
with non-prestressed NSM CFRP strips.
Up to 56% and 64% increase in the yielding load of the strengthened beams in set
BS-R and set BS-F, respectively, were observed with respect to the corresponding un-
strengthened control beam of each set. Enhancements of 15% out of the 56% and 22%
out of the 64% are related to the increase due to CFRP strengthening and the rests (which
are 41% and 42%, respectively) are due to the prestressing effect. Besides, up to 78% and
53% increase in ultimate load of the strengthened beams in set BS-R and set BS-F,
respectively, were recorded with respect to the corresponding un-strengthened control
beam of each set; 61% out of the 78% and 35% out of the 53% are reached by
strengthening with non-prestressed CFRP strip and the remaining (which are 17% and
18%, respectively) are due to the prestressing effects. In fact, strengthening has more
contribution in enhancement of the ultimate load while prestressing has more
contribution in enhancement of the yield load than the ultimate load.
Five exposed beams in set BS-F showed a typical failure mode, i.e., tension steel
reinforcements yielding followed by CFRP rupture or concrete crushing. The type of
failure modes are marked in Figure 4-31. Comparing the load-deflection curves of the
165
exposed and unexposed beams reveals that freeze-thaw exposure has its major effects on
the ultimate stage, particularly on failure mode; by shifting the mode of failure from
CFRP rupture to concrete crushing as presented in Figure 4-31 for beams BS-NP-F and
BS-P1-F in comparison with beams BS-NP-R and BS-P1-R, respectively. This shift
resulted in 2.1% and 12.2% decrease in ultimate load and deflection at ultimate load of
beam BS-NP-F in comparison with beam BS-NP-R, respectively; furthermore, it resulted
in 9% and 20% decrease in ultimate load and deflection at ultimate load of beam BS-P1-
F in comparison with beam BS-P1-R, respectively. On the other hand, for the beams with
high prestressing level, BS-P2-F and BS-P3-F, the negative effects of freeze-thaw
exposure is negligible. In fact, when the beam is highly prestressed the failure is
governed by CFRP rupture and occurs while the concrete strain in the extreme
compression fibre is small; hence, the damage done to the concrete due to freeze-thaw
exposure should be extremely high to result in a significant reduction in concrete
crushing strain and leads to changing the mode of failure from CFRP rupture to concrete
crushing at small strain. Such behaviour has not been experienced in the cases of beams
BS-P2-F and BS-P3-F.
4.5.3.2 Beams Strengthened with CFRP Rebar
Results of the beams strengthened with CFRP rebars subjected to freeze-thaw
exposure (set BR-F) are compared with similar unexposed beams (set BR-R) as presented
in Figure 4-32 and Table 4-8. The beams showed typical failure modes either by CFRP
rupture or concrete crushing. As shown in Figure 4-32, it is not appropriate to compare
BR-P3-F with BR-P3-R, since the unexposed beam was prestressed much less than the
166
planned prestrain. an upward camber ranging between 0.48-1.71 mm for beams from set
BR-F and between 0.5-1.3 mm for beams from set BR-R were recorded one week after
prestressing. An average prestressing loss of 5.4±3% occurred one week after
prestressing computed by taking the average of the strain values at the constant moment
region of the six beams. Enhancements of 87% and 177% in cracking load for set BR-F
and BR-R was reached, respectively, with respect to the non-prestressed strengthened
beam of each set.
The exposed and unexposed beams had similar yielding loads (with an average
difference of 1.6% ranging from -1% to 6.3% with respect to corresponding unexposed
beam) as presented in Table 4-8. The exposed beams showed smaller deflection at
yielding than the unexposed beams. Up to 66% and 49% increase in the yielding load of
the strengthened beams in set BR-F and set BR-R, respectively, were observed with
respect to the corresponding un-strengthened control beam of each set. Enhancements of
21% out of the 66% and 14% out of the 49% are related to increase due to NSM CFRP
strengthening and the rest (which are 45% and 35%, respectively) are due to prestressing
effect.
Besides, up to 61% and 69% increase in ultimate load of the strengthened beams
in set BR-F and set BR-R, respectively, were recorded with respect to the corresponding
un-strengthened control beam of each set; 35% out of the 61% and 63% out of the 69%
are reached by strengthening with non-prestressed NSM CFRP strip and the remaining
(which are 26% and 6%, respectively) are due to prestressing. In fact, strengthening has
more contribution in enhancement of the ultimate load while prestressing has more
contribution in enhancement of the yield load than the ultimate load. Also, an average
167
difference of -7.4% at ultimate load for the exposed beams with respect to the
corresponding unexposed beams was obtained ranging from -3% to 16.9%.
168
0
20
40
60
80
100
120
140
160
-5 15 35 55 75 95 115 135 155 175
Lo
ad
(k
N)
Mid-span deflection (mm)
BR-NP-F BR-P1-F BR-P2-F BR-P3-F B0-F
BR-NP-R BR-P1-R BR-P2-R BR-P3-R B0-R
: Concrete crushing : FRP rupture
Figure 4-32: Comparison between exposed and unexposed beams strengthened with CFRP rebars.
168
169
Table 4-8: Summary of the test results for strengthened beam using CFRP rebars. S
et
Beam ID ɛp
(µɛ)
ɛpe
(µɛ)
Δoe
(mm)
Pcr
(kN)
Δcr
(mm)
Δop
(mm)
Py
(kN)
Δy
(mm)
Pu
(kN)
Δu
(mm) μD
Φ
(kN. mm)
ɛfrp@u
(µɛ) FM
BR
-R,
un
exp
ose
d*
B0-R N.A. N.A. N.A. 12.5 1.25 N.A. 78.9 25.13 83.8 109.89 4.37 8050 N.A. CC
BR-NP-R 0 0 0 18.4 1.6 N.A. 90.2 25.3 136.4 114.5 4.53 11899 16250 FR
BR-P1-R 3460 3240 -0.5 22.1 1.5 N.A. 105.7 27.7 141.0 92.5 3.34 9917 17710 FR
BR-P2-R 6610 6210 -0.6 27.9 1.7 N.A. 114.5 28.6 141.7 79.3 2.77 8669 18910 FR
BR-P3-R 9910 8960 -1.3 34.4 2.4 N.A. 117.7 28.2 134.7 49.7 1.76 6529 17450 FR
BR
-F,
exp
ose
d B0-F N.A. N.A. N.A. 10.4 2.22 0.65 75.5 18.78 97.8 142.88 7.61 7052
† N.A. CC
BR-NP-F 0 0 0 13.1 1.23 0.595 91.6 23.78 132.3 102.71 4.32 10344 14599 CC
BR-P1-F 3801 3662 -0.48 18 1 -0.065 105.1 24.98 147.5 102.62 4.31 12658 22067 CC
BR-P2-F 6585 6548 -0.92 26 1.2 -0.52 113.4 25.86 157.5 98.05 3.79 11797 23879 CC
BR-P3-F 10272 9950 -1.71 36.3 1.21 -1.395 125.2 25.36 157.5 71.28 2.81 8734 24247 FR
F = the beam under freeze-thaw exposure ɛp = initial prestrain due to prestressing
R = the beam under room temperature ɛpe and Δoe = effective prestrain and camber at 7 days after prestressing
Pcr and Δcr = load and deflection at cracking Δop = camber after initial cracking
Py and Δy = load and deflection at yielding ɛfrp@u = CFRP strain at failure at mid-span
Pu and Δu = load and deflection at ultimate Φ = area under P-Δ curve
μD = ductility index = Δu /Δy FM = failure mode
CC = concrete crushing CCS = concrete cover spalling FR = CFRP rupture † calculated based on concrete strain 0.004125 to be consistent with the other beams failed by crushing
* (El-Hacha and Gaafar, 2011)
169
170
4.5.3.3 Beams Strengthened with CFRP Rebar versus Strips
Effects of freeze-thaw exposure on the load-deflection behaviour of the NSM
strengthened RC beams are presented in Figure 4-33. Furthermore, a summary of the test
results is presented in Table 4-7 and Table 4-8. For the NSM strengthened beams tested
in this research the freeze-thaw exposure has its major effects on the concrete materials.
The damage done to the concrete due to the freeze-thaw exposure reduces the ultimate
capacity and ductility of the beams by shifting the failure mode from CFRP rupture to
concrete crushing, as marked in Figure 4-33 for beams BS-NP-F and BR-NP-F in
comparison with beams BS-NP-R and BR-NP-R, respectively. The exposed non-
prestressed strengthened beams (BS-NP-F and BR-NP-F) have an average of 13.4%
smaller energy absorption (Φ) than the unexposed beams (BS-NP-R and BR-NP-R) kept
at room temperature. Furthermore, thermal incompatibility which is a result of different
thermal expansion coefficients of concrete, epoxy, and CFRP likely produces residual
stresses in the CFRP during the freeze-thaw cycles at low and high temperatures which
affects the bond behaviour. High temperature causes tension on the CFRP reinforcement
and increases the strain in the CFRP while the low temperature causes compression in
CFRP reinforcement and decreases the strain in the CFRP. A slight strain fluctuation of
0.0002 in the CFRP rebars and strips strain values were monitored during the freeze-thaw
cycling. For the prestressed NSM CFRP strengthened RC beams (BS-P2-R, BS-P2-F,
BR-P2-R, and BR-P2-F), comparison of the load-deflection curves in Figure 4-33 reveals
negligible effects of the freeze-thaw exposure on the flexural behaviour. The difference at
ultimate stage is caused by the differences in the CFRP ultimate tensile strains (that is
171
0.0226 for BS-P2-F versus 0.018 for BS-P2-R and 0.0239 for BR-P2-F versus 0.0189 for
BR-P2-R).
172
0
20
40
60
80
100
120
140
160
-5 15 35 55 75 95 115 135 155 175 195 215
Lo
ad
(k
N)
Mid-span deflection (mm)
B0-R BS-NP-R BR-NP-R BS-P2-R BR-P2-R
B0-F BS-NP-F BR-NP-F BS-P2-F BR-P2-F
: Concrete crushing : FRP rupture: Concrete cover spallingR: Room temperature (unexposed beams)F: Freeze-thaw (exposed beams)
Figure 4-33: Comparison between exposed and unexposed beams.
172
173
4.5.4 Effects of Prestressing
The effects of prestressing on cracking, yield, and ultimate loads, and deflection
at ultimate load are plotted in Figure 4-34 to Figure 4-37 with respect to the non-
prestressed strengthened beam in each set of tested beams. For cracking load, the highest
increase occurred in set BR-F with a value of 177%, as shown in Figure 4-34. The sets
BS-R and BS-F showed almost similar behaviour with maximum enhancements of 151%
and 153%, respectively, with respect to the corresponding non-prestressed strengthened
beams. In set BR-R, a low percentage of increase in cracking load was reached, up to
87%, with respect to the non-prestressed strengthened beam in this set; the reason is that
beam BR-NP-R (that comparison is performed based on this beam) showed a high
cracking load in comparison with beams BS-NP-F, BS-NP-R, and BR-NP-F. It should be
mentioned that the cracking loads were obtained when all beams were unexposed.
0
40
80
120
160
200
0 0.002 0.004 0.006 0.008 0.01
Ch
an
ge in
cra
ck
ing
lo
ad
(%
)
Prestrain in CFRP strips or rebar
BS-F w.r.t BS-NP-F
BS-R w.r.t BS-NP-R
BR-F w.r.t BR-NP-F
BR-R w.r.t BR-NP-R
Figure 4-34: Effects of prestressing on cracking load w.r.t non-prestressed NSM
CFRP strengthened beam in each set.
174
The percentage of change in yield load versus prestrain in CFRP strip or rebar is
presented in Figure 4-35 for the unexposed and exposed beams. The two exposed sets of
the beams (BS-F and BR-F) showed similar results with a maximum increase of 37% in
yield load of the BR-F set. The two unexposed sets (sets BS-R and BR-R tested by
Gaafar (2007)) did not show perfect similar trend, however, the average of the two sets is
in a very good correlation with the exposed beam curve. Based on the results, it can be
concluded that the effect of 500 freeze-thaw cycling exposure on the yield load of the RC
beams strengthened with prestressed NSM CFRP strips or rebar appears to be negligible.
0
5
10
15
20
25
30
35
40
0 0.002 0.004 0.006 0.008 0.01
Ch
an
ge in
yie
ld l
oad
(%
)
Prestrain in CFRP strips or rebar
BS-F w.r.t BS-NP-F
BS-R w.r.t BS-NP-R
BR-F w.r.t BR-NP-F
BR-R w.r.t BR-NP-R
Figure 4-35: Effects of prestressing on yield load w.r.t non-prestressed NSM CFRP
strengthened beam in each set.
The percentage of changes in the ultimate load and deflection for the exposed and
unexposed sets are presented in Figure 4-36 and Figure 4-37, respectively. Percentage of
175
change in the ultimate load is affected by the type of the failure and does not follow a
specific trend. It can be concluded that by increasing the prestressing level, whenever the
failure is governed by concrete crushing, the ultimate load increases with respect to the
non-prestressed strengthened beam. For any prestressing level greater than the balanced
prestressing level (which causes CFRP rupture and concrete crushing, simultaneously),
the failure is due to CFRP rupture and the ultimate load stays almost constant. Among
compared sets, set BR-F showed highest percentages of increase at ultimate load due to
prestressing (19%) while set BR-R showed the lowest percentage of increase due to
prestressing (4%). Sets BS-F and BS-R showed maximum increases of 13% and 10% at
ultimate load, respectively.
-5
0
5
10
15
20
25
0 0.002 0.004 0.006 0.008 0.01
Ch
an
ge
in
ult
ima
te lo
ad
(%
)
Prestrain in CFRP strips or rebar
BS-F w.r.t BS-NP-F
BS-R w.r.t BS-NP-R
BR-F w.r.t BR-NP-F
BR-R w.r.t BR-NP-R
Figure 4-36: Effects of prestressing on ultimate load w.r.t non-prestressed
strengthened beam in each set.
176
One of the main concerns for prestressed beams is decreasing the deflection at
ultimate load as well as the ductility (conventional definition, i.e. displacement,
curvature, and rotational ductility indices). The percentage of change in deflection at
ultimate load versus prestrain in CFRP rebar or strip is presented in Figure 4-37. Sets BR-
F and BR-R showed the lowest (up to 31%) and highest (up to 58%) decreases in
deflection at ultimate load, respectively, with respect to the deflection at ultimate load of
the corresponding non-prestressed NSM CFRP strengthened beam of each set. The
exposed beams showed lower decreases in deflection at ultimate load than the unexposed
beam. This behaviour is a result of the freeze-thaw cycling exposure that caused the
exposed non-prestressed strengthened beams (which are the reference of the comparison
for the sets BR-F and BS-F) to fail due to concrete crushing with deflections at ultimate
loads less than the ones for unexposed non-prestressed strengthened beams in sets BS-R
and BR-R.
The energy absorptions of the beams which are defined as the area under the load-
deflection curve up to the peak load are presented in Figure 4-38. For the beams
strengthened with NSM CFRP strips, the decreases of 13.8% and 26.7% in energy
absorption of beams BS-NP-F and BS-P1-F obtained with respect to the corresponding
unexposed beams, BS-NP-R and BS-P1-R, respectively. The reason is that the freeze-
thaw exposed beams showed different failure mode than the unexposed beams resulting
in smaller peak load and deflection at ultimate load. Highly prestressed beams, BS-P3-F
and BS-P3-R, showed similar energy absorption values that reveals the negligible effect
of freeze-thaw on them; on the other hand, the difference in energy absorption of beam
BS-P2-F and beam BS-P2-R is not caused by freeze-thaw exposure since the mode of
177
failure of the exposed and unexposed beam is the same; The difference is due to the
different CFRP rupture strains at ultimate (that is 0.0226 for BS-P2-F versus 0.018 for
BS-P2-R). For the beams strengthened with NSM CFRP rebar, a 13.1% decrease in
energy absorption of beam BR-NP-F was observed in comparison with BR-NP-R. For the
other beams, the difference is due to the different CFRP rupture strain at ultimate causing
the exposed beams to have greater energy absorption values than the unexposed beams
where failure is governed by CFRP rupture. According to results of the tested beams, it
can be concluded that at low prestressing levels (less than 26% of the ultimate tensile
strain of the CFRP strips, and 6% for CFRP rebar) the energy absorption of the exposed
beams are smaller than the unexposed beams mainly caused by shifting the mode of
failure from CFRP rupture to concrete crushing due to freeze-thaw cycling exposure.
-60
-50
-40
-30
-20
-10
0
10
0 0.002 0.004 0.006 0.008 0.01Ch
an
ge in
de
fle
cti
on
at
ult
ima
te lo
ad
(%
)
Prestrain in CFRP strips or rebar
BS-F w.r.t BS-NP-F
BS-R w.r.t BS-NP-R
BR-F w.r.t BR-NP-F
BR-R w.r.t BR-NP-R
Figure 4-37: Effects of prestressing on deflection at ultimate load w.r.t non-
prestressed NSM CFRP strengthened beam in each set.
178
0
2000
4000
6000
8000
10000
12000
14000
0 0.002 0.004 0.006 0.008 0.01
En
erg
y a
bso
rpti
on
(a
rea u
nd
er
load
-d
efl
ecti
on
cu
rve)
kN
.mm
Prestrain in CFRP strips or rebar
Energy absorption (BS-F set)
Energy absorption (BS-R set)
Energy absorption (BR-F set)
Energy absorption (BR-R set)
Figure 4-38: Effects of prestressing on the energy absorption of the exposed and
unexposed NSM CFRP strengthened RC beams.
4.6 Deformability and Ductility of NSM CFRP Strengthened RC Beams
The prestressed or non-prestressed NSM CFRP strengthened RC beams should be
designed for adequate strength and ductility to satisfy the ultimate limit states and avoid
brittle failure. The concept of ductility is related to the safety of the structure to provide
an opportunity for the deflections to be observed if the loads become too large. Therefore
appropriate remedial actions can be performed before failure.
Ductility is the ability of a member to undergo deformation after its initial
yielding without any significant reduction in yield strength while deformability is the
member capability to deform before failure (Bertero, 1988). Conventional ductility
indices, which are developed for conventional steel RC beams, use displacement,
179
curvature, or rotation at yielding and ultimate stages as basis for the computations. In this
case, the load-deflection response is almost an elasto-plastic curve where there is a
negligible difference between the yield and ultimate loads. From a design perspective, the
ductility index of a concrete beam reinforced with steel bars (conventional RC beam)
provides a measure of the energy absorption capability (Naaman and Jeong, 1995; Jaeger
et al., 1997). Since beams reinforced with FRP materials do not have the yield point to be
considered in the calculation of the conventional ductility indices, and also, the RC
beams strengthened with FRP materials acquire a significant portion of their capacity in
plastic range (there is a significant difference between the yield and ultimate loads in the
load-deflection response), hence, for those type of beams, the conventional ductility
indices are not an appropriate measure of the energy absorption capacity. Therefore, the
use of the concept of deformability as a measure of the energy absorption is more
appropriate than the concept of conventional ductility which is a measure of deflection
capability.
In spite of the conventional ductility indices (displacement or curvature ductility)
which are appropriate for steel reinforced concrete members, a variety of deformability
indices are proposed by different researchers for concrete members reinforced with
prestressed/non-prestressed FRP (Naaman and Jeong, 1995; Abdelrahman et al., 1995;
Zou, 2003; Rashid et al., 2005; ACI 440.1R, 2006; CAN/CSA–S6–06, 2011). In this
context, there is a gap for an appropriate deformability index for prestressed/non-
prestressed FRP strengthened RC members, and reasonable deformability limit for each
model to be applicable for design purposes.
180
In this section, a brief review is performed on the available deformability/ductility
indices. Then, three deformability indices are modified to be applicable for NSM CFRP
strengthened RC beams. Afterwards, to validate the models and compare with the
conventional models, results of four series of tests on eighteen large scale (5.15 m long)
RC beams are employed to evaluate their ductility and deformability based on the
modified models and conventional indices. The RC beams were strengthened with
prestressed and non-prestressed NSM CFRP strips and rebars as presented in Table 3-1.
The test variables include prestressing level (0, 20, 40 and 60% of ultimate tensile
strength of the CFRP reinforcement), CFRP reinforcement geometry (strip versus rebar
with the same axial stiffness), and environmental exposure (room temperature versus
freeze-thaw cycling as mentioned earlier in this chapter). Furthermore, the design Codes’
limits for ductility and deformability of the beams are checked and new limits were
proposed and validated for different models to be used in practice.
The conventional definition of structural ductility refers to the behaviour of an
under-reinforced concrete member reinforced with steel bars. In this case, the yielding of
the steel bars provides a base for a rational definition of ductility. When an RC member is
strengthened with material other than steel without a yield plateau (such as FRP) or when
a concrete member is reinforced with FRP, in these cases, the conventional definition of
structural ductility is not valid and needs to be modified. Hence, Naaman and Jeong
(1995) and Mufti et al. (1996) proposed new definitions of structural deformability for
concrete members reinforced with FRP materials. However, there is no appropriate
model for a concrete beam reinforced with conventional steel and strengthened with
prestressed or non-prestressed FRP materials where the load capacity is partly
181
supplemented by FRP materials. These members shows various load-deflection responses
affected by the ratio of existing internal steel area to the balanced steel area, ratio of
equivalent reinforcement area (i.e., transformed FRP plus internal steel) to the balanced
steel area, FRP strength and stiffness, ratio of the external to internal reinforcement areas
(area of transformed external reinforcement to area of internal reinforcement), failure
mode, and debonding issues and the effectiveness of anchorage system. Furthermore, the
prestressing effects on the load-deflection response need to be considered in the proposed
ductility model. A brief review of the existing ductility and deformability models are
presented in the following sections.
4.6.1 Existing Ductility and Deformability Models
4.6.1.1 Displacement Ductility Index
Displacement ductility is defined as the ratio of the displacement at ultimate (Δu)
to the displacement at the commencement of yielding (Δy), as represented in Equation 4-
12 This conventional index of ductility is appropriate for concrete beams reinforced with
steel bars.
y
uD
Equation 4-12
where µD is the displacement ductility index, Δu the mid-span deflection at peak load or
75% of post-peak load (for the cases in which the failure occurs gradually i.e. concrete
crushing), and Δy is the mid-span deflection at yielding.
182
4.6.1.2 Curvature Ductility Index
Curvature ductility is defined as the ratio of the angle of curvature in the member
at ultimate to that at the commencement of yielding as presented in Equation 4-13. This
ductility index is appropriate for concrete beams reinforced with steel bars and loaded by
a bending moment.
y
u
Equation 4-13
where µ is the curvature ductility index, u the mid-span curvature at peak load or 75%
of post-peak load, and y is the mid-span curvature at yielding.
4.6.1.3 Rotational Ductility Index
Rotation ductility is defined as the ratio of the rotation of the plastic hinge at
ultimate to the value at commencement of yielding, as presented in Equation 4-14. This
ductility index is appropriate for conventional RC members under bending moment and
axial force.
y
u
Equation 4-14
where µ is the rotation ductility index, u the plastic hinge rotation at peak load or 75%
of post-peak load, and y is the value of rotation at plastic hinge location at
commencement of yielding.
183
4.6.1.4 Deformability Factor
Deformability factor is defined as the ratio of the energy absorption at ultimate to
the energy absorption at service or a limiting curvature or yielding, as presented in
Equation 4-15 (ACI 440.1R, 2006). The energy absorption is the area under load-
deflection curve. The deformability factor can be applied to any type of structure.
s
uE
E
E
Equation 4-15
where µE is the deformability factor, Eu the area under load-deflection curve up to peak
load or 75% of post-peak load, and Es is the area under load-deflection curve at service
(which can be at a limiting curvature or at yielding).
4.6.1.5 Naaman and Jeong (1995) Index
The Naaman and Jeong index is a deformability model proposed by Naaman and
Jeong (1995) given as Equation 4-16. This index is based on the assumption that the
prestressed concrete beam has a fully elasto-plastic behaviour.
150
el
totJN
E
E.
Equation 4-16
where Etot is the total energy absorption (area under load-deflection curve up to peak load
or failure load) and Eel is the part of the total energy as demonstrated in Figure 4-39. In
the absence of an experimental unloading curve, the slope S for calculation of Eel can be
defined as Equation 4-17.
184
2
21211
P
S)PP(SPS
Equation 4-17
The first and second slopes, S1 and S2 in Equation 4-17, corresponding to applied
load P1 and P2, are presented in Figure 4-39.
Figure 4-39: Total, elastic, and inelastic energies (Retrieved from Naaman and
Jeong, 1995).
4.6.1.6 Abdelrahman Index
Abdelrahman et al. (1995) established a deformability index for concrete beams
prestressed by FRP tendons. This index is defined as the ratio of the maximum deflection
corresponding to the failure or peak load to the equivalent deflection of the uncracked
section for peak load given as:
l
ubA
Equation 4-18
185
where Ab is the Abdelrahman deformability index, Δu the mid-span deflection at peak
load, and Δl is the equivalent uncracked deflection at peak load as demonstrated in Figure
4-40.
Figure 4-40: Equivalent deflection, Δ1, and failure deflection, Δu (Retrieved from
Abdelrahman et al., 1995).
The Abdelrahman index overestimates the ductility as much as three times greater
than the value of deflection ductility given by displacement ductility index for concrete
beams prestressed with steel tendons (Abdelrahman et al., 1995). As can be seen this
index is developed for a beam that its load-deflection response consists of two slopes
(from zero to cracking and from cracking to ultimate).
4.6.1.7 CHBDC Deformability Factor
The CHBDC (CAN/CSA-S6-06, 2011) proposes a deformability factor (called J
factor) for concrete members reinforced with FRP materials, as presented in Equation 4-
186
19. The factor is based on both strength and deformability and can be regarded as the
ratio of two energy values calculated from a linear moment-curvature response, one
associated with the ultimate limit state condition and the other when concrete at the
extreme compression fibre reaches its proportional limit. Jaeger et al. (1995) proposed the
J factor and Mufti et al. (1996) and Jaeger et al. (1997) elaborated on its concept. The J
factor is defined as:
cc
uu
M
MJ
Equation 4-19
where Mu and u are the moment and curvature at ultimate state, respectively, and Mc and
c are the moment and curvature corresponding to maximum concrete compressive strain
of 0.001, respectively.
4.6.1.8 Zou Index
Zou (2003) proposed a deformability index for concrete beam prestressed with
FRP based on deflection and moment values given as:
cr
u
cr
u
M
MZ
Equation 4-20
where Mu and Δu are the moment and deflection at ultimate state, respectively, while Mcr
and Δcr are the moment and deflection at cracking, respectively.
187
4.6.1.9 Rashid Index
Rashid et al. (2005) developed a deformability index for FRP reinforced high
strength concrete beams with confined concrete in compression zone given as:
crush
uR
Equation 4-21
where R is the Rashid index, Δu the mid-span deflection at peak load, and Δcrush is the
mid-span deflection at the initiation of concrete cover crushing. The Rashid index is
applicable when the load-deflection response of FRP reinforced concrete beam shows a
first peak at the initiation of concrete crushing and a second peak, usually higher than the
first one, before the confined concrete in the compression zone finally disintegrated.
A summary of the existing ductility and deformability indices and their
applications are presented in Table 4-9.
188
Table 4-9: Summary of existing ductility and deformability indices.
Description Equation Parameters Application
Displacement
ductility y
uD
µD = the displacement ductility index
Δu = the mid-span deflection at peak load
or 75% of post-peak load Δy = the mid-span deflection at yielding
conventional ductility index;
appropriate for RC beams;
not suitable for beams reinforced with FRP
Curvature
ductility y
uφ
φ
φμ
µ = the curvature ductility index
u = the mid-span curvature at peak load
or 75% of post-peak load
y = the mid-span curvature at yielding
appropriate for RC beams
loaded by a bending moment
Rotation
ductility y
uθ
θ
θμ
µ = the rotation ductility index
u = the plastic hinge rotation at peak load
or 75% of post-peak load
y = the rotation at plastic hinge location at
commencement of yielding
appropriate for RC members
under bending moment and
axial force
Abdelrahman
index
(Abdelrahman
et al., 1995) l
ub
Δ
ΔA
Ab = the Abdelrahman deformability index
Δu = the mid-span deflection at peak load
Δl =the equivalent un-cracked deflection at peak load
appropriate for concrete
beams prestressed by FRP tendons; overestimates the
ductility as much as three
times greater than the value of deflection ductility; for
prestressed concrete beams
with steel tendons
Naaman and
Jeong index
(Naaman and
Jeong, 1995)
150
el
totJ-N
E
E.μ
µN-J = the Naaman and Jeong index
Etot = the total energy absorption Eel = the elastic energy released at failure
due to unloading
based on the assumption that
the prestressed concrete
beams has a fully elasto-plastic behaviour;
appropriate for prestressed
RC beams
Deformability
factor (ACI
440.1R, 2006) s
uE
E
Eμ
µE = the deformability factor Eu = the area under load-deflection curve
up to peak load or 75% of post-peak load
Es = the area under load-deflection curve at service or a limiting curvature
applicable to any type of structure
Rashid index
(Rashid et al.,
2005) crush
u
Δ
ΔR
R = the Rashid index
Δu = the mid-span deflection at peak load Δcrush = the mid-span deflection at the
initiation of concrete cover crushing.
appropriate for FRP reinforced high strength
concrete beams with
confined concrete in compression zone
CHBDC
deformability
(J) factor
(CAN/CSA-S6-
06, 2011) cc
uu
φM
φMJ
J = the CHBDC deformability factor
Mu and u = the ultimate moment capacity
and curvature of the section
Mc and c = the moment and curvature
corresponding to maximum concrete
compressive strain of 0.001.
appropriate for concrete
members reinforced with
FRP
Zou index
(Zou, 2003)
cr
u
cr
u
M
M
Δ
ΔZ
Z = the Zou index
Mu and Δu = the moment and deflection at
ultimate state Mcr and Δcr = the moment and deflection at
cracking
appropriate for concrete
beam prestressed with FRP
189
4.6.2 Modification of the Deformability Models for FRP Strengthened RC Beams
As mentioned earlier, the deformability and ductility for a member needs to be
computed based on a reference point in the load-deflection or moment-curvature
response. For an RC beam strengthened with FRP material the yielding is a rational
reference point. On the other hand, the FRP strengthened beams gain a significant portion
of their capacity at plastic range after steel yielding. Therefore, assuming elasto-plastic
behaviour in deriving the deformability/ductility index leads to a major difference with
reality and underestimation of the actual ductility or deformability values. On the other
hand, strengthening using prestressed FRP causes a significant increase in cracking stage;
therefore, it is required to consider this stage in the deformability model. In this context,
the appropriate available deformability indices are modified to be applicable for
prestressed and non-prestressed FRP strengthened RC beams.
4.6.2.1 Modified Deformability Factor
For RC beams strengthened with prestressed FRP reinforcements which have the
yielding point in their responses, the deformability factor can be defined as Equation 4-22
and can be modified as Equation 4-23, which is derived by idealizing the actual load-
deflection curve with a tri-linear slope load-deflection response as shown in Figure 4-41.
yielding
start
ultimate
startEm
dΔP
dΔPμ
Equation 4-22
190
Figure 4-41: Idealized tri-linear slope load-deflection response.
cryyyocr
yuuy
EmΔΔPΔΔP
ΔΔPP1μ
Equation 4-23
where µEm is the modified deformability factor, Δo the deflection due to prestressing
(absolute value should be used in Equation 4-23), Pcr and Δcr the load and deflection at
cracking, respectively, Py and Δy the load and deflection at yielding, respectively, and Pu
and Δu are the load and deflection at ultimate, respectively.
4.6.2.2 Modified CHBDC Deformability Index
For reinforced concrete beams strengthened with prestressed FRP material which
has the yielding point the J factor can be modified as below by considering the area under
moment-curvature curve:
yielding
start
ultimate
startm
dφM
dφMJ
Equation 4-24
191
By idealizing a moment-curvature curve with a tri-linear slope moment-curvature
response as shown in Figure 4-42, Jm is simplified as:
Figure 4-42: Idealized tri-linear slope moment-curvature response.
cryyyocr
yuuym
φφMφφM
φφMM1J
Equation 4-25
where Jm is the modified J factor, o the curvature due to prestressing (absolute value
should be used in Equation 4-25), Mcr and cr the moment and curvature at cracking,
respectively, My and y the moment and curvature at yielding, respectively, and Mu and
u are the moment and curvature at ultimate, respectively.
4.6.2.3 Modified Zou Index
The Zou index is developed for concrete beams prestressed using FRP
reinforcements where the load-deflection curve mainly can be considered as a two–slope
curve (from zero to cracking and from cracking to peak load). For an RC beam
192
strengthened with prestressed FRP reinforcement, which has the yielding point in its
response, the Zou index can be modified as:
y
u
y
um
M
M
Δ
ΔZ
Equation 4-26
where Zm is the modified Zou index, Mu and Δu the moment and deflection at ultimate
state, respectively, and My and Δy are the moment and deflection at yielding, respectively.
4.6.3 Deformability of NSM-CFRP Strengthened RC Beam
4.6.3.1 Considered Beams
Results from eighteen beams were considered to assess the deformability and
ductility: (nine beams tested in phase I and nine beams tested by Gaafar (2007)). The
variables in the experimental program comprise CFRP reinforcement geometry (rebar
versus strip with the same axial stiffness), prestressing level in the CFRP reinforcement
(0-60% of ultimate tensile strength of CFRP reinforcements), and environmental
exposure (room temperature versus freeze-thaw cycling). Results of the beams are
presented in Table 4-10 and Table 4-11.
193
Table 4-10: Results of the beams (load-deflection). S
et
Beam ID ɛp (µɛ) ɛpe
(µɛ)
Δoe
(mm)
Pcr
(kN)
Δcr
(mm)
Δop
(mm)
Py
(kN)
Δy
(mm)
Pu
(kN)
Δu
(mm)
ɛfrp@u
(µɛ) FM
Gro
up A
-un
expo
sed
*
B0-R N.A. N.A. N.A. 12.5 1.25 N.A. 78.9 25.13 83.8 109.89 N.A. CC
BS
-R
BS-NP-R 0 0 0 16.8 1.55 N.A. 90.8 25.83 135.1 118.79 14190 CCS
BS-P1-R 3474 3454 -0.47 22.1 1.24 N.A. 103 24.12 148 103.65 19405 FR
BS-P2-R 5868 5805 -0.93 30.1 1.69 N.A. 105.8 23.62 148.2 77.96 17978 FR
BS-P3-R 10287 10237 -1.60 42.1 2.64 N.A. 122.8 25.77 149.2 58.13 20000 FR
BR
-R
BR-NP-R 0 0 0 18.4 1.6 N.A. 90.2 25.3 136.4 114.5 16250 FR
BR-P1-R 3460 3240 -0.5 22.1 1 N.A. 105.7 27.2 141 92 17710 FR
BR-P2-R 6610 6210 -0.6 27.9 1.1 N.A. 114.5 28 141.7 78.7 18910 FR
BR-P3-R 9910 8960 -1.3 34.4 1.1 N.A. 117.7 26.9 134.7 48.4 17450 FR
Gro
up B
-ex
po
sed
B0-F N.A. N.A. N.A. 10.4 2.22 0.65 75.5 18.78 97.8 142.88 N.A. CC
BS
-F
BS-NP-F 0 0 0 14 1.36 0.61 92.4 22.53 132.2 104.26 14900 CC
BS-P1-F 3574 3463 -0.49 21.6 1.43 0.13 104.1 23.99 134.7 82.9 16592 CC
BS-P2-F 6900 6723 -1.09 27.3 1.24 -0.81 114.8 25.56 149.5 87.85 21464 FR
BS-P3-F 10112 9884 -1.70 35.5 1.45 -1.43 124.3 25.91 141.7 58.55 21118 FR
BR
-F
BR-NP-F 0 0 0 13.1 1.23 0.6 91.6 23.78 132.3 102.71 14914 CC
BR-P1-F 3801 3662 -0.48 18 1 -0.07 105.1 24.98 147.5 107.62 22067 CC
BR-P2-F 6585 6548 -0.92 26 1.2 -0.52 113.4 25.86 157.5 98.05 23879 CC
BR-P3-F 10272 9950 -1.71 36.3 1.21 -1.4 125.2 25.36 157.5 71.28 24247 FR
BS = the beam strengthened with CFRP strips BR = the beam strengthened with CFRP rebar
F = the beam under freeze-thaw exposure ɛp = initial prestrain due to prestressing R = the beam under room temperature ɛpe and Δoe = effective prestrain and camber at 7 days after prestressing
Pcr and Δcr = load and deflection at cracking ɛfrp@u = CFRP strain at failure at mid-span
Py and Δy = load and deflection at yielding FM = failure mode Pu and Δu = load and deflection at ultimate CC = concrete crushing CCS = concrete cover spalling
Δop = camber after initial cracking FR = CFRP rupture
*(Gaafar, 2007; El-Hacha and Gaafar, 2011)
194
Table 4-11: Results of the beams (moment-curvature).
Set
Beam ID
oe
(µ rad/mm)
Mcr (kN.m)
cr (µ rad/mm)
Mc (kN.m)
c (µ rad/mm)
My (kN.m)
y (µ rad/mm)
Mu (kN.m)
u (µ rad/mm)
Gro
up A
-un
expo
sed
*
B0-R 0 12.5 1.09 71.3 10.22 78.9 11.61 83.8 71.73
BS
-R
BS-NP-R 0 16.8 2.38 62.8 7.95 90.8 11.62 135.1 55.53
BS-P1-R -0.19 22.1 0.74 73.7 7.51 103 11.45 148 53.28
BS-P2-R -0.35 30.1 1.56 80.6 8.19 105.8 11.19 148.2 44.35
BS-P3-R -0.91 42.1 1.71 83.0 7.32 122.8 12.37 149.2 34.37
BR
-R
BR-NP-R 0 18.4 2.16 64.4 9.17 90.2 12.86 136.4 52.45
BR-P1-R -0.24 22.1 1.42 63.1 7.82 105.7 13.77 141 51.23
BR-P2-R -0.41 27.9 1.08 84.3 8.52 114.5 12.29 141.7 37.02
BR-P3-R -0.52 34.4 1.47 72.0 6.66 117.7 13.08 134.7 26.36
Gro
up B
-ex
po
sed
B0-F 0 10.4 1.49 61.6 7.22 75.5 9.19 97.8 82.43
BS
-F
BS-NP-F 0 14 0.7464 82.9 9.06 92.4 10.43 132.2 51.9
BS-P1-F -0.13 21.6 0.86 93.2 9.26 104.1 10.71 134.7 42.67
BS-P2-F -0.65 27.3 0.39 101.9 9.34 114.8 11.23 149.5 47.74
BS-P3-F -0.67 35.5 0.44 94.9 7.87 124.3 11.79 141.7 38.05
BR
-F
BR-NP-F 0 13.1 0.54 86.4 9.41 91.6 10.25 132.3 43.95
BR-P1-F -0.4 18 0.31 84.3 8.17 105.1 11.01 147.5 43.22
BR-P2-F -0.56 26 0.38 99.4 9.03 113.4 10.63 157.5 40.09
BR-P3-F -0.9 36.3 0.38 99.4 7.61 125.2 10.44 157.5 37.03
BS = the beam strengthened with CFRP strips oe = effective curvature 7 days after prestressing
BR = the beam strengthened with CFRP rebar Mcr and cr = moment and curvature at cracking
R = the beam under room temperature My and y = moment and curvature at yielding
F = the beam under freeze-thaw exposure Mu and u = moment and curvature at ultimate
Mc and c = the moment and curvature corresponding to maximum concrete compressive strain of 0.001
4.6.3.2 Deformability Analysis and Discussions
Results of the five models applied to the eighteen beams listed in Table 4-10 and
Table 4-11 are presented in Figure 4-43 and Figure 4-44, and also in Table 4-12. The
results reveal that the conventional displacement ductility (µD) and curvature ductility
(µ) almost result in the same values while for some sets of the tested beams the value of
195
the curvature ductility is slightly higher, see Figure 4-43b and Figure 4-44b. This
anomalous behaviour can be easily interpreted. The curvatures for the tested beams was
calculated based on the measured concrete surface strain from LSCs installed at the mid-
span section. The mid-span section is under the maximum cracking density, which affects
the actual magnitudes of the measured surface strain. Also, curvatures based on surface
strains do not accurately reflect the parameters involved in measurements of rotational
capacity (Spadea et al., 2001). Therefore, it can be generally concluded that ductility
based on surface concrete measurements are likely to be less reliable. The modified Zou
index (Zm) results in a value greater than those obtained from displacement and curvature
ductility indices but smaller than those obtained from modified J factor (Jm) and modified
deformability factor (µEm). The modified J factor results in higher values than the other
models. The CHBDC (CAN/CSA-S6-06, 2011) requires that the J factor should be
greater than 4 and 6 for rectangular and T-sections concrete beams reinforced with FRP
reinforcements, respectively. However, there are no deformability limits for the other
models considered in this study. The statistical analysis of the results obtained from
sixteen strengthened beams reveals that the average value obtained by µEm, Zm, µD and µ
are 88%, 69%, 57%, and 52% of the value obtained by Jm, respectively. Therefore,
considering a limit of 4 for Jm and based on statistical analysis of the results, the
corresponding limits for µEm, Zm, µD and µ are 3.5±0.5, 2.8±0.3, 2.3±0.3, and 2.1±0.2,
respectively. This finding covers a major gap in ductility and deformability of the FRP
strengthened RC beam and provides an opportunity for designers to use different
equations in order to check the ductility or deformability of RC beams strengthened with
FRP. Furthermore, comparison between ductility/deformability values of the un-
196
strengthened control beams with those values for strengthened beams, presented in Table
4-12, reveals that in most cases the un-strengthened beam shows larger
deformability/ductility; this fact is more obvious for the exposed beam in Group B.
Table 4-12: Ductility or deformability indices of beams.
Set
Beam ID ɛpe
(µɛ) µD µ µE µEm J Jm Z Zm
Gro
up A
-un
expo
sed
B0-R N.A. 4.37 6.18 7.38 7.28 8.25 11.03 591.44 4.64
BS
-R
BS-NP-R 0 4.60 4.78 9.42 8.96 15.02 10.59 616.30 6.84
BS-P1-R 3454 4.30 4.65 7.69 7.88 14.25 8.72 559.78 6.17
BS-P2-R 5805 3.30 3.96 5.55 5.51 9.96 7.16 227.13 4.62
BS-P3-R 10237 2.26 2.78 3.19 3.20 8.43 4.20 78.03 2.74
BR
-R
BR-NP-R 0 4.53 4.08 9.27 8.76 12.12 8.47 530.50 6.84
BR-P1-R 3240 3.38 3.72 5.57 5.73 14.64 6.72 586.97 4.51
BR-P2-R 6210 2.87 3.01 4.18 4.47 7.30 4.86 363.37 3.55
BR-P3-R 8960 1.80 2.01 2.32 2.35 7.40 2.83 172.29 2.06
Gro
up B
-ex
po
sed
B0-F N.A. 7.61 8.97 14.12 15.88 18.11 19.75 604.99 9.85
BS
-F
BS-NP-F 0 4.63 4.97 8.70 9.08 9.13 9.94 722.84 6.62
BS-P1-F 3463 3.46 3.98 5.69 5.89 6.66 7.06 362.18 4.47
BS-P2-F 6723 3.44 4.25 5.43 5.68 7.50 7.15 388.00 4.48
BS-P3-F 9884 2.26 3.23 3.02 3.16 7.22 4.77 161.15 2.58
BR
-F
BR-NP-F 0 4.32 4.29 8.09 8.43 7.15 8.37 845.63 6.24
BR-P1-F 3662 4.31 3.93 7.62 8.01 9.25 7.12 882.08 6.05
BR-P2-F 6548 3.79 3.77 6.30 6.60 7.04 6.49 494.96 5.27
BR-P3-F 9950 2.81 3.55 4.07 4.24 7.71 5.50 255.69 3.54
µD = the displacement ductility index µ = the curvature ductility index
µE = the deformability factor µEm = the modified deformability factor
J = the original J factor Jm = the modified J factor
Z = the original Zou index Zm = the modified Zou index
ɛpe = effective prestrain in CFRP at 7 days after prestressing
197
0
2
4
6
8
10
12
0 0.002 0.004 0.006 0.008 0.01
Du
cti
lity
or
de
form
ab
ilit
y
Prestrain in CFRP rebar
Em
Jm
Zm
Dd
Cd
µEm
Jm
Zm
µD
µ
(a) Beams strengthened using NSM CFRP rebar.
0
2
4
6
8
10
12
0 0.002 0.004 0.006 0.008 0.01
Du
cti
lity
or
de
form
ab
ilit
y
Prestrain in CFRP strip
Em
Jm
Zm
Dd
Cd
µEm
Jm
Zm
µD
µ
(b) Beams strengthened using NSM CFRP strips.
Figure 4-43: Deformability and ductility models applied to the unexposed beams.
198
0
2
4
6
8
10
12
0 0.002 0.004 0.006 0.008 0.01
Du
cti
lity
or
de
form
ab
ilit
y
Prestrain in CFRP rebar
Em
Jm
Zm
Dd
Cd
µEm
Jm
Zm
µD
µ
(a) Beams strengthened using NSM CFRP rebar.
0
2
4
6
8
10
12
0 0.002 0.004 0.006 0.008 0.01
Du
cti
lity
or
defo
rmab
ilit
y
Prestrain in CFRP strip
Em
Jm
Zm
Dd
Cd
µEm
Jm
Zm
µD
µ
(b) Beams strengthened using NSM CFRP strips.
Figure 4-44: Deformability and ductility models applied to the exposed beams.
199
A comparison between the original and the modified deformability models is
presented in Figure 4-45 and Figure 4-46 and also in Table 4-12. The results reveal that
there is a large difference between the modified Zou index (Zm) and the original one (Z).
For the beams listed in Table 4-12, the average value obtained by Z is 90.4 times the
value obtained by Zm. The reason is that the original Zou index is appropriate for the
concrete beams prestressed with FRPs and defined is based on Mcr and Δcr (the moment
and deflection at cracking, respectively, see Equation 4-20), while the modified Zou
index is defined based on My and Δy (the moment and deflection at yielding, respectively,
see Equation 4-26) to be applicable to the FRP strengthened steel reinforced concrete
beams. The modified deformability factor (µEm) obtained from Equation 4-23 and the
deformability factor (µE) calculated based on actual energy result in similar values (less
than 3% difference); µEm has the advantage of simplicity in application which does not
have the difficulty in calculation of the actual energy absorption in comparison with µE.
Comparison between the modified J factor (Jm) and the original J factor (J) shows that
the original J factor results in higher value than the modified one for the unexposed
beams (Figure 4-45), while it gives similar value to the modified one for the exposed
beams (Figure 4-46). The average value obtained by J is 1.7 and 1.1 times the value
obtained by Jm for the unexposed and exposed beams, respectively. It should be noted
that the original J factor is defined based on Mc and c, the moment and curvature
corresponding to maximum concrete compressive strain of 0.001, which makes it seems
to be appropriate for concrete beams reinforced with FRPs that have no yield points in
their load-deflection responses. On the other hand, as mentioned earlier, the curvatures
for the tested beams were calculated based on the measured concrete surface strain from
200
LSCs installed at the mid-span section. Since, the mid-span section is under the
maximum cracking density, which affects the actual magnitudes of the measured surface
strain and ductility based on surface concrete measurements are likely to be less reliable.
0
3
6
9
12
15
18
0 0.002 0.004 0.006 0.008 0.01
Du
cti
lity
or
de
form
ab
ilit
y
Prestrain in CFRP rebar
Jm
Dd
Em
Df
Zm
Cd
Jm
J
µEm
µE
Zm
Z/100
(a) Beams strengthened using NSM CFRP rebar.
0
3
6
9
12
15
18
0 0.002 0.004 0.006 0.008 0.01
Du
cti
lity
or
de
form
ab
ilit
y
Prestrain in CFRP strip
Jm
Dd
Em
Df
Zm
Cd
Jm
J
µEm
µE
Zm
Z/100
(b) Beams strengthened using NSM CFRP strips.
Figure 4-45: Comparison between the original and the modified deformability
models applied to the unexposed beams.
201
0
3
6
9
12
15
18
0 0.002 0.004 0.006 0.008 0.01
Du
cti
lity
or
defo
rmab
ilit
y
Prestrain in CFRP rebar
Jm
Dd
Em
Df
Zm
Cd
Jm
J
µEm
µE
Zm
Z/100
(a) Beams strengthened using NSM CFRP rebar.
0
3
6
9
12
15
18
0 0.002 0.004 0.006 0.008 0.01
Du
cti
lity
or
defo
rmab
ilit
y
Prestrain in CFRP strip
Jm
Dd
Em
Df
Zm
Cd
Jm
J
µEm
µE
Zm
Z/100
(b) Beams strengthened using NSM CFRP strips.
Figure 4-46: Comparison between the original and the modified deformability
models applied to the exposed beams.
202
The results from each deformability and ductility model applied to the
strengthened beams are presented in Figure 4-47 to Figure 4-51. On the other hand, the
calculated limit for each model is applied and plotted in the figures considering upper
bound values mentioned earlier. The investigation reveals that the limits used for
different models present almost the same prestrain in the CFRP rebar/strip that can be
applied to meet the ductility criteria and have an acceptable design. In this context and
based on the proposed upper bound limit, the modified deformability factor (µEm)
represents the most conservative model which results in a smaller prestrain to be applied
to meet the limit. The results obtained from µEm show that for sets BS-R, BR-R, BS-F,
and BR-F, prestressing by the maximum values presented in Table 4-10 leads to
decreases of 64.2%, 73.1%, 65.2%, and 49.7%, respectively, in comparison with the
corresponding non-prestressed strengthened beam of each set; an average decrease of
63.1% is obtained in this case. Correspondingly, the results obtained from Zm (the
modified Zou index) for sets BS-R, BR-R, BS-F, and BR-F reveal that prestressing
causes the decreases of 59.9%, 69.9%, 61.1%, and 43.3%, respectively, in comparison
with the corresponding non-prestressed strengthened beam of each set; an average
decrease of 58.6% occurred in this case.
203
0
2
4
6
8
10
12
0 0.00275 0.0055 0.00825 0.011
Cu
rvatu
re d
ucti
lity
in
dex
(µ)
Prestrain in CFRP strip or rebar
µj (BS-F set)
µj (BS-R set)
µj (BR-F set)
µj (BR-R set)
µ
µ
µ
µ
µ upper bound limit
µ limit
Figure 4-47: Verification of proposed limit for curvature ductility index (µ).
0
2
4
6
8
10
12
0 0.00275 0.0055 0.00825 0.011
Dis
pla
ce
me
nt
du
cti
lity
in
de
x (
µD)
Prestrain in CFRP strip or rebar
µD (BS-F set)
µD (BS-R set)
µD (BR-F set)
µD (BR-R set)
µD
µD
µD
µD
µD upper bound limit
µD limit
Figure 4-48: Verification of proposed limit for displacement ductility index (µD).
204
0
2
4
6
8
10
12
0 0.00275 0.0055 0.00825 0.011
De
form
ab
ilit
y i
nd
ex
(J
m)
Prestrain in CFRP strip or rebar
Jm (BS-F set)
Jm (BS-R set)
Jm (BR-F set)
Jm (BR-R set)
Jm
Jm
Jm
Jm
Jm limit (CAN/CSA–S6–06)
Figure 4-49: Verification of proposed limit for modified J factor (Jm).
0
2
4
6
8
10
12
0 0.00275 0.0055 0.00825 0.011
De
form
ab
ilit
y i
nd
ex
(Z
m)
Prestrain in CFRP strip or rebar
Zm (BS-F set)
Zm (BS-R set)
Zm (BR-F set)
Zm (BR-R set)
Zm
Zm
Zm
Zm
Zm upper bound limit
Zm limit
Figure 4-50: Verification of proposed limit for modified Zou index (Zm).
205
0
2
4
6
8
10
12
0 0.00275 0.0055 0.00825 0.011
De
form
ab
ilit
y i
nd
ex (
µE
m)
Prestrain in CFRP strip or rebar
µEm (BS-F set)
µEm (BS-R set)
µEm (BR-F set)
µEm (BR-R set)
µEm upper bound limit
µEm limit
µEm
µEm
µEm
µEm
Figure 4-51: Verification of proposed limit for modified deformability factor (µEm).
Also, the results calculated from Jm model (the modified J factor) show that for
sets BS-R, BR-R, BS-F, and BR-F, prestressing causes the decreases of 60.3%, 66.6%,
52%, and 34.3%, respectively, in comparison with the corresponding non-prestressed
strengthened beam of each set; an average decrease of 53.3% is obtained in this case.
Analyzing the results obtained from µD (the displacement ductility index) for sets BS-R,
BR-R, BS-F, and BR-F reveal that prestressing leads to decreases of 51%, 60.2%, 51.2%,
and 34.9%, respectively, in comparison with the corresponding non-prestressed
strengthened beam from each set; an average decrease of 49.3% is obtained in this case.
Furthermore, the results calculated from µ (the curvature ductility index) for sets BS-R,
BR-R, BS-F, and BR-F show that prestressing causes the decreases of 41.8%, 50.6%,
35.1%, and 17.3%, respectively, in comparison with the corresponding non-prestressed
206
strengthened beam; an average decrease of 36.2% is obtained in this case. In fact,
comparison between the averages of decreases for each index reveals the sensitivity of
each index to prestressing which increases by the following order: µ, µD, Jm, Zm, and
µEm.
4.7 Phase II: Prestressed NSM-CFRP Strengthened RC Beams under Combined
Sustained Load and Freeze-Thaw Exposure
Five beams were tested in phase II including one un-strengthened control beam
and four beams strengthened using NSM CFRP strips with target prestressing level of
0%, 20%, 40%, and 60% of the ultimate tensile strength of the CFRP strips reported by
manufacturer. The test matrix is presented in Table 3-1. The beams in phase II were
exposed to 500 freeze-thaw cycles as described in Section 3.6 while each beam was
subjected to a sustained load of 62 kN, equal to 47% of the theoretical ultimate load of
the non-prestressed NSM CFRP strengthened RC beam (BS-NP in Table 3-3). Geometry
of the beams and details of the experimental program are presented in Chapter Three.
4.7.1 Test Beams and Material Properties
Five beams subjected to sustained load and 500 cycles of freeze-thaw (based on
the test matrix presented in Table 3-1) were tested in phase II. The material properties of
the strengthened beams including steel reinforcements, concrete, and CFRP strip obtained
from ancillary tests are presented in Appendix C in detail. However, a brief description is
presented in this section.
207
4.7.1.1 Steel Reinforcements
The tension and compression steel bars (3-15M and 2-10M) possessed the yield
strengths of 5330.8 MPa and 48816 MPa, and the yield strains of 0.002660.00022
and 0.002440.00027, respectively, obtained from tension tests having a modulus of
elasticity of 200 GPa. Also, the stirrups (25-10M) had the same properties as the
compression steel bars.
4.7.1.2 Concrete
The beams in phase II were cast from the same concrete batch with a 28 days
average concrete compressive strength of 37.81.2 MPa. After subjecting to 500 freeze-
thaw cycles, the concrete cylinders were severely damaged due to exposure so that
nothing was left from the cylinders to be tested. However, a 19.18.5 MPa average
concrete compressive strength was obtained using the Schmidt hammer test on the
exposed beams at the time of testing to failure. It should be mentioned that the top
surfaces of the beams (to a depth of 50 mm) were severely deteriorated in comparison to
the other parts of the beams. More detailed investigations showed average exposed
concrete compressive strengths of 10.16.8 MPa and 28.110.1 MPa for the top layer
and side of the beams. More details about the concrete compressive strengths are
presented in Table C-1. The capacity and also failure mode of the beams were mostly
related to the concrete strength in the compression region.
208
4.7.1.3 CFRP Strips
The material properties of the CFRP strips are presented in Table 4-13. Beam BS-
P3-FS was strengthened using different batch of CFRP strips due to shortage of the CFRP
strips, however, the CFRP material property from the two batches are almost similar.
Table 4-13: CFRP material properties obtained from tension tests.
CFRP product
(Manufacturer)
Dimension
(mm)
Afrp
(mm2)
ffrpu
(MPa)
Efrp
(GPa) ɛfrpu
Aslan 500 CFRP tape*
(Hughes Brothers Inc) 2×16 31.2 2624±28 124.4±6.7 0.021±0.0009
Aslan 500 CFRP tape**
(Hughes Brothers Inc) 2×16 31.2 2707±5 132±3.1 0.0205±0.0005
* Used for beams BS-NP-FS, BS-P1-FS, and BS-P2-FS ** Only used for beam BS-P3-FS
4.7.1.4 Epoxy Adhesives
Two types of epoxy adhesives were used similar to phase I with the properties
presented in Section 3.3.3.4.
4.7.1.5 Anchor Bolts
The anchors bolts used in phase II are the same as the ones used in phase I. The
material properties of the bolts are presented in Section 3.3.3.4.
4.7.2 Results from Sustained Load and Freeze-Thaw Exposure
After strengthening, the beams in phase II were placed inside the environmental
chamber and the sustained load was applied to the beams using the system and procedure
described in Section 3.3.6. Prior to sustained loading, two trial instant loadings were
209
applied to the system to check the performance of the frame system developed for
loading and the instrumentations. Then, the sustained load was applied and the system
was locked. The system was monitored for three days and the loss in load was measured,
then the applied load was modified and checked in regular time period of one week to
keep the value of the load constant. Therefore, three stages of sustained loading were
applied during the period of the exposure (204 days). The average sustained load value
was to 47% of the analytical ultimate load of beam BS-NP-FS. The load-deflection
history for each beam is presented in Figure 4-52 to Figure 4-56 showing the two instant
loadings and unloadings, and three sustained loading and unloading stages. The sustained
load history is presented in Figure 4-61 to Figure 4-61, which shows the beams were
under slightly different sustained loads (ranging from 59.8 kN to 64.6 kN) which is
expected due to the different stiffness of the beams under the loading system. The
deflection history for each beam is presented in Figure 4-62 to Figure 4-66. In the first
stage, the beams were subjected to sustained load for 4 days at room temperature to
investigate the performance of the developed sustained loading system. In the second
stage, the beams were subjected to sustained load and freeze-thaw cycles for 3 weeks.
Then, the load was adjusted for the third stage, and the beams were subjected to sustained
load and freeze-thaw cycles for 6 months. During the exposure, the system was checked
and adjusted in regular period of one week, also, the strain in tension and compression
steel bars at mid-span, strain in CFRP strip at mid-span, and vertical deflection at mid-
span were all recorded at a rate of one reading every 1 min. It should be noted that the
LSCs placed at mid-span of the beams B0-FS, BS-NP-FS, BS-P1-FS, and BS-P2-FS
were damaged under freeze-thaw cycles and the after exposure permanent deflection in
210
these beams was estimated using the trend-line as shown in Figure 4-62 to Figure 4-66. It
should be noted that in Figure 4-52 to Figure 4-61, the sustained load corresponding to
the recorded deflection of each beam was calculated using the load-deflection responses
of the beams from set BS-F (presented in Figure 4-1) that were similar to the beams in set
BS-FS (for example the value of measured deflection under sustained load for each beam
was pluged into Figure 4-1 and the corresponding load was determined for the same
beam, this value of the load is used in Figure 4-52 to Figure 4-61). The effects of the
applied exposure (combined sustained load and 500 freeze-thaw cycles) on the beams
were significantly severe in phase II, and therefore, resulted in large permanent
deflections ranging from 8-15.6 mm.
0
10
20
30
40
50
60
70
80
0 3 6 9 12 15 18 21 24 27 30
Lo
ad
(k
N)
Mid-span deflection of beam B0-FS (mm)
Instant loading Sustained loading-stage 1
Sustained loading-stage 2 Sustained loading-stage 3
O : Estimated Permanent deflection
The fluctuation at peak load is due to load adjustment and freeze-thaw cycles
Figure 4-52: Load-deflection history for beam B0-FS.
211
0
10
20
30
40
50
60
70
80
0 3 6 9 12 15 18 21 24 27 30
Lo
ad
(k
N)
Mid-span deflection of beam BS-NP-FS (mm)
Instant loading Sustained loading-stage 1
Sustained loading-stage 2 Sustained loading-stage 3
O : Estimated Permanent deflection
The fluctuation at peak load is due to load adjustment and freeze-thaw cycles
Figure 4-53: Load-deflection history for beam BS-NP-FS.
0
10
20
30
40
50
60
70
80
0 3 6 9 12 15 18 21 24 27 30
Lo
ad
(k
N)
Mid-span deflection of beam BS-P1-FS (mm)
Instant loading Sustained loading-stage 1
Sustained loading-stage 2 Sustained loading-stage 3
O : Estimated Permanent deflection
The fluctuation at peak load is due to load adjustment and freeze-thaw cycles
Figure 4-54: Load-deflection history for beam BS-P1-FS.
212
0
10
20
30
40
50
60
70
80
0 3 6 9 12 15 18 21 24 27 30
Lo
ad
(k
N)
Mid-span deflection of beam BS-P2-FS (mm)
Instant loading Sustained loading-stage 1
Sustained loading-stage 2 Sustained loading-stage 3
O : Estimated Permanent deflection
The fluctuation at peak load is due to load adjustment and freeze-thaw cycles
Figure 4-55: Load-deflection history for beam BS-P2-FS.
0
10
20
30
40
50
60
70
80
0 3 6 9 12 15 18 21 24 27 30
Lo
ad
(k
N)
Mid-span deflection of beam BS-P3-FS (mm)
Instant loading Sustained loading-stage 1
Sustained loading-stage 2 Sustained loading-stage 3
O : Recorded Permanent deflection
The fluctuation at peak load is due to load adjustment and freeze-thaw cycles
Figure 4-56: Load-deflection history for beam BS-P3-FS.
213
Sustained load = 63.3-0.0114×(days)
0
15
30
45
60
75
30 60 90 120 150 180 210
Su
sta
ine
d lo
ad
on
b
eam
B0-F
S (
kN
)
Time (day)
Sustained loading-stage 1 Sustained loading-stage 2
Sustained loading-stage 3 Trendline
Figure 4-57: Sustained load history for beam B0-F.
Sustained load = 62.5-0.0155×(days)
0
15
30
45
60
75
30 60 90 120 150 180 210
Su
sta
ine
d lo
ad
on
b
eam
BS
-NP
-FS
(kN
)
Time (day)
Sustained loading-stage 1 Sustained loading-stage 2
Sustained loading-stage 3 Trendline
Figure 4-58: Sustained load history for beam BS-NP-FS.
Sustained load = 64.6-0.0167×(days)
0
15
30
45
60
75
30 60 90 120 150 180 210
Su
sta
ine
d lo
ad
on
b
eam
BS
-P1-F
S (
kN
)
Time (day)
Sustained loading-stage 1 Sustained loading-stage 2
Sustained loading-stage 3 Trendline
Figure 4-59: Sustained load history for beam BS-P1-FS.
214
Sustained load = 60.1-0.0037×(days)
0
15
30
45
60
75
30 60 90 120 150 180 210
Su
sta
ined
lo
ad
on
b
eam
BS
-P2-F
S (
kN
)
Time (day)
Sustained loading-stage 1 Sustained loading-stage 2
Sustained loading-stage 3 Trendline
Figure 4-60: Sustained load history for beam BS-P2-FS.
0
15
30
45
60
75
30 60 90 120 150 180 210
Su
sta
ined
lo
ad
on
b
eam
BS
-P3-F
S (
kN
)
Time (day)
Sustained loading-stage 1 Sustained loading-stage 2
Sustained loading-stage 3
Figure 4-61: Sustained load history for beam BS-P3-FS.
Δ = 25.02-0.0044×(days)
0
5
10
15
20
25
30
0 30 60 90 120 150 180 210
Mid
-sp
an
defl
ecti
on
of
be
am
B0-F
S (
mm
)
Time (day)
Sustained loading-stage 1 Sustained loading-stage 2
Sustained loading-stage 3 Trendline
Figure 4-62: Deflection history for beam B0-FS.
215
Δ = 22.03-0.0059×(days)
0
5
10
15
20
25
30
0 30 60 90 120 150 180 210
Mid
-sp
an
defl
ecti
on
of
be
am
BS
-NP
-FS
(m
m)
Time (day)
Sustained loading-stage 1 Sustained loading-stage 2
Sustained loading-stage 3 Trendline
Figure 4-63: Deflection history for beam BS-NP-FS.
Δ = 19.40-0.0056×(days)
0
5
10
15
20
25
30
0 30 60 90 120 150 180 210
Mid
-sp
an
defl
ecti
on
of
beam
BS
-P1-F
S (
mm
)
Time (day)
Sustained loading-stage 1 Sustained loading-stage 2
Sustained loading-stage 3 Trendline
Figure 4-64: Deflection history for beam BS-P1-FS.
Δ =15.91 -0.0016×(days)
0
5
10
15
20
25
30
0 30 60 90 120 150 180 210
Mid
-sp
an
defl
ecti
on
of
beam
BS
-P2-F
S (
mm
)
Time (day)
Sustained loading-stage 1 Sustained loading-stage 2
Sustained loading-stage 3 Trendline
Figure 4-65: Deflection history for beam BS-P2-FS.
216
0
5
10
15
20
25
30
0 30 60 90 120 150 180 210
Mid
-sp
an
de
flec
tio
n o
f b
eam
BS
-P3-F
S (
mm
)
Time (day)
Sustained loading-stage 1 Sustained loading-stage 2
Sustained loading-stage 3
Figure 4-66: Deflection history for beam BS-P3-FS.
On the other hand, after removing the beams from the environmental chamber it
was observed that debonding occurred at the end regions of the NSM CFRP strips at the
concrete-epoxy interface. The schematic and lengths of the debonded regions are
presented in Figure 4-67 and Table 4-14. Further, the beams were cracked extensively
due to exposure as can be seen in Figure 4-68 to Figure 4-72. These observations
revealed that the RC beam strengthened with prestressed NSM CFRP strip is prone to
debonding up to 65% of the total prestressing length; on the other hand, the non-
prestressed NSM CFRP strengthened RC beam is not susceptible to debonding under
freeze-thaw exposure and sustained load since no sign of debonding was observed after
removing the beam from the chamber. The reason is that the concrete surrounding the
prestressed NSM CFRP strips is under shear stress and due to its degradation because of
the freeze-thaw exposure, the bond capacity at the concrete-epoxy interface gradually
decreases and leads to debonding. The debonded length increases when the prestressing
level in the NSM CFRP increases. Also, the debonded length at the jacking end of the
217
NSM CFRP (named as “DL-JE” in Table 4-14) is higher than that at the fixed end
(named as “DL-FE” in Table 4-14). The reason is that the concrete-epoxy interface is
under more shear stress at the jacking end than the fixed end since the steel anchor at
jacking end was bolted after adhesive cured (24hrs after prestressing) and then the
jacking force was released. This procedure applies more shear stress at the concrete-
epoxy interface at the jacking end. This issue can be solved by modifying the prestressing
procedure, i.e., bolting the steel anchor at the jacking end and releasing the jacking force
prior to hardening the adhesive in the groove. The concern with this solution might be
having more prestressing loss in the NSM CFRP reinforcement due to seating of the steel
anchor on the bolts.
Figure 4-67: Debonding occurred at concrete-epoxy interface due to freeze-thaw
exposure and sustained load.
Table 4-14: Debonded length of the beams shown in Figure 4-67.
Beam ID
DL-FE
(debonded length at fixed
end of NSM CFRP) (mm)
DL-JE
(debonded length at jacking
end of NSM CFRP) (mm)
Total
debonded
length (mm)
Debonded
length to total
length (%)
B0-FS N.A. N.A. N.A. N.A.
BS-NP-FS 0 0 0 0
BS-P1-FS 150 600 750 19.3
BS-P2-FS 905 1435 2340 60.3
BS-P3-FS 665 1865 2530 65.2
218
Figure 4-68: Images of beam B0-FS after exposure.
Left end Mid-span Right end
Side view
218
219
Figure 4-69: Images of beam BS-NP-FS after exposure.
Side view
Top view at location #1 Top view at location #2
Bottom view at left end anchor Left end Right end
Location #1 Location #2
219
220
Figure 4-70: images of beam BS-P1-FS after exposure.
Side view
Bottom view at left end anchor
Left end Right end
Bottom view at location #2 Bottom view at right end
Mid-span
Top view at location #1
Location #1
Location #2
220
221
Figure 4-71: Images of beam BS-P2-FS after exposure.
Side view
Mid-span Right end Left end
Bottom view at left end
Bottom view
at left end
Bottom view
at right end
Top view at location #1
Bottom view at right end
Location #1
221
222
Figure 4-72: Images of beam BS-P3-FS after exposure.
Bottom view at left end
Mid-span Left end Right end
Bottom view
at left end
Bottom view
at right end
Side view
Top view at location #1
Bottom view at right end
Location #1
222
223
4.7.3 Load-Deflection Response
The load-deflection responses of the beams tested to failure in phase II are plotted
in Figure 4-73 and Figure 4-74. The permanent deflections due to sustained loading are
included in the plotted curves in Figure 4-73; while these values are not included in
Figure 4-74 to have a better comparison on the post-exposure behaviour of the beams
tested in phase II with the beams tested in phase I, hereafter. In addition, a summary of
the results is presented in Table 4-15. It should be noted that the cracking loads and the
corresponding deflections for the beams are not presented in the table. Since all the
beams work interdependently under the loading frame used to apply the sustained load
(see Section 3.3.6), finding the exact cracking load for each beam is not possible. Also,
the limited space in the chamber during loading did not allow for the discovery of the
cracking load for each beam by visual inspection.
The load-deflection responses in phase II are significantly different from the ones
in phase I (Figure 4-1) where the load-deflection responses of the prestressed NSM CFRP
strengthened RC beams are typically made of three-linear slopes. In phase II, the
responses include the negative camber due to prestressing, yielding of tension steel
rebars, and failure due to concrete crushing or CFRP debonding. Also, the large drop in
load-deflection response at failure (as the ones observed in Figure 4-1) does not occur
and the failure is ductile even though the ultimate load is significantly smaller than one
observed in phase I.
After prestressing the beams in phase II, an upward instant deflection (Δo) ranging
from 0.44-1.38 mm was observed; seven days later, these ranges changed to 0.34-1.71
mm as presented in Table 4-15 as the effective negative camber (Δoe). As explained
224
earlier in Section 4.2.2.1, removing the temporary bracket and less likely the creep within
one week are the reasons for increasing the upward deflection.
The initial and effective prestrain values obtained from the strain gauges installed
at constant moment region of the beams are provided in Table 4-15. The effective
prestrain values were obtained seven days after prestressing which show an average loss
of 2.41±0.34%. Thereafter, the beams were subjected to sustained load and freeze-thaw
cycles and experienced the permanent deflections ranging from 8-15.6 mm, as explained
in Section 4.7.2.
Since, the concrete components of the beams were severely deteriorated due to
combined exposure and sustained load, as shown in Figure 4-68 to Figure 4-72, all beams
showed the failures related to concrete, i.e., concrete crushing followed by CFRP
debonding at concrete-epoxy interface. In this regards, the failure occurred shortly after
tension steel yielding showing a completely non-typical behaviour. In reinforced concrete
structures, creep results in gradual transfer of load from the concrete to the
reinforcements. Once the steel yields, any increase in load is taken by the concrete so that
the full strength of both the steel and the concrete is developed before failure takes place.
The failure mode of each beam is marked on Figure 4-74. Photos of the beams at failure
are presented in Figure 4-75 to Figure 4-79.
225
0
20
40
60
80
100
120
0 20 40 60 80 100 120 140 160 180
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-NP-FS BS-P1-FS BS-P2-FS BS-P3-FS B0-FS
: Concrete crushingO : Concrete crushing and NSM CFRP debonding, simultaneously
Figure 4-73: Load-deflection curves of the beams subjected to combined sustained load and freeze-thaw exposure (phase II, set
BS-FS, including permanent deflection after sustained load and freeze-thaw exposure).
225
226
0
20
40
60
80
100
120
-5 15 35 55 75 95 115 135 155 175
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-NP-FS BS-P1-FS BS-P2-FS BS-P3-FS B0-FS
: Concrete crushingO : Concrete crushing and NSM CFRP debonding, simultaneously
Figure 4-74: Load-deflection curves of the beams subjected to combined sustained load and freeze-thaw exposure (phase II, set
BS-FS).
226
227
Table 4-15: Summary of the test results for phase II (beams subjected to combined sustained load and freeze-thaw exposure).
Beam ID ɛp
(µɛ)
Δo*
(mm)
ɛpe
(µɛ)
Δoe
(mm)
Δop
(mm)
Py
(kN)
Δy*
(mm) Py/Py0 Py/Pyn
Pu
(kN)
Δu*
(mm) Pu/Pu0 Pu/Pun
Φ
(kN. mm)
Failure
mode
B0-FS N.A. N.A. N.A. N.A. 15.6 62.3 13.3 1.00 N.A. 77.9 80.9 1.00 N.A. 5462.9 CC
BS-NP-FS 0 0 0 0.00 13.7 74.4 15.5 1.19 1.00 98.3 57.6 1.26 1.00 4496.6 CC
BS-P1-FS 3644 -0.44 3550 -0.34 11.5 83.8 17.5 1.35 1.13 96.8 35.1 1.24 0.98 2534.5 CC
BS-P2-FS 6907 -0.93 6726 -1.07 10.1 90.5 20.6 1.45 1.22 91.4 21.9 1.17 0.93 1343.8 CC-DB
BS-P3-FS 10290 -1.38 10082 -1.71 8 101.5 19.4 1.63 1.36 106.7 36.7 1.37 1.09 3174.6 DB-CC
ɛp and Δo = initial prestrain and initial camber due to prestressing Δop = permanent deflection after sustained loading and freeze-thaw exposure
Py and Δy = load and deflection at yielding ɛpe and Δoe = effective prestrain and camber at 7 days after prestressing
Pu and Δu = load and deflection at ultimate Φ = energy absorption (area under load-deflection curve) up to peak load
Py/Py0 and Pu/Pu0 = ratios of the yielding and ultimate loads of each beam to those from B0-FS
Py/Pyn and Pu/Pun = ratios of the yielding and ultimate load of each beam to those from corresponding non-prestressed strengthened beam
CC-DB= concrete crushing followed by the NSM CFRP debonding, almost simultaneously CC = concrete crushing
DB-CC= failure initiated by the NSM CFRP debonding and concrete crushing almost simultaneously, and then followed by the concrete crushing
* Δo, Δy, and Δu do not include the values of Δop
227
228
(a) Side view of the beam
(b) The other side view of the beam
(c) Bottom view of the beam
Figure 4-75: Photos of beam B0-FS at failure.
Concrete crushing
Concrete crushing
229
(a) Side view of the beam
(b) The other side view of the beam
(c) Bottom view of the beam
Figure 4-76: Photos of beam BS-NP-FS at failure.
Concrete crushing
Concrete crushing
230
(a) Side view of the beam
(b) The other side view of the beam
(c) Bottom view of the beam
Figure 4-77: Photos of beam BS-P1-FS at failure.
Concrete crushing
Concrete crushing
231
(a) Side view of the beam
(b) The other side view of the beam
(c) Bottom view of the beam
Figure 4-78: Photos of beam BS-P2-FS at failure.
Concrete crushing
Concrete crushing
232
(a) Side view of the beam
(b) The other side view of the beam
(c) Bottom view of the beam
Figure 4-79: Photos of beam BS-P3-FS at failure.
Concrete crushing
Concrete crushing
233
The un-strengthened control RC beam (B0-FS as shown in Figure 4-74) showed
a typical behaviour and failed due to concrete crushing occurred between two point loads
after yielding of the tension steel reinforcements. The major flexural cracks already
occurred in the beam due to freeze-thaw exposure and sustained load. These cracks got
wider as the applied monotonic load increased further and led to a large ultimate
deflection at mid-span of the beam. Then, the beam failed due to concrete crushing at the
load and deflection values lower than the expected.
For the non-prestressed strengthened RC beam, BS-NP-FS, debonding cracks at
the concrete-epoxy interface initiated from the point load location at a deflection and
corresponding load of 23 mm and 83.3 kN, and propagated towards the supports as the
monotonic loading applied further. Then, the concrete crushing started at a deflection and
corresponding load of 32.9 mm and 90 kN (after yielding of the tension steel bars) and
gradually propagated that caused a slight change in the slope of the load-deflection curve.
Major concrete crushing occurred at mid-span at a deflection and corresponding load of
49 mm and 97.3 kN and increased further to a deflection and corresponding load of 57.6
mm and 98.3 kN, which caused a large drop in the load-deflection curve. While the test
continued, complete debonding of the NSM-CFRP strips from the concrete substrate
occurred (from point load to the support at the right end of the beam that was the jacking
end at the time of prestressing). At this point, the force in the NSM CFRP reinforcement
was completely transferred to the end anchor leading to formation of cracks at the
location of the anchor bolts. Images of the beams BS-NP-FS at failure are presented in
Figure 4-75.
234
For beam BS-P1-FS, strengthened using prestressed NSM CFRP strips with
prestress level of 17%, the NSM CFRP debonded from both ends that occurred at the
concrete-epoxy interface due to combined freeze-thaw exposure and sustained load
before starting the static test. The length of the debonded NSM CFRP at each end is
provided in Table 4-14. At a load and corresponding deflection of 90 kN and 22 mm, the
debonded length reached to 750 mm from the right end (jacking end at the time of
prestressing) as shown in Figure 4-67. The concrete crushing started at mid-span location
at a load and corresponding deflection of 95 kN and 29.2 mm and gradually increased as
the monotonic loading applied further. By continuing the test, debonding from the right
end extended to a wide flexural crack at the point load location and stopped. The beam
failed due to concrete crushing (at a load of 96.8 kN and a corresponding deflection of
35.1 mm) that caused a large drop in the load-deflection response. Afterwards, more
crushing occurred as the secondary failure, and no future increase in the load was
recorded. Finally, the end anchor was separated due to concrete block failure surrounding
the bolts. Photos of beam BS-P1-FS at failure are presented in Figure 4-77.
Beam BS-P2-FS, strengthened using prestressed NSM CFRP strips with prestress
level of 33%, had a long debonded length before starting of the static test. The debonded
length included 60.3% of the total NSM CFRP length (front-to-front of the anchor), more
details can be found in Table 4-14 and Figure 4-71. Due to significant debonding and also
deterioration of concrete materials, the beam failed due to concrete crushing followed by
CFRP debonding almost simultaneously at a load of 91.4 kN and a corresponding
deflection of 21.9 mm shortly after yielding of the tension steel reinforcements (as shown
in Figure 4-74). By continuing the test, more concrete crushing occurred at mid-span that
235
caused a drop in the load-deflection response (at a deflection of 35 mm and a
corresponding load of 90.2 kN). The debonding (from the right end of the beam that was
the jacking end at the time of prestressing) reached a wide flexural crack at the location
of the point load and did not extend further. The debonded length from the left end of the
beam (fixed end at the time of prestressing) did not increase significantly during the static
test. No further increase in the load was observed as the test continued and more crushing
occurred at a deflection and corresponding load of 116 mm and 81.3 kN causing a large
drop in the load-deflection response and then the test was terminated.
Beam BS-P3-FS, strengthened using prestressed NSM CFRP strips with high
prestress level of 50%, showed the longest debonded length under combined freeze-thaw
exposure and sustained load (65.2% of total NSM CFRP length) as presented in Table
4-14 and Figure 4-72. The debonded length from the right end of the beam (jacking end
at the time of prestressing of the NSM CFRP strips) reached the point load location
before starting of the static test. The beam experienced debonding followed by crushing,
almost simultaneously, at a deflection of 22.3 mm and a corresponding load of 103.9 kN
shortly after yielding that caused a small drop in the load deflection response as shown in
Figure 4-74. By continuing the test further, an increase in the load was observed and the
beam failed due to crushing between mid-span location and point load at a deflection of
36.7 mm and a corresponding load of 106.7 kN as marked on the curve in Figure 4-74.
The debonded length from the right end of the beam extended to a wide flexural crack at
the location of the point load and did not extend further. The third drop in the load
deflection curve is due to more debonding that reached to mid-span from the right side of
the beam (jacking end at the time of prestressing). Debonding from the left end of the
236
beam (fixed end at the time of prestressing) did not increase significantly. Finally, by
continuing the test the end anchor separated due to concrete block failure (at the right
end) and the test was terminated.
Comparison between load deflection response of the tested beams in phase II
reveals that the non-prestressed NSM CFRP strengthening system can increase the
yielding load of the un-strengthened control beam up to 17.7%, furthermore, prestressed
NSM CFRP strengthening system with prestress level ranging from 0-50% can increase
the yielding load of the un-strengthened control beam up to 64.8% where 17.7% of this
value is related to strengthening and the rest, 47.1%, is related to prestressing effects. On
the other hand, the prestressed NSM CFRP strengthening increases the ultimate load of
the un-strengthened control beam up to 36.7% while 26.1% of this value is related to
strengthening and the rest, 10.7%, is related to prestressing effects.
4.7.4 Load-Strain Response
The relation between the load and strains in the extreme concrete compression
fibre, compression steel, tension steel, and CFRP strips at mid-span location of the tested
beams are presented in Figure 4-80 to Figure 4-87.
For the extreme concrete compression fibre, tension steel, and CFRP strips, the
load-strain relation consists of two parts: from the start of the static test to yielding of
tensile steel, and from yielding of tensile steel to failure. Since, the beams were already
cracked before starting of the static tests due to the applied sustained load; therefore, the
load-strain relation is linear from beginning of the test up to yielding of the tensile steel.
Yielding of the tension steel leads a significant reduction in flexural stiffness of the beam
237
that causes a decrease in the slope of the load-strain curves. By continuing the test
further, the curves reach a point at which the concrete crushing occurs. The load versus
tensile steel strain relations are obtained based on the LSCs installed at the level of the
longitudinal tension steel, since the strain gauges on the tension steel reinforcements were
damaged before yielding; therefore, no yielding plateau is observed in the plotted curves
for tension steel in Figure 4-80 to Figure 4-87.
Strain in the concrete, top steel, bottom steel, and CFRP strips at different stages
are presented in Table 4-16. After prestressing, a negative camber occurs that leads the
top steel and top concrete goes to tension while the bottom steel goes to compression,
these tension and compression strain values are small.
Results of beams BS-NP-FS and BS-P1-FS reveals that these beams experienced
a large concrete compression strain, as presented in Figure 4-85. This behaviour is due to
the severe environmental damage that has been done to the concrete materials of the
beams due to the freeze-thaw cycling, which decreases the concrete strength and
increases the ductility of the concrete materials due to presence of the thermal cracks. On
the other hand, although the instrumentation was performed at mid-span but the location
of the concrete crushing might not be at the centre of the beam to capture the maximum
strain reached at failure; this fact results in underestimation of the actual concrete
compressive strain at failure. For beams BS-P2-FS and BS-P3-FS, debonding of the NSM
CFRP at end regions prior to starting of the static test due to combined freeze-thaw
exposure and sustained load affected the ultimate capacity, which resulted in premature
failure in comparison. Therefore, these beams failed shortly after yielding of the tension
steel stage and did not experience high ductility as beams BS-NP-FS and BS-P1-FS. To
238
have a better comparison, the concrete strain at extreme compression fibre, the strain in
CFRP strips, and the strain in tension steel reinforcements versus the load are presented
in Figure 4-84 to Figure 4-86, respectively.
The strains in the compression steel reinforcements are compared in Figure 4-87
for all beams. The curves are plotted based on the reading from strain gauges installed on
the compression steel at mid-span. The compression steel strain almost showed linear
elastic behaviour prior to failure. For beams BS-NP-FS and B0-FS as can be seen in
Figure 4-80 and Figure 4-87, respectively, the strain in compression steel decreases
shortly before failure; as mentioned earlier in Section 4.2.3, this is due to local buckling
of the compression steel at mid-span location after the start of the concrete crushing. For
beams BS-P1-FS, BS-P2-FS, and BS-P3-F, a sudden increase can be seen in compression
steel strain shortly before failure, this is due to the reason that after the start of the
concrete crushing in these beams more load is transferred to the compression steel.
239
0
20
40
60
80
100
120
-0.018 -0.0135 -0.009 -0.0045 0 0.0045 0.009 0.0135
Lo
ad
(k
N)
Strain at mid-span
BS-NP-FS, Concrete Strain
BS-NP-FS, Top Steel Strain
BS-NP-FS, Bottom Steel Strain
BS-NP-FS, CFRP Strain
TensionCompression
Ultimate load = 98.3 kN
Figure 4-80: Load-strain curves for BS-NP-FS.
0
20
40
60
80
100
120
-0.018 -0.0135 -0.009 -0.0045 0 0.0045 0.009 0.0135
Lo
ad
(k
N)
Strain at mid-span
BS-P1-FS, Concrete Strain
BS-P1-FS, Top Steel Strain
BS-P1-FS, Bottom Steel Strain
BS-P1-FS, CFRP Strain
TensionCompression
Ultimate load = 96.8 kN
Figure 4-81: Load-strain curves for BS-P1-FS.
240
0
20
40
60
80
100
120
-0.018 -0.0135 -0.009 -0.0045 0 0.0045 0.009 0.0135
Lo
ad
(k
N)
Strain at mid-span
BS-P2-FS, Concrete Strain
BS-P2-FS, Top Steel Strain
BS-P2-FS, Bottom Steel Strain
BS-P2-FS, CFRP Strain
TensionCompression TensionCompression
Ultimate load = 91.4 kN
Figure 4-82: Load-strain curves for BS-P2-FS.
0
20
40
60
80
100
120
-0.018 -0.0135 -0.009 -0.0045 0 0.0045 0.009 0.0135
Lo
ad
(k
N)
Strain at mid-span
BS-P3-FS, Concrete Strain
BS-P3-FS, Top Steel Strain
BS-P3-FS, Bottom Steel Strain
BS-P3-FS, CFRP Strain
TensionCompression TensionCompression TensionCompression TensionCompression
Ultimate load = 106.7 kN
Figure 4-83: Load-strain curves for BS-P3-FS.
241
0
20
40
60
80
100
120
0 0.003 0.006 0.009 0.012 0.015
Lo
ad
(k
N)
Strain in CFRP strips at mid-span
BS-NP-FS BS-P1-FS BS-P2-FS BS-P3-FS
Figure 4-84: Load-CFRP strain for all beams.
0
20
40
60
80
100
120
-0.021 -0.018 -0.015 -0.012 -0.009 -0.006 -0.003 0
Lo
ad
(k
N)
Concrete strain in extreme compression fiber at mid-span
BS-NP-FS BS-P1-FS BS-P2-FS BS-P3-FS B0-FS
Figure 4-85: Load-concrete strain in extreme compression fibre for all beams.
242
0
20
40
60
80
100
120
-0.0005 0.004 0.0085 0.013 0.0175 0.022 0.0265
Lo
ad
(k
N)
Strain in tension steel at mid-span
BS-NP-FS BS-P1-FS BS-P2-FS BS-P3-FS B0-FS
Figure 4-86: Load-tension steel strain curves for all beams.
0
20
40
60
80
100
120
-0.005 -0.004 -0.003 -0.002 -0.001 0
Lo
ad
(k
N)
Strain in compression steel at mid-span
BS-NP-FS BS-P1-FS BS-P2-FS BS-P3-FS B0-FS
Figure 4-87: Load-compression steel strain curves for all beams.
243
Table 4-16: Strain in CFRP strips or rebar, extreme compression fibre of concrete,
compression steel, and tension steel at mid-span at different stages.
Beam ID ɛf-i
(µɛ)
ɛf-7days
(µɛ)
ɛf-su
(µɛ)
ɛc-i
(µɛ)
ɛc-7days
(µɛ)
ɛc-su
(µɛ)
ɛsc-i
(µɛ)
ɛsc-7days
(µɛ)
ɛsc-su
(µɛ)
ɛst-i
(µɛ)
ɛst-7days
(µɛ)
ɛst-su
(µɛ)
B0-FS N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. -418 N.A. N.A. 1753
BS-NP-FS 0 0 1507 N.A. N.A. N.A. N.A. N.A. -468 N.A. N.A. 1221
BS-P1-FS 3644 3550 4809 75 25 N.A. 16 11 -179 -38 -23 1641
BS-P2-FS 6907 6726 7516 90 220 N.A. 41 30 -414 -76 -100 864
BS-P3-FS 10290 10082 10850 131 109 N.A. 53 46 -285 -121 -149 588
ɛf-i, ɛc-i, ɛsc-i, and ɛst-i = initial prestrain in CFRP strips or rebar, extreme concrete fibre at top, top steel and bottom steel due
to prestressing ɛf-7days, ɛc-7days, ɛsc-7days, and ɛst-7days = strain in CFRP strips or rebar, extreme concrete fibre at top, top steel and bottom steel
at 7 days after prestressing
ɛf-su, ɛc-su, ɛsc-su, and ɛst-su = strain in CFRP strips or rebar, extreme concrete fibre at top, top steel, and bottom steel under
sustained load and freeze-thaw exposure
4.7.5 Strain Profile along the CFRP Strips
The strain profiles along the length of the NSM CFRP strip at yielding, and
ultimate loads are presented in Figure 4-89 and Figure 4-90, respectively. The profiles are
plotted based on the reading of strain from the installed strain gauges at specified
locations on the CFRP strips. For beam BS-NP-FS the strains are close to zero at the ends
of the CFRP strip at yielding and ultimate load levels (as shown in Figure 4-89 and
Figure 4-90). This implies the presence of the full bonding at the end and also complete
contribution of the epoxy adhesive in transferring the forces between the CFRP strip and
the surrounding concrete. Furthermore, the concrete-epoxy interface at the end of the
NSM CFRP strip is highly affected by stress concentration which caused debonding at
the end portion of the NSM CFRP strips under sustained load in the prestressed
strengthened beams, BS-P1-FS, BS-P2-FS, and BS-P3-FS. The end anchors have full
contribution in transferring the load after occurrence of debonding. Therefore, it is very
important that during the prestressing process, i.e., after removing the temporary
244
brackets, the end anchors are in contact with the bolts and there is no gap between them
An instance of this gap is shown in Figure 4-88. If there is any, these gaps will results in
prestressing loss (seating loss) after debonding. It should be mentioned that this loss (if
there were any) was not captured during the sustained loading under freeze-thaw
exposure. Capturing this strain loss needs waterproof instrumentation along the length of
the NSM-CFRP strips that can provide reading under freeze-thaw exposure and sustained
loading.
Figure 4-88: Gap between bolt and jacking end anchor causing future prestress loss.
As observed in Section 4.2.4, when there is no debonding the highest strain in the
CFRP strip occurs at the constant moment region of the beams (location 2000-3000 mm).
This fact is not valid for the prestressed strengthened beams tested in phase II. Since the
Gaps between bolt and anchor plate
245
prestressed strengthened beams debonded under exposure, the strain profile is almost
constant within the NSM CFRP length.
Comparison between strain profiles for beam BS-NP-FS in Figure 4-89 and
Figure 4-90 shows that the strain at both ends near the end anchors almost remained
constant during the static test showing no slippage at the ends of the NSM CFRP strip
and appropriate performance of the epoxy in transferring the forces.
0
0.003
0.006
0.009
0.012
0.015
0 1000 2000 3000 4000 5000
Str
ain
in
CF
RP
str
ip a
t yie
ldin
g
Distance from the support (mm)
BS-NP-FS BS-P1-FS BS-P2-FS BS-P3-FS
Figure 4-89: Strain profile along the length of the NSM CFRP strip at yielding.
246
0
0.003
0.006
0.009
0.012
0.015
0 1000 2000 3000 4000 5000
Str
ain
in
CF
RP
str
ip a
t u
ltim
ate
Distance from the support (mm)
BS-NP-FS BS-P1-FS BS-P2-FS BS-P3-FS
Figure 4-90: Strain profile along the length of the NSM CFRP strip at ultimate.
4.7.6 Strain Distribution at Mid-span
The strain distributions at mid-span section along the depth of the beams at
yielding and ultimate loads are presented in Figure 4-91, Figure 4-92 and Table 4-17. The
strain distributions are plotted using the strain values in concrete, compression steel,
tension steel, and CFRP strip including the effective strain due to prestressing.
The strain distributions are nonlinear at yielding, in which the nonlinearity is
caused by concrete and can be observed in top portion of the strain distributions in Figure
4-91.
The un-strengthened control RC beam, B0-FS, showed the highest curvature
among the tested beams at ultimate stage. During the test, debonding was observed at
mid-span regions at concrete-epoxy interface. Using the slope procedure, analyzing the
247
results revealed that the slope of the strain distribution between steel level and the CFRP
level at yielding and ultimate loads changes for the strengthened beams confirming the
occurrence of debonding.
-400
-350
-300
-250
-200
-150
-100
-50
0
-0.005 0 0.005 0.01 0.015
Secti
on
dep
th (
mm
)
Strain at yielding
B0-FS BS-NP-FS BS-P1-FS BS-P2-FS BS-P3-FS
Bottom steel centroid @ 343 mm
NSM CFRP strip centroid @ 387.5 mm
Top steel centroid @ 35 mm
Top fibres of the beam
Figure 4-91: Strain distribution at mid-span at yielding.
36
248
-400
-350
-300
-250
-200
-150
-100
-50
0
-0.02 -0.01 0 0.01 0.02 0.03
Secti
on
dep
th (
mm
)
Strain at ultimate
B0-FS BS-NP-FS BS-P1-FS BS-P2-FS BS-P3-FS
Bottom steel centroid @ 343 mm
NSM CFRP strip centroid @ 387.5 mm
Top steel centroid @ 35 mm
Top fibres of the beam
Figure 4-92: Strain distribution at mid-span at ultimate.
Table 4-17: Strain in extreme compression fibre of concrete, compression steel,
tension steel, and CFRP strip or rebar at mid-span section.
Beam ID ɛc-y
(µɛ)
ɛsc-y
(µɛ)
ɛst-y
(µɛ)
ɛf-y
(µɛ)
ɛc-u
(µɛ)
ɛsc-u
(µɛ)
ɛst-u
(µɛ)
ɛf-u
(µɛ)
B0-FS -1700 -834 1600 N.A. -19450 -1480 25275 N.A.
BS-NP-FS -2975 -925 1575 1710 -16200 -321 9450 7510
BS-P1-FS -3225 -1184 1475 5154 -7725 -2075 4300 6713
BS-P2-FS -1961 -1503 1604 8347 -2136 -1589 1235 8367
BS-P3-FS -1644 -911 1485 12107 -3019 -1352 2915 12073
ɛc = strain in extreme compression fibre of concrete (compression is negative) ɛsc = strain in compression steel
ɛst = strain in tension steel ɛf = strain in CFRP rebar or strip
y = at yielding u = at ultimate
4.8 Combined Effects of Freeze-Thaw Cycling Exposure and Sustained Load
In Section 4.5, the effects of the applied freeze-thaw cycling exposure in phase I
were analyzed by comparing the exposed and unexposed beams strengthened using NSM
CFRP strips and rebars showing the insignificant effects of the applied cycling exposure
36
249
on the overall flexural performance of the beams. In this section, the overall flexural
behaviour of the RC beams strengthened with non-prestressed and prestressed NSM
CFRP strips subjected to freeze-thaw cycling exposure (phase I: BS-F) are compared to
similar beams subjected to combined sustained load and freeze-thaw cycling exposure
(phase II: BS-FS).
4.8.1 Material Properties of the Compared Beams
A summary of the material properties of the beams strengthened with NSM CFRP
strips in phase I and phase II is provided in Sections 4.2.1 and 4.7.1, respectively.
4.8.2 Error Analysis
An error analysis is performed for the considered beams in phase I and phase II
(BS-F set and BS-FS set) to obtain the uncertainty of the comparison based on the
material properties. The analysis is done using the Equation 4-1 to Equation 4-4 and the
results are presented in Table 4-18. The results confirm validity of the comparisons
between the beams under freeze-thaw cycling exposure (set BS-F) and the beams
subjected to sustained load and freeze-thaw cycling exposure (set BS-FS) in which a
maximum uncertainty of 12.2% is probable due to difference between material properties
in sets BS-FS and BS-F.
250
Table 4-18: Uncertainty in comparison of sets BS-FS and BS-F based on material
properties.
Set
Uncertainty (%)
Up to
yielding (Eq. 4-1)
Yielding up
to failure (Eq. 4-2)
At failure
CFRP rupture (Eq. 4-3)
Concrete crushing (Eq. 4-4)
BS-FS w.r.t. BS-F 4.6 9.5 9.5 12.2
4.8.3 Load-Deflection Response
The results of the beams tested in phase I and phase II (RC beams strengthened
with NSM CFRP strips) are presented in Figure 4-93 and Table 4-19. The beams were
categorized into two sets: set BS-F subjected to freeze-thaw cycling exposure and set BS-
FS subjected to combined sustained load and freeze-thaw cycling exposure. For set BS-F,
the load-deflection curves include the negative camber due to prestressing, initiation of
flexural cracks, yielding of tension steel rebar, CFRP rupture or concrete crushing which
causes a large drop in load at ultimate stage, and post failure behaviour. On the other
hand, for set BS-FS, the load deflection curves comprise the negative camber due to
prestressing, yielding of the tension steel rebar, concrete crushing or NSM CFRP
debonding, and post failure.
An upward camber ranging between 0.49-1.71 mm for beams from set BS-F and
between 0.34-1.71 mm for beams from set BS-FS were recorded one week after
prestressing. The values of the initial and effective pre-strain in the CFRP strip, computed
by taking the average of the strain values at the constant moment region of the beams, are
presented in Table 4-19 showing an average prestressing loss of 2.52±0.37% one week
after prestressing. The beams in set BS-F were cracked after strengthening; the obtained
251
cracking loads show significant increase due to prestressing (up to 153% for set BS-F)
with respect to the non-prestressed strengthened beam of each set. The un-strengthened
control beams showed a low cracking load which is due to the presence of the micro-
cracks in the large-scale beams before testing, mainly caused from moving the beams
during the testing process. After this stage, the freeze-thaw exposure started on both sets.
Set BS-F was placed in the environmental chamber under 500 freeze-thaw cycles, and set
BS-FS was placed in the chamber under 500 freeze-thaw cycles while each beam was
subjected to a sustained load of 62 kN, equal to 47% of the theoretical ultimate load of
the non-prestressed NSM CFRP strengthened RC beam (BS-NP-F in Table 3-3). Then
both sets were removed and tested under four-point static monotonic loading.
252
0
20
40
60
80
100
120
140
160
-5 15 35 55 75 95 115 135 155 175
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-NP-F BS-P1-F BS-P2-F BS-P3-F B0-F
BS-NP-FS BS-P1-FS BS-P2-FS BS-P3-FS B0-FS
: CFRP rupture : Concrete crushingO : Concrete crushing and NSM CFRP debonding, simultaneouslyF : Freeze-thaw exposed beams
FS: Freeze-thaw and sustained load exposed beams
Figure 4-93: Comparison between exposed beams tested in phase I and II (freeze-thaw exposure versus combined sustained
load and freeze-thaw exposure).
252
253
Table 4-19: Summary of the test results for strengthened beam using CFRP strips (phases I & II). S
et
Beam ID ɛp
(µɛ)
ɛpe
(µɛ)
Δoe
(mm)
Pcr
(kN)
Δcr
(mm)
Δop
(mm)
Py
(kN)
Δy
(mm)
Pu
(kN)
Δu
(mm)
ɛfrp@u
(µɛ) μD
Φ
(kN. mm)
Failure
Mode
BS
-FS
, su
bje
cted
to
co
mb
ined
free
ze-t
haw
and
su
stai
ned
lo
ad
B0-FS N.A. N.A. N.A. N.A. N.A. 15.6 62.3 13.26 77.9 80.86 N.A. 6.10 5462.9 CC
BS-NP-FS 0 0 0.00 N.A. N.A. 13.7 74.4 15.47 98.3 57.59 7510 3.72 4496.6 CC
BS-P1-FS 3644 3550 -0.34 N.A. N.A. 11.5 83.8 17.52 96.8 35.13 6713 2.01 2534.5 CC
BS-P2-FS 6907 6726 -1.07 N.A. N.A. 10.1 90.5 20.60 91.4 21.95 8367 1.07 1343.8 CC-DB
BS-P3-FS 10290 10082 -1.71 N.A. N.A. 8 101.5 19.41 106.7 36.74 12073 1.89 3174.6 DB-CC
BS
-F,
sub
ject
ed t
o
free
ze-t
haw
B0-F N.A. N.A. N.A. 10.4 2.22 0.65 75.5 18.78 97.8 142.88 N.A. 7.61 7052†
CC
BS-NP-F 0 0 0 14 1.36 0.61 92.4 22.53 132.2 104.26 14900 4.63 10649 CC
BS-P1-F 3574 3463 -0.49 21.6 1.43 0.13 104.1 23.99 134.7 82.9 16592 3.46 8667 CC
BS-P2-F 6900 6723 -1.09 27.3 1.24 -0.81 114.8 25.56 149.5 87.85 21464 3.44 10214 FR
BS-P3-F 10112 9884 -1.70 35.5 1.45 -1.43 124.3 25.91 141.7 58.55 21118 2.26 6510 FR
ɛp = initial prestrain due to prestressing, ɛpe and Δoe = effective prestrain and camber at 7 days after prestressing,
Pcr and Δcr = load and deflection at cracking Δop = camber after exposure for set BS-FS and after initial loading (cracking) for set BS-F
Py and Δy = load and deflection at yielding ɛfrp@u = CFRP strain at failure at mid-span
Pu and Δu = load and deflection at ultimate μD = ductility index = Δu /Δy
CC and FR= concrete crushing and CFRP rupture Φ = energy absorption (area under P-Δ curve)
CC-DB= concrete crushing followed by the NSM CFRP debonding, almost simultaneously
DB-CC= failure initiated by the NSM CFRP debonding and concrete crushing almost simultaneously, and then followed by the concrete crushing † calculated based on concrete strain 0.004125 to be consistent with the other beams failed by concrete crushing
253
254
Comparison between yield loads shows the average decreases of 19.2±1.4% and
26.4±4.6% in the load and the deflection at yielding of the beams in set BS-FS with
respect to the corresponding beams in set BS-F, respectively. Besides, an average
decrease of 27.5±7% was observed in ultimate load of the beams in set BS-FS in
comparison to set BS-F. Furthermore, the deflection at ultimate for the beams in set BS-
FS shows an average decrease of 51.6±15% in comparison with beams BS-F.
Five exposed beams in set BS-F showed a typical failure mode, i.e., tension steel
reinforcements yielding followed by CFRP rupture or concrete crushing while the
exposed beams in set BS-FS failed at early stage after yielding due to concrete crushing;
concrete crushing followed by the NSM CFRP debonding, almost simultaneously; or an
initial NSM CFRP debonding and concrete crushing, almost simultaneously, followed by
the concrete crushing. The failure modes of the beams are marked in Figure 4-93.
Comparing the load-deflection curves of set BS-FS and BS-F reveals that in set BS-FS
the concrete materials were significantly affected and the beams were damaged more than
that in set BS-F. This damage caused an early concrete crushing failure and in some cases
NSM CFRP debonding shortly after the concrete crushing as the secondary failure.
The energy absorptions (Φ) of the beams defined as the area under the load-
deflection curve up to the peak load are presented in Figure 4-94 showing two sets of
beams. It is clear in Figure 4-94 that the beams tested in phase II (set BS-FS) showed a
significant reduction in energy absorption in comparison with the other set (phase I: BS-
F). An average of 63.9±14.9% decrease in energy absorption was observed for set BS-FS
in comparison with set BS-F. Besides, the results presented in Table 4-19 shows an
255
average decrease of 33.3±22.4% in ductility indices of the set BS-FS in comparison with
set BS-F.
0
2000
4000
6000
8000
10000
12000
14000
0 0.002 0.004 0.006 0.008 0.01
En
erg
y a
bso
rpti
on
(a
rea u
nd
er
load
-d
efl
ecti
on
cu
rve)
kN
.mm
Prestrain in CFRP strips
Energy absorption (BS-F set) Energy absorption (BS-FS set)
Figure 4-94: Effects of exposure on the energy absorption of the prestressed NSM
CFRP strengthened RC beams.
The overall comparison of the beams tested in this research reveals that the beams
strengthened with the prestressed NSM-CFRP strips subjected to combined severe
environmental exposure and sustained loading, tested to failure in flexure under static
monotonic loading, do not perform well especially after yielding of tension steel
reinforcements. In particular, the NSM-CFRP debonding at end regions of the prestressed
strengthened beams and low ductility and energy absorption resulted from the severe
256
damage to the concrete material are the issues that should be considered in long-term
performance of the prestressed NSM CFRP strengthened RC beams under freeze-thaw
exposure and sustained loading.
4.9 Prestress Losses in Phases I & II
Results of twelve RC beams strengthened with prestressed NSM CFRP strips and
rebars were considered to perform a comprehensive study on the prestress losses. The
beams were classified in three groups; Group A: four beams strengthened with CFRP
rebar subjected to freeze-thaw cycling exposure, Group B: four beams strengthened with
CFRP strips similar to Group A (in terms of prestressing level, CFRP axial stiffness, and
geometry) and subjected to freeze-thaw cycling exposure, and Group C: four beams
similar to Group B kept at room temperature. Strain loss is a reduction in the initial
prestrain in the NSM CFRP rebar or strips that can be categorized into two types,
instantaneous losses and long-term losses. Instantaneous losses occur quickly after
jacking (upon release of the jack and transfer of the prestress in the CFRP reinforcements
to the anchors) including seating losses (anchorage slip due to removing the temporary
brackets) and elastic shortening of concrete which are presented in Figure 4-95 to Figure
4-98 up to 168 hrs (7 days) after prestressing (obtained from beams in Group A and
Group B). In these figures, the losses are plotted for the beams strengthened with CFRP
strip and rebar at mid-span location.
Time-dependent prestressing losses including creep and shrinkage of the concrete
and CFRP relaxation occur gradually over the life-time of the beam strengthened with
prestressed NSM CFRP reinforcements. The long-term losses of the unexposed beams
257
(obtained from beams in Group C) are presented in Figure 4-98 up to five months; the
reason that these losses are calculated for five months is that the beams in Group C were
only kept five months after fabrication at room temperature prior to placing in the
chamber, waiting for phase I of the experimental program and also sustained loading
setup of phase II to be accomplished in the chamber. In addition, the long-term losses of
the exposed beams (obtained from beams in Group A and B under freeze-thaw cycling
exposure) are presented in Figure 4-99 to Figure 4-105 up to 74 days during exposure
(since the instrumentation were damaged under freeze-thaw cycling exposure after this
period). A 2%-6.2% strain loss is observed after 7 days with an average loss of 2.7±0.9%
for beams strengthened with NSM CFRP strips (Group B), 3.9±2.1% for beams
strengthened with NSM CFRP rebars (Group A) and 3.3±1.6% for all beams (Group A
plus Group B). Analyzing Figure 4-95 to Figure 4-97 reveals that significant amount of
the 7-day losses (60%-85%) occurs during the 24 hrs after prestressing. In this context,
82.2±4.1% of the 7-day losses of the beams strengthened with NSM-CFRP strips,
70.7±9.6% of the 7-day losses of the beams strengthened with NSM-CFRP rebars, and
76.4±9.1% of the 7-day losses of all beams occurs during the 24 hrs after prestressing.
The strain loss values are 133 µɛ, 172 µɛ, 200 µɛ, 208 µɛ, 126 µɛ, and 375 µɛ for beams
BS-P1-F, BS-P2-F, BS-P3-F, BR-P1-F, BR-P2-F, and BR-P3-F, respectively;
corresponding to the percentages of loss of 3.8%, 2.5%, 2%, 6.2%, 1.9%, and 3.6% for
beams BS-P1-F, BS-P2-F, BS-P3-F, BR-P1-F, BR-P2-F, and BR-P3-F, respectively. In
fact, by increasing the prestressing level in the NSM CFRP strip or rebar, the value of
instantaneous strain loss increases while the percentage of instantaneous loss decreases.
258
0
1
2
3
4
5
6
7
0.003
0.0031
0.0032
0.0033
0.0034
0.0035
0.0036
0 24 48 72 96 120 144 168
Pe
rce
nta
ge
of lo
ss
Pre
str
ain
in
CF
RP
Time (hr)
BS-P1-F
BR-P1-F
BS-P1-F (% of loss)
BR-P1-F (% of loss)
Figure 4-95: Losses in prestressed NSM CFRP strip or rebar: BS-P1-F and BR-P1-F.
0
0.5
1
1.5
2
2.5
3
0.0064
0.0065
0.0066
0.0067
0.0068
0.0069
0.007
0 24 48 72 96 120 144 168
Perc
en
tag
e o
f lo
ss
Pre
str
ain
in
CF
RP
Time (hr)
BS-P2-F
BR-P2-F
BS-P2-F (% of loss)
BR-P2-F (% of loss)
Figure 4-96: Losses in prestressed NSM CFRP strip or rebar: BS-P2-F and BR-P2-F.
259
0
0.5
1
1.5
2
2.5
3
3.5
4
0.0099
0.01
0.0101
0.0102
0.0103
0.0104
0.0105
0.0106
0 24 48 72 96 120 144 168
Perc
en
tag
e o
f lo
ss
Pre
str
ain
in
CF
RP
Time (hr)
BS-P3-F
BR-P3-F
BS-P3-F (% of loss)
BR-P3-F (% of loss)
Figure 4-97: Losses in prestressed NSM CFRP strip or rebar: BS-P3-F and BR-P3-F.
-140
-120
-100
-80
-60
-40
-20
0
0 30 60 90 120 150
Pre
str
ain
lo
ss in
CF
RP
str
ips (
µɛ)
Time (day)
BS-NP
BS-P1
BS-P2
BS-P3
Figure 4-98: Losses in NSM CFRP strip (BS sets) at room temperature.
260
The long-term strain losses in the CFRP strips (at room temperature) up to 150
days after 7 days of initial recording are presented in Figure 4-98 for four beams (Group
C). The losses are mainly due to creep and shrinkage of the concrete and CFRP
relaxation. The prestressed strengthened beams showed higher strain losses than strain
changes in non-prestressed strengthened beam, BS-NP. The creep and shrinkage effects
exist and are active for all beams; therefore, the difference between strengthened and un-
strengthened strain losses is mainly due to relaxation of CFRP reinforcement, which is a
relatively small component of the total long-term losses. The maximum strain loss is 123
µɛ for the prestressed beams while it is 96µɛ for the non-prestressed beam after 150 days.
The difference which is 27 µɛ is likely related to relaxation of the CFRP strips.
Therefore, considering a maximum long term loss of 123µɛ, the total strain loss values
(instantaneous plus long-term for five months) are 256 µɛ (7.2%), 295 µɛ (4.3%), 323 µɛ
(3.2%), 331 µɛ (8.7%), 249 µɛ (3.8%), and 498 µɛ (4.8%) for beams BS-P1-F, BS-P2-F,
BS-P3-F, BR-P1-F, BR-P2-F, and BR-P3-F, respectively.
The changes in strain for RC beams strengthened with NSM CRRP strips and
rebars under freeze-thaw cycling exposure are presented in Figure 4-99 to Figure 4-105.
Due to damage that occurred in instrumentation (strain gauge), the strain fluctuation
graph is not provided for beam BR-P3-F, and also, the results of the other beams are
provided for 74 days. A maximum fluctuation of 220 µɛ is reached due to changes in
temperature from +34oC to -34
oC. The linear average of changes versus time as presented
on the graphs in Figure 4-99 to Figure 4-105 are insignificant for 74 days; maximum
average values of 37 µɛ as gain (the increase in CFRP strain) and 19.6 µɛ as loss for the
beams strengthened with CFRP strips, and 52 µɛ as gain and 39 µɛ as loss for the beams
261
strengthened with CFRP rebars are monitored after 74 days. On the other hand, the
average of changes in the CFRP strain over the time (linear equations in Figure 4-99 to
Figure 4-105) increases (called as gain) in some cases while this behaviour does not
occur at room temperature, as shown in Figure 4-98. Based on the applied freeze-thaw
cycles in this study and estimated corresponding years in real life (at least 12.8 years for
500 cycles), maximum strain changes of -536 µɛ (loss) and 710 µɛ (gain) are predicted
over 50 years. In this context, the value of loss is more important which should be
considered in design of the prestressed NSM CFRP strengthened RC beams. In fact, by
combining the instantaneous and long-term prestressing losses of the member under
freeze-thaw exposure, there is a possibility that an 8.5-22.8% loss depending on the
induced prestressing level occurs in the CFRP reinforcement during 50 years life-time of
the member strengthened with prestressed NSM CFRP reinforcements.
262
y = -0.0878x
-150
-100
-50
0
50
100
150
0 15 30 45 60 75
Str
ain
flu
ctu
ati
on
in
CF
RP
str
ips
(µɛ)
Time (day)
BS-NP-F
Linear (BS-NP-F)
Figure 4-99: CFRP Strain fluctuation in beam BS-NP-F under freeze-thaw exposure.
y = 0.5x
-150
-100
-50
0
50
100
150
0 15 30 45 60 75
Str
ain
flu
ctu
ati
on
in
CF
RP
str
ips
(µɛ)
Time (day)
BS-P1-F
Linear (BS-P1-F)
Figure 4-100: CFRP Strain fluctuation in beam BS-P1-F under freeze-thaw exposure.
263
y = 0.127x
-150
-100
-50
0
50
100
150
0 15 30 45 60 75
Str
ain
flu
ctu
ati
on
in
CF
RP
str
ips
(µɛ)
Time (day)
BS-P2-F
Linear (BS-P2-F)
Figure 4-101: CFRP Strain fluctuation in beam BS-P2-F under freeze-thaw exposure.
y = -0.265x
-150
-100
-50
0
50
100
150
0 15 30 45 60 75
Str
ain
flu
ctu
ati
on
in
CF
RP
str
ips
(µɛ)
Time (day)
BS-P3-F
Linear (BS-P3-F)
Figure 4-102: CFRP Strain fluctuation in beam BS-P3-F under freeze-thaw exposure.
264
y = 0.2405x
-150
-100
-50
0
50
100
150
0 15 30 45 60 75
Str
ain
flu
ctu
ati
on
in
CF
RP
re
ba
r (µɛ)
Time (day)
BR-NP-F
Linear (BR-NP-F)
Figure 4-103: CFRP Strain fluctuation in beam BR-NP-F under freeze-thaw exposure.
y = -0.5272x
-150
-100
-50
0
50
100
150
0 15 30 45 60 75
Str
ain
flu
ctu
ati
on
in
CF
RP
re
ba
r (µɛ)
Time (day)
BR-P1-F
Linear (BR-P1-F)
Figure 4-104: CFRP Strain fluctuation in beam BR-P1-F under freeze-thaw exposure.
265
y = 0.6984x
-150
-100
-50
0
50
100
150
0 15 30 45 60 75
Str
ain
flu
ctu
ati
on
in
CF
RP
re
ba
r (µɛ)
Time (day)
BR-P2-F
Linear (BR-P2-F)
Figure 4-105: CFRP Strain fluctuation in beam BR-P2-F under freeze-thaw exposure.
4.10 Modification of Temporary and Fixed Brackets of the Anchorage System for
Prestressing
The prestressing and anchorage system used in this research was first developed
by Gaafar (2007). The system is presented in Figure 4-106 showing the fixed and
movable brackets that are temporarily used for prestressing the NSM CFRP strips or
rebar. The brackets are connected by threaded rods used for maintaining the prestressing
force after releasing the hydraulic jacks. For prestressing the NSM CFRP in phases I and
II of this research, the steel brackets developed by Gaafar (2007) were modified, as
shown in Figure 4-107, by welding steel plates to the sides of the fixed bracket and to the
top of the movable bracket, and by drilling more holes to improve the system and avoid
rotation of the brackets at jacking stage.
266
Figure 4-106: Prestressing system developed by Gaafar (2007).
Figure 4-107: Steel brackets used for prestressing NSM CFRP in phases I and II.
In spite of all efforts performed on the modification of the brackets, although the
performance of the system improved, but still the cracks formed at the location of the
fixed bracket at high prestress levels (above about 40% of the CFRP ultimate strength).
These types of cracks are shown in Figure 4-108, and similar issues were reported by
Gaafar (2007) and Oudah (2011). The aim of this short section is to modify the
Temporary brackets
267
prestressing system to avoid these types of cracks and investigate the possible cracking
patterns at very high prestress levels (up to 75% of the CFRP ultimate strength).
Figure 4-108: Cracks at the locations of steel brackets at high prestress level.
A schematic of the interaction between the temporary steel brackets and beam is
presented in Figure 4-109 that shows the applied forces on the bolts. The forces applied
to the fixed bracket transferred to the beam through the bolts. The applied prestressing
force by the jack produce a moment due to eccentricity with respect to the centre of the
Cracks at location
of fixed bracket
Crack at location
of fixed bracket
Cracks at location
of fixed bracket
268
bolt group (cg). Therefore, the bolts at the fixed brackets need to resist the jacking force
(prestressing force) and the moment due to eccentricity. This combination applies a
downward shear force on the corner bolts at the left side of the fixed bracket as shown in
Figure 4-109, that is the main reason for the observed cracks as shown in Figure 4-108.
Figure 4-109: Interaction between temporary steel brackets and beam.
Two types of cracks were observed at the locations of the bolts: cracks due to
crushing of concrete on a small area around the bolts and tension cracks that extended to
the bottom face of the beams. To avoid these types of cracking, one solution is to increase
the number of the bolts so that the applied shear force on each bolt decreases; In this
regard, to avoid possible crushing around the bolts, the compression stress applied to the
concrete through the bolts should be less than the stress at which the concrete material
starts to crack at compression (about 0.7f′c). The second solution (the most economical
one) is to reduce the force applied to the bolts by reducing the eccentricity of the applied
269
prestressing load with cg of the bolts. To search the feasibility of the second solution,
three concrete specimens (1500×200×400 mm) were made and the fixed and movable
brackets were modified to be capable of changing the eccentricity (location of the jacks)
during the prestressing.
4.10.1 Modified Prestressing System and Material Properties
The modified prestressing system applied to the specimens and its components
are presented in Figure 4-110. The temporary steel brackets were modified by welding
steel plates to the sides to be capable of changing the location of the jacks. The three
fabricated concrete specimens had identical cross-section (200×400 mm) to the RC
beams tested in phases I and II except that they were shorter in length, having a length of
1500 mm. The concrete specimens had pre-formed grooves. A dywidag steel bar with
two adjustable nuts at the ends was used instead of the CFRP reinforcements to facilitate
the execution of the experiment. The end anchors were made to have enough bolts to
carry the applied load up to ultimate capacity of the dywidag bar. The material properties
of the specimens are presented in the following sections.
270
(a) Modified prestressing system with jacks placed at maximum eccentricity
(b) Modified prestressing system with jacks placed at low eccentricity
Figure 4-110: Modified prestressing system applied to the specimens.
Movable bracket Fixed bracket
Fixed end anchor
Dywidag bar Nut Nut Jacking end anchor Hydraulic jacks
(c) Side view
Holes for placing the jacks
at different eccentricities
Load cells
270
271
4.10.1.1 Concrete
The test specimens were cast from one concrete batch with a 28 days concrete
compressive strength of 45.24.4 MPa, and a concrete compressive and tensile strengths
of 43.45 MPa and 3.280.16 MPa at the time of testing (ten months after casting)
obtained from concrete cylinders. Furthermore, results of the Schmidt hammer tests show
the concrete compressive strength of the 41 MPa, 42 MPa, and 37.5 MPa for specimens
SP-1, SP-2, and SP-3, respectively, at the time of testing.
4.10.1.2 Steel Reinforcements
The properties of the tension and compression steel reinforcements (3-15M and 2-
10M), and stirrups (7-10M) were the same as the steel reinforcements presented in
Section 4.7.1.1.
4.10.1.3 Dywidag Thread-Bar and Nuts
The used dywidag thread-bar (Ø19) had a cross-sectional area, a yield load, an
ultimate load, and a modulus of elasticity of 284 mm2, 147 kN, 196 kN, and 205 GPa,
respectively, having corresponding nuts that can carry the ultimate load of the dywidag
bar (DSI, 2013).
4.10.1.4 Steel Bolts
Carbon Steel Kwik Bolt 3 Expansion Anchor was used to connect the end anchor
to the substrate concrete. Properties of these bolts are presented in Section 3.3.3.5.
272
4.10.2 Testing Procedure
The test was performed on each specimen by doing three steps and the occurrence
of the cracks was checked during each step; step I: placing the jacks at low eccentricity (e
= 110 mm) and prestressing to a load equivalent to 75% of the CFRP tensile strength;
step II: placing the jacks at medium eccentricity (e = 180 mm) and prestressing to load
equivalent to 75% of the CFRP tensile strength; and step III: placing the jacks at high
eccentricity (e = 215 mm) and prestressing to a load equivalent to 75% of the CFRP
tensile strength. The applied steps including low, medium, and high eccentricity values
are presented in Figure 4-111. The values of the applied load by hydraulic jacks and the
corresponding prestressing load in the dywidag bar at each step were checked by reading
the load values from load cells and strain values obtained from two strain gauges installed
on the dywidag bar, respectively.
273
(a) Low eccentricity
(b) Medium eccentricity
(c) High eccentricity
Figure 4-111: Applied test steps: low, medium, and high eccentricities.
4.10.3 Results and Discussion
The results of the test are presented in Table 4-20 including the test steps, the
prestress level (load in the dywidag bar), the applied load by the hydraulic jacks, prestress
loss due to friction of the system, and the prestress level corresponding to the initiation of
the cracks at location of the brackets and end anchor. Also, the photos of the specimens
after three steps of each test are shown in Figure 4-112.
Eccentricity to cg bolts=110 mm
Eccentricity to cg bolts=180 mm
Eccentricity to cg bolts=215 mm
274
Table 4-20: Modification of the prestressing system test results. S
pec
imen
ID Test
step
Eccentricity
[from jack
level to cg of
bolts at fixed
bracket (mm)]
Prestress level (%)
[Load in dywidag
bar (kN)]
Applied
load by
jacks
(kN)
Prestress loss
due to friction
of the system
(%)
Occurrence of cracks at brackets
[prestress level corresponding to
initiation of cracks (%)]
Prestress level (%)
corresponding to initiation
of cracks at end anchor
Other type of
cracks
SP
-1
I Low
[110]
75.4
[123.4] 174.9 29.4 ― 27 (minor cracks)
Very minor
crushing
around the
bolts at fixed
and movable
brackets
II Medium
[180]
75.8
[124] 160.0 22.5 ―
No extension of previous
crack
III High
[215]
75.8
[124] 160.0 22.5 Fixed bracket [74.1]
No extension of previous
crack
SP
-2
I Low
[110]
74.5
[122] 175.4 30.5 ― 28.5 (minor cracks)
Very minor
crushing
around the
bolts at fixed
and movable
brackets
II Medium
[180]
74.7
[122.3] 143.8 14.9 Fixed bracket [74.3]
Minor extension of previous
crack
III High
[215]
75.8
[124.2] 174.7 28.9
Extension at fixed bracket [67.6]
Movable bracket [74.7]
Minor extension of previous
crack
SP
-3
I Low
[110]
70.0
[114.7] 171.2 33.0 ―
21.3 (minor cracks)
74.7 (start of block rupture) Very minor
crushing
around the
bolts at fixed
and movable
brackets
II Medium
[180]
76.7
[125.7] 181.9 30.9 ―
76.4 (extension of the block
rupture cracks)
III High
[215]
82.4
[134.9] 168.2 19.8
Fixed bracket [78.2]
Movable bracket [81.8]
81.8 (extension of the block
rupture cracks)
274
275
(a) SP-1
(b) SP-2
(c) SP-3
Figure 4-112: Damage done to the specimens after three steps of test.
276
The results, presented in Table 4-20, show that at low eccentricity (110 mm from
the jack level to cg of bolts) no cracks occurred at the location of the brackets while the
cracks were observed for medium and high eccentricity cases. The minor cracks at end
anchor locations were observed at prestress levels ranging from 21.3% to 28.5%. These
minor cracks can be avoided by increasing the bolt spacing at end anchor location and
providing longer edge distance for the bolts. Specimens SP-1 and SP-2 showed no
significant issues at the end anchor location as can be seen in Figure 4-112a and Figure 4-
93b. Specimen SP-3 experienced cracks due to concrete block rupture around the end
anchor, during step I of the test at prestress level of 74.7%, these cracks propagated
further in steps II and III, as can be seen in Figure 4-112c. In addition, a very minor
surface crushing around the bolts at the locations of the brackets was observed. The tests
show an average of 26% difference between the applied load by the jacks and the
prestress load in the dywidag bar determined from the strain gauges; this difference is due
to the friction of the system caused by the movable bracket and corresponding bolts.
As can be seen in the results, the cracks at the location of the fixed bracket
occurred at very high prestress level (a load equivalent to 74% of the CFRP tensile
strength) while they ocurred in lower prestress level (about 40-48% of the CFRP tensile
strength) for the beams in phases I and II of the experimental program. The difference
might be due to the accumulation of the following reasons. The specimens were
prestressed upside down while the beams in phases I and II were prestressed as in field
condition; therefore, the self-weight of the specimen (although it is small) produces a
compression at top (location of the brackets) that delay the occurrence of the cracks while
the self-weight of the beam results a tension stress at the location of the brackets that
277
expedites the occurrence of the cracks. The specimens are in small scale and the
prestressing length is shorter than the one for the long beams (5 m span), therefore, the
disturbed area (stress concentration) from the end anchors in the specimen applies more
compression to the location of the brackets that delays the occurrence of the cracks in
specimens. Also, the specimens and the beams had different concrete compressive
strengths (the specimens had slightly higher concrete compressive strength by 6%). The
concrete compressive strengths of the concrete cylinders, representing the beams, at the
time of strengthening are presented in Table C-1 for more details.
In general, the results confirm that the modified prestressing system performs
properly and the occurrence of the cracks during the prestressing at the location of the
fixed bracket is avoided by selecting a low value of eccentricity.
4.11 Summary
In this chapter, the experimental test results of fourteen RC beams strengthened
using prestressed and non-prestressed NSM CFRP strips and rebars including two control
un-strengthened RC beams were presented. The test variables comprise freeze-thaw
cycling exposure, sustained loading, prestressing level, and CFRP geometry. Nine beams
were tested in phase I and the results were analyzed. The beneficial and optimum
prestressing levels were defined and calculated for the tested beams. Then, the static
performance of the beams was compared with results of similar beams without any
environmental exposure tested by Gaafar (2007). A general comparison was performed
between the beams in order to evaluate the effect of freeze-thaw exposure, prestressing,
and CFRP geometry (strips versus rebar). Afterward, ductility of the tested beams was
278
examined and appropriate deformability models and corresponding limits were proposed
for FRP strengthened RC beams. Then, results of the five beams tested in phase II were
discussed in detail followed by a general comparison with similar beams in phase I to
investigate the effects of applied freeze-thaw cycles and sustained load in phase II. Then,
the instantaneous and long-term prestress losses in the NSM CFRP were evaluated under
exposure and also at room temperature. At the end, the prestressing system used in phases
I and II was modified to avoid cracking in the concrete at the location of the temporary
brackets during prestressing.
In the next chapter, a comprehensive study was conducted on the numerical
(using finite element method) and analytical simulations of the prestressed NSM CFRP
strengthened RC beams.
279
Chapter Five: Numerical and Analytical Simulations
5.1 Introduction
Comprehensive Finite Element (FE) and analytical simulations of the prestressed
Near-Surface Mounted Carbon Fibre Reinforced Polymer (NSM-CFRP) strengthened
Reinforced Concrete (RC) beams were performed and are presented in this chapter.
Firstly, the unexposed RC beams strengthened using prestressed NSM-CFRP strips are
modeled by developing a nonlinear 3D FE model considering debonding and prestressing
aspects. Then, a parametric study considering the effects of concrete, steel reinforcement,
and prestressing level is performed to present a better understanding of the effects of
these parameters and to cover the gaps in this field. Afterward, the behaviour of the steel
anchor employed to prestress the NSM-CFRP reinforcement is investigated by
conducting a parametric study considering the effects of anchor’s dimensions and bond
characteristics on the performance of the anchorage system. Then, the load-deflection
responses of the exposed RC beams strengthened with prestressed NSM-CFRP strips and
rebars subjected to freeze-thaw exposure are predicted by developing an analytical
model. Finally, a 3D FE model is developed to simulate the behaviour of the exposed RC
beams strengthened with prestressed NSM-CFRP strips subjected to combined freeze-
thaw exposure and sustained load, and the predicted results are compared to experimental
ones.
The results presented in this chapter were published in refereed journal paper
(Omran and El-Hacha, 2012b) and refereed conference papers (Omran and El-Hacha,
2010b and c, 2012e, and 2013a).
280
5.2 Finite Element Modeling of RC Beams Strengthened with Prestressed NSM-FRP
Although many researchers simulated the behaviour of Externally Bonded (EB)
strengthened RC flexural members using 2D/3D FE models considering perfect bond
between interfaces (concrete-epoxy and epoxy-FRP) due to the fact that debonding
failure was not observed in relevant tests (Kachlakev et al. 2001; Chansawat, 2003; Jia,
2003; Supaviriyakit, 2004; Chansawat et al., 2006; Rafi et al, 2007; Camata et al. 2007;
Nour et al., 2007), however, FE modeling of NSM FRP strengthened RC beams is rarely
carried out (Kang et al., 2005; Soliman et al., 2010). Based on an extensive literature
review performed in Chapter Two, the FE modeling of prestressed-NSM-FRP
strengthened RC beams has never been investigated by taking into account the debonding
effects. Therefore, a 3D FE model is developed to simulate the behaviour of RC beams
strengthened with prestressed-NSM-CFRP strips. The FE model is compared and
validated with experimental test results reported by Gaafar (2007). The model considers
the debonding at the concrete-epoxy interface by assigning fracture energies including a
bilinear shear stress-slip model and a bilinear normal tension stress-gap model.
Furthermore, the prestressing is applied to the CFRP strip elements using the equivalent
temperature method. The predicted results and experimental ones are compared in terms
of load-deflection curve, strain profile, failure mode, energy absorption, and bond
performance.
5.2.1 Experimental Program Overview and Material Properties
Five unexposed RC beams were tested by Gaafar (2007): one un-strengthened
control beam, and four beams strengthened with prestressed NSM CFRP strips. Details of
281
the strengthened beams are presented in Figure 5-1.
(a) Geometry of the beams tested by Gaafar (2007).
(b) Cross-section of the beams and end-anchor.
Figure 5-1: Details of the modeled beams.
Each beam was strengthened using two 2×16 mm CFRP strips glued together on
their sides and embedded in one groove pre-cut in the concrete cover on the tensile face
of the beams. The beams were, 5150 mm long, simply supported with rectangular cross
section of 200×400 mm. Various prestressing levels of 0%, 17%, 29.3%, and 51% of the
282
ultimate tensile strain of the CFRP strips were applied (corresponding to prestrain of 0,
0.0034, 0.0058, and 0.0102 in CFRP strips, respectively). The beams were not subjected
to environmental exposure and were tested under monotonic static loading in four-point
bending configuration.
5.2.1.1 Steel Reinforcements
The stress-strain curves of the tension and compression steel bars (3-15M and 2-
10M) determined from the uni-axial tension tests are depicted in Figure 5 2 (Gaafar,
2007). The compression and tension steel reinforcements had the yield strengths of 500
MPa and 475 MPa, respectively, having a modulus of elasticity of 200 GPa.
0
100
200
300
400
500
600
700
0 0.02 0.04 0.06 0.08 0.1 0.12
Str
es
s (M
Pa
)
Strain (mm/mm)
10M Steel Bar
15M Steel Bar
Figure 5-2: Stress-strain curves of steel bars.
283
5.2.1.2 Concrete
The concrete material possessed a maximum compressive strength of 40 MPa, a
strain at ultimate strength of 0.002233, and a modulus of elasticity of 27.84 GPa, which
are the average values obtained from the compression tests of concrete cylinders (Gaafar,
2007). Modeling of the concrete stress-strain behaviour is described in Section 5.2.3.1.
5.2.1.3 CFRP Strips
The CFRP strip was type Aslan 500 produced by Hughes Brothers with a tensile
strength of 2610 MPa, an ultimate strain of 0.02, and a modulus of elasticity of 130.5
GPa determined from the tension test (Gaafar, 2007) with a linear-elastic behaviour up to
failure.
5.2.1.4 Epoxy Adhesives
Two types of epoxy adhesives were used for NSM strengthening: Sikadur®
330
with a modulus of elasticity of 4.5 GPa and an ultimate tensile strength of 30 MPa (Sika,
2010a) used to connect the CFRP strip into the end steel anchors, and Sikadur®
30 with a
modulus of elasticity of 4.5 GPa and ultimate tensile strength of 24.8 MPa (Sika, 2010b)
used to fill in the groove in concrete.
5.2.1.5 Anchor Bolts
The anchor bolts, used to connect the end anchor to the substrate concrete, were
type Carbon steel Kwik Bolt 3 Expansion Anchor with nominal bolt diameter of 15.9 mm
and shear strength of 54.4 kN (Hilti, 2008).
284
5.2.2 Description of Finite Element Model
The developed FE model is 3D in which all constitutive materials including
concrete, CFRP strips, internal steel reinforcements, epoxy adhesive, bolts, and end
anchor were simulated using appropriate elements available in the ANSYS program
library (SAS, 2009). As shown in Figure 5-3, only one quarter of the beam was modeled
due to the symmetry in geometry and loading conditions, to reduce the computer
computational time, modeling time and volume of the output. Out of two existing mesh
generation techniques: solid modeling and direct generation, the FE model was generated
based on the latter due to intricacy of the NSM strengthened RC beams. Although the
direct mesh generation technique is very time consuming for generating large-scale
model and the modeller needs to focus more on every detail of the mesh, but it has the
advantage of complete control over the geometry of every element and every node in the
complicated models.
Figure 5-3: Quarter of the beam to be modeled.
285
5.2.3 Modeling of Materials
5.2.3.1 Concrete
The concrete material was modeled using eight-node solid brick element
(Solid65). Geometry of a Solid65 element is depicted in Figure 5-4. This element,
considering a 2×2×2 set of Gaussian Integration points, has eight nodes with three
degrees of freedom at each node, translations in the nodal x, y, and z directions with
capability of plastic deformation, cracking in three orthogonal directions and crushing.
The crushing capability of Solid65 element is omitted in the FE analysis. This procedure
was executed by researchers in the FE models of RC beams (Kachlakev et al., 2001;
Chansawat, 2003; Jia, 2003; Wolanski, 2004; Chansawat et al., 2006). The reason is that,
the FE model prematurely fails when the crushing capability of the Solid65 element is
turned on. This behaviour occurs due to high stress concentration under the loading plate
that leads the crushing to start and develop within a small load and the local stiffness
sharply decreases, afterward, the solution diverges displaying a large displacement
warning. However, when the crushing capability of Solid65 is omitted, the secondary
tensile strain produced by the Poisson’s effect leads to cracking and finally failure of the
beam (Kachlakev et al., 2001). To properly model the concrete, the considered model for
concrete comprises linear and multi-linear elastic/isotropic material properties in addition
to the concrete model defined in ANSYS (Wolanski, 2004; Chansawat et al., 2006; Al-
Darzi, 2007; Özcan et al., 2009). The multi-linear isotropic or elastic material uses the
Von Mises failure criterion or actual stress-strain curve, respectively, along with the
Willam and Warnke model (Willam and Warnke, 1975) to define the failure of the
286
concrete. A Poisson’s ratio of 0.18 was assigned to the concrete material (Wight and
MacGregor, 2009).
Figure 5-4: Geometry of Solid65 element (SAS, 2009).
After choosing the concrete element for the FE model, the next step is assigning
the appropriate stress-strain curve. The actual concrete stress-strain curve, obtained from
experimental tests, has been rarely used in FE modeling, and most researchers employed
available analytical stress-strain curve models from the literature. The reason is the
difficulty in identifying the appropriate descending branch of the curve. The descending
branch of the concrete stress-strain curve in compression is affected by test conditions
including loading rate, type of testing machine, gauge length of the measured axial
deformation, etc. and existence of stirrups. To estimate the unconfined concrete
behaviour in compression, the available analytical models in the literature such as
Modified Hognestad (Hognestad, 1951), Thorenfeldt et al. (1987), Desayi and Krishnan
(1964), Todeschini (Todeschini et al., 1964), CEB-FIP model code (CEB-FIP, 1993), and
287
Loov (1991) almost result in similar ascending branch, but produce different strain at
ultimate and also different descending branch. Most of the researchers used Desayi and
Krishnan’s stress-strain curve in the FE models (Kachlakev et al., 2001; Jia, 2003;
Wolanski, 2004; Chansawat et al., 2006; Coronado and Lopez, 2006; Özcan et al., 2009).
On the other hand, the equations proposed by Thorenfeldt et al. (1987) and Loov (1991)
can be used to match an experimental concrete compressive stress-strain curve. The latter
is presented in Equation 5-1. Many researchers used the unconfined concrete stress-strain
curve while some did not even considered the descending branch in modeling the stress-
strain curve of concrete and used perfectly plastic behaviour after maximum concrete
compressive strength (Kachlakev et al., 2001; Jia, 2003). On the other hand, few
researchers considered the confined concrete stress-strain curve in FE modeling
(Chansawat, 2003, Chansawat et al., 2006). Concrete behaves confined due to lateral
support of the steel stirrups, and this happens when the stresses are approaching the uni-
axial strength in disturbed area of a beam. Confinement enhances the stress-strain
behaviour of the concrete at high strain locations (under the loading plate). In the
developed FE model, a confined concrete constitutive model was adopted based on the
experimental ancillary test results in order to perform an exact FE modeling. Most of the
available analytical models for concrete confined by rectangular ties are derived for the
members under axial compression loading and consider enhancement in both strength
and ductility (Chan, 1955; Roy and Sozen, 1965; Soliman and Yu, 1967; Sargin, 1971;
Vallenas et al., 1977; Sheikh and Uzameri, 1980; Park et al., 1982; Mander et al., 1988).
Kemp (1998) proposed a confined concrete model applicable for beams by enhancing
both strength and ductility based on parameters affecting ductility. Kent and Park (1971)
288
derived a confined concrete model which considers the enhancement in ductility due to
confinement by stirrups; Equation 5-2 proposed by these authors for ε50h, results in the
additional ductility due to rectangular stirrups at stress value of 0.5f′c. The Loov’s
equation (Equation 5-1) was used to define an unconfined concrete compressive stress-
strain curve based on two points (points 1 and 2 in Figure 5-5) which were obtained from
the experimental concrete stress-strain curve reported by Gaafar (2007).
n
o
c
o
c
o
c
cc
nB
nB
ff
1
11
1
11
Equation 5-1
where o = strain at maximum concrete compressive strength cf and c = strain at
concrete compressive stress cf . The two constants, n and B, in Equation 5-1 can be
calculated based on two points so that the analytical curve can match any experimental
concrete stress-strain curve. Therefore, the following values of n and B are reached for
the unconfined concrete using points 1 and 2 obtained from the experimental concrete
stress-strain curve.
123
120
MPa26and004202Point
MPa12and00043101Point
MPa40at0022330
.n
.B
f.:
f.:
f.
unconfined
unconfined
cc
cc
co
289
Figure 5-5: Concrete constitutive model in compression under flexural loading.
Then, point 3 on the confined curve in Figure 5-5 was calculated based on the
strain h50 at cf. 50 that gives additional ductility due to the stirrups given by Equation
5-2. The ratio of volume of one stirrup to volume of concrete core measured to outside of
the stirrup, ρs, is calculated using Equation 5-3. The strain c50 on the descending branch
of the confined concrete curve at cf. 50 is determined using Equation 5-4.
sh
shS
b
4
350 Equation 5-2
sh
shs
Sdb
Adb
2 Equation 5-3
huc 505050
Equation 5-4
290
where b = width of confined core measured to outside of the stirrup, shS = spacing of
stirrups, b= width of the stirrup (between centre lines of the bar) , d = depth of the
stirrup (between centre lines of the bar), shA = area of one leg of the stirrup, d = depth of
confined core measured to outside of the stirrup, and u50 = unconfined concrete strain on
the descending branch at cf. 50 .
For the tested beams, c50 is determined using Equation 5-2 to Equation 5-4 as
below:
0109230
005017050atcurveunconfined
for15EquationApplying
0059050
mm200
mm6154
0089560
50
50
50
.
.f.f
.
S
.b
.
c
ucc
h
sh
s
At the end, the Loov’s equation was applied considering points 3 and 1 to
calculate n and B for confined concrete and to define the descending branch of confined
curve up to stress 0.2f′c.
31
123
MPa20and01092303Point
MPa12and00043101Point
MPa400022330
.n
.B
f.:
f.:
fat.
confined
confined
cc
cc
co
291
The final relation for the stress-strain curve of the concrete is presented by
Equation 5-5. Comparison, performed by the author, showed that the stress-strain curve
defined by this method is similar to that defined by Desayi and Krishnan’s stress-strain
curve, and the advantage is that the proposed curve is derived based on the actual
material properties of the concrete reported by Gaafar (2007).
067346020
06734600022330692627613981
67552
00223307811551
4714
31
123
.f.
....
.f
...
.f
f
cc
c.cc
cc
c.cc
cc
c
Equation 5-5
The applied stress-strain curve of the concrete in tension is depicted in Figure 5-6
(SAS, 2009). The contribution of the concrete in the tension zone to the rigidity of the
beam is known as tension stiffening. Considering Figure 5-6, as the tensile stress meet the
concrete tensile strength, ft, and the crack forms, a tensile stress relaxation occurs. The
defined curve allows considering the strain-softening behaviour for cracked concrete.
Furthermore, it considers the effects of the reinforcement interaction with concrete to be
simulated in a simple manner. In a cracked reinforced concrete, the section between two
cracks is susceptible to carry the forces in the steel reinforcement at the crack. Although
after cracking, the stiffening effect of tension carried by concrete between cracks has much
less significance, and the cracked section properties can be used with little error, but
applying non-zero relaxation after cracking helps in convergence of the problem. For the
292
FE model, a bilinear stress-strain relation, predefined in ANSYS program, is employed to
model the tension stiffening as shown in Figure 5-6.
Figure 5-6: Concrete constitutive model in tension (Retrieved from SAS, 2009).
5.2.3.2 Steel Reinforcements
Steel reinforcements can be simulated in FE modeling of RC structures using
three methods: discrete model, embedded model, and smeared model as depicted in
Figure 5-7 (Tavarez, 2001). In the discrete model (Figure 5-7a), the steel reinforcement,
simulated using link, truss or beam elements, is connected to the concrete element nodes.
The main drawbacks of discrete model are that the concrete mesh configuration is
restricted by the location of the reinforcement and the volume of the steel reinforcement
is not deducted from the concrete volume.
293
(a) Discrete model
(b) Embedded model
(c) Smeared model
Figure 5-7: Different approaches for modeling of reinforcement (Tavarez, 2001).
294
In the embedded model (Figure 5-7b), the reinforcement is embedded into the
concrete which overcome mesh dependency restriction in the discrete model, therefore,
the stiffness is evaluated separately for the concrete material and steel reinforcements.
Displacements of the embedded elements are compatible with those of the surrounding
concrete elements; therefore, the concrete elements and their interaction points with
reinforcement are identified and employed to recognize the nodal location of the
reinforcement mesh. The embedded reinforcing method is beneficial when it is used with
higher order elements or where the reinforcement configuration in concrete member is
complex. A drawback of this approach is that the additional nodes, required for the
reinforcements, increase the degrees of freedom in the model and causes a longer
computer computational time in comparison with the discrete approach. In the smeared
model (Figure 5-7c), the reinforcement is uniformly distributed over the concrete
elements. In this approach, the properties of the material model in the element are formed
from individual properties of concrete and reinforcement using composite theory. The
smeared reinforcing method is beneficial for large structural models in which the
reinforcement does not affect the overall response of the model.
In the developed FE model, the discrete model (Figure 5-7a) of steel
reinforcement is employed. A two-node link element, Link8, was chosen to simulate the
steel reinforcements as shown in Figure 5-8. The Link8 is a 3D spar with three
translational degrees of freedom at each node in x, y, and z directions, and is capable of
plastic deformation. A multi-linear material model was assigned to the Link8 elements, as
presented in Figure 5-2, in addition to the related real constant (i.e. the area of cross-
section) assigned to each steel rebar.
295
Figure 5-8: Geometry of Link8 element (SAS, 2009).
5.2.3.3 CFRP Strips
Eight-node solid brick element, Solid45, was used to model the CFRP strips.
Geometry of a Solid45 element is depicted in Figure 5-9. Solid45 element considering a
2×2×2 set of Gaussian integration points, has eight nodes with three translational degrees
of freedom at each node in x, y, and z directions. This element is capable of assigning
multi-linear elastic material model. The multi-linear stress-strain curve of the CFRP strip
is presented in Figure 5-10. In the 3D FE model, to minimize mesh intricacy, a CFRP
strip with the dimension of 5×16 mm was modeled instead of 2-2×16 mm plus 1mm
epoxy in-between (as shown in Figure 5-1). Therefore, an equivalent modulus of
elasticity of 104.4 GPa (2×2×16×130.5/(5×16)=104.4 GPa), a tensile strength of 2088
MPa (104400×0.02=2088 MPa), and an ultimate strain of 0.02 were assigned to the
CFRP material in the FE model, to have an identical stress-strain curve with the one
shown in Figure 5-10. A Poisson’s ratio of 0.35 was assumed for CFRP (Kabir and
Hojatkashani, 2008).
296
Figure 5-9: Geometry of Solid45 element (SAS, 2009).
Figure 5-10: Strain-strain curve assigned to CFRP strip elements.
5.2.3.4 Epoxy Adhesives
Two types of epoxy adhesive were used in the FE model. Sikadur® 330, with a
modulus of elasticity of 4.5 GPa and ultimate tensile strength of 30 MPa (Sika, 2010a),
was used to bond the CFRP strip to the steel anchor while Sikadur® 30, with a modulus
of elasticity of 4.5 GPa and ultimate tensile strength of 24.8 MPa (Sika, 2010b), was used
to fill in the groove and bond the CFRP strip to the concrete. Both types were modeled
297
using Solid45 elements. The multi-linear elastic material stress-stress curves assigned to
the epoxy adhesives are depicted in Figure 5-11 and Figure 5-12. A Poisson’s ratio of
0.37 is assumed for the epoxy adhesives (Kabir and Hojatkashani, 2008).
Figure 5-11: Strain-strain curve assigned to epoxy elements, Sikadur® 330.
Figure 5-12: Strain-strain curve assigned to epoxy elements, Sikadur® 30.
298
5.2.3.5 End Anchor and Loading and Supporting Steel Plates
The end anchor, loading and supporting plates were modeled using Solid45
elements. A linear elastic material is assigned to these elements with a modulus of
elasticity of 200 GPa and a Poisson’s ratio of 0.3.
5.2.3.6 Bolts at End Anchors
The two-node beam element, Beam4, was employed to model the steel bolts at the
end steel anchor. The geometry of a Beam4 element is presented in Figure 5-13. This
element has two nodes with three translational and three rotational degrees of freedom at
each node with capabilities of tension, compression, torsion and bending. The Beam4
element is capable to take into account the shear effects by assigning the shear deflection
constants (1.11 for circular cross-section). A linear elastic material property and
corresponding real constants for the anchor bolt including a diameter of 16 mm, a cross-
sectional area of 201 mm2, and a moment of inertia of 3217 mm
4 were assigned to this
element.
299
Figure 5-13: Geometry of Beam4 element (SAS, 2009).
5.2.4 Debonding Model
Debonding at the concrete-epoxy interface, which is the weakest layer, is
simulated using contact pairs and Cohesive Zone Material (CZM) model. To implement
debonding aspects in the FE analysis, a normal stress-gap model and a shear stress-slip
model are employed enabling mixed-mode debonding. It should be mentioned that,
considering both models provides an opportunity to appropriately analyze the debonding
behaviour; considering only the shear stress-slip model, as used in most studies (Chen
and Teng, 2001; Buyle-Bodin et al., 2002; Pham and Al-Mahaidi, 2005; Coronado and
Lopez, 2006), leads to an interface mode of separation where the slip dominates the
separation normal to the interface (gap); on the other hand, considering just the tension
stress-gap model leads to a mode of failure where the gap dominates the slip at the
300
interface. Hence, defining the debonding according to only one of the two models means
ignoring the effect of the other and making a difference with what actually happens in
reality, where both models contribute to debonding in NSM strengthened RC beam. In
the developed FE model, the bilinear shear stress-slip and normal stress-gap models are
calculated based on the appropriate fracture energies of the concrete-epoxy interface,
which are identified in the next sections.
Fine mesh was mapped inside the strengthening groove to increase the accuracy
of the results, and there was no need to map fine mesh outside the groove to decrease the
modeling time and computer computational time. Surface-to-surface contact pairs were
assigned to the concrete-epoxy interface to separate the fine mesh mapped inside the
groove from surrounding mesh. The interfacial surface on concrete (target surface) was
modeled using TARGE170 and the interfacial surface on epoxy adhesive (contact
surface) was modeled with CONTA173. Geometry of the assigned elements for the
concrete-epoxy interface is plotted in Figure 5-14. TARGE170 is capable of simulating
various 3D target surfaces for the associated contact elements. CONTA173 is employed
to simulate contact and sliding between 3D target surfaces and deformable surfaces,
defined by this element. This element is generated using four nodes, considering a 22
set of Gaussian integration points, and is applicable to 3D structural and coupled field
contact analyses. The related shear stress-slip and tensile stress-gap model were assigned
to the contact surface by developing a subroutine in ANSYS command menu. The CZM
is used for bonded contacts with the Augmented Lagrangian method that needs to be
assigned to the contact properties.
301
(a) Geometry of TARGE170 (b) Geometry of CONTA173
Figure 5-14: Geometry of elements for concrete-epoxy interface (SAS, 2009).
The interface separation in mixed-mode debonding depends on both normal and
shear stress components. The bilinear shear stress-slip and normal tension stress-gap
models are plotted in Figure 5-15 and Figure 5-16. The area under each bilinear model is
equal to the fracture energy of the interface in shear or tension which is the energy
dissipated due to debonding. As shown in Figure 5-15 and Figure 5-16, debonding
initiates when debonding parameter (dm) is equal to zero. As debonding propagates, dm
increases, and finally, reaches unity as debonding terminates. After this point, any further
separation at the interface occurs without any normal or shear contact stress.
302
Figure 5-15: Bilinear shear stress-slip model.
Figure 5-16: Bilinear normal tension stress-gap model.
The equations for the contact shear and normal stresses based on the bilinear
models are defined as Equation 5-6 and Equation 5-7, respectively.
)d(uK mttt 1 Equation 5-6
303
)d(uK mnnn 1 Equation 5-7
where τt= contact shear stress, Kt= contact shear stiffness, ut= contact slip, σn= contact
normal stress, Kn= contact normal stiffness, un= contact gap, and dm= debonding
parameter (scalar) which is defined through Equations. 5-8 to 5-10 (SAS, 2009).
xdm
mm
1 Equation 5-8
22
t
t
n
nm
u
u
u
u Equation 5-9
tct
ct
ncn
cn
uu
u
uu
ux
Equation 5-10
where ūn= contact gap at the maximum contact normal stress (tension), ūt= contact slip at
the maximum contact shear stress, unc= contact gap at the completion of debonding, and
utc= contact slip at the completion of debonding. Note that dm, Δm, and x are scalars. In
the above equations, dm= 0 for Δm ≤ 1 and 0 < dm ≤ 1 for Δm > 1. The constraint on x
(Equation 5-10) is enforced automatically by appropriate scaling the contact stiffness
values.
In mixed-mode, debonding usually occurs before dissipation of the critical
fracture energy because both shear and normal contact stresses contribute to the total
fracture energy dissipation. In the model, it is assumed that no slip occurs at the concrete-
304
epoxy interface under pure normal compressive stress for mixed-mode debonding. There
are two main reasons for this assumption: first, in the NSM strengthening, the concrete-
epoxy interface is mostly under shear and normal tension stresses; and second, debonding
is a combination of shear stress and normal tension stress (as a result of the produced slip
and gap) and even under compressive stress this is the secondary effect of the
compression that causes tension or shear stresses at some regions of the interface and
results in slip or gap which are considered in the FE model based on the defined shear
stress-slip and tension stress-gap models. Therefore, the following energy criterion
(Equation 5-11) is used to define the termination of debonding in the mixed-mode (SAS,
2009).
1
cn
nn
ct
tt
G
du
G
du Equation 5-11
where Gct and Gcn are the total values of shear and normal fracture energies, respectively.
These values need to be identified for the NSM strengthened RC beams as described in
the next two sections.
5.2.4.1 Identification of Shear Stress-Slip Model
In the NSM FRP strengthened RC beam, the debonding occurs at the concrete-
epoxy interface which is the weakest interface and the main reason for shortage of
research in this field is the identification of appropriate bond behaviour that can be
reasonably applicable to the NSM technique. Many shear stress-slip models were
305
proposed for the EB strengthening technique the most well-known ones are the models
developed by Chen and Teng (2001) and Lu et al. (2005). However, these models are not
appropriate for the NSM technique because they are developed according to the geometry
of the FRP plate which is approximately considered as the geometry of the debonding
plane in the EB technique. In the NSM strengthening method, it is not a valid assumption
to consider the geometry of the plate/strip instead of the geometry of the actual
debonding plane. Also, the strain in the NSM FRP reinforcement at debonding is
significantly greater than that in the EB technique due to confinement of the surrounding
concrete. Seracino et al. (2007) examined debonding resistance of the EB and NSM
plate-to-concrete joints and overcame the drawbacks of the previous bond-slip models by
considering the geometry of the debonding plane; these authors proposed a fracture
energy and an ultimate shear stress equations for bond based on the statistical analysis of
many experimental test results. The considered shear stress-slip model, used in the FE
model, (Figure 5-15) is derived from fracture energy of the interface in NSM
strengthened specimens (Equations 5-12 to 5-15).
6007808020 .cmax f)..( Equation 5-12
2
9760 605260 .c
.
ct
f.G
Equation 5-13
07808020
9760 5260
..
.u
.ct
Equation 5-14
mm2widthgroove
mm1depthgroove
Equation 5-15
306
where τmax= maximum shear stress of contact (MPa), γ= aspect ratio of the interface
failure plane (mm/mm), f′c= concrete compressive strength (MPa), Gct= shear fracture
energy (N/mm), and utc= contact slip at the completion of debonding (mm). The values of
τmax= 8.37 MPa and utc= 1.295 mm are derived using Equations 5-12 to 5-15 for the shear
stress-slip model.
5.2.4.2 Identification of Normal Tension Stress-Gap Model
The tensile resistance at the concrete-epoxy interface is assumed to be limited to
the tensile capacity of the weakest material which is the concrete tensile strength
(presented in Equation 5-16 (CAN/CSA-A23.3-04, 2004)). Therefore, when the
interfacial tensile stress exceeds the concrete tensile strength, the debonding occurs due
to cracking of the concrete adjacent to the interface. This behaviour was also observed
during the experimental tests performed by Gaafar (2007). Similar procedure was
employed by Kishi et al. (2005) for debonding analysis of the EB strengthened RC
beams. Therefore, the fracture energy of the interface under tensile stress is considered to
be equal to the fracture energy of the concrete presented in Equation 5-17 proposed by
the CEB-FIP Model Code (1993). The contact gap (Equation 5-18) is derived using
Equation 5-16 and Equation 5-17 to satisfy the tensile fracture energy based on the
concrete tensile strength.
cmax f. 60 Equation 5-16
307
70
10
.
cfocn
fGG
Equation 5-17
20
324
10.
cfo
cn
.
fGu
Equation 5-18
where σmax= maximum tensile stress of contact (MPa), f′c= concrete compressive strength
(MPa), Gcn= total value of the normal fracture energy (N/mm), unc= contact gap at the
completion of debonding (mm), and Gfo= the base value of fracture energy (N/mm),
which depends on the maximum aggregate size. For concrete with maximum aggregate
size of 20 mm, Gfo is calculated as 0.03475 N/mm by nonlinear interpolation between
different values of aggregate size reported in the CEB-FIP Model Code (1993). The
values of σmax= 3.79 MPa and unc= 0.048 mm are derived using Equation 5-16 to
Equation 5-18 for the tension stress-gap model.
5.2.5 Modeling of Prestressing
So far, there exist three methods to enforce prestressing in FE modeling: apply
initial stress, apply initial strain, and apply equivalent temperature to meet the prestrain in
relevant materials. For simplicity in the pre-processing and post-processing operations
and for the considered type of elements as well the assigned material properties for the
CFRP strips, the equivalent temperature method was implemented to enforce the
prestressing effect. The thermal expansion of the CFRP strip in longitudinal direction,
αfrp, is set as -9×10-6
/oC based on the FRP material data sheet (Hughes Brothers, 2010a).
308
The equivalent temperature is computed using Equation 5-19 and applied to the CFRP
strip elements to make the exact prestrain for each prestressed beam. After assigning the
computed equivalent temperature (Δt) to the FE model it was found that the produced
prestrain is slightly (1-1.5%) smaller than the applied prestrain value (εP). In fact, the
slight change in prestressing is a result of the straining of the beam as the self-
equilibrating stress state establishes itself during an equilibrating static analysis step.
Applying the prestressing transfers load to the concrete beam, causing compressive
stresses in the concrete. The resulting deformation due to elastic shortening of the
concrete beam reduces the strain in the CFRP strip due to prestressing. Therefore, the
applied equivalent temperature (Δtapplied) is calculated somehow (by trial and error) to
produce the exact value of εP for each beam. It can be seen from the following values that
the difference between Δt and Δtapplied (strain loss due to elastic shortening) is very small
and even can be ignored without significant effect on the results.
tfrpP Equation 5-19
C.tC.t.
C.tCt.
C.tC.t.
oapplied
oP
oapplied
oP
oapplied
oP
16114833113301020
556596520058680
053837837700340
5.2.6 Mesh Sensitivity Analysis
Principally, the developed FE analysis should be objective and the results should
not depend on subjective aspects including element type or mesh size. Sensitivity
analysis is not necessary when there are sufficient experimental results to validate the FE
309
model. In this case, the model can be built based on the modeller experience on the type
of the element and mesh size, and validity and accuracy of the predicted results can be
evaluated to be sufficient by comparing them with experimental ones. In the case of pure
FE analysis (with no experimental results available to check the validity and accuracy),
performing a mesh sensitivity analysis is necessary to make sure about the accuracy and
consistency of the results. However, a mesh sensitivity analysis was performed to identify
the optimum mesh density and appropriate element sizes for the FE model of the tested
beams. In this context, a non-prestressed NSM-CFRP strengthened RC beam was
modeled with five different numbers of elements as shown in Figure 5-17. A summary of
the models developed for mesh sensitivity analysis are presented in Table 5-1. The
number of the elements varies from 2587 to 22417. The size of the output file (.rst) is
presented which is normalized with respect to the BS-NP-S1; this parameter shows the
volume of the output file for BS-NP-S5 with 22417 elements is 11.93 times the one for
BS-NP-S1 with 2587 elements.
To find the optimum number of elements, the mid-span deflection, concrete
compressive stress at mid-span location at extreme top fibre (at the centre of the top face
of the beam), stress in tension steel at mid-span, and stress in CFRP strip at mid-span
versus the number of elements are plotted in Figure 5-18 at load 20 kN, which is in the
linear stage of the load-deflection curve (before cracking). It should be mentioned that the
sensitivity analysis is reasonable when it is evaluated in linear stage of the load-deflection
curve. Many parameters interfere in convergence and the sensitivity curve does not
follow a reasonable trend when the structure (especially concrete member) goes to
nonlinear stages. The optimum is practically achieved when an increase in the mesh
310
density has a negligible effect on the results. On the other hand, the computer
computational time (which is different based on the computer capabilities) should be
considered in achievement of the optimum number of elements. According to the author
best experience, it’s more rational to select the optimum model based on the sensitivity
curve of the deflection versus the number of elements. Eventually, the model with 13614
elements is employed for FE analysis that yields a minimum of 99.2% reliability in
predicted results (as presented in Figure 5-18).
311
Table 5-1: Mesh sensitivity models.
Beam ID
Total
number of
elements
Total
number
of nodes
Number of elements for: Output
volume
(relative) Solid65
(concrete)
Link8
(steel bar)
Solid45
(CFRP, epoxy,
steel plate)
Beam4
(steel bolt)
Contact
(concrete-epoxy
interface)
BS-NP-S1 2587 2858 900 230 860 10 587 1
BS-NP-S2 6762 7394 2572 329 2660 14 1187 2.78
BS-NP-S3 13614 14914 4754 425 5854 14 2567 5.76
BS-NP-S4 20443 22792 9440 626 7076 14 3287 8.76
BS-NP-S5 22417 24924 11386 626 7104 14 3287 11.93
311
312
(a) BS-NP-S1 (b) BS-NP-S2
(c) BS-NP-S3 (d) BS-NP-S4
(e) BS-NP-S5
Figure 5-17: Mesh sensitivity models.
313
1.46
1.462
1.464
1.466
1.468
1.47
0 5000 10000 15000 20000 25000
Mid
-sp
an
de
fle
cti
on
(m
m)
Number of elements
Selected model99.95% reliability
6.8
7
7.2
7.4
7.6
7.8
0 5000 10000 15000 20000 25000Ten
sil
e s
tress in
CF
RP
(M
Pa)
Number of elements
Selected model99.16% reliability
16.7
16.72
16.74
16.76
16.78
16.8
0 5000 10000 15000 20000 25000
Te
ns
ile
str
es
s in
ste
el (M
Pa
)
Number of elements
Selected model99.92% reliability
-3.33
-3.31
-3.29
-3.27
-3.25
0 5000 10000 15000 20000 25000
Co
mp
ressiv
e s
tress
in c
on
cre
te (M
Pa)
Number of elements
Selected model99.96% reliability
Figure 5-18: Mesh sensitivity at 20 kN.
314
The meshed beam (selected model) is presented in Figure 5-19 to Figure 5-24. At
the location of the end anchors, the groove width is 25 mm to account for the embedded
anchors and in between along the length of the CFRP strip the groove width is 16 mm
which is the reason for using some larger aspect ratio elements at the side of the groove
with respect to other regions as shown in Figure 5-20.
Figure 5-19: The meshed beam (quarter of the tested beam).
Figure 5-20: Cross-section of the beam.
315
Figure 5-21: Steel reinforcements.
Figure 5-22: Mesh at the end groove.
Figure 5-23: Contact around the groove.
316
Figure 5-24: End-steel anchor.
5.2.7 Nonlinear Analysis
The nonlinear solution was executed using displacement control method in which
the non-zero displacement constraints were assigned to the model (at the loading plate
location) and the corresponding reaction forces were calculated. Therefore, the reaction
load-deflection curve obtained from the nonlinear analysis is the same as the applied
load-deflection curve obtained from the test. Another procedure for the FE analysis is
load control method in which the load is assigned to the model and the deflection is
calculated. The displacement control has a few advantages versus load control that can
overcome both the convergence difficulties and the rigid body modes when two bodies
are disconnected in contact pairs, and analyze the model with assigned material stress-
strain curve having descending branch. Each prestressed strengthened beam was solved
by defining seven load-steps as presented in Table 5-2. For instance, the ANSYS files
generated for FE model of the prestressed NSM CFRP strengthened beam, BS-P2-R, are
presented in Appendix D.
317
Table 5-2: Summary of load-steps assigned for nonlinear analysis.
Load-step
Time at
end of
load-step
Sub-step Max
number of
iterations
Displacement
convergence
criteria tolerance No. Min Max
1. Zero load-camber
induced by prestressing* 0.0001 1 1 1 40 0.01
2. Applied prestressing-
before first cracking 1.2 10 5 40 40 0.01
3. Before first cracking-
after first cracking 4 80 50 100 40 0.05
4. After first cracking-
before steel yielding 20 20 10 10000 40 0.05
5. Before steel yielding-
after steel yielding 26 40 15 10000 40 0.05
6. After steel yielding-
before ultimate 60 20 10 10000 60 0.05
7. Before ultimate-after
ultimate 120 20 10 10000 60 0.05
* used for prestressed NSM-CFRP strengthened beams
Generally, the number of load-steps in a FE analysis is arbitrary chosen by the
modeller based on the type of the problem, convergence behaviour of the FE model or
system, in particular, response of the structure, and the cost in term of computer
computational time. The main reasons for using seven load-steps instead of one were to:
i) assign the effect of prestressing on the model, and ii) apply the load gradually by
assigning different maximum and minimum numbers of the sub-steps defined for each
load-step. The latter leads to the following advantages: to increase the accuracy of the
results and properly calculate the loads and deflections at different steps (i.e., at
prestressing, surrounding cracking, yielding, and ultimate), to control computer
computational time so as to minimize the number of Newton-Raphson equilibrium
iterations required, and to assist in convergence of the nonlinear problem. After several
trials, a maximum displacement convergence tolerance of 0.05 is applied to the model
based on the convergence sensitivity analysis. To take into account the effect of the self-
318
weight of the beam, a preliminary analysis was performed on the model by applying
density and inertia and the deflection, sw, was calculated at the point load. Then, another
analysis was conducted by applying the same deflection sw as a boundary condition to
the model without the effect of self-weight and the reaction forces which are equivalent
to the reactions due to self-weight are calculated, called Psw. Then, Psw and sw were
subtracted from the reaction forces and deflections obtained from the nonlinear solution
of each beam. By this way, the predicted load-deflection response is in the same manner
as the experimental load-deflection response that already included the self-weight effects.
5.2.8 FE Results, Validation, and Discussion
5.2.8.1 Load-Deflection Curve
Comparison between experimental and numerical load-deflection responses is
depicted in Figure 5-25 to Figure 5-28 including the un-strengthened control beam, B0-R,
the strengthened beam with non-prestressed NSM CFRP strip, BS-NP-R, and the
strengthened beams with prestressed NSM CFRP strip, BS-P1-R, BS-P2-R, and BS-P3-
R. The FE solutions of the beams were terminated after CFRP rupture or concrete
crushing whichever occurred first accompanied by a non-convergence message from the
program. The predicted load-deflection responses include the negative camber due to
prestressing, initiation of flexural cracks, yielding of tensile steel rebar, local debonding
(which causes small fluctuations at large deflection), and CFRP rupture which causes a
large drop of total load at ultimate stage.
A summary of the results obtained from the tests versus the FE analysis is
presented in Table 5-3, including type of failure, ductility index (the ratio of the ultimate
319
deflection to the deflection at yielding), energy absorption (the area under load-deflection
curve up to the peak load), and percentage of difference between corresponding
experimental and numerical values.
At cracking, a relatively large percentage of difference is observed (an average
error of 0.8%±16.1% for cracking load with a maximum of 28% for B0-R, and an
average error of -22%±18.8% for cracking deflection with a maximum of -49.6% for BS-
P3-R) which might be due to presence of the micro cracks in the beams before testing.
Also, the cracking load and corresponding deflection in the tested beams were obtained
based on the visual inspections during the test and in some cases might be overestimated,
as can be seen for beam BS-P3-R. The other reason for underestimation or overestimation
of the cracking load using the FE analysis might be due to difference between concrete
compressive strength in the model and in tested beams; an average concrete compressive
strength was assigned to the FE models (40 MPa for all beams), that might be slightly
different for each beam in reality. Therefore, the obtained difference between FE and test
at cracking is most possibly the accumulation of the mentioned errors.
At yielding stage, the differences between FE and experimental results are
negligible (an average error of 2.3%±2.5% for yield load with a maximum of 5.2% for
BS-P2-R, and an average error of 1.7%±5% for yield deflection with a maximum of -
9.3% for BS-P2-R).
At ultimate stage, the predicted loads are almost the same as those obtained from
the test; however, the predicted ultimate deflections are smaller than those from the
experimental values. This behaviour might be due to the fact that the rupture of the CFRP
strip in FEM occurs when the first fibre in the CFRP strip reaches its ultimate tensile
320
strain, while during the test there is a possibility that the CFRP strip ruptured gradually.
On the other hand, the material properties (i.e., CFRP ultimate strain) are not absolutely
constant values and could be slightly smaller or greater than the specified values that
would lead to a difference at ultimate deflection when the failure governs by CFRP
rupture. An average error of 0.6%±6.1% for ultimate load with a maximum of 10.7% for
B0-R, and an average error of -5.1%±5.9% for ultimate deflection with a maximum of -
14.8% for BS-P1-R were obtained at the ultimate stage. The modeled beams showed
similar type of failure to the tested beams which is concrete crushing for the un-
strengthened control beam, B0-R, and CFRP rupture for the prestressed strengthened
beams except beam BS-NP-R strengthened with non-prestressed NSM CFRP strips
which failed due to concrete cover spalling. The fluctuation of the FE curve for BS-NP-R
observed in Figure 5-25 is due to major flexural cracks and also local debonding initiated
from top face of the groove, which could be a warning for this type of failure. Therefore,
the performed comparison indicates that the load-deflection curves obtained from the FE
models are matched with those from the experimental ones.
321
0
20
40
60
80
100
120
140
160
0 15 30 45 60 75 90 105 120 135
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-NP-R (Experimental)
BS-NP-R (FE Analysis)
B0-R (Experimental)
B0-R (FE Analysis)
Figure 5-25: Comparison between FE and experimental results for B0-R and BS-
NP-R.
0
20
40
60
80
100
120
140
160
-5 15 35 55 75 95 115 135
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-P1-R (Experimental)
BS-P1-R (FE Analysis)
Figure 5-26: Comparison between FE and experimental results for BS-P1-R.
322
0
20
40
60
80
100
120
140
160
-5 15 35 55 75 95 115 135
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-P2-R (Experimental)
BS-P2-R (FE Analysis)
Figure 5-27: Comparison between FE and experimental results for BS-P2-R.
0
20
40
60
80
100
120
140
160
-5 15 35 55 75 95 115 135
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-P3-R (Experimental)
BS-P3-R (FE Analysis)
Figure 5-28: Comparison between FE and experimental results for BS-P3-R.
323
Table 5-3: Summary of the results.
Beam
ID#
Prestrain
in CFRP Results
Δo
(mm)
Pcr
(kN)
Δcr
(mm)
Py
(kN)
Δy
(mm)
Pu
(kN)
Δu
(mm) μD
Φ
(kN. mm)
Failure
Mode
B0-R N.A.
FE 0 16 1.18 81.9 24.29 92.8 107.49 4.43 8446.6 CC
Test‡ 0 12.5 1.25 78.9 25.13 83.8 109.89 4.37 8050.2 CC
Error % 0 28 -5.6 3.8 -3.3 10.7 -2.2 1.4 4.9 ―
BS-NP-R 0
FE 0 15.4 1.14 93.6 25.42 136.8 111.9 4.4 11816.2 FR
Test‡ 0 16.8 1.55 90.8 25.83 135.1 118.79 4.6 12357.4 CCS
Error % 0 -8.3 -26.5 3.1 -1.6 1.3 -5.8 -4.3 -4.4 ―
BS-P1-R 0.0034
FE -0.48 22.7 1.2 102.1 25.04 140.4 88.26 3.52 9501.8 FR
Test‡ -0.47 22.1 1.24 103 24.12 148 103.65 4.3 11828.7 FR
Error % -2.1 2.7 -3.2 -0.9 3.8 -5.1 -14.8 -18.1 -19.7 ―
BS-P2-R 0.00587
FE -0.82 28.1 1.27 111.3 25.81 144.3 78.27 3.03 8582 FR
Test‡ -0.93 30.1 1.69 105.8 23.62 148.2 77.96 3.3 8813.1 FR
Error % 11.8 -6.6 -24.9 5.2 9.3 -2.6 0.4 -8.2 -2.6 ―
BS-P3-R 0.0102
FE -1.42 37.1 1.33 123.3 25.84 147.3 56.41 2.18 6223.4 FR
Test‡ -1.6 42.1 2.64 122.8 25.77 149.2 58.13 2.26 6529 FR
Error % 11.3 -11.9 -49.6 0.4 0.3 -1.3 -3.0 -3.5 -4.7 ―
Pcr and Δcr = load and deflection at cracking Δo = camber due to prestressing CC = Concrete crushing
Py and Δy = load and deflection at yielding μD = ductility index = Δu /Δy CCS = Concrete cover spalling
Pu and Δu = load and deflection at ultimate Φ = area under P-Δ curve up to Pu FR = CFRP rupture ‡
Gaafar (2007).
323
324
5.2.8.2 Strain Profiles and Distributions
Strain profiles along the length of the NSM CFRP strip and strain distribution
across the depth at mid-span of the beams are presented in Figure 5-29 to Figure 5-36.
The curves are plotted at three different load levels for each beam: cracking, yielding, and
ultimate. The experimental values are based on the reading of the strains in the CFRP
strip, steel rebars, and in the concrete at extreme compression fibre. For all beams, the
predicted strain profiles along the length of the CFRP strip are very well matched with
the experimental values at cracking and yielding. At ultimate stage, a very good
correlation is observed between the experimental and predicted strain profile except for
the non-prestressed strengthened beam, BS-NP-R. The reason is that this beam failed due
to concrete cover spalling at the tension face before CFRP strips reaches its ultimate
strain while in the FE model, the beam failed due to CFRP rupture. It can be seen from
the strain profile at ultimate that the maximum strain in the CFRP strips occurs
somewhere between the applied point load location and mid-span of the beam (from 2000
mm to 2500 mm on the x axis of the graph) which could not be captured experimentally
due to the location of the installed strain gauges. The FE strain distributions at mid-span
in Figure 5-33 to Figure 5-36 are calculated at the location of the experimental measured
strains and linearly connected together. The distribution shows very good correlation at
cracking and yielding and with negligible difference at ultimate. It should be noticed that
the strain distribution at mid-span section is not linear due to the effect of pre-strain
applied to the CFRP strip. However, the distribution along the effective depth is almost
linear at yielding and nonlinear at ultimate mostly due to concrete behaviour at
compression zone.
325
0
0.005
0.01
0.015
0.02
0 1000 2000 3000 4000 5000
Str
ain
Distance from the support (mm)
@ Cracking Load, 15.4 kN, FEM-ANSYS @ Cracking Load, 16.8 kN, Experimental
@ Yielding Load, 93.6 kN, FEM-ANSYS @ Yielding Loading, 90.8 kN, Experimental
@ Ultimate Load, 136.8 kN, FEM-ANSYS @ Ultimate Load, 135.1 kN, Experimental
Figure 5-29: Comparison between experimental and numerical strain profile along
the CFRP strip for beam BS-NP-R.
0
0.005
0.01
0.015
0.02
0 1000 2000 3000 4000 5000
Str
ain
Distance from the support (mm)
@ Cracking Load, 22.7 kN, FEM-ANSYS @ Cracking Load, 22.1 kN, Experimental
@ Yielding Load,102.1 kN, FEM-ANSYS @ Yielding Load, 103 kN, Experimental
@ Ultimate Load, 140.4 kN, FEM-ANSYS @ Ultimate Load, 148 kN, Experimental
Figure 5-30: Comparison between experimental and numerical strain profile along
the CFRP strip for beam BS-P1-R.
326
0
0.005
0.01
0.015
0.02
0 1000 2000 3000 4000 5000
Str
ain
Distance from the support (mm)
@ Cracking Load, 28.1 kN, FEM-ANSYS @ Cracking Load, 30.1 kN, Experimental
@ Yielding Load, 102.8 kN, FEM-ANSYS @ Yielding Load, 105.8 kN, Experimental
@ Ultimate Load, 144.3 kN, FEM-ANSYS @ Ultimate Load, 148.2 kN, Experimental
Figure 5-31: Comparison between experimental and numerical strain profile along
the CFRP strip for beam BS-P2-R.
0
0.005
0.01
0.015
0.02
0 1000 2000 3000 4000 5000
Str
ain
Distance from the support (mm)
@ Cracking Load, 37.1 kN, FEM-ANSYS @ Cracking Load, 42.1 kN, Experimental
@ Yielding Load, 123.3 kN, FEM-ANSYS @ Yielding Load, 122.8 kN, Experimental
@ Ultimate Load, 147.3 kN, FEM-ANSYS @ Ultimate Load, 149.2 kN, Experimental
Figure 5-32: Comparison between experimental and numerical strain profile along
the CFRP strip for beam BS-P3-R.
327
-400
-350
-300
-250
-200
-150
-100
-50
0
-0.01 -0.005 0 0.005 0.01 0.015 0.02
Se
cti
on
De
pth
(m
m)
Strain
@ Cracking Load, 15.4 kN, FEM-ANSYS @ Cracking Load, 16.8 kN, Experimental
@ Yielding Load, 93.6 kN, FEM-ANSYS @ Yielding Load, 90.8 kN, Experimental
@ Ultimate Load, 136.8 kN, FEM-ANSYS @ Ultimate Load, 135.1 kN, Experimental
Bottom Steel Level
CFRP Strips Level
Top Steel Level
Top Fibre of the Beam
Figure 5-33: Comparison between experimental and numerical strain distribution
across the depth at mid-span for beam BS-NP-R.
-400
-350
-300
-250
-200
-150
-100
-50
0
-0.01 -0.005 0 0.005 0.01 0.015 0.02
Se
cti
on
De
pth
(m
m)
Strain
@ Cracking Load, 22.7 kN, FEM-ANSYS @ Cracking Load, 22.1 kN, Experimental
@ Yielding Load, 102.1 kN, FEM-ANSYS @ Yielding Load, 103 kN, Experimental
@ Ultimate Load, 140.4 kN, FEM-ANSYS @ Ultimate Load, 148 kN, Experimental
Bottom Steel Level
CFRP Strips Level
Top Steel Level
Top Fibre of the Beam
Figure 5-34: Comparison between experimental and numerical strain distribution
across the depth at mid-span for beam BS-P1-R.
328
-400
-350
-300
-250
-200
-150
-100
-50
0
-0.01 -0.005 0 0.005 0.01 0.015 0.02
Se
cti
on
De
pth
(m
m)
Strain
@ Cracking Load, 28.1 kN, FEM-ANSYS @ Cracking Load, 30.1 kN, Experimental
@ Yielding Load, 102.8 kN, FEM-ANSYS @ Yielding Load, 105.8 kN, Experimental
@ Ultimate Load, 144.3 kN, FEM-ANSYS @ Ultimate Load, 148.2 kN, Experimental
Bottom Steel Level
CFRP Strips Level
Top Steel Level
Top Fibre of the Beam
Figure 5-35: Comparison between experimental and numerical strain distribution
across the depth at mid-span for beam BS-P2-R.
-400
-350
-300
-250
-200
-150
-100
-50
0
-0.01 -0.005 0 0.005 0.01 0.015 0.02
Se
cti
on
De
pth
(m
m)
Strain
@ Cracking Load, 37.1 kN, FEM-ANSYS @ Cracking Load, 42.1 kN, Experimental
@ Yielding Load, 123.3 kN, FEM-ANSYS @ Yielding Load, 122.8 kN, Experimental
@ Ultimate Load, 147.3 kN, FEM-ANSYS @ Ultimate Load, 149.2 kN, Experimental
Bottom Steel Level
CFRP Strips Level
Top Steel Level
Top Fibre of the Beam
Figure 5-36: Comparison between experimental and numerical strain distribution
across the depth at mid-span for beam BS-P3-R.
329
5.2.8.3 Debonding aspects
The initiation of debonding and its propagation at ultimate load for two FE
models (BS-NP-R and BS-P2-R) are shown in Figure 5-37 and Figure 5-38 to examine
the effect of debonding phenomenon. The debonding parameter value (dm) ranging from
0 to 1 is presented in these figures. Debonding is initiated when dm = 0 and by further
propagation dm approaches to unity. The termination of debonding is defined by Equation
5-11 when the total fracture energy is dissipated. Analysis of the FE results reveals that
debonding occurs at the horizontal concrete-epoxy interface on the top surface of the
NSM groove. Furthermore, the area of the debonded surface at ultimate load is less for
the prestressed NSM CFRP strengthened beam in comparison with the non-prestressed
NSM CFRP strengthened beam. In fact, debonding is a result of high interfacial shear and
tensile stresses caused by high deflection and large crack openings while prestressing
reduces the ductility of the beam, and therefore, avoids the debonding to occur. Results
revealed no debonding occured for beam BS-P3-R up to failure, while for beam BS-P1-
R, debonding occurred before failure and it was much less than beam BS-NP-R.
Therefore, less debonding occurs with increasing the prestressing level in the NSM
CFRP, i.e. the area of the debonded interface at failure decreases.
330
BS-NP-R Debonding Parameter (dm) Contour.983916
HI: Horizontal concrete-epoxy interface
VI: Vertical concrete-epoxy interface
HI
VI
Concrete
Epoxy
CFRP
strips
(a)
BS-NP-R Debonding Parameter (dm) Contour
HI
VI
HI: Horizontal concrete-epoxy interface
VI: Vertical concrete-epoxy interface
Concrete
Epoxy
CFRP
strips
(b)
Figure 5-37: Debonding Parameter (dm) contour at the concrete-epoxy interface in
the model: (a) BS-NP-R at initiation of debonding (load = 130.4 kN, deflection =
80.14 mm) and (b) BS-NP-R at ultimate.
331
BS-P2-R Debonding Parameter (dm) Contour
HI
VI
HI: Horizontal concrete-epoxy interface
VI: Vertical concrete-epoxy interface
Concrete
Epoxy
CFRP
strips
(a)
BS-P2-R Debonding Parameter (dm) Contour
HI
VI
HI: Horizontal concrete-epoxy interface
VI: Vertical concrete-epoxy interface
Concrete
Epoxy
CFRP
strips
(b)
Figure 5-38: Debonding Parameter (dm) contour at the concrete-epoxy interface in
the model: (a) BS-P2-R at initiation of debonding (load = 140.4 kN, deflection =
68.32 mm) and (b) BS-P2-R at ultimate.
332
5.3 Parametric Study on RC Beams Strengthened with Prestressed NSM-FRP
Conducting experimental investigations is indispensable to assess the actual
performance of structural elements, on the other hand, testing is usually a time
consuming and costly procedure for solving a problem. Therefore, researchers are
encouraged toward numerical or analytical solutions of a problem, even if it is
complicated to figure them out. In this section a parametric study is conducted on RC
beams strengthened with prestressed NSM CFRP. A Finite Element (FE) modeling
procedure similar to what has been presented in Section 5.2 is employed but with
simplified material properties to decrease the solution time for doing the parametric
study. First, the simplified developed 3D nonlinear FE model was validated with the
experimental data to simulate the behaviour of RC beam strengthened with prestressed
NSM-CFRP strips. Afterwards, the model was used and 23 beams were analyzed to
assess the prestressing level in the NSM CFRP strips, the tensile steel reinforcement
ratio, and the concrete compressive strength. The effects of these parameters on the
negative camber caused by prestressing; cracking, yielding, and ultimate loads and
corresponding deflections; mode of failure; and energy absorption were investigated. In
addition, the optimum prestressing level, which preserves the amount of energy
absorption of the NSM CFRP strengthened beam equal to the un-strengthened control
beam was estimated for the beams with different tension steel reinforcement ratios.
5.3.1 Modeled Beams
Geometry of the modeled beams is presented in Figure 5-1. More description
about the geometry is provided in Section 5.2.1. To perform a comprehensive parametric
333
study 23 beams were modeled as presented in Table 5-4.
Table 5-4: Properties of the modeled beams.
Beam ID ɛp
[ɛp/ɛfrpu %]
Afrp (mm2)
[Afrp/(bh) %]
Concrete Properties Area of Steel
f′c (MPa)
fr
(MPa)
Ec
(MPa)
Asc (mm2)
[Asc/(bh) %]
Ast (mm2)
[Ast/(bh) %]
B0-0.75-40 0 0
40 3.79 28460.5 200
[0.25]
600
[0.75]
BS-0-0.75-40 0
64
[0.08]
BS-19-0.75-40 0.0034
[19]
BS-36-0.75-40 0.0065
[36]
BS-58-0.75-40 0.0104
[58]
B0-1.25-40 0 0
40 3.79 28460.5 200
[0.25]
1000
[1.25]
BS-0-1.25-40 0
64
[0.08]
BS-19-1.25-40 0.0034
[19]
BS-36-1.25-40 0.0065
[36]
BS-58-1.25-40 0.0104
[58]
B0-1.75-40 0 0
40 3.79 28460.5 200
[0.25]
1400
[1.75]
BS-0-1.75-40 0
64
[0.08]
BS-19-1.75-40 0.0034
[19]
BS-36-1.75-40 0.0065
[36]
BS-58-1.75-40 0.0104
[58]
B0-2.25-40 0 0
40 3.79 28460.5 200
[0.25]
1800
[2.25]
BS-0-2.25-40 0
64
[0.08]
BS-19-2.25-40 0.0034
[19]
BS-36-2.25-40 0.0065
[36]
BS-58-2.25-40 0.0104
[58]
BS-36-1.25-30 0.0065
[36]
64
[0.08]
30 3.29 24647.5 200
[0.25]
1000
[1.25] BS-36-1.25-50 50 4.24 31819.8
BS-36-1.25-60 60 4.65 34856.9 ɛp= prestrain in CFRP strips ɛfrpu= ultimate tensile strain of CFRP strips
Afrp= area of CFRP strips b and h= width and height of RC beam
f′c, fr, and Ec= compressive strength, tensile strength and modulus of elasticity of the concrete material
Asc and Ast= area of compression and tension steel reinforcements
334
Properties of the modeled beams are presented in Table 5-4 including the concrete
properties of each beam, area and reinforcement ratio of CFRP strips, area and
reinforcement ratio of reinforcing steel, and prestressing level as prestrain in CFRP strips
and percentage of the ultimate tensile strain of the CFRP strips. The strengthened beam
ID in Table 5-4 refer to: the first part as the type of the beam (BS: beams strengthened
with NSM CFRP strip), the second part as the prestressing level (percentage of the
ultimate tensile strain of the CFRP strips), the third part as the tension steel ratio, and the
fourth part as the concrete compressive strength. It should be mentioned that the un-
strengthened beam ID is similar to the one used for the strengthened beam excepts that it
starts with B0 instead of BS at the first part and the second part used for strengthened
beam is excluded.
5.3.2 Description of FE Model
The developed FE models are 3D and all materials including concrete, CFRP
strips, longitudinal steel reinforcements, steel stirrups, epoxy adhesive, steel bolts, and
steel end anchor were simulated using appropriate elements in the ANSYS program
(SAS, 2004). In this section, it is tried to generate a simplified model for performing the
parametric study, therefore, to reduce the computer computational time, modelling time
and volume of the results, only one quarter of the beam was modeled due to the
symmetry in cross-section and loading span. Furthermore, complete bond was assumed
between different interfaces in the model since the overall flexural behaviour of the NSM
CFRP strengthened beams is not affected by any debonding as reported by Gaafar (2007)
and also to facilitate the trend of the parametric study. The aim of this section is to
335
conduct a parametric study, which is independent from the material properties and the
applied prestressing values in the beams tested by Gaafar (2007), on the other hand, the
simplified developed 3D FE models needs to be validated to be used for parametric study
that is accomplished later on in this section.
5.3.3 Modeling of Materials
5.3.3.1 Concrete
The Solid65 element was considered to model the concrete. Characteristics of this
element are presented in Section 5.2.3.1. The modulus of elasticity and tensile strength of
the concrete are calculated from equations 5-20 and 5-21 (CAN/CSA-A23.3-04, 2004). A
Poisson’s ratio of 0.18 is assigned to the concrete (Wight and MacGregor, 2009). To
properly model the concrete, the considered model for concrete includes linear and multi-
linear material properties in addition to the concrete model defined in ANSYS
(Kachlakev et al., 2001; Wolanski, 2004) as describes in the rest of this section. The
simplified compressive stress-strain curve for the concrete model was obtained by
applying equations 5-22 to 5-25 to form the multi-linear stress-strain curve as plotted in
Figure 5-39 (Wolanski, 2004; Wight and MacGregor, 2009).
cc fE 4500 Equation 5-20
cr f.f 60 Equation 5-21
10if cc Ef Equation 5-22
336
o
o
cc
Ef
12if
1
Equation 5-23
cuocc ff if Equation 5-24
c
c
E
f
20 Equation 5-25
where Ec, fr, f′c, 1, fc, , and 0 are the concrete modulus of elasticity (MPa), the concrete
tensile strength (MPa), the concrete compressive strength (MPa), the strain at the end of
the linear part up to fc= 0.3f′c (Wight and MacGregor, 2009), the concrete compressive
stress at strain , the strain at stress fc, and the strain at maximum concrete strength,
respectively.
Figure 5-39: Simplified concrete compressive stress-strain curves.
337
5.3.3.2 Steel Reinforcements
The Link8 element was selected to model steel reinforcements. Characteristics of
this element are mentioned in Section 5.2.3.2. The stress-strain curve of the internal steel
reinforcements was determined from the uniaxial tension tests as shown in Figure 5-2.
Multi-linear elastic material was considered to model the steel rebars with a Poisson’s
ratio of 0.3 (Wight and MacGregor, 2009).
5.3.3.3 CFRP Strips
The Solid45 element was employed to model the CFRP strips with characteristics
listed in Section 5.2.3.3. A linear-elastic material behaviour up to failure was assigned to
the CFRP elements with a modulus of elasticity of 145 GPa and a tensile strength of 2610
MPa, an ultimate strain of 0.018 (Gaafar, 2007). A Poisson’s ratio of 0.35 was considered
for this material (Kabir and Hojatkashani, 2008). In the model, to minimize mesh
intricacy, a 5×16 mm CFRP strip was modeled instead of 2-2×16 mm CFRP strips plus
1mm epoxy in-between (Figure 5-1). Therefore, an equivalent modulus of elasticity of
116 GPa (2×2×16×145/(5×16)=116 GPa), a tensile strength of 2088 MPa
(116000×0.018=2088 MPa), and an ultimate strain of 0.018 were allocated to the CFRP
material in the model, which yielded an identical axial stiffness with the CFRP in the test.
5.3.3.4 Epoxy Adhesive
The epoxy adhesive was modeled using Solid45 elements. It is assumed that the
epoxy adhesive behaves as linear-elastic up to failure, and possessed a Young's modulus
338
of 2.4 GPa and an ultimate tensile strength of 24 MPa (Sika, 2007b). A Poisson’s ratio of
0.37 was assigned to this material (Kabir and Hojatkashani, 2008).
5.3.3.5 Bolts at Steel End Anchor
The Beam4 element was considered to model the steel bolts at the end anchor.
Characteristics of this element are presented in Section 5.2.3.6. A linear elastic material
was assigned to these elements with a modulus of elasticity of 200 GPa and a Poisson’s
ratio of 0.3 (Wight and MacGregor, 2009).
5.3.3.6 Steel End Anchor and Loading and Supporting Steel Plates
The steel end anchors and loading and supporting steel plates were modeled using
Solid45 elements with a linear elastic material assigned to these elements having a
modulus of elasticity of 200 GPa and a Poisson’s ratio of 0.3 (Wight and MacGregor,
2009).
5.3.3.7 Bond at Concrete-Epoxy Interface
Although the complete bond was considered between different materials at the
interfaces, but the surface-to-surface contact elements with multi point constraint (MPC)
algorithm were assigned to interface between concrete and adhesive to separate the fine
mesh mapped inside the groove from surrounding mesh. The target surface (on concrete)
was modeled with TARGE170 and the contact surface (on adhesive) was modeled with
CONTA173. Properties and capabilities of these elements are mentioned in Section 5.2.4.
339
5.3.3.8 Modeling of Prestressing
Prestressing in the NSM CFRP was applied by assigning the initial stress to
Solid45 elements.
5.3.4 Nonlinear Solution
The meshed beam is depicted in Figure 5-40. The nonlinear solution was executed
using load control where the load is assigned to the model and the corresponding
deflection is computed. The nonlinearity problem was solved by defining five load-steps
for each model to accurately calculate the cracking, yielding, and ultimate loads and
deflections, to assign the effect of prestressing on the model, to control computer
computational time, and to assist in convergence of the problem. A summary of the
applied load-steps are presented in Table 5-5. Based on the developed FE models, the
ultimate load was attained either due to concrete crushing or CFRP rupture whichever
occurred first.
Table 5-5: Summary of load-steps assigned for nonlinear analysis.
Load-step Time at end of
load-step**
Sub-step** Max
number of
iterations
Displacement
convergence
criteria
tolerance No. Min Max
1. Zero load- induced
prestressing level* 1 1 N.A. N.A. 80 0.01
2. Applied prestressing-
before first cracking 5000-8000 10 5 50 80 0.01
3. Before first cracking-
after first cracking 8000-14000 15-75 15-40 100 100 0.03
4. After first cracking-
before steel yielding 20000-60000 20 10 100 100 0.03
5. Before steel yielding-
failure 28000-90000 50-10000 40-70 1000-40000 100 0.03
* used for prestressed NSM-CFRP strengthened beams
** varies
340
Figure 5-40: Meshed beam.
5.3.5 Validation of the Model
Results of one beam, BS-58-0.75-40, are compared to the experimental results
reported by Gaafar (2007) to validate the simplified developed 3D FE model. The load-
deflection response of the modeled beam is stiffer than the experimental one, as shown in
Figure 5-41. The difference starts before cracking, extended up to yielding, and slightly
increases in the plastic region. The difference might be due to ignoring the self-weight of
the beam in the FE models (which is ignored to facilitate the parametric study) and also
the slight difference between the reported CFRP material properties obtained from
tension tests and what was observed during the test under flexural performance.
Comparison between the FE and the experimental results for the strain profile along the
length of the CFRP strip in beam BS-58-0.75-40, at cracking, yielding, and ultimate loads
is presented in Figure 5-42. At cracking and yielding loads, the predicted strain profile
along the CFRP strip is matched with the experimental values. The modeled and
experimental beams showed similar mode of failure governed by CFRP rupture.
However, the recorded ultimate strain in the NSM CFRP strips for the tested beam is
341
greater than the ultimate tensile strain of 0.018 obtained from the tension test by Gaafar
(2007). Due to this difference, the FEM strain profile at ultimate and also the ultimate
deflection of the beam BS-58-0.75-40 are smaller than those from the experiment.
0
20
40
60
80
100
120
140
160
-5 0 5 10 15 20 25 30 35 40 45 50 55 60
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-58-0.75 (Experimental)
BS-58-0.75 (FE Analysis)
: CFRP rupture
Figure 5-41: Comparison between experimental and numerical load-deflection
curves of beam BS-58-0.75-40.
342
0
0.004
0.008
0.012
0.016
0.02
0 1000 2000 3000 4000 5000
Str
ain
in
CF
RP
str
ips
Distance from the support (mm)
@ Cracking Load, 46 kN, FEM-ANSYS @ Cracking Load, 42.1 kN, Experimental
@ Yielding Load, 131.2 kN, FEM-ANSYS @ Yielding Load, 122.8 kN, Experimental
@ Ultimate Load, 151.9 kN, FEM-ANSYS @ Ultimate Load, 149.2 kN, Experimental
Figure 5-42: Comparison between experimental and numerical strain profile along
the length of CFRP strips of beam BS-58-0.75-40.
A summary of the comparison between predicted and experimental results are
presented in Table 5-6 including a comparison between load-deflection values at
cracking, yielding and ultimate, ductility index (defined as the ratio of deflection at
ultimate to deflection at yielding), amount of energy absorption (determined as the area
under load-deflection curve), failure mode, and the percentage of difference between FE
and test results.
343
Table 5-6: Comparison between numerical and experimental results of beam BS-58-
0.75-40.
Beam ID Results Δo
(mm)
Pcr
(kN)
Δcr
(mm)
Py
(kN)
Δy
(mm)
Pu
(kN)
Δu
(mm) µD
Φ
(kN·mm) FM
BS-58-0.75-40
Test 1.6 42.1 2.64 122.8 25.77 149.2 58.13 2.26 6529 FR
FEM 1.58 46.0 1.8 131.2 24.84 151.9 45.40 1.83 5067.2 FR
Error % 1.3 9.3 31.8 6.8 3.6 1.8 21.9 19.0 22.4
Pcr and Δcr = load and deflection at cracking Δo = negative camber due to prestressing
Py and Δy = load and deflection at yielding µD = ductility index (Δu /Δy)
Pu and Δu = load and deflection at ultimate Φ = energy absorption (area under P-Δ curve up to Pu)
FM = failure mode FR = CFRP rupture
5.3.6 Parametric Study
Results of a comprehensive parametric study performed on the prestressing level,
the tensile steel reinforcement ratio, and the concrete compressive strength of the RC
beams strengthened with prestressed NSM CFRP strips are presented and discussed in
this section.
5.3.6.1 Effects of Prestressing Level in the NSM CFRP
To assess the effects of prestressing results from four sets of beams analyzed
using FE method were employed. Each set consisted of five beams with equal tension
steel ratio: one un-strengthened control beam and four RC beams strengthened with NSM
CFRP strips. The prestressing levels in the strengthened beams included 0%, 19%, 36%,
and 58% of the ultimate tensile strain of the CFRP strips. The tension steel ratio in each
set was different from the other sets including 0.75%, 1.25%, 1.75%, and 2.25% of the
total cross-sectional area of the RC beam while all the strengthened beams had the same
CFRP reinforcement ratio of 0.08%.
344
0
25
50
75
100
125
150
175
-10 0 10 20 30 40 50 60 70 80 90 100 110 120
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-58-0.75-40 (FE Analysis)
BS-36-0.75-40 (FE Analysis)
BS-19-0.75-40 (FE Analysis)
BS-0-0.75-40 (FE Analysis)
B0-0.75-40 (FE Analysis)
: CFRP rupture : Concrete crushing
Figure 5-43: Load-deflection curves of the modeled beams-effects of prestressing
level on set BS-0.75-40.
0
25
50
75
100
125
150
175
200
225
-10 0 10 20 30 40 50 60 70 80 90 100 110 120
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-58-1.25-40 (FE Analysis)
BS-36-1.25-40 (FE Analysis)
BS-19-1.25-40 (FE Analysis)
BS-0-1.25-40 (FE Analysis)
B0-1.25-40 (FE Analysis)
: CFRP rupture : Concrete crushing
Figure 5-44: Load-deflection curves of the modeled beams-effects of prestressing
level on set BS-1.25-40.
345
0
25
50
75
100
125
150
175
200
225
250
275
-10 0 10 20 30 40 50 60 70 80 90 100 110 120
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-58-1.75-40 (FE Analysis)
BS-36-1.75-40 (FE Analysis)
BS-19-1.75-40 (FE Analysis)
BS-0-1.75-40 (FE Analysis)
B0-1.75-40 (FE Analysis)
: CFRP rupture : Concrete crushing
Figure 5-45: Load-deflection curves of the modeled beams-effects of prestressing
level on set BS-1.75-40.
0
25
50
75
100
125
150
175
200
225
250
275
300
-10 0 10 20 30 40 50 60 70 80 90 100 110 120
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-58-2.25-40 (FE Analysis)
BS-36-2.25-40 (FE Analysis)
BS-19-2.25-40 (FE Analysis)
BS-0-2.25-40 (FE Analysis)
B0-2.25-40 (FE Analysis)
: Concrete crushing
Figure 5-46: Load-deflection curves of the modeled beams-effects of prestressing
level on set BS-2.25-40.
346
Table 5-7: Summary of the results for the effects of prestressing.
Beam ID Δo
(mm)
Δcr
(mm)
Pcr
(kN)
Δy
(mm)
Py
(kN)
Δu
(mm)
Pu
(kN) µD
Φ
(kN·mm) FM
B0-0.75-40 0 1.68 23 22.3 84.8 118.47 103.8 5.31 10411 CC
BS-0-0.75-40 0 1.58 21.6 25.52 101.9 111.02 160.6 4.35 12922.5 FR
BS-19-0.75-40 0.52 1.68 30 25.29 111.0 87.68 157.2 3.47 10196.8 FR
BS-36-0.75-40 0.99 1.74 37.2 25.12 120.6 67.92 155.5 2.70 7877 FR
BS-58-0.75-40 1.58 1.80 46.0 24.84 131.2 45.4 151.9 1.83 5067.2 FR
B0-1.25-40 0 1.73 24.6 26.75 141.5 80.52 155.8 3.01 10207.8 CC
BS-0-1.25-40 0 1.61 22.9 28.06 154.0 78.69 195.9 2.80 11326.6 CC
BS-19-1.25-40 0.49 1.69 31 28.37 164.2 78.16 205.3 2.76 11975.1 CC
BS-36-1.25-40 0.93 1.76 38.3 28.83 173.7 70.22 209.4 2.44 10979.3 FR
BS-58-1.25-40 1.48 1.88 47.7 29.30 186.1 51.16 208.3 1.75 7685.6 FR
B0-1.75-40 0 1.77 26.2 30.4 195.1 66.78 208.7 2.20 10637 CC
BS-0-1.75-40 0 1.65 24.5 31.71 206.2 62.43 235.6 1.97 10384.9 CC
BS-19-1.75-40 0.46 1.75 32.6 32.09 215.9 60.91 244.4 1.90 10577.6 CC
BS-36-1.75-40 0.87 1.81 39.6 32.51 225.1 60.01 252.1 1.85 10850.4 CC
BS-58-1.75-40 1.39 1.94 49.1 32.88 236.3 53.13 257.8 1.62 9675.2 FR
B0-2.25-40 0 1.81 27.8 33.67 244.3 54.59 255.7 1.62 9712.3 CC
BS-0-2.25-40 0 1.71 26.2 34.74 255.0 52.46 275 1.51 9521.8 CC
BS-19-2.25-40 0.43 1.80 34.2 35.16 263.7 51.54 282.7 1.47 9691.7 CC
BS-36-2.25-40 0.82 1.89 41.4 35.68 272.6 50.32 289.3 1.41 9709.7 CC
BS-58-2.25-40 1.31 2.00 50.6 36.26 283.3 48.89 297.9 1.35 9738.5 CC
Comparison between load-deflection curves of the beams in each set is presented
in Figure 5-43 to Figure 5-46. A summary of the results of the modeled beams is
presented in Table 5-7. Analyzing the results reveals that increasing the prestressing level
in the NSM CFRP strips from 0-58% enlarges the negative camber up to 100% of the
cracking deflection of the non-prestressed strengthened beam in set with 0.75% of
tension steel ratio and up to 76.6% of the cracking deflection of the non-prestressed
strengthened beam in set with 2.25% of tension steel ratio, more details are provided in
Figure 5-47.
347
0
20
40
60
80
100
120
0 10 20 30 40 50 60
Neg
ati
ve
cam
be
r to
cra
kin
g d
efl
ec
tio
n
of
BS
-0 i
n e
ac
h s
et
(%
)
Prestressing level (% of CFRP ultimate strength)
Set BS-0.75-40
Set BS-1.25-40
Set BS-1.75-40
Set BS-2.25-40
Figure 5-47: Effects of prestressing on negative camber.
At cracking stage; enhancements of 93.1% in cracking load of the non-prestressed
strengthened beam for set with 2.25% of tension steel ratio, and 113.2% in cracking load
of the non-prestressed strengthened beam for set with 0.75% of tension steel ratio were
achieved due to increasing the prestressing level in the NSM CFRP from 0-58%, see
Figure 5-48 for more details. Also a maximum increase of 17.6% in cracking deflection
of the non-prestressed strengthened beam was reached by changing the prestressing level
in CFRP from 0-58% for set with 1.75% of tension steel ratio.
348
0
30
60
90
120
0 10 20 30 40 50 60
% o
f ch
an
ge
in
cra
ck
ing
lo
ad
w
.r.t
BS
-0 in
ea
ch
se
t
Prestressing level (% of CFRP ultimate strength)
Set BS-0.75-40
Set BS-1.25-40
Set BS-1.75-40
Set BS-2.25-40
Figure 5-48: Effects of prestressing on cracking load.
At yielding stage, enhancements of 28.8% and 11.1% in yielding load of the
beams with 0.75% and 2.25% tension steel ratios were obtained, respectively, with
respect to non-prestressed strengthened beam of each set by changing the prestressing
level in the NSM CFRP from 0-58%, as shown in Figure 5-49. In this context, minor
change (less than 4%) on the yielding deflection was observed. The efficiency of the
prestressing can be examined in as much as the non-prestressed strengthening increases
the yielding load of the un-strengthened control beam from 4.4% (in the beam with
2.25% of tension steel ratio) to 20.2% (in the beam with 0.75% of tension steel ratio)
whereas in strengthening with 58% of prestressing these values reach to 16% and 54.7%.
It can be concluded that a linear relationship exists between the prestressing level in
CFRP strip from 0-58% and the percentage of change in cracking and yielding loads.
349
0
10
20
30
0 10 20 30 40 50 60
% o
f ch
an
ge in
yie
ld l
oad
w
.r.t
BS
-0 in
each
set
Prestressing level (% of CFRP ultimate strength)
Set BS-0.75-40
Set BS-1.25-40
Set BS-1.75-40
Set BS-2.25-40
Figure 5-49: Effects of prestressing on yield load.
The effect of the prestressing on the ultimate load depends on the type of failure
as presented in Figure 5-50. For sets with 1.25% and 1.75% of tension steel ratios, the
ultimate load versus the prestressing level relations are almost downward parabolas,
which is due to change of the type of failure from concrete crushing to CFRP rupture as
the prestressing level increases for these sets, as presented in Table 5-7 and Figure 5-50.
If failure by CFRP rupture governs, the prestressing results in a small decrease (up to
5.4%) in the ultimate load of the non-prestressed strengthened beam (in the set with
0.75% of tension steel ratio). If failure by concrete crushing governs, the prestressing
causes a small increase (up to 8.3%) in the ultimate load of the non-prestressed
strengthened beam (in set with 2.25% of tension steel ratio). However, non-prestressed
350
strengthening enhances the ultimate load of the un-strengthened beam by 54.7% in set
with 0.75% of tension steel ratio and 7.5% in set with 2.25% of tension steel ratio, as can
be seen by comparing the results (Pu) in Table 5-7. It can be concluded that prestressing
of NSM CFRP for strengthening has no significant effect on the ultimate load of the non-
prestressed strengthened beam, as shown in Figure 5-50 for analyzed beams. At ultimate
stage, decreases of 59.1% and 6.8% in deflections at ultimate loads of the sets with
0.75% and 2.25% of tension steel ratios were reached, respectively, with respect to the
non-prestressed strengthened beam in each set by changing the prestressing level in NSM
CFRP from 0-58%, more details are provided in Figure 5-51.
-10
-5
0
5
10
0 10 20 30 40 50 60
% o
f ch
an
ge in
ult
imate
lo
ad
w
.r.t
BS
-0 in
each
set
Prestressing level (% of CFRP ultimate strength)
Set BS-0.75-40
Set BS-1.25-40
Set BS-1.75-40
Set BS-2.25-40
Figure 5-50: Effects of prestressing on ultimate load.
351
-60
-50
-40
-30
-20
-10
0
0 10 20 30 40 50 60
% o
f ch
an
ge in
ult
imate
defl
ecti
on
w
.r.t
BS
-0 in
each
set
Prestressing level (% of CFRP ultimate strength)
Set BS-0.75-40
Set BS-1.25-40
Set BS-1.75-40
Set BS-2.25-40
Figure 5-51: Effects of prestressing on ultimate deflection.
Due to decreasing the ultimate deflection, prestressing reduces the ductility index
(deflection at ultimate to deflection at yielding). In this context, decreases of 58% and
10.7% in ductility indices of the sets with 0.75% and 2.25% of tension steel ratios were
achieved, respectively, with respect to the non-prestressed strengthened beam in each set
by changing the prestressing level in NSM CFRP from 0-58%, see Figure 5-52 for more
details.
The amount of energy absorption (area under load-deflection response up to peak
load) depends on the type of failure. As shown in Figure 5-53 by changing the
prestressing level from 0-58%, a decrease of 60.8% in energy absorption of the set with
0.75% of tension steel ratio occurred with respect to the non-prestressed strengthened
beam in this set. In this context, the amount of decrease is smaller for sets with higher
352
tension steel ratios. The highest amount of energy absorption is reached when balanced
failure occurs (CFRP rupture and concrete crushing simultaneously). This type of failure
utilizes the full capacity of materials. As presented in Table 5-7 and Figure 5-54 to Figure
5-57, the maximum energy absorption is reached when the type of failure changes from
concrete crushing to CFRP rupture. When failure by CFRP rupture governs for a non-
prestressed NSM CFRP strengthened beam, applying and increasing the prestressing
level decreases the energy absorption. When failure by concrete crushing governs for a
non-prestressed NSM CFRP strengthened beam, applying and increasing the prestressing
level enhances the energy absorption. Further, when the tension steel ratio is low
strengthening can cause a wide changes in the energy absorption (e.g., in set with 0.75%
of tension steel ratio, it changes from 24.1% to -51.3% with respect to the un-
strengthened beam, see Figure 5-54) but, the changes in the energy absorption are very
small when the tension steel ratio is high (e.g., in set with 2.25% of tension steel ratio, it
changes from -2% to 0.3% with respect to the un-strengthened beam, see Figure 5-57).
The type of failure of the strengthened beams changes from concrete crushing to CFRP
rupture with increasing the prestressing level in the NSM CFRP strips.
353
-60
-50
-40
-30
-20
-10
0
0 10 20 30 40 50 60
% o
f ch
an
ge
in
du
cti
lity
in
de
x
w.r
.t B
S-0
in
eac
h s
et
Prestressing level (% of CFRP ultimate strength)
Set BS-0.75-40
Set BS-1.25-40
Set BS-1.75-40
Set BS-2.25-40
Figure 5-52: Effects of prestressing on ductility index.
-70
-60
-50
-40
-30
-20
-10
0
10
0 10 20 30 40 50 60
% o
f ch
an
ge in
en
erg
y a
bso
rpti
on
w.r
.t B
S-0
in
each
set
Prestressing level (% of CFRP ultimate strength)
Set BS-0.75-40
Set BS-1.25-40
Set BS-1.75-40
Set BS-2.25-40
Figure 5-53: Effects of prestressing on energy absorption.
354
The optimum prestressing level is defined in the previous chapter as the
prestressing level in the NSM CFRP strips (taken as a percentage of the ultimate tensile
strength of the CFRP strips) which maintains the amount of energy absorption in the
strengthened beam equal to the un-strengthened control beam. Calculation of the
optimum prestressing level is illustrated in Figure 5-54 to Figure 5-57 for each set of
beams. Based on the defined procedure, an optimum prestressing level of 17.5%, 41.1%,
22.8% or 40%, and 38% is obtained for beams with 0.75%, 1.25%, 1.75%, and 2.25% of
tension steel ratio, respectively. It can be seen that as the tension steel ratio increases the
optimum prestressing level increases, however, at a steel ratio of 1.75% two optimum
prestressing levels were obtained (22.8% and 40%) because of the shape of the energy
absorption curve in each steel ratio, which depends on the mode of failure that happens in
the range of applied prestressing levels from 0-58%. If failure by concrete crushing
governs throughout the prestressing range, the curve is ascending. If failure by FRP
rupture governs throughout the prestressing range, the curve is descending. When
balanced failure happens in the prestressing range (i.e., there is a transition in mode of
failure within the prestressing range from concrete crushing to CFRP rupture) the curve is
downward facing parabola, and in this case, there is possibility to have two optimum
prestressing levels that each one is related to separate type of failure.
355
0
2000
4000
6000
8000
10000
12000
14000
0 10 20 30 40 50 60
Are
a u
nd
er
loa
d-d
efl
ec
tio
n c
urv
e
(kN
.mm
)
Prestress level (% of CFRP ultimate strength)
Energy absorption (BS-0.75 set)
Energy absorption of unstrengthened beam
: CFRP rupture : Concrete crushing
Figure 5-54: Determination of optimum prestressing level for set BS-0.75.
0
2000
4000
6000
8000
10000
12000
14000
0 10 20 30 40 50 60
Are
a u
nd
er
loa
d-d
efl
ec
tio
n c
urv
e
(kN
.mm
)
Prestress level (% of CFRP ultimate strength)
Energy absorption (BS-1.25 set)
Energy absorption of unstrengthened beam
: CFRP rupture : Concrete crushing
Figure 5-55: Determination of optimum prestressing level for set BS-1.25.
356
0
2000
4000
6000
8000
10000
12000
14000
0 10 20 30 40 50 60
Are
a u
nd
er
load
-de
flec
tio
n c
urv
e
(kN
.mm
)
Prestress level (% of CFRP ultimate strength)
Energy absorption (BS-1.75 set)
Energy absorption of unstrengthened beam
: CFRP rupture : Concrete crushing
Figure 5-56: Determination of optimum prestressing level for set BS-1.75.
0
2000
4000
6000
8000
10000
12000
14000
0 10 20 30 40 50 60
Are
a u
nd
er
loa
d-d
efl
ec
tio
n c
urv
e
(kN
.mm
)
Prestress level (% of CFRP ultimate strength)
Energy absorption (BS-2.25 set)
Energy absorption of unstrengthened beam
: CFRP rupture : Concrete crushing
Figure 5-57: Determination of optimum prestressing level for set BS-2.25.
357
5.3.6.2 Effects of Tension Steel Reinforcement
To assess the effect of tension steel ratio, the modeled beams were categorized as
presented in Table 5-8 in which each set consists of beams with the same prestressing
level and various tension steel ratios.
Table 5-8: Summary of the results for the effects of tension steel ratio.
Beam ID Δo
(mm)
Δcr
(mm)
Pcr
(kN)
Δy
(mm)
Py
(kN)
Δu
(mm)
Pu
(kN) µD
Φ
(kN·mm) FM
B0-0.75-40 0 1.68 23.0 22.30 84.8 118.47 103.8 5.31 10411 CC
B0-1.25-40 0 1.73 24.6 26.75 141.5 80.52 155.8 3.01 10207.8 CC
B0-1.75-40 0 1.77 26.2 30.40 195.1 66.78 208.7 2.20 10637 CC
B0-2.25-40 0 1.81 27.8 33.67 244.3 54.59 255.7 1.62 9712.3 CC
BS-0-0.75-40 0 1.58 21.6 25.52 101.9 111.02 160.6 4.35 12922.5 FR
BS-0-1.25-40 0 1.61 22.9 28.06 154.0 78.69 195.9 2.80 11326.6 CC
BS-0-1.75-40 0 1.65 24.5 31.71 206.2 62.43 235.6 1.97 10384.9 CC
BS-0-2.25-40 0 1.71 26.2 34.74 255.0 52.46 275 1.51 9521.8 CC
BS-19-0.75-40 0.52 1.68 30.0 25.29 111.0 87.68 157.2 3.47 10196.8 FR
BS-19-1.25-40 0.49 1.69 31.0 28.37 164.2 78.16 205.3 2.76 11975.1 CC
BS-19-1.75-40 0.46 1.75 32.6 32.09 215.9 60.91 244.4 1.90 10577.6 CC
BS-19-2.25-40 0.43 1.80 34.2 35.16 263.7 51.54 282.7 1.47 9691.7 CC
BS-36-0.75-40 0.99 1.74 37.2 25.12 120.6 67.92 155.5 2.70 7877 FR
BS-36-1.25-40 0.93 1.76 38.3 28.83 173.7 70.22 209.4 2.44 10979.3 FR
BS-36-1.75-40 0.87 1.81 39.6 32.51 225.1 60.01 252.1 1.85 10850.4 CC
BS-36-2.25-40 0.82 1.89 41.4 35.68 272.6 50.32 289.3 1.41 9709.7 CC
BS-58-0.75-40 1.58 1.80 46.0 24.84 131.2 45.4 151.9 1.83 5067.2 FR
BS-58-1.25-40 1.48 1.88 47.7 29.30 186.1 51.16 208.3 1.75 7685.6 FR
BS-58-1.75-40 1.39 1.94 49.1 32.88 236.3 53.13 257.8 1.62 9675.2 FR
BS-58-2.25-40 1.31 2.00 50.6 36.26 283.3 48.89 297.9 1.35 9738.5 CC
Analyzing the predicted results shows that increasing the tension steel ratio from
0.75% to 2.25%:
Reduces the negative camber up to 17% for all sets, as shown in Figure 5-58
Increases negligibly the cracking deflection up to 8.2% for the non-prestressed
strengthened set and up to 10.8% for the set with 58% of prestressing
358
Enhances the cracking load up to 9.9% for set with 58% of prestressing and up
to 21.3% for the non-prestressed strengthened set, as shown in Figure 5-59
Enlarges the deflection at yielding up to 36.1% for the non-prestressed
strengthened set and up to 45.9% for the strengthened set with 58% of
prestressing
Enlarges the deflection at yielding in the un-strengthened set up to 51%
Increases the yielding load up to 150.2% for the non-prestressed strengthened
set and up to 115.9% for the strengthened set with 58% of prestressing, as
shown in Figure 5-60
Enhances the yielding load in un-strengthened set up to 188.1%;
Decreases the ultimate deflection when failure by concrete crushing governs
(as represented in Figure 5-62 and Table 5-8 for non-prestressed strengthened
set)
Enhances the ultimate deflection when the failure by CFRP rupture governs
(as represented in Figure 5-62 and for the strengthened set with 58% of
prestressing)
Results from Table 5-8 reveal that the maximum deflection occurs when the type
of failure changes from CFRP rupture to concrete crushing.
Furthermore, changing the steel ratio from 0.75% to 2.25%:
Increases the ultimate load up to 71.2% for the non-prestressed strengthened
set and up to 96.1% for the strengthened set with 58% of prestressing, as
shown in Figure 5-61
359
Decreases the ductility index up to 65.2% for the non-prestressed strengthened
set and up to 26.2% for the strengthened set with 58% of prestressing, as
shown in Figure 5-63;
Changes the failure mode from CFRP rupture to concrete crushing
The changes in the amount of energy absorption versus tension steel ratio is
plotted in Figure 5-64. The curve reaches to its highest value when there is a transition in
mode of failure (From CFRP rupture to concrete crushing). As long as failure by CFRP
rupture governs, increasing the steel ratio enhances the energy absorption and as long as
failure by concrete crushing governs, increasing the steel ratio decreases the energy
absorption, as can be seen in Figure 5-64.
-20
-15
-10
-5
0
0.75 1 1.25 1.5 1.75 2 2.25
% o
f ch
an
ge in
neg
ati
ve c
am
ber
w.r
.t o
f B
S-0
.75 in
each
set
Tension steel ratio (%)
Set BS-19-40
Set BS-36-40
Set BS-58-40
Figure 5-58: Effects of tension steel ratio on negative camber.
360
0
5
10
15
20
25
0.75 1 1.25 1.5 1.75 2 2.25
% o
f c
ha
ng
e in
cra
ck
ing
lo
ad
w
.r.t
BS
-0.7
5 in
ea
ch
se
t
Tension steel ratio (%)
Set BS-0-40
Set BS-19-40
Set BS-36-40
Set BS-58-40
B0-40
Figure 5-59: Effects of tension steel ratio on cracking load.
0
50
100
150
200
0.75 1 1.25 1.5 1.75 2 2.25
% o
f ch
an
ge in
yie
ld l
oad
w
.r.t
BS
-0.7
5 in
eac
h s
et
Tension steel ratio (%)
Set BS-0-40
Set BS-19-40
Set BS-36-40
Set BS-58-40
B0-40
Figure 5-60: Effects of tension steel ratio on yield load.
361
0
40
80
120
160
0.75 1 1.25 1.5 1.75 2 2.25
% o
f ch
an
ge in
ult
imate
lo
ad
w
.r.t
BS
-0.7
5 in
eac
h s
et
Tension steel ratio (%)
Set BS-0-40
Set BS-19-40
Set BS-36-40
Set BS-58-40
B0-40
Figure 5-61: Effects of tension steel ratio on ultimate load.
-60
-40
-20
0
20
0.75 1 1.25 1.5 1.75 2 2.25
% o
f c
ha
ng
e in
ult
ima
te d
efl
ec
tio
n
w.r
.t B
S-0
.75
in
ea
ch
se
t
Tension steel ratio (%)
Set BS-0-40
Set BS-19-40
Set BS-36-40
Set BS-58-40
B0-40
Figure 5-62: Effects of tension steel ratio on ultimate deflection.
362
-80
-60
-40
-20
0
0.75 1.25 1.75 2.25
% o
f ch
an
ge in
du
cti
lity
in
dex
w.r
.t B
S-0
.75 in
eac
h s
et
Tension steel ratio (%)
Set BS-0-40
Set BS-19-40
Set BS-36-40
Set BS-58-40
B0-40
Figure 5-63: Effects of tension steel ratio on ductility index.
-40
-20
0
20
40
60
80
100
0.75 1 1.25 1.5 1.75 2 2.25
% o
f c
ha
ng
e in
en
erg
y a
bs
orp
tio
nw
.r.t
BS
-0.7
5 in
ea
ch
se
t
Tension steel ratio (%)
Set BS-0-40
Set BS-19-40
Set BS-36-40
Set BS-58-40
B0-40
Figure 5-64: Effects of tension steel ratio on energy absorption.
363
5.3.6.3 Effects of Concrete Compressive Strength
To examine the effect of concrete compressive strength on the behaviour of the
RC beams strengthened with prestressed NSM CFRP strips, four beams with tension steel
ratio of 1.25% and strengthened with the same prestressing level (36% of CFRP ultimate
tensile strength) but using different concrete compressive strengths of 30 MPa, 40 MPa,
50 MPa, and 60 MPa were analyzed. The load-deflection curves of the strengthened
beams with different concrete compressive strengths are presented in Figure 5-65. A
summary of the results for the effects of concrete compressive strength is presented in
Table 5-9.
0
25
50
75
100
125
150
175
200
225
-10 0 10 20 30 40 50 60 70 80
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-36-1.25-60 (f'c = 60MPa, FE Analysis)
BS-36-1.25-50 (f'c = 50MPa, FE Analysis)
BS-36-1.25-40 (f'c = 40MPa, FE Analysis)
BS-36-1.25-30 (f'c = 30MPa, FE Analysis)
: CFRP rupture : Concrete crushing
Figure 5-65: Effects of concrete compressive strength on the load-deflection curve.
364
When the concrete compressive strength increases: the type of failure changes
from concrete crushing to CFRP rupture; the ductility index slightly increases; the energy
absorption decreases slightly when CFRP rupture governs and reaches to its maximum
value when balanced failure occurs; the camber due to prestressing decreases (up to
22.8%); the cracking and yielding deflections decrease negligibly (up to 4.4% and 13.8%,
respectively); the ultimate deflection slightly decreases when the failure by CFRP rupture
governs; and the cracking, yielding, and ultimate loads increase (up to 17.4%, 2.8%, and
9.8%, respectively). It can be concluded that changing the concrete compressive strength
has a very slight effect on the overall flexural behaviour of the RC beams strengthened
with prestressed NSM CFRP strips.
Table 5-9: Summary of the results for the effects of concrete compressive strength.
Beam ID Δo
(mm)
Pcr
(kN)
Δcr
(mm)
Py
(kN)
Δy
(mm)
Pu
(kN)
Δu
(mm) µD
Φ
(kN·mm) FM
BS-36-1.25-30 1.04 36.4 1.85 171.2 30.71 197.2 61.93 2.02 8911.2 CC
BS-36-1.25-40 0.93 38.3 1.76 172.4 28.26 209.4 70.22 2.49 10979.3 FR
BS-36-1.25-50 0.85 40.3 1.73 173.9 27.03 213.7 68.05 2.52 10846.7 FR
BS-36-1.25-60 0.80 42.7 1.77 175.9 26.47 216.3 66.86 2.53 10774.2 FR
5.4 FE Modeling of Steel End Anchor and Parametric Study
In this section, a 3D FE model is developed using ANSYS program to simulate
the behaviour of the end-steel end anchor used for the prestressed NSM CFRP
strengthening system. This type of anchor , as shown in Figure 5-66, was first developed
and used by Gaafar (2007) to implement a practical prestressing system for the NSM
strengthening and to overcome the drawbacks of the previous systems available in the
literature (Nordin and Täljsten, 2006; De Lorenzis and Teng, 2007; Badawi and Soudki,
2009) explained in more details in Chapter Two. After developing the FE model and
365
making sure about the accuracy of the results, a parametric study was performed, as
presented in this section, to analyze the effects of the adhesive thickness, the bond
characteristics, and the anchor length on the performance of the anchor and interfacial
shear stress distribution.
Figure 5-66: Anchorage system for prestressed NSM-CFRP strengthening.
5.4.1 Description of the FE Model
The modeled end anchor is 3D consisting of CFRP strips, epoxy adhesive, steel
anchor and steel bolts which are simulated by using the appropriate solid elements
available in the ANSYS program. Due to symmetry, only half of the anchor was modeled
to facilitate the preprocessing and post processing steps. The CFRP-epoxy and epoxy-
anchor interfaces were modeled by applying contact elements and assigning well-known
Steel end anchor
Kwik anchor bolt
Temporary fixed bracket
CFRP strips
Temporary movable bracket
366
Coulomb friction model (based on cohesion and internal friction) to consider the
interaction between normal and shear stresses. Since this part of the research is a pure FE
one, the accuracy of the model was confirmed by conducting a sensitivity analysis on the
results, then, a parametric study (including 14 models as presented in Table 5-10) was
performed to investigate the effects of bond cohesion, anchor length, anchor width, and
anchor height on the interfacial stress distributions and bond performance. The model ID
specifies Lt (the length of anchor tube, mm)-C (cohesion, MPa)-Ha (height of the
adhesive between CFRP and steel tube in the vertical direction, mm)-Wa (width of the
adhesive between CFRP and steel tube in the horizontal direction, mm). More details
about the geometry of the modeled end anchors are presented in Figure 5-67.
Table 5-10: Summary of the modeled steel end anchors.
Model ID
Anchor tube Interface Adhesive CFRP Bolt Anchor plate
Lt×Wt×Ht×Tt
(mm)
C
(MPa) µ
Ha
(mm)
Wa
(mm)
Lf×Wf×Tf
(mm)
db-dh
(mm)
Lp×Wp×Tp
(mm)
Lt250-C5-Ha1.5-Wa7
250×25×25×3
5
0.65
1.5
7
400×16×5
16-19 150×140×9.5
Lt250-C10-Ha1.5-Wa7 10
Lt250-C15-Ha1.5-Wa7 15
Lt250-C20-Ha1.5-Wa7 20
Lt150-C10-Ha1.5-Wa7 150×25×25×3
10
300×16×5
Lt200-C10-Ha1.5-Wa7 200×25×25×3 350×16×5
Lt300-C10-Ha1.5-Wa7 300×25×25×3 450×16×5
Lt350-C10-Ha1.5-Wa7 350×25×25×3 500×16×5
Lt400-C10-Ha1.5-Wa7 400×25×25×3 550×16×5
Lt450-C10-Ha1.5-Wa7 450×25×25×3 600×16×5
Lt250-C10-Ha1.5-Wa3.5 250×18×25×3 3.5
400×16×5
Lt250-C10-Ha1.5-
Wa10.5 250×32×25×3 10.5
Lt250-C10-Ha4.5-Wa7 250×25×31×3 4.5 7
Lt250-C10-Ha7.5-Wa7 250×25×37×3 7.5
Lt= length of anchor tube Wt= width of anchor tube Ht= height of anchor tube Tt= thickness of anchor tube
Lf= length of CFRP strips Wf= width of CFRP strips Ha= height of adhesive Tf= thickness of CFRP strips
Lp= length of anchor plate Wp= width of anchor plate C= cohesion µ= friction coefficient
db=bolt diameter Wa=adhesive width dh=hole diameter
367
Figure 5-67: Details of the modeled end anchors and abbreviation of dimensions.
5.4.2 Modeling of Materials
5.4.2.1 Steel End Anchor
Eight-node solid brick element (Solid45) was employed to model the steel
material of the anchor. Characteristics of this element are provided in Section 5.2.3.3. A
multi-linear stress-strain curve assigned to the steel material is presented in Figure 5-68.
Also, a Poissons’s ratio of 0.3 was considered for the steel material (Emam, 2007).
368
Figure 5-68: Stress-strain curve of anchor steel (Emam, 2007).
5.4.2.2 CFRP Strip
The CFRP strip was modeled using the Soild45 element. Based on the stress-
strain curve of the CFRP material, a multi-linear elastic material model was assigned to
them as shown in Figure 5-10 obtained from experimental results, with a Poisson’s ratio
of 0.22 for CFRP material (Kachlakev et al., 2001).
5.4.2.3 Epoxy Adhesive
In the NSM strengthening system the epoxy adhesive had been used to fill in the
groove and bond the CFRP strip to the inside of the steel anchor. The epoxy was
simulated using the Solid45 element. The employed epoxy adhesive was Sikadur® 330
with a multi-linear elastic material stress-strain curve presented in Figure 5-11. A
Poisson’s ratio of 0.3 was assigned to Sikadur® 330 (Haghani, 2010).
369
5.4.2.4 Anchor Bolt
In the developed anchorage system for the prestressed NSM-CFRP strengthening
system (Gaafar, 2007), the end steel anchors are mounted on the substrate concrete using
anchor bolts (Kwik bolt 3 expansion anchor) made of carbon steel (Hilti Inc.). These
bolts were simulated using Solid45 elements in the FE analysis. A multi-linear material
model, obtained from data sheet of these bolts, was assigned to bolt elements as shown in
Figure 5-69. A Poisson’s ratio of 0.29 for carbon steel was assigned to the bolts
(Engineers edge, 2012).
Figure 5-69: Stress-strain curve for anchor bolts (Hilti Inc).
5.4.2.5 Bond
The CFRP-epoxy, steel-epoxy, and bolt-hole interfaces were modeled using
contact elements. The Coulomb friction model was applied to the interfaces to take into
account the interaction between interface materials in terms of interfacial shear and
pressure. A surface-to-surface contact pairs were applied to the interfaces, the target
surface on stiffer material of the corresponding interface was modeled using TARGE170
370
and the contact surface on softer material of the interface was modeled using CONTA
173. Characteristics of these elements are provided in Section 5.2.4.
The failure at steel-epoxy and CFRP-epoxy interfaces was defined using Coulomb
friction model criteria. In the Coulomb friction model, two contacting materials can carry
shear stresses up to a certain magnitude across their interface before they start sliding
relative to each other; this state is known as sticking. The Coulomb friction model defines
an equivalent shear stress at which sliding on the surface begins as a fraction of the
contact pressure as presented in Equation 5-26 (SAS, 2009):
Cp Equation 5-26
where τ is the shear strength (MPa), µ the friction coefficient, p the contact pressure
(MPa), and C is the cohesion sliding resistance (MPa). Once the shear stress exceeds the
shear strength calculated from Equation 5-26, the two surfaces slides relative to each
other; this state is known as sliding. The surface friction coefficient depends on
temperature, time, normal pressure, sliding distance, or sliding relative velocity. In the FE
analysis, a friction coefficient of 0.65 was assigned to the interfaces (Varastehpour &
Hamelin, 1997).
5.4.3 Mesh Sensitivity Analysis
As mentioned earlier in Section 5.2.6, the FE results should not depend on the
element type or size; and since this part is an FE analysis where there is no experimental
results available to validate the FE model, therefore, performing a sensitivity analysis is
371
required. To identify the optimum number of elements four primary FE models,
considering complete bond between interfaces, with 1509, 2813, 5077, and 8309 number
of elements were developed for a 250 mm tube length steel anchor (model Lt250-C5-
Ha1.5-Wa7). These FE models are presented in Figure 5-70 to Figure 5-73. The optimum
model was selected based on the sensitivity curve obtained for displacement at loaded
end of the CFRP strips at 100 kN applied load, as shown in Figure 5-74. As can be seen
in Figure 5-74, the major change of the curve occurs at about 2800 number of elements,
therefore, any model with number of elements greater than 2800 leads to high accuracy
whereas the model with 5077 elements was selected (with about 99.3% result reliability
calculated with respect to the model with high number of the elements, 8309 elements).
The selected model based on sensitivity analysis was a primary model considering
complete bond, the final model was developed by assigning the contact elements to the
steel-epoxy and CFRP-epoxy interfaces of the selected primary model and the number of
elements was reached to 7371. It should be mentioned that the optimum model should
result in both the accurate responses and a reasonable computer computational time.
Although picking a model with a very high number of elements (from the last flat part of
the sensitivity curve) leads to the accurate responses, but it does not necessarily mean the
picked model is optimum since it results in an excessive long computer computational
time.
372
Figure 5-70: Anchorage model with 1509 elements developed for sensitivity analysis.
Figure 5-71: Anchorage model with 2813 elements developed for sensitivity analysis.
373
Figure 5-72: Anchorage model with 5077 elements developed for sensitivity analysis.
Figure 5-73: Anchorage model with 8309 elements developed for sensitivity analysis.
374
2.5
2.54
2.58
2.62
2.66
2.7
0 1500 3000 4500 6000 7500 9000Dis
pla
cem
en
t at
lo
ad
ed
en
d
of
CF
RP
str
ips (
mm
)
Number of elements
Selected model99.3% reliability
Figure 5-74: Mesh sensitivity (at 100 kN).
5.4.4 Nonlinear Analysis
The nonlinear solution was executed using a displacement control method in
which non-zero displacement constraints were assigned to the nodes at the CFRP free
end. The main reasons for applying displacement control were to obtain any descending
branch in the load-displacement response and a better recognition of failure. After several
trials on convergence of the model, a maximum displacement convergence tolerance of
0.01 was applied to the model. Based on the load response of the anchor, convergence
behaviour, and computer computational time only one load-step was defined with number
of sub-steps varies from a minimum (20) to a maximum (20000) value. The typical
meshed anchor is presented in Figure 5-75. Due to symmetry, only half of the steel
anchor was modeled and appropriate constraint was assigned to the plan of symmetry.
The assigned constraints are presented in Figure 5-76. It is assumed that the Kwik bolts
are fixed in the concrete; therefore, the fixed constraints were assigned to the model at the
375
top parts of the bolts. The nuts on the bolts which are in contact with the plate were
simulated by assigning the vertical constraints to the steel plate in the bolt vicinity.
376
(a) Isometric view (b) Cross-section
(c) Plan view
Figure 5-75: Meshed anchor (steel tube length = 250 mm).
Bolt
Steel plate
Steel tube
CFRP strip
Epoxy adhesive
Wa Ha
376
377
(a) Isometric view (b) Elevation
(c) Plan view (d) Cross-section
Figure 5-76: Assigned constraints to the anchor model.
377
378
5.4.5 Numerical Results and Discussion
5.4.5.1 Effects of Bond Cohesion
Four FE models (presented in Table 5-11) with different cohesion values for
CFRP-epoxy and steel-epoxy interfaces varies from 5-20 MPa were considered to
investigate the effects of bond cohesion on the performance of the steel end anchor. The
results are plotted in Figure 5-77 to Figure 5-79 showing the load-displacement at the
CFRP free end response and the interfacial shear stress (friction) distribution at the
CFRP-epoxy and the steel-epoxy interfaces.
0
30
60
90
120
150
180
0 1 2 3 4 5 6 7
Lo
ad
(k
N)
Displacement at CFRP loaded-end (mm)
Lt250-C5-Ha1.5-Wa7 Lt250-C10-Ha1.5-Wa7
Lt250-C15-Ha1.5-Wa7 Lt250-C20-Ha1.5-Wa7
Figure 5-77: Effects of cohesion value (5-20 MPa) on load-displacement curves.
379
0
5
10
15
20
0 50 100 150 200 250
Fri
cti
on
at
vert
ical in
terf
ace b
etw
een
C
FR
P a
nd
ep
oxy (
MP
a)
Distance from anchor end (mm)
Lt250-C5-Ha1.5-Wa7 Lt250-C10-Ha1.5-Wa7
Lt250-C15-Ha1.5-Wa7 Lt250-C20-Ha1.5-Wa7
Figure 5-78: Effects of cohesion value (5-20 MPa) on shear stress at CFRP-epoxy
vertical interface at 50 kN.
0
5
10
15
20
0 50 100 150 200 250
Fri
cti
on
at
vert
ical in
terf
ace b
etw
een
s
tee
l a
nd
ep
ox
y (
MP
a)
Distance from anchor end (mm)
Lt250-C5-Ha1.5-Wa7 Lt250-C10-Ha1.5-Wa7
Lt250-C15-Ha1.5-Wa7 Lt250-C20-Ha1.5-Wa7
Figure 5-79: Effects of cohesion value (5-20 MPa) on shear stress at steel-epoxy
vertical interface at 50 kN.
CFRP-epoxy
vertical interface
Steel-epoxy
vertical interface
380
Table 5-11: Summary of FE results, cohesion effects.
Model ID Pu (kN) Δu (mm) FM
Lt250-C5-Ha1.5-Wa7 53.5 2.54 DB
Lt250-C10-Ha1.5-Wa7 106.9 4.52 DB
Lt250-C15-Ha1.5-Wa7 153.5 5.87 DB
Lt250-C20-Ha1.5-Wa7 161.4 5.89 FR Pu and Δu= load and displacement at ultimate FM= failure mode
DB= debonding at CFRP-epoxy interface FR= CFRP rupture
The results reveal that the ultimate load significantly increases by improving the
bond cohesion property. A 201.5% increase in ultimate capacity was obtained by
changing the cohesion value from 5-20 MPa; on the other hand, the mode of failure
changes from debonding at the CFRP-epoxy interface to CFRP rupture. Furthermore,
analyzing Figure 5-77 reveals that the debonding failure in the models with low value of
bond cohesion occurs gradually causing a plastic deformation for anchors Lt250-C5-
Ha1.5-Wa7 and Lt250-C10-Ha1.5-Wa7 at ultimate stage.
The shear stress (friction) distributions at the CFRP-epoxy and the steel-epoxy
vertical interfaces at load 50kN is plotted in Figure 5-78 and Figure 5-79. These results
reveal that the shape of the distribution is a left-skewed curve where the peak is located
within the last 20 mm of the steel tube at the loaded end. In this context, the superior part
of the skewed curve is limited by the interface strength as can be seen in Figure 5-78.
When the cohesion value of the interface decreases more length of the anchor is utilized
to dissipate the energy and transfer the applied load, therefore, the maximum value of the
stress decreases. The smaller area of the CFRP-epoxy interface than the steel-epoxy
interface causes the higher interfacial shear stress at this interface in comparison with
steel-epoxy interface, as it can be seen in comparison between corresponding curves in
Figure 5-78 and Figure 5-79.
381
5.4.5.2 Effects of Anchorage Length
The effect of the NSM CFRP anchorage bond length was examined by
considering seven different FE models where anchor tube length varies from 150-450
mm as presented in Figure 5-80 and Table 5-12. The predicted load-displacement curves
and interfacial shear stress distributions are plotted in Figure 5-81 to Figure 5-83. The
results show that increasing the NSM CFRP anchorage bond length from 150-400 mm
enhances the ultimate capacity up to 145.9% while the mode of failure changes from
debonding at the CFRP-epoxy interface to CFRP rupture occurred at the tip of the steel
tube at the loaded-end. Furthermore, increasing the anchorage bond length from 400-450
mm has no effect on the capacity of the anchorage system. Based on the results, a
minimum bond length of 378 mm avoids debonding failure and allows the CFRP to
achieve its full tensile capacity.
382
(a) Lt150-C10-Ha1.5-Wa7
(b) Lt200-C10-Ha1.5-Wa7
(c) Lt250-C10-Ha1.5-Wa7
(d) Lt300-C10-Ha1.5-Wa7
(e) Lt350-C10-Ha1.5-Wa7
(f) Lt400-C10-Ha1.5-Wa7
(g) Lt450-C10-Ha1.5-Wa7
Figure 5-80: Developed FE models for the effects of anchorage length.
383
0
30
60
90
120
150
180
0 1 2 3 4 5 6 7 8
Lo
ad
(kN
)
Displacement at CFRP loaded-end (mm)
Lt150-C10-Ha1.5-Wa7 Lt200-C10-Ha1.5-Wa7 Lt250-C10-Ha1.5-Wa7
Lt300-C10-Ha1.5-Wa7 Lt350-C10-Ha1.5-Wa7 Lt400-C10-Ha1.5-Wa7
Lt450-C10-Ha1.5-Wa7
Figure 5-81: Effects of bond length (150-450 mm) on load-displacement curves.
0
2
4
6
8
10
12
0 50 100 150 200 250 300 350 400 450
Fri
cti
on
at
ve
rtic
al in
terf
ac
e b
etw
ee
n
CF
RP
an
d e
po
xy (
MP
a)
Distance from anchor end (mm)
Lt150-C10-Ha1.5-Wa7 Lt200-C10-Ha1.5-Wa7 Lt250-C10-Ha1.5-Wa7
Lt300-C10-Ha1.5-Wa7 Lt350-C10-Ha1.5-Wa7 Lt400-C10-Ha1.5-Wa7
Lt450-C10-Ha1.5-Wa7
Figure 5-82: Effects of bond length (150-450 mm) on shear stress at CFRP-epoxy
vertical interface at 50 kN.
CFRP-epoxy
vertical interface
384
0
1
2
3
4
5
6
7
8
9
10
0 50 100 150 200 250 300 350 400 450
Fri
cti
on
at
vert
ical in
terf
ace b
etw
een
ste
el an
d e
po
xy (
MP
a)
Distance from anchor end (mm)
Lt150-C10-Ha1.5-Wa7 Lt200-C10-Ha1.5-Wa7 Lt250-C10-Ha1.5-Wa7
Lt300-C10-Ha1.5-Wa7 Lt350-C10-Ha1.5-Wa7 Lt400-C10-Ha1.5-Wa7
Lt450-C10-Ha1.5-Wa7
Figure 5-83: Effects of bond length (150-450 mm) on shear stress at steel-epoxy
vertical interface at 50 kN.
Table 5-12: Summary of FE results, anchor length effects.
Model ID Pu (kN) Δu (mm) FM
Lt150-C10-Ha1.5-Wa7 65.4 2.07 DB
Lt200-C10-Ha1.5-Wa7 85.6 3.46 DB
Lt250-C10-Ha1.5-Wa7 106.9 4.52 DB
Lt300-C10-Ha1.5-Wa7 128.1 5.89 DB
Lt350-C10-Ha1.5-Wa7 149 7.26 DB
Lt400-C10-Ha1.5-Wa7 160.9 7.72 FR
Lt450-C10-Ha1.5-Wa7 160.7 7.71 FR
Pu and Δu= load and displacement at ultimate FM= failure mode
DB= debonding at CFRP-epoxy interface FR= CFRP rupture
Analyzing the shear stress distributions at 50 kN for different bond anchorage
lengths in Figure 5-82 and Figure 5-83 reveals that in spite of the change in length of the
anchor the distributions and maximum shear stress are similar. In this context, when the
anchorage bond length is short, in case of Lt150-C10-Ha1.5-Wa7 as shown in Figure
Steel-epoxy vertical interface
385
5-82, an increase in the shear stress distribution occurs to transfer the loads, which
gradually causes debonding as the applied load increases.
5.4.5.3 Effects of Adhesive Width
The effects of the adhesive width (Wa in Figure 5-57) on the load-displacement
curves and interfacial stress distributions were analyzed by developing three FE models
(as presented in Figure 5-84) where the adhesive width varies from 3.5-10.5 mm
corresponding to 0.7-2.1 times the CFRP thickness. The results are presented in Figure
5-85 to Figure 5-89 and Table 5-13. All the FE models failed due to debonding at the
CFRP-epoxy interface. Analyzing the results reveals that changing the width of the
adhesive has insignificant effects on the load-displacement response, as presented in
Figure 5-85 and Table 5-13. On the other hand, comparing the interfacial shear stress
distributions reveals that increasing the adhesive width from 3.5-10.5 mm decreases the
maximum interfacial shear stress at the steel-epoxy vertical interface up to 54.3% as
plotted in Figure 5-87, while has insignificant effects on the shear stress distributions at
other interfaces as presented in Figure 5-86, Figure 5-88, and Figure 5-89. It should be
mentioned that if the failure occurs due to debonding at the steel-epoxy interface, any
increase in adhesive width, which leads to a major decrease in steel-epoxy interfacial
stress, results in a significant enhancement on the capacity of anchorage.
386
(a) Lt250-C10-Ha1.5-Wa3.5 (b) Lt250-C10-Ha1.5-Wa7 (c) Lt250-C10-Ha1.5-Wa10.5
Figure 5-84: Developed FE models for the effects of adhesive width.
386
387
0
20
40
60
80
100
120
0 1 2 3 4 5 6
Lo
ad
(kN
)
Displacement at CFRP loaded-end (mm)
Lt250-C10-Ha1.5-Wa3.5
Lt250-C10-Ha1.5-Wa7
Lt250-C10-Ha1.5-Wa10.5
Figure 5-85: Effects of adhesive width (Wa=3.5-10.5 mm) on load-displacement
curves.
Table 5-13: Summary of FE results, adhesive width effects.
Model ID Pu (kN) Δu (mm) FM
Lt250-C10-Ha1.5-Wa3.5 106.2 4.43 DB
Lt250-C10-Ha1.5-Wa7 106.9 4.52 DB
Lt250-C10-Ha1.5-Wa10.5 107 4.56 DB
Pu and Δu= load and displacement at ultimate FM= failure mode
DB= debonding at CFRP-epoxy interface
388
0
2
4
6
8
10
12
0 50 100 150 200 250
Fri
cti
on
at
ho
rizo
nta
l in
terf
ace b
etw
een
ste
el an
d e
po
xy (
MP
a)
Distance from anchor end (mm)
Lt250-C10-Ha1.5-Wa3.5 Lt250-C10-Ha1.5-Wa7 Lt250-C10-Ha1.5-Wa10.5
Figure 5-86: Effects of adhesive width (Wa=3.5-10.5 mm) on shear stress at steel-
epoxy horizontal interface at 50 kN.
0
2
4
6
8
10
12
0 50 100 150 200 250
Fri
cti
on
at
vert
ical in
terf
ace b
etw
een
ste
el an
d e
po
xy (
MP
a)
Distance from anchor end (mm)
Lt250-C10-Ha1.5-Wa3.5 Lt250-C10-Ha1.5-Wa7 Lt250-C10-Ha1.5-Wa10.5
Figure 5-87: Effects of adhesive width (Wa=3.5-10.5 mm) on shear stress at steel-
epoxy vertical interface at 50 kN.
Steel-epoxy
horizontal interface
Steel-epoxy
vertical interface
389
0
2
4
6
8
10
12
0 50 100 150 200 250Fri
cti
on
at
ho
rizo
nta
l in
terf
ace b
etw
een
C
FR
P a
nd
ep
oxy (
MP
a)
Distance from anchor end (mm)
Lt250-C10-Ha1.5-Wa3.5 Lt250-C10-Ha1.5-Wa7 Lt250-C10-Ha1.5-Wa10.5
Figure 5-88: Effects of adhesive width (Wa=3.5-10.5 mm) on shear stress at CFRP-
epoxy horizontal interface at 50 kN.
0
2
4
6
8
10
12
0 50 100 150 200 250
Fri
cti
on
at
vert
ical in
terf
ace b
etw
een
C
FR
P a
nd
ep
oxy (
MP
a)
Distance from anchor end (mm)
Lt250-C10-Ha1.5-Wa3.5 Lt250-C10-Ha1.5-Wa7 Lt250-C10-Ha1.5-Wa10.5
Figure 5-89: Effects of adhesive width (Wa=3.5-10.5 mm) on shear stress at CFRP-
epoxy vertical interface at 50 kN.
CFRP-epoxy
horizontal interface
CFRP-epoxy vertical interface
390
5.4.5.4 Effects of Adhesive Height
The effects of adhesive height (Ha in Figure 5-57) on the performance of the
NSM CFRP anchorage were analyzed by developing three models as presented in Figure
5-90 where the adhesive height varies from 1.5-7.5 mm corresponding to 0.094-0.47
times the CFRP width. The results are plotted in Figure 5-91 to Figure 5-95. Analyzing
Figure 5-92 to Figure 5-95 shows that increasing the adhesive height has a significant
effect on the shear stress distribution at the horizontal steel-epoxy interface. In this
context, a 62.9% decrease in the maximum interfacial shear stress is reached by
increasing the adhesive height from 1.5-7.5 mm as presented in Figure 5-92. On the other
hand, the effects of adhesive height on the shear stress distribution at the CFRP-epoxy
interfaces and the vertical steel-epoxy interface are insignificant as presented in Figure
5-93 to Figure 5-95. The FE models failed due to debonding at the CFRP-epoxy interface
and increasing the adhesive height almost has no effect on the load-displacement
response of the anchor since it has minor effects on the stress distribution at CFRP-epoxy
interfaces.
391
(a) Lt250-C10-Ha1.5-Wa7 (b) Lt250-C10-Ha4.5-Wa7 (c) Lt250-C10-Ha10.5-Wa7
Figure 5-90: Developed FE models for the effects of adhesive height.
391
392
0
20
40
60
80
100
120
0 1 2 3 4 5 6
Lo
ad
(k
N)
Displacement at CFRP loaded-end (mm)
Lt250-C10-Ha1.5-Wa7
Lt250-C10-Ha4.5-Wa7
Lt250-C10-Ha7.5-Wa7
Figure 5-91: Effects of adhesive height (Ha=1.5-7.5 mm) on load-displacement
curves.
Table 5-14: Summary of FE results, adhesive height effects.
Model ID Pu (kN) Δu (mm) FM
Lt250-C10-Ha1.5-Wa7 106.9 4.52 DB
Lt250-C10-Ha4.5-Wa7 106.9 4.42 DB
Lt250-C10-Ha7.5-Wa7 106.9 4.46 DB
Pu and Δu= load and displacement at ultimate FM= failure mode
DB= debonding at CFRP-epoxy interface
393
0
2
4
6
8
10
12
0 50 100 150 200 250
Fri
cti
on
at
ho
rizo
nta
l in
terf
ac
e b
etw
een
s
tee
l a
nd
ep
ox
y (
MP
a)
Distance from anchor end (mm)
Lt250-C10-Ha1.5-Wa7 Lt250-C10-Ha4.5-Wa7 Lt250-C10-Ha7.5-Wa7
Figure 5-92: Effects of adhesive height (Ha=1.5-7.5 mm) on shear stress at steel-
epoxy horizontal interface at 50 kN.
0
2
4
6
8
10
12
0 50 100 150 200 250
Fri
cti
on
at
ve
rtic
al in
terf
ac
e b
etw
ee
n
ste
el a
nd
ep
ox
y (
MP
a)
Distance from anchor end (mm)
Lt250-C10-Ha1.5-Wa7 Lt250-C10-Ha4.5-Wa7 Lt250-C10-Ha7.5-Wa7
Figure 5-93: Effects of adhesive height (Ha=1.5-7.5 mm) on shear stress at steel-
epoxy vertical interface at 50 kN.
Steel-epoxy
horizontal interface
Steel-epoxy vertical interface
394
0
2
4
6
8
10
12
0 50 100 150 200 250Fri
cti
on
at
ho
rizo
nta
l in
terf
ac
e b
etw
een
C
FR
P a
nd
ep
ox
y (
MP
a)
Distance from anchor end (mm)
Lt250-C10-Ha1.5-Wa7 Lt250-C10-Ha4.5-Wa7 Lt250-C10-Ha7.5-Wa7
Figure 5-94: Effects of adhesive height (Ha=1.5-7.5 mm) on shear stress at CFRP-
epoxy horizontal interface at 50 kN.
0
2
4
6
8
10
12
0 50 100 150 200 250
Fri
cti
on
at
ve
rtic
al in
terf
ac
e b
etw
ee
n
CF
RP
an
d e
po
xy (
MP
a)
Distance from anchor end (mm)
Lt250-C10-Ha1.5-Wa7 Lt250-C10-Ha4.5-Wa7 Lt250-C10-Ha7.5-Wa7
Figure 5-95: Effects of adhesive height (Ha=1.5-7.5 mm) on shear stress at CFRP-
epoxy vertical interface at 50 kN.
CFRP-epoxy
horizontal interface
CFRP-epoxy
vertical interface
395
5.5 Analytical Modeling of RC Beams Strengthened With Prestressed NSM-CFRP
Reinforcements Subjected to Freeze-Thaw Exposure
The Load-deflection responses of the nine tested beams in phase I are predicted
analytically by developing a code in Wolfarm Mathematica software (Wolfarm Research,
2008). It should be mentioned that, since the freeze-thaw cycling exposure had minor
effects on the concrete material and bond at the concrete-epoxy interface, the developed
FE model described in Section 5.2 could have been employed to model the exposed
beams in phase I by assigning the appropriate material properties. But, the FE modeling
of the tested beams in phase II, which is presented in Section 5.6, has all the aspects
required for FE modeling of the beams in phase I and to avoid repetition, the beams in
phase I have been modeled analytically. The developed analytical code aims to generate
the load-deflection response for strengthened/un-strengthened rectangular RC beams with
prestressed/non-prestressed FRP material under four-point bending configuration. It has
the capabilities of assigning the actual concrete stress-strain curve based on Loov's
equation (Loov, 1991), elasto-plastic behaviour for the compression and tension
reinforcing steel bars, linear behaviour for the FRP reinforcements (strip or rebar), and
different prestressed CFRP length along the length of the beam. Since the overall flexural
behaviour of the tested beams in phase I is not affected by debonding as was observed
during the tests, the perfect bond is assumed in the analytical model, therefore, two
failure modes, CFRP rupture or concrete crushing, are considered. The analytical code
can be modified for different type of the loading by making a few changes on the applied
moment along the length of the beam. Conceptually, the mid-span deflection at each
applied moment is calculated using integration of curvatures along the length of the beam
396
(from support to mid-span). To achieve accurate results, the half-length of the beam was
divided to 51 elements in the shear span and one element in the constant moment region.
The main advantage of the developed analytical code versus FE analysis is that the
developed code has a much shorter computer computational time (6 min for analytical
model versus 8 hrs for FE model). Furthermore, the predicted results are in a very good
correlation with the experimental ones.
5.5.1 Experimental Program Overview
Nine RC beams tested in phase I of the experimental program were analyzed by
considering the effects of freeze-thaw exposure. One beam was considered as the un-
strengthened control RC beam, four beams were strengthened using NSM CFRP strips
(2×16 mm strips glued together from the side and mounted in one groove on the tension
side of the beam), and the other four beams were strengthened using NSM CFRP rebars
(9.5 mm diameter rebar). A summary of the test results including the prestrain in the
CFRP rebar or strip was presented in Table 4-2. Details of the beams were plotted in
Figure 3-1. The beams were exposed to 500 freeze-thaw cycles. Each cycle, consisting of
eight intervals programmed to be accomplished in 8hrs, include the lower temperature
bound of -34oC and the upper temperature bound of +34
oC with a relative humidity of
75% for temperature above +20oC. Details of the intervals and trend of three freeze-thaw
cycles were presented in Section 3.6.
397
5.5.2 Description of Algorithm
The developed analytical model generates the load-deflection response of the
tested RC beams using numerical integration of the curvatures along the length of the
beam. The algorithm includes seven steps to produce the load-deflection response and the
source code is written in Wolfarm Mathematica (Wolfarm Research, 2008), a powerful
automated technical computing software. The inputs include twenty-five constants, which
represent material properties and geometry of the beam. The code is written based on
different variables, arrays for loads, deflections, moments, and curvatures, different loops
and functions available in the software. The output is set to present the type of failure; a
plot of the load-deflection response; and load, deflection, moment, and mid-span
curvature for twenty-four points on the load-deflection curve including prestressing,
cracking, yielding, and ultimate stages.
5.5.2.1 Concepts for Calculation of Deflection at an Arbitrary Load Level
The deflection of a beam at mid-span at an arbitrary load level is calculated by
integration of curvatures along the length as presented in Equation 5-27, where the
curvature at every point is calculated using Equation 5-28. To calculate the mid-span
deflection of a prestressed beam under four-point-bending configuration as shown in
Figure 5-96, Equation 5-27 can be expanded as Equation 5-29.
2
0
/L
dxx)xφ(Δ (Park & Paulay, 1975) Equation 5-27
398
)xEI(
)xM()xφ( (Park & Paulay, 1975) Equation 5-28
IV
2
IIIII
0
I
2
/L
Lp
pL
x
x
gtc
/L
Logtc
p
p
p
cr
cr
xdx)LEI(
)LM(xdx
)xEI(
M(x)xdx
IE
M(x)xdx
IE
)x(MΔ Equation 5-29
where Δ is the deflection, x the distance from the support, (x) the curvature at distance x,
M(x) the applied moment at distance x, EI(x) the flexural stiffness at distance x, Mp(x) the applied
moment on the beam at distance x due to prestressing, Lo the un-strengthened length, Ec the
modulus of elasticity of concrete, Igt the moment of inertia of the gross transformed
section, xcr the distance from the support to a point where the applied moment is equal to
the cracking moment of the section, Lp the distance from the support to the point load, M(Lp)
the moment value at point load location (x= Lp), and EI(Lp) is the flexural stiffness at point
load location. More details about the calculations and values of the parameters can be
found in the source code in Appendix E.
The upward deflection at mid-span due to prestressing is calculated using part I of
the integral in Equation 5-29 assuming that the beam remains un-cracked in this part.
Integration of curvatures along the un-cracked length of the beam is calculated using part
II of Equation 5-29. Contribution of the cracked length of the beam in resulted deflection
is computed using parts III and IV of Equation 5-29, in which part IV is related to the
constant moment regions. In the developed analytical model, first, the cracking, yielding,
and ultimate capacities of the beam are calculated. Then, the mid-span deflections are
calculated at 10th
point between cracking to yielding loads on the load-deflection curve,
399
and also, at 10th
point between yielding to ultimate loads. To calculate the corresponding
deflection for an arbitrary applied load (e.g., at a load value between yielding and
ultimate), the integration limit xcr in Equation 5-29 needs to be specified for the applied
load. This integration limit is calculated based on the moment diagram and knowing the
cracking moment capacity of the section (e.g., under four-point bending xcr=Mcr/Papplied)
as shown in Figure 5-96. After specifying the integration limits, Equation 5-29 can be
solved by knowing the EI (flexural stiffness) for parts III and IV related to the cracked
regions of the beam. The value of EI in the cracked region depends on the applied
moment and curvature at each section which changes from a point to another point along
the cracked length (EI=M/φ). Therefore, to solve parts III and IV of Equation 5-29, the
cracked length of the beam is divided into equal segments (small lengths) and assumed
that the curvature is constant along each small length. Afterwards, the applied moment at
the centre of each small length is easily calculated by having the moment diagram of the
applied load. Then, the curvature (and also EI) at the centre of each small length was
calculated by applying the force and moment equilibriums of the section and finding the
unknowns (c and c) at each small length (φsegment= c/c, EIsegment= Msegment/φsegment). In the
developed code, for each applied load, part III of Equation 5-29 is calculated by fifty
integrals from xcr to Lp and part IV is calculated by one integral (since the curvature is
constant along the integration limits in part IV). The number of the segments (fifty for
part III) is selected based on a sensitivity analysis on the output. It should be noted that
the load-deflection response is generated based on twenty-four different applied loads
and corresponding deflections. More details can be found in the source code in Appendix
E.
400
Figure 5-96: Finding the integration limits for Equation 5-29 using moment
diagram.
It should be clarified that Equation 5-29 is the simplified form of a more detailed
equation for calculation of the mid-span deflection. In fact, in a beam that is not
strengthened for entire length with prestressed NSM-CFRP, the length of the beam
consists of two portions, strengthened and un-strengthened, that both should be
considered in calculation of the deflection. If the cracks form within the un-strengthened
length of the beam (the applied moment along the un-strengthened length is larger than
the cracking moment capacity of the un-strengthened section), therefore, parts II and III
of Equation 5-29 should be replaced with Equation 5-30. On the other hand, if no cracks
401
form within the un-strengthened length of the beam, parts II and III of Equation 5-29
should be replaced with Equation 5-31. For the beams that properly strengthened (same
as the ones employed in this paper), Equation 5-31 can be simplified to Equation 5-32
and be used in Equation 5-29 with insignificant effect on the resulted deflection. The
latter is employed in this research.
xdx)xEI(
M(x)xdx
IE
M(x)
xdx)xEI(
M(x)xdx
IE
M(x)
p
stcr
stcr
uncr
uncr
L
x
x
Lostgtc
Lo
x
x
ungtc
0
IIIII
Equation 5-30
xdx)xEI(
M(x)xdx
IE
M(x)xdx
IE
M(x) p
stcr
stcr L
x
x
Lostgtc
Lo
ungtc
0IIIII Equation5-31
xdx)xEI(
M(x)xdx
IE
M(x) p
stcr
stcr L
x
x
stgtc
0IIIII Equation 5-32
where xcr-un and xcr-st are the distance from the support to a point where the applied
moment is equal to the cracking moment capacity of the un-strengthened and
strengthened sections, respectively, Igt-un and Igt-st the moment of inertia of the gross
transformed un-strengthened and strengthened sections, respectively, and the other
parameters are described earlier.
402
5.5.3 Modeling of Materials
5.5.3.1 Concrete of Exposed Beam
The exposed concrete stress-strain curve was defined based on Loov’s equation
(Loov, 1991). The concrete compressive strength of the exposed beams in phase I was
obtained using Schmidt hammer test performed on the specimens. The other properties of
the exposed concrete including modulus of elasticity and strain at peak stress were
calculated based on the study performed by Duan et al. (2011) on the effects of freeze-
thaw cycles on the stress-strain curves of unconfined and confined concrete. Since the
freeze-thaw cycle used by Duan et al. (2011) was different than the one conducted in this
study, therefore, the equivalent number of the cycles (N) is obtained using Equation 5-33
(Duan et al., 2011) by having the concrete compressive strength at different stages:
0355328200
1
.c
unexposedc
exposedc
f
f
f
N
Equation 5-33
where fc exposed is the concrete compressive strength after exposure (MPa), fc unexposed the
concrete compressive strength before exposure (MPa), fc28 the concrete compressive
strength at 28 days (MPa), and N is the number of freeze-thaw cycles.
The strain at peak stress and modulus of elasticity after exposure were calculated
using Equations 5-34 and 5-35 proposed by Duan et al. (2011).
403
)Nf(
exposedun
exposed .ce
1406528661742
0
0
Equation 5-34
)Nf.(
unexposedc
exposedc .ce
E
E 7089528
71013451
Equation 5-35
where 0 exposed is the concrete strain at peak stress after exposure, 0 unexposed the concrete
strain at peak stress before exposure, Ec exposed the modulus of elasticity of concrete after
exposure (MPa), and Ec unexposed is the modulus of elasticity of concrete before exposure
(MPa).
Finally by finding the properties of the exposed concrete and apply two points of
the stress-strain curve to the Loov’s equation (as presented in Equation 5-1), Equation 5-
36 is derived for the exposed concrete. More details about the calculation of the concrete
stress-strain curve can be found in the source code in Appendix E.
4.9112102.08 173.22 1
709.86 04
cc
ccf
Equation 5-36
where fc and ɛc are the compressive stress of concrete (MPa) and the concrete strain,
respectively.
5.5.3.2 Steel Reinforcement
An elasto-plastic behaviour was considered for the steel reinforcements in the
analytical model. The assigned material properties are listed in the input file of the source
code (Appendix E) for the top and bottom steel reinforcements.
404
5.5.3.3 CFRP Strip or Rebar
A linear elastic behaviour was considered for the CFRP strips and rebars with the
material properties presented in the input file of the source code in Appendix E.
5.5.4 Nonlinear Analysis
The nonlinear analysis in the model is performed by satisfying the moment and
the force equilibriums for cross-section of the beam shown in Figure 5-97 and finding the
unknowns (concrete strain at extreme compression fibre and depth of the neutral axis).
These equilibrium equations are presented in Equations 5-37 and 5-38.
00 cssf CCTTF
Equation 5-37
appliedstsffscsCcc M)cd(T)cd(T)dc(CyCM 0 Equation 5-38
where Tf is the force in CFRP strip or rebar, Ts the force in bottom steel rebars, Cs the
force in compression steel rebars, Cc the compressive force carried by concrete, ӯCc the
distance between neutral axis and point of action of the resultant compressive force on
concrete, c the depth of neutral axis, dsc the depth to the centroid of the top steel rebars, df
the depth to the centroid of the CFRP strips or rebars, dst the depth to the centroid of the
bottom steel rebars, and Mapplied is the applied moment. The components of Equations 5-
37 and 5-38 are calculated using the following equations.
)(EAT peffrpfrpf
Equation 5-39
405
ytstytst
ytstststst
s iffA
ifEAT
Equation 5-40
ycscycsc
ycscscscsc
s iffA
ifEAC
Equation 5-41
c
cc dy)y(fbC0
Equation 5-42
c
c
c
c
cC
dy)y(fb
dy)y(fbyy
0
0
Equation 5-43
4.91
12102.08 173.22 1
709.86
04
c
y
c
y
c
y
)y(f
cccc
cc
c
Equation 5-44
where Afrp is the area of CFRP rebars or strips (mm2), Efrp the modulus of elasticity of
CFRP rebars or strips (MPa), f the strain in CFRP rebar or strip, pe the prestrain in
CFRP rebar or strips, Ast the area of bottom steel rebras (mm2), Est the modulus of
elasticity of bottom steel rebars (MPa), st the strain in bottom steel rebars, fyt the yield
stress of the bottom steel rebars (MPa), yt the yield strain of bottom steel rebars, Asc the
area of top steel rebras (mm2), Esc the modulus of elasticity of top steel rebars (MPa), sc
the strain in top steel rebars, fyc the yield stress of top steel rebars (MPa), yc the yield
strain of bottom steel rebars, b the width of the beam (mm), fc(y) the compressive stress
on concrete at height y defined based on Equation 5-41 (MPa), cc the concrete strain at
406
extreme compression fibre, y the vertical distance from the neutral axis (mm), and c is the
depth of the neutral axis (mm).
Figure 5-97: Strain and stress distribution on a prestressed NSM-CFRP
strengthened section.
5.5.5 Analytical Results and Discussion
5.5.5.1 Load-Deflection Curve
Comparison between experimental and analytical load-deflection responses is
presented in Figure 5-98 and Figure 5-99. The analytical solutions of the beams were
terminated after concrete crushing or CFRP rupture whichever occurred first. The
estimated load-deflection responses include the negative camber due to prestressing,
initiation of flexural cracks, yielding of tensile steel rebar, and failure at ultimate stage. A
summary of the results obtained from the tests versus the analytical solutions are
presented in Table 5-15 and Table 5-16 for sets BS-F and BR-F, respectively, including
type of failure, ductility index (the ratio of the deflection at ultimate load to the deflection
at yielding), energy absorption (the area under load-deflection curve up to the peak load),
and percentage of difference between corresponding experimental and analytical values.
407
At cracking, a relatively large percentage of difference is observed between
experimental and analytical values. Considering the strengthened beams, an average error
of 11.7±7.8% for cracking load of set BS-F with a maximum of 22% for BS-NP-F, and
an average error of 38.8±10.9% for cracking deflection with a maximum of 54.9% for
BS-P2-F are observed. Furthermore, considering the strengthened beams, an average
error of 22.5±15.2% for cracking load of set BR-F with a maximum of 37.8% for BR-P1-
F, and an average error of 23.9%±12.7% for cracking deflection with a maximum of
40.5% for BR-P1-F are reached. Also, the differences of 62.4% and -18.5% are observed
for cracking load and deflection of B0-F, respectively. The high percentage of the
difference at cracking stage might be due to the presence of the micro cracks in the beams
before testing. The other reason for underestimation or overestimation of the cracking
load using the analytical solution might be due to a difference between concrete
compressive strength in the model and in tested beams. The beams were cracked after
strengthening before being subjected to freeze-thaw exposure, while in the analytical
solution an average exposed concrete compressive strength was assigned to the beams
(40 MPa for all beams), that might be slightly different for each beam that was cracked in
reality. The resulted difference between the analytical solution and the test values at
cracking is most possibly the accumulation of the mentioned errors.
At yielding stage, the differences between analytical solutions and experimental
results are negligible. Considering the strengthened beams, An average error of -3±2.2%
for yield load of set BS-F with a maximum of -5% for BS-P3-F and an average error of
0±9.2% for yield deflection with a maximum of 11.8% for BS-NP-F are reached.
Similarly, considering the strengthened beams, an average error of -1.8±2.4% for yield
408
load of set BR-F with a maximum of -4.5% for BR-P3-F and an average error of -
4.2±6.1% for yield deflection with a maximum of -8.8% for BR-P3-F are obtained.
At ultimate stage, the predicted loads are almost the same as those from the test;
however, the predicted ultimate deflections are different than those from the test values.
On the other hand, the material properties (i.e., CFRP ultimate strain or concrete stress-
strain curve) could be slightly smaller or greater than the specified values that would lead
to a difference at ultimate deflection when the failure governs by CFRP rupture or
concrete crushing. In set BS-F, considering the strengthened beams, an average error of
2.5±4% for ultimate load with a maximum of 6.7% for BS-P1-F, and an average error of
3.3±10.9% for ultimate deflection with a maximum of 16.7% for BS-P1-F are observed at
the ultimate stage. In set BR-F, considering the strengthened beams, an average error of
0.6±3.5% for ultimate load with a maximum of 5.2% for BR-NP-F, and an average error
of -0.6±13.5% for ultimate deflection with a maximum of 18.2% for BR-P3-F are
reached at the ultimate stage. The modeled beams showed similar types of failure to the
tested beams. The fluctuation of the experimental curve at ultimate stage is not observed
in analytical solution which is mainly due to the elimination of local debonding in the
analytical model. Therefore, the performed comparison indicates that the load-deflection
curves obtained from the analytical solutions can accurately predict those values from the
experimental ones.
409
0
20
40
60
80
100
120
140
160
-5 15 35 55 75 95 115 135 155 175
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-P3-F (Experimental) BS-P3-F (Analytical)
BS-P2-F (Experimental) BS-P2-F (Analytical)
BS-P1-F (Experimental) BS-P1-F (Analytical)BS-NP-F (Experimental) BS-NP-F (Analytical)B0-F (Experimental) B0-F (Analytical)
: Concrete crushing : FRP rupture
Figure 5-98: Comparison between experimental and analytical load-deflection responses for BS-F set.
409
410
Table 5-15: Summary of the results for BS-F set.
Beam
ID#
Prestrain
in CFRP Results
Δo
(mm)
Pcr
(kN)
Δcr
(mm)
Py
(kN)
Δy
(mm)
Pu
(kN)
Δu
(mm) μD
Φ
(kN. mm)
Failure
Mode
B0-F N.A.
Analytical 0 16.9 1.81 75.5 18.78 97.8 142.88 7.61 11646.7 CC
Test‡ 0 10.4 2.22 84.8 24.81 87.0 155.31 6.26 12368.6 CC
Error % 0 62.4 -18.5 -10.9 -24.3 12.4 -8.0 21.6 -5.8
BS-NP-F 0
Analytical 0 17.1 1.81 92.4 25.19 137.1 103.59 4.11 10398.9 CC
Test‡ 0 14.0 1.36 92.4 22.53 132.2 104.26 4.63 10649.0 CC
Error % 0 22.0 33.4 0.0 11.8 3.7 -0.6 -11.1 -2.3
BS-P1-F 0.003463
Analytical -0.48 23.9 1.87 101.5 24.61 143.7 96.77 3.93 10419.3 CC
Test‡ -0.49 21.6 1.43 104.1 23.99 134.7 82.90 3.46 8667.1 CC
Error % -1.7 10.6 31.2 -2.5 2.6 6.7 16.7 13.8 20.2
BS-P2-F 0.006723
Analytical -0.94 30.4 1.92 109.9 24.09 145.2 79.81 3.31 8774.7 FR
Test‡ -1.09 27.3 1.24 114.8 25.56 149.5 87.85 3.44 10214.1 FR
Error % -14.2 11.2 54.9 -4.3 -5.7 -2.9 -9.2 -3.6 -14.1
BS-P3-F 0.009884
Analytical -1.38 36.6 1.97 118.1 23.62 145.1 62.11 2.63 6832.1 FR
Test‡ -1.70 35.5 1.45 124.3 25.91 141.7 58.55 2.26 6509.8 FR
Error % -19.1 3.1 35.9 -5.0 -8.8 2.4 6.1 16.4 5.0
Pcr and Δcr = load and deflection at cracking Δo = camber due to prestressing CC = concrete crushing
Py and Δy = load and deflection at yielding μD = ductility index = Δu /Δy FR = CFRP rupture
Pu and Δu = load and deflection at ultimate Φ = energy absorption (area under P-Δ curve up to Pu)
Note: the results include the self-weight effects.
410
411
0
20
40
60
80
100
120
140
160
-5 15 35 55 75 95 115 135 155 175
Lo
ad
(k
N)
Mid-span deflection (mm)
BR-P3-F (Experimental) BR-P3-F (Analytical)
BR-P2-F (Experimental) BR-P2-F (Analytical)
BR-P1-F (Experimental) BR-P1-F (Analytical)
BR-NP-F (Experimental) BR-NP-F (Analytical)
: Concrete crushing : FRP rupture
Figure 5-99: Comparison between experimental and analytical load-deflection responses for BR-F set.
411
412
Table 5-16: Summary of the results for BR-F set.
Beam
ID#
Prestrain
in CFRP Results
Δo
(mm)
Pcr
(kN)
Δcr
(mm)
Py
(kN)
Δy
(mm)
Pu
(kN)
Δu
(mm) μD
Φ
(kN. mm)
Failure
Mode
B0-F N.A.
Analytical 0 16.9 1.81 75.5 18.78 97.8 142.88 7.61 11646.7 CC
Test‡ 0 10.4 2.22 84.8 24.81 87.0 155.31 6.26 12368.6 CC
Error % 0.0 62.4 -18.5 -10.9 -24.3 12.4 -8.0 21.6 -5.8
BR-NP-F 0
Analytical 0 17.1 1.34 92.9 24.74 139.2 102.40 4.14 10423.6 CC
Test‡ 0 13.1 1.23 91.6 23.78 132.3 102.71 4.32 10344.4 CC
Error % 0 30.4 9.7 1.4 4.1 5.2 -0.3 -4.2 0.8
BR-P1-F 0.003662
Analytical -0.5 24.8 1.41 103.1 24.09 146.6 94.92 3.94 10442.3 CC
Test‡ -0.5 18.0 1.00 105.1 24.98 147.5 107.62 4.31 12357.7 CC
Error % 12.9 37.8 40.5 -1.9 -3.5 -0.6 -11.8 -8.6 -15.5
BR-P2-F 0.006548
Analytical -1.0 30.9 1.45 111.1 23.61 152.5 89.54 3.79 10432.9 CC
Test‡ -0.9 26.0 1.20 113.4 25.86 157.5 98.05 3.79 11796.5 CC
Error % 5.9 18.7 21.1 -2.1 -8.7 -3.2 -8.7 0.0 -11.6
BR-P3-F 0.009950
Analytical -1.5 38.0 1.51 120.4 23.08 157.5 79.13 3.43 9671.7 FR
Test‡ -1.7 36.3 1.21 125.2 25.36 157.5 71.28 2.81 8733.6 FR
Error % -13.9 4.7 24.9 -3.8 -9.0 0.0 11.0 22.0 10.7
Pcr and Δcr = load and deflection at cracking Δo = camber due to prestressing CC = concrete crushing
Py and Δy = load and deflection at yielding μD = ductility index = Δu /Δy FR = CFRP rupture
Pu and Δu = load and deflection at ultimate Φ = energy absorption (area under P-Δ curve up to Pu)
Note: the results include the self-weight effects.
412
413
5.6 FE Modeling of RC Beams Strengthened with Prestressed NSM-CFRP
Reinforcement Subjected to Freeze-Thaw Exposure and Sustained Load
The beams tested in phase II of the experimental program, subjected to freeze-
thaw exposure and sustained load, are simulated using FEM as presented in this section
and the predicted load-deflection responses are compared with the experimental ones.
The concepts and aspects of the developed model are similar to Section 5.2 (FE modeling
of unexposed beams) except that in the current analysis the material properties are
different since the beams were exposed to the environmental and loading conditions.
5.6.1 Experimental Program Overview
Five RC beams tested in phase II of the experimental program including one un-
strengthened control beam and four beams strengthened using NSM CFRP strips were
modeled. The beams were subjected to 500 freeze-thaw cycles while each beam was
under a sustained load of 62 kN (47% of analytical ultimate load of the non-prestressed
NSM CFRP strengthened RC beam, BS-NP-F in Table 3-3), and tested under four-point
bending static monotonic loading to failure. A summary of the test results including
prestrain in CFRP strips was presented in Table 4-15. Details of the beams and test setup
were plotted in Figure 3-1. Furthermore, details of three freeze-thaw cycling exposure
and sustained loading were presented in Sections 3.6 and 3.7, respectively.
5.6.2 Description of finite element model
The aim of the FE analysis developed in this section is to predict the flexural
behaviour of the beams after exposure not the behaviour during exposure. Therefore,
414
details of the developed 3D FE model is the same as the unexposed strengthened RC
beams described in Section 5.2.2. The major difference between the model presented in
this section and the model developed for the unexposed beams (Section 5.2.2) is in the
material properties of the exposed beams including concrete, bond at concrete-epoxy
interface, and steel reinforcement. Also, the observed total debonded length after
exposure, as presented in Table 4-14, was assigned to the FE model of each beam (by
assigning a zero value for shear and normal fracture energies of the interface) to simulate
the conditions of the beams prior to static testing to failure.
5.6.3 Debonding Model of Exposed Beams
The debonding for the exposed beams were simulated using contact pairs and
Cohesive Zone Material (CZM) model considering a bond-slip model and a normal stress
gap model as described in the following sections. More details on the considered
debonding model can be found in Section 5.2.4.
5.6.3.1 Bond-Slip Model for Exposed Beams
The bilinear shear stress-slip model is obtained based on the procedure described
in Section 5.2.4.1 using the exposed concrete compressive strength of 28.1 MPa
surrounding the groove. The values of maximum shear stress of contact, τmax= 6.62 MPa,
and contact slip at the completion of debonding, utc= 1.19 mm, are derived using
Equations 5-12 to 5-15 for the shear stress-slip model. Comparing the exposed and
unexposed bilinear models shows a decrease of 27.3% in shear fracture energy due to the
exposure applied in phase II.
415
5.6.3.2 Normal Tension Stress-Gap Model for Exposed Beams
The bilinear normal tension stress-gap model is calculated based on the procedure
described in Section 5.2.4.2. The values of maximum tensile stress of contact, σmax= 3.18
MPa, and contact gap at the completion of debonding, unc= 0.045 mm, are derived using
Equations 5-16 to 5-18 and the exposed concrete compressive strength of 28.1 MPa
surrounding the groove. Comparing the exposed and unexposed bilinear models shows a
decrease of 21.3% in normal fracture energy due to exposure applied in phase II.
5.6.4 Modeling of Prestressing
The prestressing was applied by assigning the temperature to the CFRP elements
(equivalent temperature method) as explained in Section 5.2.5. Considering the
longitudinal thermal expansion of the CFRP strip, αfrp, as -9×10-6
/oC (based on the FRP
material data sheet, Hughes Brothers Inc) and using Equation 5-19, the following
temperatures were assigned to the CFRP elements in the FE model to meet the prestrain
in CFRP strip. On the other hand, since the NSM CFRP strip experienced debonding at
the end regions due to exposure (see Section 4.7.2 and Table 4-14), the value of prestrain
in the CFRP strip prior to testing is less than that prior to being subjected to
environmental exposure. This loss happens due to seating loss (anchorage slip at the
bolts) after debonding, and therefore, reduces the prestrain in the CFRP strip. Regarding
the debonded lengths presented in Table 4-14 and based on the occurred debonding and
end anchor inspections after exposure the values of anchor movement, presented at the
end of this section, are considered for the beams strengthened using prestressed NSM
416
CFRP strips. Furthermore, as explained earlier in Section 5.2.5, the resulting deformation
due to elastic shortening of the concrete beam reduces the strain in the CFRP strip due to
prestressing. Therefore, the applied equivalent temperature (Δtapplied) was calculated by
trial and error to produce the exact value of prestrain, εP, for each beam.
Ct&.
Ct&.
Ct&.
oappliedP
oappliedP
oappliedP
1070debondingtoduemovementanchor1mmgconsiderin010080
510debondingtoduemovementanchor4mmgconsiderin006730
340debondingtoduemovementanchor1mmgconsiderin003550
5.6.5 Modeling of Materials
5.6.5.1 Concrete of Exposed Beams
The concrete material is modeled with Solid65 elements using the procedure
described in Section 5.2.3.1. Observations and inspections on the exposed beams
confirmed that the severity of the exposure at the top part of the cross-section was
different from the sides and bottom, and core of the beam’s cross-section. The top surface
of the beam had a concrete compressive strength of 10.1 MPa while the sides and bottom
surfaces had a concrete compressive strength of 28.1 MPa obtained from Schmidt
hammer tests presented in Appendix C. The exposure damage done to the core of the
beams was insignificant, and therefore, a concrete compressive strength of 34.5 MPa was
assigned to that part, which is the average strength obtained from compression test of the
unexposed concrete cylinders at the time of the testing to failure. Therefore, the beams
were modeled using three different concrete material properties (stress-strain curves)
assigned to the cross-sections as shown in Figure 5-100.
417
Figure 5-100: Simulation of the beams with exposed concrete materials.
Results of the static test show that the exposed beams have stiffer load-deflection
response than the unexposed beam before yielding. This behaviour also was observed by
Oldershaw (2008), described in Section 2.10.7 and Table 2-12. The increase in stiffness
is a result of creep on the beams. In fact, the concrete material showed higher modulus
and lower strength than the unexposed specimens. The increase in the modulus of
elasticity is a result of creep and wet condition. The concrete material gets stiffer when it
undergoes creep (Oldershaw, 2008; Neville, 2011). On the other hand, in a saturated
cement paste, the absorbed water in the calcium silicate hydrate (C-S-H) phase is load-
bearing, the disjoining pressure in C-S-H tends to reduce the van-der-Waals force of
attraction, thus lowering the strength of the concrete (Mehta and Monteiro, 2006).
It should be mentioned that finding the exact concrete properties of the heavily
deteriorated beams in phase II was not possible due to variation in concrete properties.
418
Equations 5-45, 5-46 and 5-47 represent the concrete stress-strain curves, assigned to the
beams, obtained using Loov’s equation (Equation 5-1). More details about the calculation
of the concrete stress-strain curves can be found in Appendix E.
95728682804711
81121110
.cc
cc
.
..f
Equation 5-45
996391073889457571
69520128
.cc
cc
..
..f
Equation 5-46
91941210599454754331
751055534
.cc
cc
..
..f
Equation 5-47
where fc and ɛc are the concrete compressive stress (MPa) and the corresponding concrete
strain, respectively.
5.6.5.2 Steel Reinforcement
The steel reinforcement bars were simulated using the procedure described in
Section 5.2.3.2, employing two-node link element, Link8, as shown in Figure 5-8. A
multi-linear material model was assigned to the Link8 elements in addition to the related
real constants assigned to cross-section of each steel rebar. Comparison between the un-
strengthened control beam and non-prestressed strengthened beam (in which the yield
load is directly related to the yield stress of tension steel) from phase II and similar beams
from phase I revealed an average decrease of 18.6% at yield load due to the combined
sustained load and freeze-thaw cycles. In fact, subjecting the beams to the sustained load
and freeze-thaw cycles decreased the yield stress of the tension steel reinforcements
419
while had negligible effects on the modulus of elasticity. On the other hand, the tension
steel reinforcements used in phase II had a different yield stress from those used in phase
I, considering this difference, the yield stress of the tension steel reinforcements
decreased by 26% in phase II. Therefore, the following multi-linear stress-strain curves
assigned to the steel reinforcement elements are presented in Figure 5-101 in which the
decrease in yield stress is considered.
0
100
200
300
400
500
600
0 0.02 0.04 0.06 0.08 0.1 0.12
Str
ess (
MP
a)
Strain
10M Steel Bar
15M Steel Bar
Figure 5-101: Stress-strain curves of the steel bars for exposed beams in phase II.
5.6.5.3 CFRP Strip
The CFRP strips were modeled using Solid45 elements as explained in Section
5.2.3.3. An equivalent multi-linear stress-strain curve was assigned to the CFRP element
for each stress-strain curve presented in Figure 5-102a and b obtained from experimental
420
results (Section 4.7.1.3). A Poisson’s ratio of 0.22 was assigned to the CFRP elements
(Kachlakev et al., 2001).
(a) For BS-NP-FS,BS-P1-FS, and BS-P2-FS (b) For BS-P3-FS
Figure 5-102: Stress-strain curves assigned to the CFRP strip elements.
5.6.5.4 Epoxy Adhesive, Loading Plate, Steel Anchors, and Steel Bolts
The Epoxy adhesive, loading plate, steel anchors, and steel bolts were modeled
using the elements, materials, and procedures mentioned in Sections 5.2.3.5 and 5.2.3.6.
5.6.6 Nonlinear Analysis
The nonlinear solution was performed using displacement control method as
explained in Section 5.2.7. Details of the load-steps defined for solving the FE models are
presented in Table 5-17.
421
Table 5-17: Summary of load-steps assigned for nonlinear analysis.
Load-step
Time at
end of
load-step
Sub-step Max
number of
iterations
Displacement
convergence
criteria tolerance No. Min Max
1. Zero load-camber
induced by prestressing* 0.0001 1 1 1000 40 0.01
2. Applied prestressing-
before first cracking 1.2 10 5 40 40 0.01
3. Before first cracking-
after first cracking 4 80 50 100 40 0.05
4. After first cracking-
before steel yielding 18 20 10 10000 40 0.05
5. Before steel yielding-
after steel yielding 26 40 15 10000 40 0.05
6. After steel yielding-
ultimate 60 20 10 10000 60 0.05
7. Before ultimate-after
ultimate** 200 80 40 20000 60 0.05
* used for prestressed NSM-CFRP strengthened beams
** used for un-strengthened control beam
5.6.7 Numerical Results and Discussion
Comparison between experimental and numerical load-deflection curves is
presented in Figure 5-103 which includes the five beams tested in phase II (un-
strengthened control beam, B0-FS, strengthened beam with non-prestressed NSM CFRP
strip, BS-NP-FS, and strengthened beams with prestressed NSM CFRP strips, BS-P1-FS,
BS-P2-FS, and BS-P3-FS). The FE models were terminated due to concrete crushing
accompanied by a non-convergence message from the program which causes a large drop
of the total load at ultimate stage. A comparison between the results obtained from the
tests versus the FE analysis are provided in Table 5-18, including the type of failure,
ductility index (the ratio of the ultimate deflection to the deflection at yielding), energy
absorption (the area under load-deflection curve up to the peak load), and percentage of
difference between corresponding experimental and numerical values.
422
0
20
40
60
80
100
120
-5 15 35 55 75 95 115 135 155 175
Lo
ad
(k
N)
Mid-span deflection (mm)
BS-P3-FS (Experimental) BS-P3-FS (FE)
BS-P2-FS (Experimental) BS-P2-FS (FE)
BS-P1-FS (Experimental) BS-P1-FS (FE)
BS-NP-FS (Experimental) BS-NP-FS (FE)
B0-FS (Experimental) B0-FS (FE)
Figure 5-103: Comparison between experimental and numerical load-deflection curves.
422
423
Table 5-18: Summary of the results.
Beam
ID#
Assigned
prestrain
to CFRP
Total debonded
length after
exposure (mm)
Results Py
(kN)
Δy
(mm)
Pu
(kN)
Δu
(mm) μD
Φ
(kN. mm)
Failure
Mode
B0-FS N.A. N.A.
FE 65.9 20.7 72.9 68.4 3.3 4088.4 CC
Test‡ 62.3 13.3 77.9 80.9 6.1 5462.9 CC
Error % 5.7 56.5 -6.5 -15.4 -46.0 -25.2 ―
BS-NP-FS 0 0
FE 73.3 20.6 97.3 53.4 2.6 3641.2 CC
Test‡ 74.4 15.5 98.3 57.6 3.7 4496.6 CC
Error % -1.4 32.9 -1.0 -7.2 -30.2 -19.0 ―
BS-P1-FS 0.003034 750
FE 82.5 21.2 106.3 54.9 2.6 4238.6 CC
Test‡ 83.8 17.5 96.8 35.1 2.0 2534.5 CC
Error % -1.6 20.9 9.9 56.3 29.3 67.2 ―
BS-P2-FS 0.004664 2340
FE 85.3 20.8 110.4 55.6 2.7 4515.5 CC
Test‡ 90.5 20.6 91.4 21.9 1.1 1343.8 CC-DB
Error % -5.7 0.8 20.7 153.4 151.4 236.0 ―
BS-P3-FS 0.009567 2530
FE 98.0 20.8 118.5 46.8 2.2 4149.2 CC
Test‡ 101.5 19.4 106.7 36.7 1.9 3174.6 DB-CC
Error % -3.4 7.2 11.1 27.3 18.7 30.7 ―
Py and Δy = load and deflection at yielding μD = ductility index = Δu /Δy
Pu and Δu = load and deflection at ultimate Φ = energy absorption (area under P-Δ curve up to Pu) CC = concrete crushing
CC-DB= concrete crushing followed by the NSM CFRP debonding, almost simultaneously
DB-CC= failure initiated by the NSM CFRP debonding and concrete crushing almost simultaneously, and then followed by the concrete crushing
423
424
From starting the test up to the yielding stage, the FE and experimental curves
match satisfactorily with insignificant differences at the yield load and significant
differences at the yield deflection. An average error of -1.3±4.3% for yield load with a
maximum of 5.7% for B0-FS, and an average error of -23.6±22.2% for yield deflection
with a maximum of 56.5% for B0-FS are reached. The experimental load-deflection
responses are stiffer than the predicted ones before yielding. The increase in stiffness
might be a result of creep of the beams which makes the concrete material stiffer at
regions that are not affected by the freeze-thaw cycles such as the core of the beams. It
should be mentioned that finding the amount of this possible increase in concrete
stiffness (modulus of elasticity) was not possible in the test, and therefore, was not
considered in the FE model.
At ultimate stage, the predicted loads are higher than those from the tests; this
difference might be due to combination of a few reasons. The fact is that due to high
exposure the variability in material property is high, and even for one specimen the
concrete behaviour is different from one point to the other point. Therefore, the exact
stress-strain curve of the concrete material might be slightly different than what was
assigned to the FE model. Also, the debonding occurred at the end regions of the NSM
CFRP strip under exposure caused a prestressing loss in CFRP strip due to seating of the
steel anchor on the steel bolts. Finding the exact value of this loss needs extensive
waterproof instrumentations along the length of the NSM CFRP strip while the beams are
under exposure (in the experiment, the strain in the CFRP strip at mid-span was
monitored during the exposure). Therefore, the prestrain in the CFRP strip after exposure
might be different from what was assigned to the models. In addition to the above
425
mentioned reasons, in reinforced concrete members creep results in a gradual transfer of
load from the concrete to the reinforcement, and once the steel reinforcement yields, any
increase in the applied load is carried by the concrete so that full strength of both the steel
and the concrete is developed prematurely before expected failure takes place.
Due to the above mentioned reasons, there is no rational trend in the results
obtained from the tests at failure, and large error are observed between the predicted and
the experimental results. An average error of 6.8±10.7% for ultimate load with a
maximum of 20.7% for BS-P2-FS, and an average error of 42.9±68.1% for deflection at
ultimate load with a maximum of 153% for BS-P2-FS are reached at the ultimate stage.
Also, an average error of 24.7±77.6% for ductility index with a maximum of 151% for
BS-P2-FS, and an average error of 58±106.5% for energy absorption with a maximum of
236% for BS-P2-FS are reached. The modeled beams showed similar type of failure to
the tested beams which is concrete crushing in all cases.
Therefore, the performed comparison indicates that the load-deflection curves
obtained from the FE models shows an acceptable match with those from the
experimental ones up to yielding, but after yielding the trend of the predicted curves are
not in a very good correlation with the experimental ones.
5.7 Summary
In this chapter, the FE and analytical simulations related to RC beams
strengthened using prestressed NSM CFRP strips and rebars were presented. First, five
unexposed RC beams including one un-strengthened control beam, one beam
strengthened using non-prestressed NSM CFRP strips, and three beams strengthened
426
using prestressed NSM CFRP strips were modeled by developing a nonlinear 3D FE
model. Then, a parametric study was performed in which 23 beams were analyzed to
assess the effects of the prestressing level in the NSM CFRP strips, the tensile steel
reinforcement ratio, and the concrete compressive strength on the flexural behaviour of
the NSM CFRP strengthened RC beams. Afterward, the anchorage system used for
prestressing the NSM CFRP strips was modeled followed by a parametric study in which
fourteen anchorage were modeled to investigate the effects of bond cohesion, anchorage
length, adhesive width, and adhesive height on the pullout capacity and interfacial shear
stress distributions at steel-epoxy and CFRP-epoxy interfaces. Then, the load-deflection
responses of nine beams exposed to freeze-thaw cycles, tested in phase I, were simulated
by developing an analytical solution. Finally, the load-deflection responses of five beams
exposed to combined freeze-thaw cycles and sustained loading, tested in phase II, were
simulated by developing a FE model.
In the next chapter, the conclusions and recommendations resulted from this
research are presented.
427
Chapter Six: Conclusions and Recommendations
6.1 Introduction
The research presented herein aims at studying the gaps in the field of prestressed
and non-prestressed NSM CFRP strengthening of RC beams. In this chapter, the
conclusions of this work and the recommendations for future research are presented.
In the experimental part of the research, the conclusions were drawn based on the
studies of the flexural performance of the beams exposed to freeze-thaw cycles, the
deformability of the NSM CFRP strengthened RC beams, the effects of CFRP geometry
strips versus rebar, the flexural performance of the beams exposed to combined freeze-
thaw cycles and sustained loading, the prestress losses in the NSM CFRP strengthened
beams, and the modification of the NSM CFRP prestressing system.
In the numerical and analytical parts of the research, the conclusions were drawn
based on the finite element modeling of the beams strengthened using prestressed NSM
CFRP strips, the parametric study on RC beams strengthened with prestressed NSM
CFRP, the finite element modeling and parametric study on the steel end anchor,
analytical modeling of RC beams strengthened with prestressed NSM CFRP strips and
rebars subjected to freeze-thaw exposure, and the finite element modeling of the beams
strengthened using prestressed NSM CFRP strips subjected to combined freeze-thaw
exposure and sustained load.
On the other hand, the results might not be statistically significant due to the
limited number of the tested beams reported in this research, however, they would
428
provide a better understanding on the performance of the prstressed NSM CFRP
strengthened RC beams subjected to freeze-thaw cycles and sustained load.
6.2 Conclusions
6.2.1 Experimental Test Results
6.2.1.1 Phase I: Experimental Study on RC Beams Strengthened with Prestressed NSM-
CFRP Strips and Rebar Subjected to Freeze-Thaw Exposure
The flexural performance of the RC beams strengthened with prestressed and
non-prestressed NSM-CFRP strips and rebars exposed to 500 freeze-thaw cycles were
examined in phase I. Each freeze-thaw cycle in phase I consisted of eight intervals that
was programmed to be accomplished in 8hrs, including the lower temperature bound of -
34oC and the upper temperature bound of +34
oC with a relative humidity of 75% for
temperatures above +20oC. Based on this part of the research, the following conclusions
can be drawn:
1. The freeze-thaw cycling exposure mainly affects the concrete, concrete-epoxy
interface, and causes residual stress in the NSM-CFRP reinforcement due to
thermal incompatibility of the components.
2. The effects of freeze-thaw cycling exposure on the flexural performance of the
beams strengthened using prestressed NSM CFRP strips and rebars with high
prestress levels of 48% and 41%, respectively, where the failure is governed by
CFRP rupture while the concrete strain in extreme compression fibre is small, are
negligible.
429
3. The damage done to the concrete, due the freeze-thaw cycling exposure, affects
the ultimate state, and particularly the failure mode of the beams, by shifting the
mode of failure from CFRP rupture to concrete crushing and results in smaller
ultimate load, deflection at ultimate load, and energy absorption. A 12.2-20%
decrease in ultimate deflection and a negligible (2.1-9%) decrease in ultimate load
of the exposed beams were observed in comparison with the similar unexposed
beams. The exposed beams experienced a decrease of 13.1-26.7% in energy
absorption in comparison with unexposed beams.
4. The initiation of the longitudinal debonding cracks at the concrete-epoxy interface
appears to be related to the fracture energy of the interface; these cracks almost
initiate at a constant beam’s deflection independent from prestressing level for the
particular beams in this study. Since, prestressing decreases the ductility index
(deflection at ultimate to deflection at yielding), therefore, the longitudinal
debonding cracks at the concrete epoxy interface is less likely to occur in beams
strengthened using prestressed NSM CFRP reinforcements.
5. The beams strengthened using prestressed NSM CFRP strips and rebar with high
prestress levels of 48% and 41%, respectively, showed no sign of debonding
while the beams strengthened using prestressed NSM CFRP strips and rebar with
prestress levels of 33% and 26%, respectively, and lower, showed longitudinal
debonding cracks at the concrete-epoxy interface localized at the constant moment
region with insignificant effects on the overall flexural performance of the beams.
6. The overall flexural performance of the beams strengthened with NSM-CFRP
rebars and strips (which have the similar axial stiffness) is almost the same, but
430
the beams strengthened with sand coated CFRP rebar showed less damage to
bond than the beams strengthened with rough textured CFRP strips.
7. Strengthening with non-prestressed NSM CFRP strips has significant effects in
the plastic range on the load-deflection behaviour while strengthening using
prestressed NSM CFRP strips has significant effects in both the elastic and plastic
ranges.
8. The prestressing of the NSM CFRP reinforcement leads to more contribution in
enhancing the yielding load than the ultimate load. Up to 64% and 66% increase
in the yielding load of the strengthened beam with CFRP strips and rebar,
respectively, were obtained with respect to the un-strengthened control RC beam
in which 22% out of 64% and 21% out of 66% are related to the increase due to
strengthening and the rests, 42% and 45%, are due to the prestressing effects.
Also, up to 53% and 61% increase in the ultimate load of the strengthened beam
with CFRP strips and rebar were recorded in which 35% out of 61% and 53% are
reached by strengthening with non-prestressed CFRP reinforcements and the
remaining is due to the prestressing effects.
9. The anchorage slippage at the jacking end of the NSM CFRP reinforcement (after
removing the brackets and transferring the prestressing force to the steel end
anchor) causes a prestressing loss along a short length (100-200 mm) of the NSM
CFRP, but it has insignificant effects on the overall flexural performance of the
beam.
10. The anchorage system performed well during the exposure and up to the failure.
431
11. An optimum prestressing level can be achieved in order to preserve the beam's
original energy before strengthening. The experimental results yield an optimum
prestressing level of 27.5% for beam strengthened with CFRP strips versus 31.5%
for beam strengthened with CFRP rebar.
12. A beneficial prestressing level is defined as a prestressing level, which produces
the maximum improvement in energy absorption of the strengthened RC beam
with respect to the un-strengthened control RC beam. The improvement is the
difference between the energy absorption of the strengthened and un-strengthened
beam calculated up to the ultimate deflection of the strengthened beam The
experimental results yield a beneficial prestressing level of 31.4% for beam
strengthened with CFRP strips versus 24.1% for beam strengthened with CFRP
rebar.
6.2.1.2 Deformability and Ductility of NSM CFRP Strengthened RC Beams
Ductility and deformability of prestressed and non-prestressed NSM-CFRP
strengthened RC beams have been studied in this research by considering the results of
four series of tests on eighteen beams. Based on this part of the research, the following
conclusions can be drawn:
1. The existing deformability models available in the literature need to be modified
to be applicable for FRP strengthened RC beams; therefore, three deformability
indices (the deformability factor, the Zou index, and the J factor) were modified
to be applicable for these types of beams.
432
2. The value calculated from the modified deformability (µEm), the modified Zou
(Zm), the displacement ductility (µD), and the curvature ductility (µ) indices is
88%, 69%, 57%, and 52% of the value obtained from the modified J factor (Jm).
3. It is recommended that deformability and ductility limits of 4, 3.1, 2.6, and 2.3
be used for checking the design of the FRP strengthened RC beams based on the
µEm, Zm, µD, and µ models, respectively. Among examined models, the modified
deformability factor (µEm) represents the most conservative model and leads to the
lowest permitted prestressing level based on its limit.
4. Due to prestressing, reductions of 63.1%, 58.6%, 53.3%, 49.3%, and 36.2%
occurred for µEm, Zm, Jm, µD, and µ, respectively, in comparison with the non-
prestressed strengthened RC beam.
6.2.1.3 Phase II: Prestressed NSM-CFRP Strengthened RC Beams under Combined
Sustained Load and Freeze-Thaw Exposure
The flexural performance of the RC beams strengthened with prestressed and
non-prestressed NSM-CFRP strips exposed to 500 freeze-thaw cycles while each beam
was subjected to a sustained load of 62 kN, equal to 47% of the theoretical ultimate load
of the non-prestressed NSM CFRP strengthened RC beam. Similar freeze-thaw cycle to
phase I was used in phase II except that the 75% relative humidity at temperatures above
+20oC was replaced with fresh water spray (18 L/min for a time period of 10 min) at
temperature +20oC to increase the severity of the applied exposure. Based on this part of
the research, the following conclusions can be drawn:
433
1. The effects of the applied exposure on the beams were significantly severe in
phase II, the concrete was severely deteriorated, the beams were cracked
extensively, and permanent deflections (after unloading the sustained load)
ranging from 8-15.6 mm occurred at mid-span of the beams.
2. Due to freeze-thaw exposure and sustained loading, debonding (up to 65% of the
total prestressing length) occurred in the prestressed NSM CFRP strengthened RC
beams at the end regions of the NSM CFRP strips at the concrete-epoxy interface;
On the other hand, no sign of debonding was observed in the non-prestressed
NSM CFRP strengthened RC beam.
3. After freeze-thaw exposure and sustained loading, the debonded length at the
jacking end of the NSM CFRP is higher than that at the fixed end.
4. Strengthening the beam using prestressed NSM CFRP strengthening system with
prestress level up to 49% increased the yielding load of the un-strengthened
control beam up to 64.8%; in which 17.7% of this value is related to strengthening
with non-prestressed NSM CFRP and the rest, 47.1%, is related to prestressing
effects.
5. The prestressed NSM CFRP strengthening increases the ultimate load of the un-
strengthened control beam up to 36.7% in which 26.1% of this value is related to
strengthening and the rest, 10.7%, appears to be related to prestressing effects.
6. Since the prestressed strengthened beams debonded under exposure, the strain
profile is almost constant within the NSM CFRP length.
7. The overall flexural behaviour of the beams in phase II is completely affected by
the combined freeze-thaw exposure and sustained load. Five exposed beams in set
434
BS-F showed a typical failure mode, i.e., tension steel reinforcements yielding
followed by CFRP rupture or concrete crushing while the exposed beams in set
BS-FS failed at early stage after yielding due to concrete crushing; concrete
crushing followed by the NSM CFRP debonding, almost simultaneously; or an
initial NSM CFRP debonding and concrete crushing, almost simultaneously,
followed by the concrete crushing.
8. Comparison between yield loads shows the average decreases of 19.2% and
26.4% in the load and the deflection at yielding of the beams in set BS-FS with
respect to the corresponding beams in set BS-F, respectively. Besides, an average
decrease of 27.5% was observed in ultimate load of the beams in set BS-FS in
comparison to set BS-F. Furthermore, the deflection at ultimate for the beams in
set BS-FS shows an average decrease of 51.6% in comparison with beams BS-F.
9. An average of 63.9% decrease in energy absorption (area under the load-
deflection curve up to the peak load) was observed for set BS-FS in comparison
with set BS-F. Besides, an average decrease of 33.3% in ductility indices
(deflection at ultimate to deflection at yielding) occurred in set BS-FS in
comparison with set BS-F.
10. The NSM-CFRP debonding at end regions of the prestressed strengthened
beams and low ductility and energy absorption resulted from the severe damage to
the concrete material are the issues that should be considered in long-term
performance of the prestressed NSM CFRP strengthened RC beams under freeze-
thaw exposure and sustained loading.
435
6.2.1.4 Prestress Losses in Prestressed NSM CFRP Strips and Rebar
The instantaneous and long-term prestress losses in NSM CFRP reinforcements
were studied using the beams strengthened with prestressed NSM CFRP strips and rebars
from phases I and II. Based on this part of the research, the following conclusions can be
drawn:
1. At room temperature and 7 days after prestressing, an average loss of 3.3% in
CFRP strain occurred in the prestressed NSM-CFRP strengthened RC beams
under self-weight in which 76.4% of this loss happened within 24 hrs after
prestressing.
2. At room temperature and 6 months after prestressing, an average loss of 5.3% in
CFRP strain occurred in the prestressed NSM-CFRP strengthened RC beams
under self-weight.
3. Under freeze-thaw exposure and 50 years after presterssing, an estimated value of
8.5-22.8% loss in CFRP strain is possible to occur in prestressed NSM-CFRP
strengthened RC beam. On the other hand, the freeze-thaw cycling exposure can
leads to a gain in CFRP strain in some cases.
6.2.1.5 Modification of the NSM CFRP Prestressing System
The fixed and movable brackets were modified to avoid the occurrence of the
cracks at the location of the fixed bracket and to investigate the possible cracking patterns
at very high prestress levels (up to 75% of the CFRP ultimate strength). Based on this
part of the research, the following conclusions can be drawn:
436
1. The modification done to the prestressing system eliminates the occurrence of the
cracks during the prestressing at the location of the fixed bracket by selecting a
low value of eccentricity.
2. The tests show that up to 26% difference between the applied load by the jacks
and the prestress load in the NSM reinforcement is possible due to friction
between the prestressing system and beam.
6.2.2 Numerical and Analytical Simulations
6.2.2.1 Finite Element Modeling of RC Beams Strengthened with Prestressed NSM-FRP
A comprehensive nonlinear 3D finite element model was developed to investigate
the behaviour of the RC beams strengthened in flexure with prestressed NSM CFRP
strips, and by considering the effect of debonding. The model was validated with the
experimental results. Based on this part of the research, the following conclusions can be
drawn:
1. The proposed 3D FE model was validated with the experimental results and a
very good correlation was observed. The validated FE model properly estimated
the behaviour of the NSM-CFRP-strengthened RC beams. The FEM procedure
and selected elements along with the assigned material constitutive models and
considered mixed-mode-debonding model (normal tension stress-gap and shear
stress-slip models) can be used to generate a FE model for future studies.
2. When a strengthened beam is tested under four-point bending configuration, the
maximum strain in the CFRP strip does not happen at mid-span section, but
occurs at a location somewhere from the point load to mid-span of the beam
437
which could not be possibly captured due to the infinite location of the installed
strain gauges along the length of the CFRP strips. Also, the strain distribution at
mid-span section is not linear due to the effect of pre-strain applied to the CFRP
strip.
3. The results show that debonding propagation at ultimate load which is mainly
caused by high deflection and crack opening is less for the prestressed beam.
6.2.2.2 Parametric Study on RC Beams Strengthened with Prestressed NSM-FRP
An extensive parametric study was performed to analyse the effects of
prestressing level in the NSM CFRP, tensile steel reinforcement, and concrete
compressive strength on the flexural behaviour of RC beams strengthened with
prestressed NSM CFRP strips. According to this study the following conclusions can be
drawn:
1. Increasing the prestressing level in the NSM CFRP reinforcement: significantly
enhances the negative camber; the cracking and yielding loads; and the cracking
deflection of the strengthened beam; on the other hand, reduces the ultimate
deflection and the ductility index of the strengthened beam.
2. Prestressing the NSM CFRP has a minor effect on the yielding deflection and
ultimate load of the strengthened beam and also on the energy absorption of RC
beams with high tension steel ratio. The type of failure of the strengthened beams
changes from concrete crushing to CFRP rupture with an increase to the
prestressing level in the NSM CFRP reinforcement.
438
3. Increasing the tensile steel reinforcement enhances: the cracking and yielding
deflections; the cracking, yielding, and ultimate loads; and the deflection at
ultimate load when CFRP rupture governs; on the other hand, reduces: the
negative camber; the ductility index; and the ultimate deflection when concrete
crushing governs. The type of failure changes from CFRP rupture to concrete
crushing with increasing the tension steel reinforcement ratio.
4. Increasing the concrete compressive strength: slightly enhances the camber due to
prestressing; the cracking and yielding deflections; and the deflection at ultimate
load when CFRP rupture governs; on the other hand, slightly reduces: the ductility
index and the cracking, yielding, and ultimate loads. The type of failure changes
from concrete crushing to CFRP rupture with increasing the concrete compressive
strength. In general, changing the concrete compressive strength has a very slight
effect on the overall flexural behaviour of the RC beams strengthened with
prestressed NSM CFRP strips.
5. The maximum amount of energy absorption happens when balanced failure
occurs. When CFRP rupture governs, the energy absorption decreases as the
prestressing level, tensile steel ratio, or concrete compressive strength increase.
When concrete crushing governs, the energy absorption increases as the
prestressing level, tensile steel ratio, or concrete compressive strength increase.
6.2.2.3 FE Modeling of Steel End Anchor and Parametric Study
A nonlinear 3D finite element model of the steel end anchor used to prestress
NSM CFRP strips for flexural strengthening of RC beams is developed to investigate the
439
effects of various parameters on the overall behaviour and interfacial shear stress
distributions. According to this part of the research, the following conclusions can be
drawn:
1. The cohesion between interfaces (CFRP-epoxy and steel-epoxy) has a significant
effect on the ultimate capacity of the anchorage. A 202% enhancement in ultimate
load is reached by changing the cohesion of the interfaces from 5 to 20 MPa.
2. Increase in the bond length from 150-450 mm leads to a 146% increase in
ultimate capacity and changing the mode of failure from debonding to CFRP
rupture.
3. Increase in the adhesive width and height leads to a significant decrease in the
interfacial shear stress distribution at vertical and horizontal steel-epoxy
interfaces, respectively. Decreases of 54.3% and 63% in the maximum shear
stresses at the steel-epoxy interfaces were reached by increasing the adhesive
width from 3.5-10.5 mm and adhesive height from 1.5-7.5 mm, respectively.
4. The shear stress distribution at interfaces is a skewed curve which is limited to
bond capacity from the top.
6.2.2.4 Analytical Modeling of RC Beams Strengthened With Prestressed NSM-CFRP
Reinforcements Subjected to Freeze-Thaw Exposure
A nonlinear analytical model was developed to generate the load-deflection
responses of the RC beams strengthened in flexure with prestressed or non-prestressed
NSM-CFRP strips and rebars subjected to freeze-thaw exposure (phase I). Based on this
part of the research, the following items can be drawn:
440
1. The reliability of the model was confirmed by comparing the predicted results
with nine experimental load-deflection responses revealing very good accuracy of
the predicted results. The proposed analytical model can be employed with
enough confidence as a predictive method in future studies.
3. The model has the capabilities of assigning the freeze-thaw exposed concrete
stress-strain curve based on Loov's equation, elasto-plastic behaviour for
compression and tension steel, linear behaviour for FRP, and partial prestressed
CFRP length along the length of the beam.
4. The developed model has the main advantage of having much shorter computer
computational time in comparison with finite element analysis of similar beams.
6.2.2.5 FE Modeling of RC Beams Strengthened with Prestressed NSM-CFRP
Reinforcement Subjected to Freeze-Thaw Exposure and Sustained Load
Five RC beams tested in phase II of the experimental program, which were
subjected to freeze-thaw exposure and sustained load, were simulated and the predicted
load-deflection responses are compared with the experimental ones. Based on this part of
the research, the following conclusion can be drawn:
1. The performed comparison indicates that the load-deflection curves obtained from
the FE models acceptably matched those from the experimental ones up to
yielding, but after yielding the trend of the predicted curves are not in a very good
correlation with the experimental ones.
441
6.3 Recommendations
1. The fatigue performance of the RC beams strengthened with prestressed NSM
CFRP reinforcements subjected to freeze-thaw cycles is an interesting issue that
needs to be investigated experimentally and numerically in the evolution of this
strengthening system.
2. Seismic and dynamic behaviour of the RC beams strengthening using prestressed
NSM CFRP reinforcements needs to be studied experimentally and numerically.
3. The performance of the RC beams strengthened using prestressed NSM CFRP
reinforcements subjected to different types of exposure such as chemical solution
(salt, alkaline, and acid), oxidation, UV radiation, etc needs to be studied.
4. There is no valid method to relate the accelerated freeze-thaw cycles to the real-
world considering the parameters involved based on the geographic location and
the weather conditions.
5. Retrofitting the large-scale bridge I girders using prestressed NSM CFRP
reinforcements should be considered by addressing different issues such as type of
prestressing systems (temporary brackets) and end anchors.
6. The behaviour of the retrofitted existing structural member using prestressed
NSM CFRP reinforcements needs to be investigated. In this case, the existing
cracks might affect the efficiency of the NSM CFRP retrofitting. Also, due to
degradation of concrete properties, the occurrence of cracks at the location of the
cracks at the time of presterssing is probable and should be considered.
7. Strengthening the beams under applied particular service loads using the
prestressed NSM CFRP technique needs to be studied in detail.
442
8. Strengthening RC slabs using prestressed NSM CFRP technique needs to be
studied.
9. The behaviour of the prestressed NSM CFRP strengthening technique under fire
needs to be studied and compared to the prestressed EB strengthening system.
10. After completion of the gaps in this field (mostly the items mentioned above),
proposing a design guideline seems necessary for the rational implementation of
the prestressed NSM CFRP retrofitting and strengthening technique.
443
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List of to Date Publications from the Research Presented in This PhD Thesis
Omran, H.Y., and El‐Hacha, R. (2010b). Finite element modelling of RC beams
strengthened in flexure with prestressed NSM CFRP strips. Proceeding of The 5th
International Conference on FRP Composites in Civil Engineering (CICE2010).
Beijing, China, September 27‐29, pp.718‐721.
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flexure using prestressed NSM CFRP strips. Proceeding of The 3rd
International
Conference on Seismic Retrofitting (ISCR2010). Tabriz, Iran, October 20‐22,
CD‐ROM, 12p.
Omran, H.Y., and El-Hacha, R. (2012a). Reinforced concrete beams strengthened using
prestressed NSM CFRP reinforcement – effects of CFRP geometry and freeze-
thaw exposure. Proceedings of the 6th
International Conference on Advanced
Composite Materials in Bridges and Structures (ACMBS-VI), Kingston, Ontario,
Canada, May 22 – 25, 8p.
Omran, H. Y., and El-Hacha, R. (2012b). Nonlinear 3D finite element modeling of RC
beams strengthened with prestressed NSM-CFRP strips. Construction and
Building Materials, 31 (June 2012): 74-85.
Omran, H.Y., and El‐Hacha, R. (2012c). Deformability and ductility of reinforced
concrete beams strengthened with NSM‐CFRP reinforcements. Proceeding of The
3rd
International Structural Specialty Conference. Edmonton, Alberta, Canada,
June 6‐9, 10p.
468
Omran, H. Y., and El-Hacha, R. (2012d). Effects of severe environmental exposure on
RC beams strengthened with prestressed NSM-CFRP strips. Proceeding of The 6th
International Conference on FRP Composites in Civil Engineering - CICE2012,
Rome, Italy, June 13-15, 8p.
Omran, H.Y., and El‐Hacha, R. (2012e). Anchorage system to prestress NSM‐CFRP
strip: effects of bond and anchor dimensions on the interfacial stress distributions
and bond performance. Proceeding of The 4th
International Symposium on Bond
in Concrete (BIC2012). Brescia, Italy, June 17‐20, 9p.
Omran, H.Y., and El‐Hacha, R. (2013a). Analytical modeling of RC beams strengthened
with prestressed NSM‐CFRP strips subjected to freeze‐thaw exposure.
Proceeding of The 2nd
Conference on Smart Monitoring, Assessment and
Rehabilitation of Civil Structures (SMAR13). Istanbul, Turkey, September 9-11,
9p.
Omran, H.Y., and El‐Hacha, R. (2013b). Effects of sustained load and freeze-thaw
exposure on RC beams strengthened with prestressed NSM-CFRP strips. The 4th
Asia-Pacific Conference on FRP in Structures (APFIS2013). Melbourne,
Australia, December 11-13, 6p (accepted).
El-Hacha, R. and Omran, H. Y. RC beams strengthened using prestressed NSM-CFRP
reinforcements: effects of freeze-thaw exposure, CFRP geometry, and prestressing
Loss. Composite Structures. (under submission)
469
Omran, H. Y. and El-Hacha, R. Experimental study on RC beams strengthened with
prestressed NSM-CFRP strips subjected to freeze-thaw exposure. Composite
Structures. (under submission)
470
Appendix A: Beam Design
A.1 Introduction
The key points of the load-deflection curves are calculated by developing a code
in Mathematica software that can account for negative camber due to prestressing,
concrete cracking, steel yielding, CFRP rupture, and concrete crushing of the prestressed
and non-prestressed NSM-CFRP strengthened RC beams. The design is performed based
on the material properties reported by the manufacturer that assigned as inputs to the
code.
A.2 Design Concepts, Source Code, and Results
The concept of the code is similar to Section 5.5 by assuming strain compatibility,
and force and moment equilibriums. The deflection at mid-span at each load increment is
calculated using integration from the curvatures along the length of the beams. The
source code includes eight steps to produce the overal load-deflection response and is
written in Wolfarm Mathematica (Wolfarm Research, 2008). The code is written based
on different variables, arrays for loads, deflections, moments, and curvatures, different
loops and functions available in the software.
For instance, the source code is provided in the following pages having the inputs
for solving the load-deflection response of beam BS-P3 followed by the obtained results,
the results for the other beams are summarized in Table A-1. The eight steps are briefly
mentioned in the source code, where Step 1 is the input, Step 2 calculates the load-
deflection response from start to cracking, Step 3 calculates the yield load, Step 4
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calculates the ultimate load due to concrete crushing, Step 5 calculates the ultimate load
due to CFRP rupture, Step 6 calculates the loads and corresponding deflections from
cracking to yielding of tension steel, Step 7 calculates the loads and corresponding
deflections from yielding of tension steel to ultimate, and the calculated load and
corresponding deflection are plotted in Step 8. More details about the steps can be found
in the source code.
The input of the source code includes twenty-five constants in N and mm units,
which represent material properties and geometry of the beam, where L is the span
length; Lp the shear span length; Lo the un-strengthened length on each side; b and h the
width and the height of the beam, respectively; dst the depth to the tension steel
reinforcements, dsc the depth to the compression steel reinforcements; df the depth to the
CFRP reinforcements; Efrp, ϵfrpu, ffrpu, Afrp, and ϵpe the modulus of elasticity, the
ultimate tensile strain, the tensile strength, the area, and the prestrain in the CFRP
reinforcements, respectively; Bcsc, ncsc, and ϵocsc the constants B, n, and ϵo in the
loov’s equation (Equation 5-1), respectively; fc, Ec, fr, and ϵcCC the compressive
strength, the modulus of elasticity, the tensile strength, and the crushing strain of the
concrete material, respectively; Ast, fyt, and Est the area, the yield stress, and the
modulus of elasticity of the tension steel reinforcements, respectively; and Asc, fyc, and
Esc are the area, the yield stress, and the modulus of elasticity of the compression steel
reinforcements, respectively.
The output is set to present the type of failure; a plot of the load-deflection
response; and load, deflection, moment, and mid-span curvature for twenty-four points on
the load-deflection curve including prestressing, cracking, yielding, and ultimate stages.
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Table A-1: Summary of designed specimens.
Beam ID ɛp Δo
(mm)
Δcr*
(mm)
Pcr*
(kN)
Δy*
(mm)
Py*
(kN)
Δu*
(mm)
Pu*
(kN) ɛc@u ɛfrp@u
Failure
Mode
B0 N.A. 0 1.70 22.70 21.85 82 121.47 85.73 0.0035 N.A. CC
BS-NP 0 0 1.71 22.91 22.16 88.88 96.92 131.78 0.00302 0.017 FR
BS-P1 0.0034 0.45 1.76 29.60 21.58 97.83 75.74 131.65 0.00259 0.017 FR
BS-P2 0.0068 0.90 1.81 36.28 21.03 106.73 56.36 131.26 0.00217 0.017 FR
BS-P3 0.0102 1.35 1.86 42.97 20.53 115.58 38.85 130.31 0.00173 0.017 FR
BR-NP 0 0 1.71 22.94 22.21 89.86 93.06 135.17 0.00295 0.016 FR
BR-P1 0.0034 0.51 1.77 30.58 21.55 100.08 71.47 134.99 0.00251 0.016 FR
BR-P2 0.0068 1.02 1.82 38.22 20.94 110.24 51.87 134.48 0.00208 0.016 FR
BR-P3 0.0102 1.54 1.88 45.85 20.37 120.33 34.34 133.20 0.00162 0.016 FR
ɛp = target prestrain value in CFRP reinforcement ɛc@u= concrete strain at extreme compression fibre at ultimate
Δo = initial camber due to prestressing ɛfrp@u= maximum CFRP strain at ultimate
Pcr and Δcr = load and deflection at cracking CC = concrete crushing
Py and Δy = load and deflection at yielding FR = CFRP rupture
Pu and Δu = load and deflection at ultimate
* self-weight is ignored in calculations (to consider the self-weight effects, values of 6 kN and 0.47 mm should be deducted from the loads and deflections,
respectively)
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477
Appendix B: Fabrication of Beams
B.1 Introduction
Fabrication of the RC beam specimens includes building the formwork, steel
cage, instrumentation, concrete casting, and strengthening are presented in this Appendix.
B.2 Fabrication of Formwork
Three formworks (two pairs and one single) were fabricated to cast a maximum of
five RC beams at once. Each pair form were fabricated by connecting two single forms
laterally using wooden bracer sitting on one base as shown in Figure B-1a. The plywood
used for formwork had 19 mm thickness. The sides of the forms were connected to each
other and to the base using angle as shown in Figure B-1b. Pictures of the formwork
fabrication are presented in Figure B-1. Prior to casting, the inner surfaces of the
formworks were sprayed with oil to facilitate the removal of the beams after curing.
(a) Fabrication of the pair forms (b) Fabricated formworks
Figure B-1: Fabrication of formwork.
Bracer
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B.3 Steel Cage
Fourteen steel cages were built for the experimental program. Each steel cage was
made of 2-5250 mm long 10M deformed steel bars used for top reinforcements, 3-5250
mm long 15M deformed steel bars used for bottom reinforcements, and 25-1200 mm long
10M deformed steel bars used for stirrups (with a 135 degree hook). Top and bottom
reinforcements had a 90 degree bent at each end with a development length of 100 mm.
All reinforcement were tied together using 100 mm long steel ties. Fabrication of steel
cage and also steel cages placed into the formwork are shown in Figure B-2a and b,
respectively. To place the cages into the formwork, plastic chairs were used between the
formwork and the cages (six 38 mm plastic chairs at bottom attach to the stirrups and
twelve 22.5 mm plastic chairs at each sides attach to the stirrups) to provide the necessary
concrete cover for the longitudinal reinforcements. The threaded rods with washers and
nuts were used to keep the width inside the formwork constant and avoid buckling of the
side of formwork during casting. Two 1000 mm long steel wires were tied to each cage at
1200 from each end to work as handle for moving the beams as shown in Figure B-2b.
Furthermore, the wires for strain gauges and thermocouple were passed through a small
hose and hanged from the edge of the formwork to avoid possible future damage to the
wires.
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(a) Fabrication of the cage (b) Cages placed into the formwork
Figure B-2: Fabrication of the steel cage and placement in the formwork.
B.4 Casting Concrete
Three batches of concrete were used to cast fourteen beams for the test matrix:
batch #1 poured on August 13, 2009 (five beams were cast, BS-F set and B0-F in Table
3-1); batch #2 on July 9, 2010 (four beams were cast, BR-F set in Table 3-1); and batch
#3 on October 12, 2010 (five beams were cast, BS-FS set and B0-FS in Table 3-1). The
concrete was poured in the formwork carefully to avoid the possible damage to the strain
gauges installed on the steel bars. Also during the casting, a vibrator was used to compact
the concrete and to avoid honeycombing. The top surfaces of the beams were levelled
using hand trowels (Figure B-3a). Cylinder specimens (100×200 mm, diameter × height)
were cast to obtain the concrete properties at different stages. At the end, the beams were
covered with plastic sheets to avoid formation of surface cracks during curing, as shown
in Figure B-3b. The beams were stripped from the formworks three days after casting.
Steel rod
Handle
Plastic
chair
Thermocouple
wire
Strain gauge
wire
480
(a) Concrete cast in formworks (b) Covering the concrete with plastic sheets
Figure B-3: Fabrication of RC beams.
B.5 Strengthening Procedure
One of the challenges for using prestressed NSM FRP method is developing a
practical method for prestressing. Most researches in this area were performed while the
beam was prestressed against entire length needing both ends of the beam as mentioned
in Chapters One and Two. The prestressing and anchorage systems used in this research
for prestressing the NSM CFRP strips and rebar was developed by Gaafar (2007), which
overcomes the drawbacks of the previous research and is practical. The steps performed
for strengthening the beams in this research are presented in this section followed by
more detailed description of the major steps.
B.5.1 General Steps
The following steps were performed for strengthening using prestressed NSM
CFRP:
481
1. Preparation of the CFRP reinforcements (the CFRP strips and rebars were cut to
provide the same prestressing length for each beam after elongation, two CFRP
strips were bonded together to from the side to have similar axial stiffness with
rebar)
2. Making end anchors and cleaning the insides of the end anchors by sand blasting
3. Bonding CFRP rebar/strips into the end anchors using epoxy Sikadur® 330 and
leaving for a week to cure (the CFRP strips and rebars were cleaned with Acetone
solvent)
4. Marking the location of the groove on the beam (the elongation of CFRP
reinforcement due to prestressing was considered in marking the groove)
5. Cutting the grooves (the beams were upside down to facilitate the trend, the
grooves at the ends were made wider and deeper to allow for placing the end
anchors)
6. Cleaning the groove with water and air pressure
7. Drilling the location of the bolts for fixed end anchor, fixed bracket, and movable
bracket (the location of the internal steel reinforcements were identified to avoid
hitting the internal steel, enough space was considered between the brackets for
placing the jacks and load cells, the bolts at movable bracket were located such
that allow moving the bracket more than CFRP elongation due to prestressing)
8. Placing the beam on the pedestal to simulate the field condition for overhead
strengthening
9. Filling the groove with epoxy, Sikadur® 30, using epoxy gun and leveling using
spatula (used for overhead applications)
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10. Attaching the fixed end anchor to the concrete using anchor bolts (that
hammered in holes), holding the anchor at the other end and pushing the CFRP
into the centre of the groove, levelling the epoxy in the groove (the CFRP
reinforcements were cleaned with Acetone before placing in the groove)
11. Installing the fixed and movable brackets, hydraulic jacks, load cells, and
threaded steel bar with adjustable nuts (placed between movable and fixed
brackets)
12. Applying the load by jacking to the about 2% higher than target perstressing
level (to consider possible loss) for each beam
13. Tightening the adjustable nut, removing the ramps of the hydraulic jack, then,
leaveing the system for 24 hrs
14. Drilling and bolting the jacking end anchor
15. Removing the temporary and movable brackets after four days and monitoring
the system up to a week. It should be noted that the end anchors at the ends of
the CFRP reinforcements remained in place.
In the case of the non-prestressed NSM CFRP strengthening the following steps
were performed:
1. Preparation of the CFRP reinforcements
2. Making end anchors and cleaning the insides of the end anchors by sand blasting
3. Bonding CFRP rebar/strips into the end anchors using epoxy Sikadur® 330 and
leaving for a week to cure (the CFRP strips and rebars were cleaned with Acetone
solvent)
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4. Marking the location of the groove on the beam
5. Cutting the grooves (the beams were upside down)
6. Cleaning the groove with water and air pressure
7. Drilling the location of the bolts for end anchors
8. Filling the groove using epoxy Sikadur® 30
9. Attaching one end anchor to the concrete using anchor bolts, holding the anchor at
the other end and pushing the CFRP into the groove (the CFRP reinforcements
were cleaned with Acetone before placing in the groove)
10. Attaching the other end anchor
11. Levelling the epoxy
B.5.2 Preparation of CFRP Strips or Rebar
The CFRP strips or rebar were cut to provide an equal strengthening length of
3880 mm for all beams. Therefore, the end anchor length and elongation of the CFRP
strips/rebar due to prestressing was considered for each beam. The length of the CFRP
(cut length) and the length of the groove (elongated CFRP length) for each beam are
presented in Table B-1.
484
Table B-1: Groove and CFRP strips/rebar lengths.
Beam ID
Target
prestrain
in CFRP
Elongation due
to prestressing
(mm)
Length of
end anchor
(mm)
Groove length
(elongated CFRP length)
(mm)
CFRP length at rest
(cut length)
(mm)
BS-NP-F
BR-NP-F
BS-NP-FS
0 0 250 4380 4380
BS-P1-F
BR-P1-F
BS-P1-FS
0.0034 13 250 4380 4367
BS-P2-F 0.0068 26 250 4380 4354
BR-P2-F
BS-P2-FS 0.0068 26 400 4680 4654
BS-P3-F
BS-P3-FS 0.0102 40 400 4680 4640
BR-P3-F 0.0102 40 450 4780 4740
After cutting the CFRP strips to the calculated lengths in Table B-1 in order to have
similar axial stiffness for the strengthened beams using CFRP strip and rebar, two strips,
after cleaning the surfaces using Acetone, were attached together from the side using a
thin layer (about 1mm) of Sikadur®
330. Then the two strips were kept in boned position
using multiple steel clamps along the length for 24 hrs. it should be mentioned that the
CFRP strips and rebars were shipped at length of 4573 mm. Therefore, to meet the
lengths calculated in Table B-1, the original length was equally extended from each end.
The CFRP strips were extended by attaching four CFRP sheets to each end, one at the
bottom face, two in between, and one at the top face of the strips. The CFRP rebars were
extended by adding multiple rolls of CFRP sheets.
B.5.3 Steel Bolts for End Anchors and Temporary Brackets
The end anchors were attached to the concrete using expansion bolts named
Carbon Steel Kwik Bolt 3 Expansion Anchor having a diameter of 15.9 mm. The steel
485
brackets were mounted on the sides of the beam using HCA Coil bolts also having a
diameter of 15.9 mm.
B.5.4 Mechanical Anchors
The CFRP mechanical anchor was made of steel plate and tube (for CFRP strips)
or pipe (for CFRP rebar), which were welded together. Different lengths of the tube/pipe
were used for different prestressing level (as presented in Figure 3-2b in detail).
The end anchors (inside the pipes or tubes) were cleaned by sand blasting and the
CFRP reinforcement was connected to the anchors using epoxy adhesive (Sikadur® 330)
and cured for one week. In the case of CFRP strips, two strips were attached together
from one side to make the target area of CFRP needed for strengthening and then, after
one day, were attached to the anchors. The small screws were placed in the anchor to
adjust the CFRP reinforcement, as shown in Figure B-4.
(a) Using CFRP strips (b) Using CFRP rebar
Figure B-4: Attaching the CFRP reinforcements to the end anchors.
486
B.5.5 Temporary Brackets
The prestressing and anchorage system used in this research was first developed
by Gaafar (2007). The system includes the fixed and movable brackets that temporarily
use for prestressing the NSM CFRP strips or rebar as presented in Figure B-5. The
brackets are connected by threaded rods used for maintaining the prestressing force after
releasing the hydraulic jacks. Then, the steel anchor at jacking end is bolted to the
concrete, the jacks are released and temporary brackets are detached.
Figure B-5: Prestressing system developed by Gaafar (2007).
For prestressing the NSM CFRP in phases I and II of this research, the steel
brackets developed by Gaafar (2007) were modified by welding the steel plates to the
sides of the fixed bracket and to the tops of the movable bracket, and drilling few more
holes to improve the system and avoid rotation of the brackets at jacking stage, as shown
in Figure B-6.
487
Figure B-6: Steel brackets used for prestressing NSM CFRP in phases I and II.
B.5.6 Cutting Grooves
The grooves were made in the beams when the beams were upside down using a 6
mm thick diamond blade concrete saw. To avoid making dust and to decrease the
temperature generated in the diamond blade throughout cutting the grooves, a water flow
was connected to the saw as shown in Figure B-7a. The groove depth was 25±2 mm for
all beams however the groove width depends on the type of the NSM strengthening
material, 16±2 mm for CFRP strips and 20±2 mm for CFRP rebar. End groove regions
were cut wider and deeper for the placement of end anchors; 28±2 mm deep and 28±2
mm wide. The finished groove is show in Figure B-7b. The grooves were cleaned with
water pressure and dried with air pressure after cutting as shown in Figure B-8. Each
groove was made in 5 hrs including marking, sawing, and cleaning the groove.
Temporary brackets
488
(a) Saw cutting the groove (b) Finished groove
Figure B-7: Cutting the groove.
(a) Cleaning the groove using water (b) Drying the groove using air pressure
Figure B-8: Groove preparation.
B.5.7 Drilling Holes for Bolts
After cutting the grooves, the beams were drilled in order to make holes for bolts
at the end anchor, temporary fixed and movable brackets. The locations of the hole for
temporary brackets and the end anchors were marked on the beam by: knowing the
Guiding angle
Water hose
Diamond
blade saw
489
locations of the stirrups and longitudinal reinforcements, considering enough space
between the brackets for placing the jacks and load cells, and allowing the CFRP
elongation due to prestressing at the movable bracket. A different number of holes,
depending on the prestress level, were made in temporary fixed bracket: four holes for
BS-P1, six holes for BS-P2, and eight holes for BS-P3. The drilling was performed to 70
mm depth in concrete using drill bit having a diameter of 15.9 mm.
B.5.8 Prestressing System for NSM CFRP
After grooving, the beams were placed on two pedestals to be prestressed in the
same situation as the field. The instrumentations were performed on the beam to measure
the upward deflection due to prestressing at the centre, locations of the point loads, strain
in top and bottom steel reinforcements at mid-span, and strain in CFRP reinforcements.
Prestressing was performed by using hydraulic jack and temporary brackets installed on
the beam. At high prestress levels, for beam BS-P3, the cracks formed at the location of
the fixed bracket during prestressing. These types of cracks are shown in Figure 4-108,
and similar issue was reported by Gaafar (2007) and Oudah (2011). Therefore, the
locations of the fixed brackets were strengthened with externally bonded CFRP sheet to
minimize the cracks. The prestressed NSM strengthening are presented in Figure B-9.
More details about prestressing procedure are described by Gaafar (2007).
490
(a) Filling the groove using epoxy (b) Prestressing system
(c) Drilling at jacking end anchor (d) Placing bolt at jacking end anchor
(e) Removing the jacks (f) Removing the brackets
(g) Strengthening using CFRP sheet at fixed bracket location
for beams with high prestress level of NSM CFRP (BR-P3)
Figure B-9: Prestessed NSM strengthening.
491
Appendix C: Ancillary Test Results
C.1 Introduction
The ancillary test results of the materials used in the research are presented in this
appendix including concrete, CFRP rebar and strips, and steel reinforcements.
C.2 Concrete
Three ready mix concrete batches were used to cast fourtheen beams. Batch #1
poured on August 13, 2009 (five beams were cast, BS-F set and B0-F in Table C-1);
batch #2 on July 9, 2010 (four beams were cast, BR-F set in Table C-1); and batch #3 on
October 12, 2010 (five beams were cast, BS-FS set and B0-FS in Table C-1). The
concrete from the batches had similar specified properties as described in Section 3.3.3.2.
The uniaxial concrete compressive strengths of the beam were measured by testing
standard cylinders specimens (100 × 200 mm, diameter × height) as shown in Figure C-1,
according to ASTM C39/C39M (2010). The rate of loading during the application of the
first half of the anticipated loading phase was 10kN/sec then it was decreased to 2-1
kN/sec for the second phase. Two Linear Strain Conversion (LSC) devices were installed
on the cylinders, at a gauge length of 150 mm, to measure the strain in compression as
shown in Figure C-1a.
The concrete compressive strengths of the beams at 28 days, at the time of
strengthening, precracking, and testing to failure are presented in Table C-1 including the
date of the cylinder test and the number of the cylinders tested. It should be mentioned
that the exposed concrete strengths at the time of testing for the beams in phase II were
492
obtained using Schmidt hammer test on the beams, since the cylinders were severely
deteriorated due to freeze-thaw exposure and nothing was left from them to be tested. A
typical concrete stress-strain curve is presented in Figure C-2.
Cylinders from batches #1 and 2 had an unexposed concrete compressive strength
of 41.56.2 MPa and 39.44.2 MPa, respectively, at the time of testing to failure. The
strength of the freeze-thaw exposed concrete cylinders from batches #1 and 2 were
32.110.8 MPa and 286.8 MPa, respectively, at the time of testing the beams to failure.
The results of the hammer test, performed on the beams from batch #1 at the time of
testing to failure, shows an average exposed concrete compressive strength of 39.94.5
MPa and 48.32.6 MPa for the top surface and sides of the beams, respectively, while
these values are 40.37.3 MPa and 44.34.7 MPa for barch #2. Cylinders from batch #3
had an unexposed concrete compressive strength of 34.53.7 MPa. The hammer test
results performed on the beams from batch #3 reveal an average exposed concrete
compressive strength of 10.16.8 MPa and 28.110.1 MPa for the top surface and sides
of the beams, respectively.
493
(a) Compression test (b) Type of failure
Figure C-1: Concrete compression test and type of failure
0
10
20
30
40
50
0 0.001 0.002 0.003 0.004
Stre
ss (
MP
a)
Strain
Specimen #1
Specimen #2
Specimen #3
Figure C-2: Typical stress-strain curves of concrete (from batch#1 at 28 days)
494
Table C-1: Concrete compression test results. P
has
e
Bat
ch
Beam ID
Concrete compressive strength at
28 days (MPa)
(date, No of tests)*
Strengthening (MPa)
(date, No of tests)
Initial cracking (MPa)
(date, No of tests)
Time of testing
Unexposed (MPa)
(date, No of tests)
Exposed (MPa)
(date, No of tests)
Exposed** (MPa)
(location, No of readings)
I
1
B0-F
45.47±2.90
(9-11-2009, 3)
N.A. 42.04±2.57
(6-25-2010, 3)
34.38±2.25
(4-29-2011, 2)
32.03±5.21
(4-29-2011, 3)
40.2±5.6 (Top, 15)
45.5±2.5 (Side, 15)
BS-NP-F 37.96±4.96
(6-15-2010, 2)
35.85±3.34
(6-17-2010, 3)
50.43±0.54
(5-05-2011, 3)
42.88±5.61
(5-05-2011, 3)
39±4.5 (Top, 15)
48±2.3 (Side, 17)
BS-P1-F 41.03±2.54
(6-07-2010, 2)
35.85±3.34
(6-17-2010, 3)
44.08±1.32
(5-07-2011, 2)
39.51±3.79
(5-07-2011, 3)
40.8±4 (Top, 15)
48.4±3.6 (Side, 16)
BS-P2-F 37.96±4.96
(6-15-2010, 2)
42.04±2.57
(6-25-2010, 3)
38.03±5.46
(5-12-2011, 3)
25.81±13.80
(5-12-2011, 3)
40.5±3.25 (Top, 15)
49.5±2.5 (Side, 20)
BS-P3-F 39.32±0.49
(7-05-2010, 3)
37.84±2.89
(7-15-2010, 3)
42.14±0.88
(5-14-2011, 2)
20.12±5.20
(5-14-2011, 3)
39±5 (Top, 15)
50±2 (Side, 18)
2
BR-NP-F
43.48±2.18
(8-07-2010, 3)
44.59±3.16
(8-11-2010, 4)
41.56±4.51
(9-02-2010, 5)
39.27±3.10
(6-09-2011, 3)
23.34±8.65
(6-09-2011, 3)
38.7±9.3 (Top, 25)
44±6 (Side, 17)
BR-P1-F 44.59±3.16
(8-11-2010, 4)
41.56±4.51
(9-02-2010, 5)
39.90±5.71
(6-15-2011, 3)
30.61±3.44
(6-15-2011, 3)
39±7.5 (Top, 17)
42.5±3.5 (Side, 18)
BR-P2-F 44.60±1.02
(8-18-2010, 3)
41.56±4.51
(9-02-2010, 5)
34.96±0.83
(6-17-2011, 3)
27.95±2.18
(6-17-2011, 3)
42±6 (Top, 18)
44±5 (Side, 15)
BR-P3-F 41.29±1.01
(8-26-2010, 3)
38.05±1.02
(9-04-2010, 3)
43.39±1.30
(6-22-2011, 3)
30.01±10.64
(6-22-2011, 3)
41.5±6.5 (Top, 15)
46.5±4.2 (Side, 18)
II
3
B0-FS
37.76±1.19
(11-08-2010, 3)
N.A. N.A. 37.12±1.83
(8-14-2012, 3) ―
9.2±4.8 (Top, 24)
31±7 (Side, 36)
BS-NP-FS 38.03±2.23
(12-04-2010, 3) N.A.
31.77±1.55
(8-17-2012, 3) ―
9±5 (Top, 16)
28±9 (Side, 27)
BS-P1-FS 38.03±2.23
(12-04-2010, 3) N.A.
36.34±5.89
(8-21-2012, 3) ―
10±7 (Top, 15)
27±12 (Side, 44)
BS-P2-FS 36.51±1.83
(12-15-2010, 3) N.A.
33.9±0.28
(8-23-2012, 3) ―
10.2±7.8 (Top, 15)
23.4±13 (Side, 39)
BS-P3-FS 35.01±1.11
(12-23-2010, 3) N.A.
32.33±4.57
(8-24-2012, 3) ―
12±9.6 (Top, 15)
31±9.7 (Side, 33)
* (date, No of tests)=( Month-Day-Year, number of the tested cylinders) **the values are based on Schmidt hammer tests performed on top surface and sides of beams
494
495
C.3 CFRP Strip and Rebar
Three batches of CFRP reinforcements were used in this project, batch #1 CFRP
strips, batch #2 CFRP rebars, and batch #3 CFRP strips. Two specimens were tested from
each batch according to ASTM D 3039/D3039M (2008) for tensile properties. The
anchors were made to avoid premature debonding before CFRP rupture. One strain gauge
(SG) was installed on the CFRP rebar/strip at the centre of each specimen to measure the
strain corresponding to the applied load. The CFRP tension test is shown in Figure C-2,
and the stress-strain relation are plotted in Figures C-3 to C-5. The material properties of
CFRP reinforcements in each batch are represented in Table C-2.
(a) CFRP tension test specimens (b) Tension test
(c) Specimens after test
Figure C-2: Tension tests on CFRP strips and rebars.
496
0
500
1000
1500
2000
2500
3000
0 0.005 0.01 0.015 0.02 0.025
Str
es
s (
MP
a)
Strain
Aslan 500, CFRP strip, Specimen 1
Aslan 500, CFRP strip, Specimen 2
● : CFRP rupture
Figure C-3: Stress-strain relation of CFRP strip from batch #1.
0
500
1000
1500
2000
2500
3000
0 0.005 0.01 0.015 0.02 0.025 0.03
Str
es
s (
MP
a)
Strain
Aslan 200, CFRP rebar, Specimen 1
Aslan 200, CFRP rebar, Specimen 2
● : CFRP ruptureO : DebondingΔ : Strain gauge damaged
Figure C-4: Stress-strain relation of CFRP rebar from batch #2.
497
0
500
1000
1500
2000
2500
3000
0 0.005 0.01 0.015 0.02 0.025
Str
es
s (
MP
a)
Strain
Aslan 500, CFRP strip, Specimen 1
Aslan 500, CFRP strip, Specimen 2
● : CFRP rupture
Figure C-5: Stress-strain relation of CFRP strip from batch #3.
Table C-2: Properties of the CFRP materials obtained from tension tests.
CFRP products
(Manufacturer)
Dimensions
(mm)
Afrp
(mm2)
ffrpu
(MPa)
Efrp
(GPa) ɛfrpu
Used for
beam
Batch #1
Aslan 500 CFRP tape
(Hughes Brothers Inc)
2×16 31.2 2624±28 124.4±6.7 0.0211±0.0009
BS-NP-F
BS-P1-F
BS-P2-F
BS-P3-F
BS-NP-FS
BS-P1-FS
BS-P2-FS
Batch #2
Aslan 200 CFRP rebar
(Hughes Brothers Inc)
Ф9.5 71.3 2896* 115.9±1.5 0.025
*
BR-NP-F
BR-P1-F
BR-P2-F
BR-P3-F
Batch #3
Aslan 500 CFRP tape
(Hughes Brothers Inc)
2×16 31.2 2707±5 132±3.1 0.0205±0.0005 BS-P3-FS
* Only one specimen reached CFRP rupture.
498
C.4 Steel Reinforcements
One batch of top reinforcements and two batches of bottom steel reinforcements
were used to make the steel cages: batch #1 includes 15M bars, batch #2 includes 10M
bars, and batch #3 includes 15M bars. Batches #1 and 2 were used to build the steel cages
for the beams in phase I while batches #2 and 3 were used to build the steel cages in
phase II. The specimens were taken from top and bottom steel rebars to obtain the
material properties and corresponding stress-strain curves in tension according to ASTM
A370 (2010). One strain gauge (SG) was installed on each steel bar specimen at the
centre to measure the strain corresponding to the applied load. The 15M bar from batch
#1 had a yield strength of 4929 MPa, a yield strain of 0.002460.00017, and an ultimate
strength of 6546, while the 15M bar from batch #3 had a yield strength of 5330.8 MPa,
a yield strain of 0.002660.00022, and an ultimate strength of 7225 MPa. The 10M bar
from batch #2 had a yield strength of 48816 MPa, a yield strain of 0.002440.00027,
and an ultimate strength of 73919 MPa. The corresponding stress-strain curves of the
steel bars from each batch are presented in Figures C-6 to C-8. It should be mentioned
that after yielding the strain gauges installed on the specimens were damaged in most
cases and therefore the curves were terminated in Figures C-6 to C-8.
499
0
100
200
300
400
500
600
700
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Str
es
s (
MP
a)
Strain
15M Specimen 1
15M Specimen 2
15M Specimen 3
Figure C-6: Stress-strain curve of 15M steel bars in batch #1.
0
100
200
300
400
500
600
700
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Str
es
s (
MP
a)
Strain
10M Specimen 1
10M Specimen 2
10M Specimen 3
Figure C-7: Stress-strain curve of 10M steel bars in batch #2.
500
0
100
200
300
400
500
600
700
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Str
ess (
MP
a)
Strain
15M Specimen 1
15M Specimen 2
Figure C-8: Stress-strain curve of 15M steel bars in batch #3.
501
Appendix D: ANSYS Logs
D.1 Introduction
In this appendix, the files related to ANSYS model generated for the prestressed
NSM-CFRP strengthened beam, BS-P2-R, are printed.
D.2 ANSYS Logs for BS-P2-R
D.2.1 BS-P2-R.mntr
SOLUTION HISTORY INFORMATION FOR JOB: BS-P2-R.mntr
ANSYS RELEASE 12.0 .1 14:54:00 04/13/2011
LOAD STEP
SUB-STEP
NO. ATTM
P
NO. ITER
TOTL ITER
INCREMENT TIME/LFACT
TOTAL TIME/LFA
CT
VARIAB 1 MONITOR
CPU
VARIAB 2 MONITOR
MxDs
VARIAB 3 MONITOR
MxPl
1 1 1 7 7 1.00E-04 1.00E-04 46.598 0.84115 1.93E-02
2 1 1 3 10 0.11999 0.12009 21.481 0.21545 3.59E-04
2 2 1 2 12 0.11999 0.24008 35.381 -0.26924 1.17E-04
2 3 1 2 14 0.17999 0.42007 49.343 -0.45912 1.23E-04
2 4 1 2 16 0.23998 0.66004 63.508 -0.7123 1.33E-04
2 5 1 2 18 0.23998 0.90002 77.548 -0.96547 1.30E-04
2 6 1 2 20 0.14999 1.05 91.495 -1.1237 1.11E-04
2 7 1 2 22 0.14999 1.2 105.57 -1.2819 1.06E-04
3 1 1 2 24 3.50E-02 1.235 14.742 -1.3188 7.47E-05
3 2 1 2 26 3.50E-02 1.27 28.829 -1.3558 7.08E-05
3 3 1 2 28 5.25E-02 1.3225 43.025 -1.4111 7.29E-05
3 4 1 2 30 5.60E-02 1.3785 57.346 -1.4702 7.27E-05
3 5 1 2 32 5.60E-02 1.4345 71.448 -1.5293 7.14E-05
3 6 1 2 34 5.60E-02 1.4905 85.489 -1.5884 6.89E-05
3 7 1 2 36 5.60E-02 1.5465 99.482 -1.6474 6.62E-05
3 8 1 2 38 5.60E-02 1.6025 113.99 -1.7066 6.60E-05
3 9 1 2 40 5.60E-02 1.6585 128.23 -1.766 6.53E-05
3 10 1 18 58 5.60E-02 1.7145 257.14 -1.8718 7.27E-04
3 11 1 2 60 5.60E-02 1.7705 272.56 -1.9327 5.33E-05
3 12 1 2 62 5.60E-02 1.8265 289.16 -1.9937 5.48E-05
3 13 1 3 65 5.60E-02 1.8825 312.06 -2.0551 8.87E-05
502
3 14 1 4 69 5.60E-02 1.9385 341.22 -2.1166 1.19E-04
3 15 1 2 71 5.60E-02 1.9945 356.37 -2.1777 5.13E-05
3 16 1 2 73 5.60E-02 2.0505 371.5 -2.2386 5.23E-05
3 17 1 2 75 5.60E-02 2.1065 386.57 -2.2997 5.23E-05
3 18 1 2 77 5.60E-02 2.1625 401.31 -2.3609 5.17E-05
3 19 1 2 79 5.60E-02 2.2185 415.85 -2.4219 5.16E-05
3 20 1 2 81 5.60E-02 2.2745 430.44 -2.4829 5.14E-05
3 21 1 4 85 5.60E-02 2.3305 458.99 -2.5444 1.14E-04
3 22 1 2 87 5.60E-02 2.3865 473.67 -2.6056 4.78E-05
3 23 1 5 92 5.60E-02 2.4425 509.47 -2.6697 1.39E-04
3 24 1 3 95 5.60E-02 2.4985 531.96 -2.7319 7.61E-05
3 25 1 4 99 5.60E-02 2.5545 560.76 -2.7966 1.00E-04
3 26 1 3 102 5.60E-02 2.6105 582.73 -2.859 7.33E-05
3 27 1 2 104 5.60E-02 2.6665 597.45 -2.9202 4.42E-05
3 28 1 2 106 5.60E-02 2.7225 611.85 -2.9816 4.47E-05
3 29 1 2 108 5.60E-02 2.7785 626.34 -3.0428 4.55E-05
3 30 1 2 110 5.60E-02 2.8345 641.37 -3.1039 4.53E-05
3 31 1 2 112 5.60E-02 2.8905 655.97 -3.1652 4.52E-05
3 32 1 3 115 5.60E-02 2.9465 677.39 -3.2266 7.34E-05
3 33 1 2 117 5.60E-02 3.0025 692.47 -3.2877 4.32E-05
3 34 1 5 122 5.60E-02 3.0585 728.45 -3.3499 1.27E-04
3 35 1 2 124 5.60E-02 3.1145 743.22 -3.4111 4.26E-05
3 36 1 2 126 5.60E-02 3.1705 757.73 -3.4724 4.41E-05
3 37 1 2 128 5.60E-02 3.2265 772.33 -3.5333 4.36E-05
3 38 1 11 139 5.60E-02 3.2825 850.44 -3.5569 3.35E-04
3 39 1 5 144 5.60E-02 3.3385 886.66 -3.6152 1.16E-04
3 40 1 4 148 5.60E-02 3.3945 915.1 -3.6738 9.23E-05
3 41 1 2 150 5.60E-02 3.4505 929.81 -3.7341 4.02E-05
3 42 1 2 152 5.60E-02 3.5065 944.4 -3.7944 4.14E-05
3 43 1 2 154 5.60E-02 3.5625 959.11 -3.8548 4.13E-05
3 44 1 2 156 5.60E-02 3.6185 974.3 -3.9147 4.03E-05
3 45 1 2 158 5.60E-02 3.6745 988.94 -3.9742 3.98E-05
3 46 1 3 161 5.60E-02 3.7305 1010.3 -4.0336 6.68E-05
3 47 1 2 163 5.60E-02 3.7865 1025.1 -4.0936 3.95E-05
3 48 1 7 170 5.60E-02 3.8425 1074.8 -4.1495 1.63E-04
3 49 1 4 174 5.60E-02 3.8985 1103.2 -4.2099 8.64E-05
3 50 1 2 176 5.60E-02 3.9545 1117.7 -4.2702 3.84E-05
3 51 1 2 178 4.55E-02 4 1132.6 -4.3191 3.83E-05
4 1 1 7 185 0.8 4.8 52.073 -5.1716 2.23E-04
4 2 1 18 203 0.8 5.6 184 -5.9885 4.38E-04
503
4 3 1 5 208 0.8 6.4 220.96 -6.8395 2.78E-04
4 4 1 5 213 1.2 7.6 258.28 -8.1193 2.06E-04
4 5 1 14 227 1.6 9.2 360.83 -9.7927 4.50E-04
4 6 1 7 234 1.6 10.8 413.22 -11.49 2.62E-04
4 7 1 35 269 1.6 12.4 671.02 -13.167 9.91E-04
4 8 7 3 512 1.88E-02 12.419 2454.5 -13.187 7.08E-05
4 9 1 16 528 1.88E-02 12.438 2572.3 -13.206 3.59E-04
4 10 1 2 530 1.88E-02 12.456 2587.6 -13.226 8.22E-05
4 11 1 2 532 2.81E-02 12.484 2603.3 -13.255 3.32E-05
4 12 1 4 536 4.22E-02 12.527 2633.6 -13.299 7.35E-05
4 13 1 2 538 4.22E-02 12.569 2648.9 -13.344 3.05E-05
4 14 1 2 540 6.33E-02 12.632 2664.1 -13.411 3.27E-05
4 15 1 5 545 9.49E-02 12.727 2701.3 -13.511 1.00E-04
4 16 1 2 547 9.49E-02 12.822 2716.8 -13.611 3.33E-05
4 17 1 2 549 0.14238 12.964 2733.3 -13.762 3.91E-05
4 18 1 2 551 0.21357 13.178 2750 -13.988 4.73E-05
4 19 1 4 555 0.32036 13.498 2780.8 -14.328 1.04E-04
4 20 1 4 559 0.32036 13.819 2811.3 -14.667 9.99E-05
4 21 1 14 573 0.48054 14.299 2917.7 -15.172 3.57E-04
4 22 1 7 580 0.48054 14.78 2973 -15.679 2.02E-04
4 23 1 13 593 0.72081 15.5 3072 -16.439 6.04E-04
4 24 1 25 618 0.72081 16.221 3266.3 -17.192 2.60E-03
4 25 1 6 624 0.72081 16.942 3311.5 -17.955 4.80E-04
4 26 1 25 649 1.0812 18.023 3510.3 -19.09 1.63E-03
4 27 1 16 665 1.0812 19.105 3636.3 -20.23 7.91E-04
4 28 1 6 671 0.89548 20 3681 -21.176 4.65E-04
5 1 1 2 673 0.15 20.15 14.851 -21.335 8.25E-05
5 2 1 17 690 0.15 20.3 134.66 -21.508 7.17E-04
5 3 1 2 692 0.15 20.45 149.29 -21.666 8.06E-05
5 4 1 5 697 0.225 20.675 185.56 -21.904 2.28E-04
5 5 1 2 699 0.225 20.9 201.68 -22.142 9.88E-05
5 6 1 3 702 0.3375 21.237 224.24 -22.499 1.80E-04
5 7 1 3 705 0.4 21.637 247.7 -22.921 2.16E-04
5 8 1 3 708 0.4 22.037 269.65 -23.344 2.08E-04
5 9 1 4 712 0.4 22.437 299.66 -23.766 2.52E-04
5 10 1 4 716 0.4 22.837 331.42 -24.188 2.16E-04
5 11 1 5 721 0.4 23.237 368.04 -24.61 3.10E-04
5 12 1 14 735 0.4 23.637 467.07 -25.031 5.32E-04
5 13 1 3 738 0.4 24.037 489.17 -25.454 1.76E-04
5 14 1 5 743 0.4 24.437 524.44 -25.876 2.30E-04
504
5 15 1 3 746 0.4 24.837 546.63 -26.3 1.76E-04
5 16 1 13 759 0.4 25.237 637.05 -26.746 5.53E-04
5 17 1 14 773 0.4 25.637 735.25 -27.196 6.17E-04
5 18 1 14 787 0.3625 26 832.5 -27.604 5.40E-04
6 1 1 13 800 1.7 27.7 89.997 -29.484 1.27E-03
6 2 1 15 815 1.7 29.4 192.38 -31.383 1.38E-03
6 3 1 13 828 1.7 31.1 281.83 -33.259 1.09E-03
6 4 1 13 841 1.7 32.8 371.42 -35.143 1.01E-03
6 5 1 14 855 1.7 34.5 467.74 -37.016 1.00E-03
6 6 1 16 871 1.7 36.2 578.7 -38.887 1.31E-03
6 7 1 12 883 1.7 37.9 662.91 -40.762 1.02E-03
6 8 1 20 903 1.7 39.6 800.77 -42.638 1.67E-03
6 9 1 12 915 1.7 41.3 884.96 -44.521 1.21E-03
6 10 1 15 930 1.7 43 989.98 -46.39 1.50E-03
6 11 1 21 951 1.7 44.7 1135.6 -48.239 1.69E-03
6 12 1 10 961 1.7 46.4 1205.8 -50.114 9.88E-04
6 13 1 17 978 1.7 48.1 1323.7 -51.985 1.60E-03
6 14 1 13 991 1.7 49.8 1414.4 -53.845 2.00E-03
6 15 1 12 1003 1.7 51.5 1497.8 -55.718 1.18E-03
6 16 1 15 1018 1.7 53.2 1602.4 -57.574 1.24E-03
6 17 1 30 1048 1.7 54.9 1810.5 -59.401 2.80E-03
6 18 1 17 1065 1.7 56.6 1928.5 -61.234 1.25E-03
6 19 1 14 1079 1.7 58.3 2027.1 -63.082 1.15E-03
6 20 1 10 1089 1.7 60 2097.9 -64.93 8.16E-04
7 1 2 6 1155 1.5 61.5 546.49 -66.556 7.84E-04
7 2 2 15 1230 0.75 62.25 1166.7 -67.346 2.67E-03
7 3 1 7 1237 0.75 63 1219.5 -68.156 8.10E-04
7 4 3 5 1362 0.28125 63.281 2264.8 -68.456 4.56E-04
7 5 1 5 1367 0.28125 63.562 2299.8 -68.756 6.39E-04
7 6 1 7 1374 0.42188 63.984 2348.4 -69.212 9.81E-04
7 7 1 5 1379 0.42188 64.406 2384.4 -69.667 2.16E-03
7 8 1 4 1383 0.63281 65.039 2415 -70.362 4.29E-04
7 9 1 5 1388 0.94922 65.988 2454.7 -71.395 4.76E-04
7 10 1 8 1396 1.4238 67.412 2513 -72.959 9.88E-04
7 11 1 12 1408 1.4238 68.836 2604.2 -74.504 1.61E-03
7 12 1 21 1429 1.4238 70.26 2772.5 -76.024 3.50E-03
7 13 1 12 1441 1.4238 71.684 2866 -77.559 1.80E-03
7 14 2 9 1510 0.71191 72.396 3456.9 -78.32 1.03E-03
7 15 2 6 1576 0.35596 72.751 4055.1 -78.698 1.44E-03
7 16 1 6 1582 0.35596 73.107 4098.6 -79.082 6.00E-04
505
7 17 4 3 1765 6.67E-02 73.174 5723.6 -79.153 7.18E-04
7 18 1 4 1769 6.67E-02 73.241 5755.8 -79.223 1.40E-02
D.2.2 BS-P2-R.BSC
=========================== = multifrontal statistics = =========================== number of equations = 42060 no. of nonzeroes in lower triangle of a = 1097883 number of compressed nodes = 14791 no. of compressed nonzeroes in l. tri. = 165588 amount of workspace currently in use = 14502137 max. amt. of workspace used = 59562212 no. of nonzeroes in the factor l = 11428652. number of super nodes = 2056 number of compressed subscripts = 285253 size of stack storage = 1000055 maximum order of a front matrix = 1124 maximum size of a front matrix = 632250 maximum size of a front trapezoid = 69856 no. of floating point ops for factor = 4.6494D+09 no. of floating point ops for solve = 4.5925D+07 actual no. of nonzeroes in the factor l = 11428652. actual number of compressed subscripts = 285253 actual size of stack storage used = 1095494 near zero pivot monitoring activated number of pivots adjusted = 0. negative pivot monitoring activated number of negative pivots encountered = 0. factorization panel size = 64 factorization update panel size = 32 solution block size = 2 time (cpu & wall) for structure input = 0.124023 0.139528 time (cpu & wall) for ordering = 0.375000 0.376673 time (cpu & wall) for symbolic factor = 0.015625 0.015230 time (cpu & wall) for value input = 0.155273 0.154428 time (cpu & wall) for numeric factor = 2.636719 1.344835 computational rate (mflops) for factor = 1763.334716 3457.240852 condition number estimate = 0.0000D+00 time (cpu & wall) for numeric solve = 0.078125 0.040978 computational rate (mflops) for solve = 587.838822 1120.723815 effective I/O rate (MB/sec) for solve = 2239.665880 4269.957671
no input or output performed
D.2.3 BS-P2-R.stat
Sparse Solver : curEqn= 42060 totEqn= 42060 Job CP sec= 8345.788 Factor done= 100% Factor Wall sec= 0.0 rate= 0.0 Mflops
506
D.2.4 BS-P2-R.s01
/COM,ANSYS RELEASE 12.0.1 UP20090415 14:53:41 04/13/2011 /NOPR /TITLE,BS-P2-R _LSNUM= 1 ANTYPE, 0 RESCONTROL,DEFINE,ALL ,ALL , 1 BFUNIF,TEMP,_TINY AUTOTS,ON NSUBST, 1, 1, 1, KUSE, 0 TIME, 1.000000000E-04 TREF, 0.00000000 ALPHAD, 0.00000000 BETAD, 0.00000000 DMPRAT, 0.00000000 CNVTOL,U , 1.00000000 , 1.000000000E-02, 2, -1.00000000 CRPLIM, 0.100000000 , 0 CRPLIM, 0.00000000 , 1 NCNV, 1, 0.00000000 , 0, 0.00000000 , 0.00000000 LNSRCH,ON NEQIT, 40 ERESX,DEFA OUTPR,BASI, ALL, OUTRES,NSOL, ALL, OUTRES,RSOL, ALL, OUTRES,ESOL, ALL, OUTRES,NLOA, ALL, OUTRES,STRS, ALL, OUTRES,EPEL, ALL, OUTRES,EPPL, ALL, OUTRES, ALL, ALL, ACEL, 0.00000000 , 0.00000000 , 0.00000000 OMEGA, 0.00000000 , 0.00000000 , 0.00000000, 0 DOMEGA, 0.00000000 , 0.00000000 , 0.00000000 CGLOC, 0.00000000 , 0.00000000 , 0.00000000 CGOMEGA, 0.00000000 , 0.00000000 , 0.00000000 DCGOMG, 0.00000000 , 0.00000000 , 0.00000000 IRLF, 0 D, 6,UZ , 0.00000000 , 0.00000000 . D, 14913,UZ , 0.00000000 , 0.00000000 D, 266,UX , 0.00000000 , 0.00000000 . D, 11716,UX , 0.00000000 , 0.00000000 D, 14806,UY , 0.00000000 , 0.00000000 . D, 14815,UY , 0.00000000 , 0.00000000 BFE, 5204,TEMP, 1, 659.550000 BFE, 5204,TEMP, 2, 659.550000 BFE, 5204,TEMP, 3, 659.550000 BFE, 5204,TEMP, 4, 659.550000 BFE, 5204,TEMP, 5, 659.550000 BFE, 5204,TEMP, 6, 659.550000 BFE, 5204,TEMP, 7, 659.550000
507
BFE, 5204,TEMP, 8, 659.550000 . BFE, 8763,TEMP, 1, 659.550000 BFE, 8763,TEMP, 2, 659.550000 BFE, 8763,TEMP, 3, 659.550000 BFE, 8763,TEMP, 4, 659.550000 BFE, 8763,TEMP, 5, 659.550000 BFE, 8763,TEMP, 6, 659.550000 BFE, 8763,TEMP, 7, 659.550000 BFE, 8763,TEMP, 8, 659.550000 /GOPR
D.2.5 BS-P2-R.s02
/COM,ANSYS RELEASE 12.0.1 UP20090415 14:57:06 04/13/2011 /NOPR /TITLE,BS-P2-R _LSNUM= 2 ANTYPE, 0 RESCONTROL,DEFINE,ALL ,ALL , 1 BFUNIF,TEMP,_TINY AUTOTS,ON NSUBST, 10, 40, 5, KUSE, 0 TIME, 1.20000000 TREF, 0.00000000 ALPHAD, 0.00000000 BETAD, 0.00000000 DMPRAT, 0.00000000 CNVTOL,U , 1.00000000 , 1.000000000E-02, 2, -1.00000000 CRPLIM, 0.100000000 , 0 CRPLIM, 0.00000000 , 1 NCNV, 1, 0.00000000 , 0, 0.00000000 , 0.00000000 LNSRCH,ON NEQIT, 40 ERESX,DEFA OUTPR,BASI, ALL, OUTRES,NSOL, ALL, OUTRES,RSOL, ALL, OUTRES,ESOL, ALL, OUTRES,NLOA, ALL, OUTRES,STRS, ALL, OUTRES,EPEL, ALL, OUTRES,EPPL, ALL, OUTRES, ALL, ALL, ACEL, 0.00000000 , 0.00000000 , 0.00000000 OMEGA, 0.00000000 , 0.00000000 , 0.00000000, 0 DOMEGA, 0.00000000 , 0.00000000 , 0.00000000 CGLOC, 0.00000000 , 0.00000000 , 0.00000000 CGOMEGA, 0.00000000 , 0.00000000 , 0.00000000 DCGOMG, 0.00000000 , 0.00000000 , 0.00000000 IRLF, 0 D, 6,UZ , 0.00000000 , 0.00000000 . D, 14913,UZ , 0.00000000 , 0.00000000 D, 266,UX , 0.00000000 , 0.00000000
508
. D, 11716,UX , 0.00000000 , 0.00000000 D, 14806,UY , 0.00000000 , 0.00000000 . D, 14815,UY , 0.00000000 , 0.00000000 D, 14824,UY , -1.20000000 , 0.00000000 D, 14830,UY , -1.20000000 , 0.00000000 D, 14839,UY , -1.20000000 , 0.00000000 D, 14842,UY , -1.20000000 , 0.00000000 D, 14851,UY , -1.20000000 , 0.00000000 D, 14854,UY , -1.20000000 , 0.00000000 BFE, 5204,TEMP, 1, 659.550000 BFE, 5204,TEMP, 2, 659.550000 BFE, 5204,TEMP, 3, 659.550000 BFE, 5204,TEMP, 4, 659.550000 BFE, 5204,TEMP, 5, 659.550000 BFE, 5204,TEMP, 6, 659.550000 BFE, 5204,TEMP, 7, 659.550000 BFE, 5204,TEMP, 8, 659.550000 . BFE, 8763,TEMP, 1, 659.550000 BFE, 8763,TEMP, 2, 659.550000 BFE, 8763,TEMP, 3, 659.550000 BFE, 8763,TEMP, 4, 659.550000 BFE, 8763,TEMP, 5, 659.550000 BFE, 8763,TEMP, 6, 659.550000 BFE, 8763,TEMP, 7, 659.550000 BFE, 8763,TEMP, 8, 659.550000 /GOPR
D.2.6 BS-P2-R.s03
/COM,ANSYS RELEASE 12.0.1 UP20090415 15:04:30 04/13/2011 /NOPR /TITLE,BS-P2-R _LSNUM= 3 ANTYPE, 0 RESCONTROL,DEFINE,ALL ,ALL , 1 BFUNIF,TEMP,_TINY AUTOTS,ON NSUBST, 80, 100, 50, KUSE, 0 TIME, 4.00000000 TREF, 0.00000000 ALPHAD, 0.00000000 BETAD, 0.00000000 DMPRAT, 0.00000000 CNVTOL,U , 1.00000000 , 5.000000000E-02, 2, -1.00000000 CRPLIM, 0.100000000 , 0 CRPLIM, 0.00000000 , 1 NCNV, 1, 0.00000000 , 0, 0.00000000 , 0.00000000 LNSRCH,ON NEQIT, 40 ERESX,DEFA OUTPR,BASI, ALL, OUTRES,NSOL, ALL,
509
OUTRES,RSOL, ALL, OUTRES,ESOL, ALL, OUTRES,NLOA, ALL, OUTRES,STRS, ALL, OUTRES,EPEL, ALL, OUTRES,EPPL, ALL, OUTRES, ALL, ALL, ACEL, 0.00000000 , 0.00000000 , 0.00000000 OMEGA, 0.00000000 , 0.00000000 , 0.00000000, 0 DOMEGA, 0.00000000 , 0.00000000 , 0.00000000 CGLOC, 0.00000000 , 0.00000000 , 0.00000000 CGOMEGA, 0.00000000 , 0.00000000 , 0.00000000 DCGOMG, 0.00000000 , 0.00000000 , 0.00000000 IRLF, 0 D, 6,UZ , 0.00000000 , 0.00000000 . D, 14913,UZ , 0.00000000 , 0.00000000 D, 266,UX , 0.00000000 , 0.00000000 . D, 11716,UX , 0.00000000 , 0.00000000 D, 14806,UY , 0.00000000 , 0.00000000 . D, 14815,UY , 0.00000000 , 0.00000000 D, 14824,UY , -4.00000000 , 0.00000000 D, 14830,UY , -4.00000000 , 0.00000000 D, 14839,UY , -4.00000000 , 0.00000000 D, 14842,UY , -4.00000000 , 0.00000000 D, 14851,UY , -4.00000000 , 0.00000000 D, 14854,UY , -4.00000000 , 0.00000000 BFE, 5204,TEMP, 1, 659.550000 BFE, 5204,TEMP, 2, 659.550000 BFE, 5204,TEMP, 3, 659.550000 BFE, 5204,TEMP, 4, 659.550000 BFE, 5204,TEMP, 5, 659.550000 BFE, 5204,TEMP, 6, 659.550000 BFE, 5204,TEMP, 7, 659.550000 BFE, 5204,TEMP, 8, 659.550000 . BFE, 8763,TEMP, 1, 659.550000 BFE, 8763,TEMP, 2, 659.550000 BFE, 8763,TEMP, 3, 659.550000 BFE, 8763,TEMP, 4, 659.550000 BFE, 8763,TEMP, 5, 659.550000 BFE, 8763,TEMP, 6, 659.550000 BFE, 8763,TEMP, 7, 659.550000 BFE, 8763,TEMP, 8, 659.550000 /GOPR
D.2.7 BS-P2-R.s04
/COM,ANSYS RELEASE 12.0.1 UP20090415 15:24:09 04/13/2011 /NOPR /TITLE,BS-P2-R _LSNUM= 4 ANTYPE, 0 RESCONTROL,DEFINE,ALL ,ALL , 1
510
BFUNIF,TEMP,_TINY AUTOTS,ON NSUBST, 20, 10000, 10, KUSE, 0 TIME, 20.0000000 TREF, 0.00000000 ALPHAD, 0.00000000 BETAD, 0.00000000 DMPRAT, 0.00000000 CNVTOL,U , 1.00000000 , 5.000000000E-02, 2, -1.00000000 CRPLIM, 0.100000000 , 0 CRPLIM, 0.00000000 , 1 NCNV, 1, 0.00000000 , 0, 0.00000000 , 0.00000000 LNSRCH,ON NEQIT, 40 ERESX,DEFA OUTPR,BASI, ALL, OUTRES,NSOL, ALL, OUTRES,RSOL, ALL, OUTRES,ESOL, ALL, OUTRES,NLOA, ALL, OUTRES,STRS, ALL, OUTRES,EPEL, ALL, OUTRES,EPPL, ALL, OUTRES, ALL, ALL, ACEL, 0.00000000 , 0.00000000 , 0.00000000 OMEGA, 0.00000000 , 0.00000000 , 0.00000000, 0 DOMEGA, 0.00000000 , 0.00000000 , 0.00000000 CGLOC, 0.00000000 , 0.00000000 , 0.00000000 CGOMEGA, 0.00000000 , 0.00000000 , 0.00000000 DCGOMG, 0.00000000 , 0.00000000 , 0.00000000 IRLF, 0 D, 6,UZ , 0.00000000 , 0.00000000 . D, 14913,UZ , 0.00000000 , 0.00000000 D, 266,UX , 0.00000000 , 0.00000000 . D, 11716,UX , 0.00000000 , 0.00000000 D, 14806,UY , 0.00000000 , 0.00000000 . D, 14815,UY , 0.00000000 , 0.00000000 D, 14824,UY , -20.0000000 , 0.00000000 D, 14830,UY , -20.0000000 , 0.00000000 D, 14839,UY , -20.0000000 , 0.00000000 D, 14842,UY , -20.0000000 , 0.00000000 D, 14851,UY , -20.0000000 , 0.00000000 D, 14854,UY , -20.0000000 , 0.00000000 BFE, 5204,TEMP, 1, 659.550000 BFE, 5204,TEMP, 2, 659.550000 BFE, 5204,TEMP, 3, 659.550000 BFE, 5204,TEMP, 4, 659.550000 BFE, 5204,TEMP, 5, 659.550000 BFE, 5204,TEMP, 6, 659.550000 BFE, 5204,TEMP, 7, 659.550000 BFE, 5204,TEMP, 8, 659.550000 . BFE, 8763,TEMP, 1, 659.550000
511
BFE, 8763,TEMP, 2, 659.550000 BFE, 8763,TEMP, 3, 659.550000 BFE, 8763,TEMP, 4, 659.550000 BFE, 8763,TEMP, 5, 659.550000 BFE, 8763,TEMP, 6, 659.550000 BFE, 8763,TEMP, 7, 659.550000 BFE, 8763,TEMP, 8, 659.550000 /GOPR
D.2.8 BS-P2-R.s05
/COM,ANSYS RELEASE 12.0.1 UP20090415 16:59:46 04/13/2011 /NOPR /TITLE,BS-P2-R _LSNUM= 5 ANTYPE, 0 RESCONTROL,DEFINE,ALL ,ALL , 1 BFUNIF,TEMP,_TINY AUTOTS,ON NSUBST, 40, 10000, 15, KUSE, 0 TIME, 26.0000000 TREF, 0.00000000 ALPHAD, 0.00000000 BETAD, 0.00000000 DMPRAT, 0.00000000 CNVTOL,U , 1.00000000 , 5.000000000E-02, 2, -1.00000000 CRPLIM, 0.100000000 , 0 CRPLIM, 0.00000000 , 1 NCNV, 1, 0.00000000 , 0, 0.00000000 , 0.00000000 LNSRCH,ON NEQIT, 40 ERESX,DEFA OUTPR,BASI, ALL, OUTRES,NSOL, ALL, OUTRES,RSOL, ALL, OUTRES,ESOL, ALL, OUTRES,NLOA, ALL, OUTRES,STRS, ALL, OUTRES,EPEL, ALL, OUTRES,EPPL, ALL, OUTRES, ALL, ALL, ACEL, 0.00000000 , 0.00000000 , 0.00000000 OMEGA, 0.00000000 , 0.00000000 , 0.00000000, 0 DOMEGA, 0.00000000 , 0.00000000 , 0.00000000 CGLOC, 0.00000000 , 0.00000000 , 0.00000000 CGOMEGA, 0.00000000 , 0.00000000 , 0.00000000 DCGOMG, 0.00000000 , 0.00000000 , 0.00000000 IRLF, 0 D, 6,UZ , 0.00000000 , 0.00000000 . D, 14913,UZ , 0.00000000 , 0.00000000 D, 266,UX , 0.00000000 , 0.00000000 . D, 11716,UX , 0.00000000 , 0.00000000 D, 14806,UY , 0.00000000 , 0.00000000
512
. D, 14815,UY , 0.00000000 , 0.00000000 D, 14824,UY , -26.0000000 , 0.00000000 D, 14830,UY , -26.0000000 , 0.00000000 D, 14839,UY , -26.0000000 , 0.00000000 D, 14842,UY , -26.0000000 , 0.00000000 D, 14851,UY , -26.0000000 , 0.00000000 D, 14854,UY , -26.0000000 , 0.00000000 BFE, 5204,TEMP, 1, 659.550000 BFE, 5204,TEMP, 2, 659.550000 BFE, 5204,TEMP, 3, 659.550000 BFE, 5204,TEMP, 4, 659.550000 BFE, 5204,TEMP, 5, 659.550000 BFE, 5204,TEMP, 6, 659.550000 BFE, 5204,TEMP, 7, 659.550000 BFE, 5204,TEMP, 8, 659.550000 . BFE, 8763,TEMP, 1, 659.550000 BFE, 8763,TEMP, 2, 659.550000 BFE, 8763,TEMP, 3, 659.550000 BFE, 8763,TEMP, 4, 659.550000 BFE, 8763,TEMP, 5, 659.550000 BFE, 8763,TEMP, 6, 659.550000 BFE, 8763,TEMP, 7, 659.550000 BFE, 8763,TEMP, 8, 659.550000 /GOPR
D.2.9 BS-P2-R.s06
/COM,ANSYS RELEASE 12.0.1 UP20090415 17:14:44 04/13/2011 /NOPR /TITLE,BS-P2-R _LSNUM= 6 ANTYPE, 0 RESCONTROL,DEFINE,ALL ,ALL , 1 BFUNIF,TEMP,_TINY AUTOTS,ON NSUBST, 20, 10000, 10, KUSE, 0 TIME, 60.0000000 TREF, 0.00000000 ALPHAD, 0.00000000 BETAD, 0.00000000 DMPRAT, 0.00000000 CNVTOL,U , 1.00000000 , 5.000000000E-02, 2, -1.00000000 CRPLIM, 0.100000000 , 0 CRPLIM, 0.00000000 , 1 NCNV, 1, 0.00000000 , 0, 0.00000000 , 0.00000000 LNSRCH,ON NEQIT, 60 ERESX,DEFA OUTPR,BASI, ALL, OUTRES,NSOL, ALL, OUTRES,RSOL, ALL, OUTRES,ESOL, ALL, OUTRES,NLOA, ALL,
513
OUTRES,STRS, ALL, OUTRES,EPEL, ALL, OUTRES,EPPL, ALL, OUTRES, ALL, ALL, ACEL, 0.00000000 , 0.00000000 , 0.00000000 OMEGA, 0.00000000 , 0.00000000 , 0.00000000, 0 DOMEGA, 0.00000000 , 0.00000000 , 0.00000000 CGLOC, 0.00000000 , 0.00000000 , 0.00000000 CGOMEGA, 0.00000000 , 0.00000000 , 0.00000000 DCGOMG, 0.00000000 , 0.00000000 , 0.00000000 IRLF, 0 D, 6,UZ , 0.00000000 , 0.00000000 . D, 14913,UZ , 0.00000000 , 0.00000000 D, 266,UX , 0.00000000 , 0.00000000 . D, 11716,UX , 0.00000000 , 0.00000000 D, 14806,UY , 0.00000000 , 0.00000000 . D, 14815,UY , 0.00000000 , 0.00000000 D, 14824,UY , -60.0000000 , 0.00000000 D, 14830,UY , -60.0000000 , 0.00000000 D, 14839,UY , -60.0000000 , 0.00000000 D, 14842,UY , -60.0000000 , 0.00000000 D, 14851,UY , -60.0000000 , 0.00000000 D, 14854,UY , -60.0000000 , 0.00000000 BFE, 5204,TEMP, 1, 659.550000 BFE, 5204,TEMP, 2, 659.550000 BFE, 5204,TEMP, 3, 659.550000 BFE, 5204,TEMP, 4, 659.550000 BFE, 5204,TEMP, 5, 659.550000 BFE, 5204,TEMP, 6, 659.550000 BFE, 5204,TEMP, 7, 659.550000 BFE, 5204,TEMP, 8, 659.550000 . BFE, 8763,TEMP, 1, 659.550000 BFE, 8763,TEMP, 2, 659.550000 BFE, 8763,TEMP, 3, 659.550000 BFE, 8763,TEMP, 4, 659.550000 BFE, 8763,TEMP, 5, 659.550000 BFE, 8763,TEMP, 6, 659.550000 BFE, 8763,TEMP, 7, 659.550000 BFE, 8763,TEMP, 8, 659.550000
D.2.10 BS-P2-R.s07
/COM,ANSYS RELEASE 12.0.1 UP20090415 17:50:07 04/13/2011 /NOPR /TITLE,BS-P2-R _LSNUM= 7 ANTYPE, 0 RESCONTROL,DEFINE,ALL ,ALL , 1 BFUNIF,TEMP,_TINY AUTOTS,ON NSUBST, 20, 10000, 10, KUSE, 0
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TIME, 120.000000 TREF, 0.00000000 ALPHAD, 0.00000000 BETAD, 0.00000000 DMPRAT, 0.00000000 CNVTOL,U , 1.00000000 , 5.000000000E-02, 2, -1.00000000 CRPLIM, 0.100000000 , 0 CRPLIM, 0.00000000 , 1 NCNV, 1, 0.00000000 , 0, 0.00000000 , 0.00000000 LNSRCH,ON NEQIT, 60 ERESX,DEFA OUTPR,BASI, ALL, OUTRES,NSOL, ALL, OUTRES,RSOL, ALL, OUTRES,ESOL, ALL, OUTRES,NLOA, ALL, OUTRES,STRS, ALL, OUTRES,EPEL, ALL, OUTRES,EPPL, ALL, OUTRES, ALL, ALL, ACEL, 0.00000000 , 0.00000000 , 0.00000000 OMEGA, 0.00000000 , 0.00000000 , 0.00000000, 0 DOMEGA, 0.00000000 , 0.00000000 , 0.00000000 CGLOC, 0.00000000 , 0.00000000 , 0.00000000 CGOMEGA, 0.00000000 , 0.00000000 , 0.00000000 DCGOMG, 0.00000000 , 0.00000000 , 0.00000000 IRLF, 0 D, 6,UZ , 0.00000000 , 0.00000000 . D, 14913,UZ , 0.00000000 , 0.00000000 D, 266,UX , 0.00000000 , 0.00000000 . D, 11716,UX , 0.00000000 , 0.00000000 D, 14806,UY , 0.00000000 , 0.00000000 . D, 14815,UY , 0.00000000 , 0.00000000 D, 14824,UY , -120.000000 , 0.00000000 D, 14830,UY , -120.000000 , 0.00000000 D, 14839,UY , -120.000000 , 0.00000000 D, 14842,UY , -120.000000 , 0.00000000 D, 14851,UY , -120.000000 , 0.00000000 D, 14854,UY , -120.000000 , 0.00000000 BFE, 5204,TEMP, 1, 659.550000 BFE, 5204,TEMP, 2, 659.550000 BFE, 5204,TEMP, 3, 659.550000 BFE, 5204,TEMP, 4, 659.550000 BFE, 5204,TEMP, 5, 659.550000 BFE, 5204,TEMP, 6, 659.550000 BFE, 5204,TEMP, 7, 659.550000 BFE, 5204,TEMP, 8, 659.550000 . BFE, 8763,TEMP, 1, 659.550000 BFE, 8763,TEMP, 2, 659.550000 BFE, 8763,TEMP, 3, 659.550000 BFE, 8763,TEMP, 4, 659.550000 BFE, 8763,TEMP, 5, 659.550000
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BFE, 8763,TEMP, 6, 659.550000 BFE, 8763,TEMP, 7, 659.550000 BFE, 8763,TEMP, 8, 659.550000
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Appendix E: Developed Computational Source Code in Mathematica
E.1 Introduction
The developed code for calculation of the load-deflection response of the exposed
beams explained in Section 5.5 is presented in this section. The first step is to define the
stress-strain curve of the exposed concrete as a function so that it can be used by the
source code for calculation of the load-deflection response.
E.2 Calculation of the Exposed Concrete Stress-Strain Curve
The concepts and procedure for the calculation of the exposed concrete stress-
stress curve is presented in Section 5.5.3.1. To facilitate the trend of the analysis the
described procedure was performed by developing a small code in Mathematica as
below:
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E.3 Computational Source Code
The computational source code for calculation of the load-deflection response of
the RC beams strengthened using NSM CFRP reinforcements subjected to the freeze-
thaw exposure is similar to the one presented in Appendix A excepts that the inputs are
different. For instance, the solution for beams BS-P3-F is presented in this section.
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