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Evaluation of deteriorated reinforced concrete channel beam bridge decks retrofit with glass fibre reinforced… Ross, Sherrill L. 2000

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E V A L U A T I O N O F D E T E R I O R A T E D R E I N F O R C E D C O N C R E T E C H A N N E L B E A M B R I D G E D E C K S R E T R O F I T W I T H G L A S S F I B R E R E I N F O R C E D P O L Y M E R S by S H E R R I L L L . R O S S B.Sc . University o f Alberta, 1998 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A P P L I E D S C I E N C E in T H E F A C U L T Y O F G R A D U A T E S T U D I E S Department o f C iv i l Engineering We accept this thesis as conforming To the required standard U N I V E R S I T Y O F B R I T I S H C O L U M B I A August, 2000 ©Sherr i l l L . R o s s , 2000 In p resen t ing this thesis in part ial fu l f i lment of the requ i rements fo r an a d v a n c e d d e g r e e at the Un ivers i ty of Br i t ish C o l u m b i a , I agree that the Library shall m a k e it f ree ly avai lable fo r re fe rence and s tudy. I fur ther agree that pe rm iss i on for ex tens ive c o p y i n g of th is thes is fo r scho lar ly p u r p o s e s may b e g ran ted by the h e a d of m y depa r tmen t o r by his o r her representat ives. It is u n d e r s t o o d that c o p y i n g o r p u b l i c a t i o n o f th is thesis for f inanc ia l ga in shal l no t b e a l l o w e d w i t h o u t m y wr i t ten p e r m i s s i o n . D e p a r t m e n t of f,/'vi."l E f l ^ i t ^ r i / y j T h e Univers i ty of Bri t ish C o l u m b i a V a n c o u v e r , C a n a d a Da te D E - 6 (2/88) ABSTRACT There are several highway bridges in British Columbia constructed of reinforced concrete channel beam sections. These beams were a standard section used for highway bridge construction in British Columbia in the late 1950s and early 1960s. With years of use, these channel beam bridges have deteriorated. Because of this damage, the existing strength of these bridges has been questioned. Bridges with excessive deterioration must either be replaced or repaired. Replacing all of the channel beam bridges in British Columbia will be very expensive. If these bridges can be repaired rather than replaced there will be a significant cost saving for the taxpayers of British Columbia. One possible retrofit alternative is to repair reinforced concrete channel beam bridges using glass fibre reinforced polymers (GFRP). GFRP consists of thin diameter fiberglass reinforcing fibres in a polymer matrix. The use of GFRP for structural repair is relatively new. GFRP has the potential to be an effective retrofit material for these structures because of its high strength and stiffness, low specific weight, and resistance to corrosion. This study presents an evaluation of deteriorated reinforced concrete channel beam highway bridges retrofit with different types of GFRP. The use of two different types of GFRP retrofit materials are investigated including a traditional GFRP wrap, and a new GFRP spray material. The structural response of channel beam bridge decks with and without GFRP retrofit is found from an experimental program, finite element analysis, and design calculations. The effects of the two different types of GFRP on bridge deck structural properties are compared to non-retrofit bridge decks based on experimental and analytical results. Study results are also used to provide a comparison between the two different types of GFRP retrofit material. The accuracy of design calculation procedures for determining structural properties of GFRP retrofit channel beams is also determined in this study by comparing design calculation and experimental values. Based on the results of this study, recommendations regarding retrofitting British Columbia's channel beam highway bridges with GFRP are made. ii TABLE OF CONTENTS A B S T R A C T ii T A B L E OF CONTENTS iii LIST O F T A B L E S xi LIST OF FIGURES xiii LIST OF PHOTOS xvi A C K N O W L E D G E M E N T S xvii C H A P T E R 1 - INTRODUCTION 1.0 Introduction 1 2.0 Channel Beam Bridges in British Columbia 1 3.0 Objectives of Study 3 C H A P T E R 2 - L I T E R A T U R E REVIEW 1.0 Introduction 5 2.0 Causes of Structural Deficiency in Reinforced Concrete Bridges 6 2.1 Alkali Aggregate Reaction 6 2.2 Freeze-Thaw and Deicing Chemicals 7 2.3 Carbonation Causing Corrosion of Reinforcing Bars 7 2.4 Corrosion of Reinforcing Steel 8 3.0 Tested Bridges Have More Strength Than Predicted by Analytical Methods 8 3.1 Stiffness 8 3.2 Conservative Design 9 iii Table of Contents 4.0 Bridge Retrofit Advantages and Options 9 4.1 Benefits of Repair Compared to Replacement 9 4.2 Retrofit Options 10 5.0 Retrofit Materials 10 5.1 Steel Plate 10 5.1.1 Application 10 5.1.2 Advantages and Disadvantages 11 5.2 Fibre Reinforced Polymers 11 5.2.1 Components of Fibre Reinforced Polymers 11 5.2.2 Advantages of FRP 12 5.2.3 Disadvantages of FRP 12 5.3 Fibre Reinforced Plastic Wrap 13 5.3.1 Application 13 5.4 Fibre Reinforced Plastic Spray 13 5.4.1 Application 14 5.4.2 Advantages and Disadvantages of Sprayed FRP Compared to FRP Wrap 14 5.5 Comparison of Different Retrofit Materials 15 5.5.1 Material Behavior 15 5.5.2 Material Properties 15 6.0 Structural Effects of Fibre Reinforced Plastic on Reinforced Concrete Members 16 6.1 Design and Analysis Using FRP 16 6.1.1 Flexural Analysis 16 6.1.2 Shear Analysis 17 6.2 Effect of FRP on Mechanical Properties of Reinforced Concrete Members 18 6.2.1 Increased Strength and Stiffness 18 6.2.2 Reduced Stress and Strain 18 6.3 Factors Influencing FRP Effectiveness 19 6.3.1 FRP Thickness 19 6.3.2 Beam Cross Section 19 6.3.3 Reinforcing Ratio 19 6.4 Failure Mode of Reinforced Concrete Members Strengthened with FRP 19 6.4.1 Reinforced Concrete Failure 20 6.4.2 Debonding at Concrete/FRP interface 21 6.4.3 FRP Failure 21 iv Table of Contents C H A P T E R 3 - E X P E R I M E N T A L P R O G R A M 1.0 Introduction 22 2.0 Channel Beam Test Specimens 23 2.1 Channel Beam Cross Section 23 2.2 Reinforcing Scheme 24 2.2.1 Longitudinal Steel Reinforcement 24 2.2.2 Shear/Torsion Reinforcement 24 2.3 Material Properties 25 2.3.1 Steel Reinforcement Tensile Properties 25 2.3.2 Concrete 25 3.0 Damage Characterization of Channel Beams Prior to Testing 26 3.1 Introduction 26 3.2 Damage Common to All Four Channel Beams 26 3.2.1 General Damage Description 26 3.2.2 Loss of Section Due to Separation 27 3.3 Individual Beam Damage Characterization 27 3.3.1 Summary of Individual Beam Damage 27 3.3.2 Beam One 28 3.3.3 Beam Two 28 3.3.4 Beam Three 29 3.3.5 Beam Four 30 4.0 Experiment Set-Up 3 0 4.1 Supports 31 4.2 Load Configuration 35 5.0 Instrumentation 36 5.1 Applied Load 36 5.2 Vertical Displacement 36 5.3 Strain 37 5.4 Horizontal Displacement 38 5.5 Data Acquisition System 39 6.0 Application of Retrofit Materials 3 9 6.1 Introduction 39 6.2 Surface Preparation 39 6.3 Application of GFRP Spray 41 6.4 Application of GFRP Wrap 43 v Table of Contents 7.0 Test Procedure 45 7.1 Initial Elastic Stiffness 46 7.1.1 Initial Elastic Flexural Stiffiiess 46 7.1.2 Initial Elastic Torsional Stiffness 46 7.2 Ultimate Load Testing 46 7.2.1 Ultimate Flexural Loading 47 7.2.2 Ultimate Flexural-Torsional Loading 47 8.0 Beam Failure Modes 48 8.1 Beam One 48 8.2 Beam Two 50 8.3 Beam Three 52 8.4 Beam Four 55 9.0 Results 5 7 9.1 Initial Elastic Stiffiiess Testing Results 57 9.1.1 Initial Elastic Flexural Stiffness 57 9.1.2 Initial Elastic Torsional Stiffness 60 9.2 Flexural Load Test Results 62 9.2.1 Total Applied Load Versus Vertical Deflection at Midspan 62 9.3 Ultimate Flexural-Torsional Load Test Results 63 9.3.1 Torsion Versus Angle of Twist per Unit Length at Third Point 63 9.4 Flexural and Flexural-Torsional Test Results 64 9.4.1 Strain 64 9.4.2 Horizontal Displacement 70 9.5 Summary of Experimental Results 70 10.0 Applicability and Accuracy of Results 71 10.1 Applicability of Results 7 1 10.1.1 Differences in Beam Damage States and Comparison ofResults 7 1 10.1.2 Damage Due to Beam Separation Process 71 10.1.3 Load Condition 71 10.1.4 Boundary Conditions 7 1 10.2 Accuracy ofResults 7 2 10.2.1 Support Seating 7 2 10.2.2 Electrical Interference 7 2 vi Table of Contents C H A P T E R 4 - F IN ITE E L E M E N T A N A L Y S I S 1.0 Introduction 73 2.0 Limitations of Model 74 3.0 Model of an Individual, Non-Retrofit, Reinforced Concrete Channel Beam 74 3.1 Finite Element Model Description 74 3.1.1 Elements 74 3.1.2 Coordinate System 75 3.1.3 Geometry 75 3.1.4 Material Properties 76 3.1.5 Boundary Conditions 76 3.2 Verification of Model 77 3.2.1 Flexural Stiffness 77 3.2.2 Torsional Stiffness 78 3.2.3 Longitudinal Stress 80 4.0 Model of an Individual Channel Beam Retrofit With GFRP 82 4.1 Finite Element Model Description 82 4.1.1 Elements 82 4.1.2 Coordinate System 82 4.1.3 Geometry 83 4.1.4 Material Properties 83 4.1.5 Boundary Conditions 84 4.2 Verification of Model 84 4.2.1 Flexural Stiffness 84 4.2.2 Torsional Stiffness 85 4.2.3 Longitudinal Stress 85 5.0 Finite Element Analysis of Channel Beam Bridge Decks 86 5.1 Model Description 87 5.1.1 Elements 87 5.1.2 Coordinate System 87 5.1.3 Geometry 87 5.1.4 Material Properties 87 5.1.5 Boundary Conditions 88 5.2 Load Configuration 88 vii Table of Contents 6.0 Channel Beam Bridge Model Results 89 6.1 Verification of Elastic Range Results 89 6.2 Vertical Deflection of Bridge Deck Flanges 90 6.3 Longitudinal Stress at Bottom of Bridge Deck Flanges 91 C H A P T E R 5 - C O M P A R I S O N A N D I N T E R P R E T A T I O N O F R E S U L T S 1.0 Introduction 93 2.0 Comparison and Interpretation of Experimental Results and Design Calculations 93 2.1 Failure Modes 93 2.1.1 Ultimate Flexural Load Tests 93 2.1.2 Ultimate Flexural-Torsional Load Tests 94 2.2 Ultimate Load Capacity 94 2.2.1 Ultimate Flexural Load Capacity 94 2.2.2 Difference in Channel Beam Flexural Load Capacity Due to GFRP Retrofit 95 2.2.3 Ultimate Torsional Load Capacity 96 2.3 Ultimate Ductility Capacity/Ultimate Vertical Deflection Capacity 96 2.3.1 Ductility Capacity/Vertical Deflection Capacity of Channel Beams in Flexural Load Test 96 2.3.2 Difference in Channel Beam Ductility Capacity Due to GFRP Retrofit 98 2.4 Elastic Stiffness 99 2.4.1 Elastic Flexural Stiffhess 99 2.4.2 Elastic Torsional Stiffhess 99 2.4.3 Difference in Channel Beam Flexural Stiffness and Torsional Stiffhess Due to GFRP Retrofit 100 2.5 Longitudinal Strain 101 2.5.1 Longitudinal Strain in Cross Section 101 2.5.2 Difference in Channel Beam Longitudinal Strain Due to GFRP Retrofit 104 3.0 Comparison and Interpretation of Finite Element Analysis Results 108 3.1 Vertical Displacement at Bottom of Flanges 108 3.2 Stresses in Flanges 109 Table of Contents C H A P T E R 6 - C O N C L U S I O N S A N D R E C O M M E N D A T I O N S 1.0 Introduction 108 2.0 Effects of Damage on Structural Behavior of Channel Beams 109 2.1 Concrete Section Loss at Top of Channel Beam One and Ultimate Load and Ductility Capacity 109 2.2 Loss of Concrete Cover From Longitudinal Reinforcing Steel and Failure Initiation 109 2.3 Initial Damage Condition and Initial Stiffness 109 3.0 Effects of GFRP Retrofit on Channel Beam Structural Properties 110 3.1 Increase in Flexural Load Carrying Capacity 110 3.2 Reduction in Ultimate Ductility Capacity 110 3.3 Increase in Flexural Stiffness and Torsional Stiffness 111 3.4 Reduction in Longitudinal Strain I l l 4.0 Effects of GFRP Retrofit on Channel Beam Bridge Deck Structural Properties I l l 4.1 Reduction in Vertical Displacement 111 4.2 Reduction in Longitudinal Stress 112 5.0 Comparison of GFRP Spray and GFRP Wrap Retrofits 112 6.0 Accuracy of Design Calculations 113 6.1 Flexural Resistance 113 6.2 Ductility CapacityAfertical Deflection Capacity 114 6.3 Elastic Flexural Stiffness 114 6.4 Longitudinal Strain 114 7.0 Recommendations 115 7.1 Recommended Retrofit Material 115 7.1.1 Application of Retrofit Material 116 7.1.2 Environmental Concerns 116 7.1.3 Durability Concerns 116 7.2 Channel Beam Bridge Repair Recommendations 116 7.3 Channel Beam Bridge Retrofit Design Recommendations 117 7.4 Channel Beam Bridge Retrofit Program Implementation Recommendations 117 ix Table of Contents R E F E R E N C E S 119 A P P E N D I X 1 - C A L C U L A T I O N S A N D M I S C E L L A N E O U S I N F O R M A T I O N 122 A P P E N D I X 2 - I N I T I A L D A M A G E C O N D T I O N O F C H A N N E L B E A M S 155 A P P E N D I X 3 - S A P 2000 O U T P U T D I A G R A M S 177 X LIST OF TABLES Table 2.1: Material Properties 14 Table 3.1: Summary of Reinforcement Tensile Properties 25 Table 3.2: Beam Designation 46 Table 3.3: Summary of Flexural Stiffhess Values 60 Table 3.4: Summary of Torsional Stiffiiess Values 62 Table 3.5: Summary of Maximum Load and Vertical Deflection 63 Table 3.6: Position of Strain Measurements Along Length of Beam 64 Table 3.7: Summary of Maximum Recorded Strain Values and Corresponding Total Load 67 Table 4.1: Summary of Flexural Stiffhess Values 78 Table 4.2: Summary of Torsional Stiffiiess Values 79 Table 4.3: Summary of Stress Values at Bottom of Flanges at Midspan 80 Table 4.4: Summary of Stress Values at Top-Centre of Web at Midspan 81 Table 4.5: Increase in Flexural Stiffiiess of Retrofit Beams Relative to Non-Retrofit Beams 84 Table 4.6: Increase in Torsional Stiffiiess Values of Retrofit Beams Relative to Non-Retrofit Beams 85 Table 4.7: Reduction in Longitudinal Stress at Bottom of Flanges of Retrofit Beams Relative to Non-Retrofit Beams (100 kN total load) 86 Table 4.8: Load Case One, Maximum Vertical Flange Deflection 91 Table 4.9: Load Case One, Maximum Tensile and Compressive Longitudinal Stresses in Flanges 92 Table 4.10: Load Case Two, Maximum Vertical Flange Deflection 94 Table 4.11: Load Case Two, Maximum Tensile and Compressive Longitudinal Stresses in Flanges 95 xi List of Tables Table 5.1: Comparison of Ultimate Flexural Capacity Values 98 Table 5.2: Increase in Flexural Capacity of Retrofit Beams Relative to Non-Retrofit Beams 99 Table 5.3: Comparison of Maximum Vertical Deflection Values 101 Table 5.4: Difference in Channel Beam Ductility Capacity Due to GFRP Retrofit Table 5.5: Comparison of Flexural Stiffhess Values 102 Table 5.6: Comparison of Torsional Stiffiiess Values 102 Table 5.7: Increase in Elastic Stiffiiess of Retrofit Beams Relative to Non-Retrofit Beams 103 Table 5.8: Comparison of Strain Values at 150 kN of Applied Load 107 Table 5.9: Decrease in Strain for Retrofit Beams Relative to Non-Retrofit Beams at 150 kN Applied Load 108 Table 5.10: Comparison of Maximum Vertical Displacement Values 109 Table 5.11: Comparison of Maximum Tensile Longitudinal Stresses in Flanges 109 Table 6.1: Comparison of GFRP Spray and GFRP Wrap Retrofits on Channel Beam and Channel Beam Bridge Structural Properties 113 xii LIST OF FIGURES Figure 2.1: Calculation of Flexural Resistance 16 Figure 3.1: Channel Beam Cross Section 23 Figure 3.2: Reinforcement Details 24 Figure 3.3: Shear Reinforcement Distribution Along Length of Channel Beam 24 Figure 3.4: Experiment Set-Up, Three Dimensional View 32 Figure 3.5: Experiment Set-Up, Side View 33 Figure 3.6: Experiment Set-Up, End View 34 Figure 3.7: End Supports 35 Figure 3.8: Beam One, Initial Flexural Loading, Total Load versus Average Centre Deflection 58 Figure 3.9: Beam Two, Initial Flexural Loading, Total Load versus Average Centre Deflection 58 Figure 3.10: Beam Three, Initial Flexural Loading, Total Load versus Average Centre Deflection 59 Figure 3.11: Beam Four, Initial Flexural Loading, Total Load versus Average Centre Deflection 59 Figure 3.12: Beam One, Initial Flexural-Torsional Loading, Torsion versus Angle of Twist per Unit Length at Third Point 60 Figure 3.13: Beam Two, Initial Flexural-Torsional Loading, Torsion versus Angle of Twist per Unit Length at Third Point 61 Figure 3.14: Beam Three, Initial Flexural-Torsional Loading, Torsion versus Angle of Twist per Unit Length at Third Point 61 Figure 3.15: Beam Four, Initial Flexural-Torsional Loading, Torsion versus Angle of Twist per Unit Length at Third Point 62 Figure 3.16: Beams 1, 3, and 4, Ultimate Flexural Loading, Total Load versus Average Centre Deflection 63 Figure 3.17: Beam Two, Torsion versus Angle of Twist per Unit Length 64 Figure 3.18: Beam One, Total Load versus Strain 65 Figure 3.19: Beam Two, Total Load versus Strain 66 Figure 3.20: Beam Three, Total Load versus Strain 66 Figure 3.21: Beam Four, Total Load versus Strain 67 xi i i List of Figures Figure 3.22: Beam One, Strain Profiles 68 Figure 3.23: Beam Two, Strain Profiles 68 Figure 3.24: Beam Three, Strain Profiles 68 Figure 3.25: Beam Four, Strain Profiles 68 Figure 3.26: Ultimate Loading, Total Load versus Horizontal Displacement 70 Figure 4.1: Cross Section of Reinforced Concrete Channel Beam Finite Element Model 75 Figure 4.2: Three Dimensional View of Reinforced Concrete Channel Beam Finite Element Model 76 Figure 4.3: Total Load versus Average Centre Deflection 78 Figure 4.4: Torsion versus Angle of Twist per Unit Length 79 Figure 4.5: Total Applied Load versus Longitudinal Stress in Bottom of Flange at Midspan 80 Figure 4.6: Total Applied Load versus Longitudinal Stress in Top-Centre of Web at Midspan 81 Figure 4.7: Cross Section of Channel Beam Finite Element Model With Applied GFRP 83 Figure 4.8: Finite Element Model of Bridge Deck 87 Figure 4.9: CL-625 Truck Load Configuration 89 Figure 4.10: Load Configuration Along Span of Bridge Deck 89 Figure 4.11: Load Configuration Along Deck Width 90 Figure 4.12: Vertical Deflection of Flange 3 92 Figure 4.13: Longitudinal Stress Distribution At Bottom of Flange 3 93 Figure 5.1: Non-Retrofit Beam, Total Load versus Vertical Deflection at Midspan 99 Figure 5.2: Beam Retrofit With GFRP Spray, Total Load versus Vertical Deflection at Midspan 100 Figure 5.3: Beam Retrofit With GFRP Wrap, Total Load versus Vertical Deflection at Midspan 100 Figure 5.4: Non-Retrofit Beam, Total Load versus Compressive Strain at Top of Beam 104 Figure 5.5: Non-Retrofit Beam, Total Load versus Tensile Strain in Longitudinal Steel 104 Figure 5.6: Beam Retrofit With GFRP Spray, Total Load versus Compressive Strain at Top of Beam 105 xiv List of Figures Figure 5.7: Beam Retrofit With GFRP Spray, Total Load versus Tensile Strain in Longitudinal Steel 105 Figure 5.8: Beam Retrofit With GFRP Wrap, Total Load versus Compressive Strain at Top of Beam 106 Figure 5.9: Beam Retrofit With GFRP Wrap, Total Load versus Tensile Strain in Longitudinal Steel 106 Figure 5.10: Total Load versus Compressive Strain at Top of Beam, Comparison of Experimental Results 107 Figure 5.11: Total Load versus Tensile Strain in Longitudinal Steel, Comparison of Experimental Results 108 xv LIST OF PHOTOS Photo 1.1: Channel Beam Bridge 2 Photo 1.2: Underside of Channel Beam Bridge 3 Photo 3.1: Experiment Set-up 31 Photo 3.2: Vertical Displacement Instrumentation on Top of Beam 37 Photo 3.3: Horizontal L V D T on Top of Beam 38 Photo 3.4: Dial Gauge and Scale at Roller Support 38 Photo 3.5: Restored Beam Cross Section 40 Photo 3.6: Primer Application 40 Photo 3.7: GFRP Spray Application Machine 41 Photo 3.8: Application of GFRP Spray 42 Photo 3.9: Condensing GFRP Spray With Serrated Rollers 42 Photo 3.10: Application of GFRP Fabric 44 Photo 3.11: Condensing GFRP Wrap With Serrated Rollers 44 Photo 3.12: Completed GFRP Wrapped Beam 45 Photo 3.13: Beam One, Initiating Shear Crack 48 Photo 3.14: Concrete Crushing in Failure Zone of Beam One 49 Photo 3.15: Concrete Crushing in Failure Zone of Beam One (Close-up) 49 Photo 3.16: Beam One, Final Deflected Shape 50 Photo 3.17: Shear Crack Causing Failure of Beam Two 51 Photo 3.18: Beam Two, Cracking in Flange Opposite to Failure Zone 51 Photo 3.19: Beam Two, Final Deflected Shape 52 Photo 3.20: Tensile Failure of GFRP, Outside of Beam 53 Photo 3.21: Tensile Failure of GFRP, Underside of Beam 53 Photo 3.22: Crack Along Longitudinal Reinforcement at Failure 54 Photo 3.23: Beam Three, Final Deflected Shape 54 Photo 3.24: Flexural Cracking 55 Photo 3.25: Tensile Failure of GFRP Wrap, Underside of Flange 56 Photo 3.26: Longitudinal Cracking 56 Photo 3.27: Beam Four, Final Deflected Shape 57 xvi ACKNOWLEDGEMENTS This research project was made possible by the Natural Sciences and Engineering Research Council of Canada (NSERC), and the British Columbia Ministry of Transportation and Highways. Their support is gratefully acknowledged. Dr. Robert Sexsmith provided patient guidance throughout the duration of this work. His valuable practical experience helped provide perspective and direction to this project. Dr. Nemy Banthia, Dr. Perry Adebar, and Dr. Carlos Ventura also provided helpful advice, which is sincerely appreciated. Martin Johnson, Andrew Boyd, and the U B C Structures Lab staff including Harald Schrempp, Doug Smith, Doug Hudniuk, Scott Jackson, John Wong, Max Nazar, and Howard Nichol were instrumental in the success of the experimental program. Their assistance in setting up and running the tests is gratefully appreciated. Tuna Onur provided finite element modeling advice. Her valuable suggestions and experience are much appreciated. Special thanks are also extended to Valentin Varga for drafting experimental configuration figures. Carol Newton helped with final revisions and editing and her efforts are also sincerely appreciated. Special thanks to my friends at U B C who have helped to make my time at UBC such a positive experience. Finally, deep gratitude is extended to my family, who have always been an important source of support and encouragement. xvii CHAPTER 1 INTRODUCTION 1.0 Introduction Several highway bridges in British Columbia were constructed during the 1950s and 1960s using reinforced concrete channel beams. Over the years these bridges have begun to deteriorate. The Neil Bridge was one such bridge that had considerable deterioration. This bridge was taken out of service because the strength of this structure was found to be questionable by the British Columbia Ministry of Transportation and Highways (BCMOTH). There are several other bridges in British Columbia built at the same time as the Neil Bridge that are also constructed of channel beam sections. To replace all of the channel beam highway bridges in British Columbia will be a great expense to the taxpayers of British Columbia. One alternative to bridge replacement is to repair these structures using glass fibre reinforced polymers (GFRP). GFRP consists of reinforcing fiberglass fibres in a polymer matrix. The use of GFRP as an external reinforcement has been shown to increase the strength and stiffness of reinforced concrete members. If these structures are repaired with GFRP, a costly replacement of several bridges could possibly be avoided. The feasibility of using different types of GFRP to retrofit British Columbia's deteriorating reinforced concrete channel beam highway bridges is evaluated in this study. Two different types of GFRP retrofit material are investigated including a GFRP spray and a GFRP wrap. The assessment of these two retrofit options is based on experimental load testing and finite element analysis. Recommendations are made regarding the use of GFRP for retrofitting British Columbia's reinforced concrete channel beam highway bridges based on the results of this study. 2.0 Channel Beam Bridges in British Columbia There are approximately twenty reinforced concrete channel beam bridges in British Columbia. The bridge deck of these bridges is made up of simply supported, precast channel beam sections. The reinforced concrete channel beam sections are approximately three feet across at their widest point and are sixteen inches tall. These sections were a standard section in bridge construction in the province of British Columbia between 1956 and the early 1960s. 1 Chapter 1 - Introduction The channel beam sections are positioned longitudinally to form a span. Bridges with this type of section range from a single span to a maximum of sixteen spans. Most bridges of this type are one to five spans. The spans are either 22 or 28 feet long. Channel beam bridges are used primarily in two lane highways. These bridges are typically ten channel beams wide. A shear key within the top seven inches of adjacent beams joins channel beams to each other. The outer beams have a 12 inch wide curb at the edge. The channel sections are covered with a layer of asphalt to create the road surface. The channel beams and the layer of pavement make up the bridge deck. The ends of the channel sections generally rest on elastomeric bearings and are supported by timber beams. A typical channel beam bridge is shown in Photo 1.1. The underside of a channel beam bridge is shown in Photo 1.2. Photo 1.1: Channel Beam Bridge 2 Chapter 1 - Introduction Photo 1.2: Underside of Channel Beam Bridge 3.0 Objectives of Study The objectives of this study are as follows: • To compare the structural behavior of non-retrofit (plain reinforced concrete) channel beam bridge decks with channel beam bridge decks retrofit with GFRP; • To compare the structural behavior of reinforced concrete bridge decks retrofit with GFRP spray with channel beam bridge decks retrofit with GFRP wrap; • To assess the accuracy of design calculation methods for determining structural properties of reinforced concrete channel beam bridge decks retrofit with GFRP; • To determine the effect of damage on structural properties of reinforced concrete channel beam bridge decks with and without GFRP retrofit; and • To make recommendations on whether GFRP is an appropriate retrofit material, the preferable type of GFRP material for retrofit, design strategies, and retrofit implementation programs for channel beam bridges in British Columbia 3 Chapter 1 - Introduction In this study, the structural response of channel beam bridge decks with and without GFRP retrofit is found from an experimental program, finite element analysis, and design calculations. The experimental program for load testing channel beam bridge girders is described in chapter three of this report. Four channel beam girders from the Neil Bridge are load tested as a part of this research project. Channel beams are tested to failure under a flexural and flexural-torsional load condition. Two channel beams receive no retrofit, one channel beam is retrofit with GFRP spray, and one channel beam is retrofit with GFRP wrap. Details of the channel beams, initial damage conditions, GFRP application procedures, the testing program, and experimental results are discussed in this chapter. The development of the bridge deck finite element models and the results of the finite element models are presented in chapter four. Finite element modeling is done using SAP2000® software. Finite element models of an individual reinforced concrete channel beam, and channel beams retrofit with GFRP spray and GFRP wrap are first developed and checked for accuracy. These sections are then used to develop finite element models of channel beam bridge decks with and without GFRP retrofit. Finite element models are tested using Canadian Highway Bridge Design Code < 1 9 ) load configurations to determine the worst case flexural and torsional load conditions. Results from design calculation values, experimental study, and finite element analysis are compared and interpreted in chapter five. Chapter six presents conclusions of this study and provides recommendations for retrofitting British Columbia's channel beam bridges. 4 CHAPTER 2 LITERATURE REVIEW 1.0 Introduction Aging reinforced concrete bridges have become a concern in North America. Many of the bridges in Canada and the United States were built in the 1950s and 1960s,' 2 3 ' 2 6 ' and are structurally deficient or functionally obsolescent by today's standards.'23' A structurally deficient bridge has a problem with its structural components such as physical deterioration, section loss, or excessive cracking. This deterioration may be due to inadequate maintenance, corrosion damage, physical damage, and/or design deficiencies. As a result, such bridges have either a load restriction, or require a retrofit in order to remain open to traffic.'2 3' A bridge may also be inadequate due to functional obsolescence. Functional obsolescence means the load carrying capacity, geometry, and approaches of a bridge no longer meet code criteria.' 2 3 ' This may occur due to increased traffic, increased vehicle weight, or changes in the code. The combination of heavier loads and deterioration of some bridges has raised structural safety concerns. Several options exist in order to deal with the problem of deteriorating concrete bridges. The bridge may be replaced, retrofit, or left in its current state. Several studies have found that existing bridges actually have sufficient strength, despite their deteriorated appearance. In this case only minor repairs may be necessary. If a reinforced concrete bridge is chosen for retrofit, an option is to provide external reinforcement using fibre reinforced polymers (FRP). The use of FRP strengthens bridge members, and is much less expensive than bridge replacement. This chapter presents a review of the existing literature on the problem of deteriorating reinforced concrete bridges. First, how and why reinforced concrete bridges become structurally deficient or functionally obsolescent are discussed in section two. This section focuses on how concrete degrades and what improvements have been made in recent years so that future concrete structures will have increased durability. Section three of this chapter presents studies in the literature that indicate deteriorated bridges actually have more strength than expected. It has been found in the past that some significantly deteriorated bridges are able to carry loads well in excess of that predicted by analysis. Examples of this phenomenon, and possible explanations for this behavior are given in this section. Section four discusses the options of replacing and repairing deficient bridges. The benefits of bridge retrofit relative to bridge replacement are emphasized. This section also outlines some common retrofitting strategies. 5 Chapter 2 - Literature Review Sections five and six focus on the use of fibre reinforced polymers for repairing reinforced concrete bridges. Section five presents materials used as external reinforcement in bridge retrofits including steel plate and different types of FRP. Section six provides structural information on the use of FRP including design and analysis of FRP reinforced members, the effects of FRP on beam mechanical properties, and failure modes of FRP strengthened beams. 2.0 Causes of Structural Deficiency in Reinforced Concrete Bridges The deterioration of concrete bridges can be attributed to a number of different factors. One cause of deterioration is chemical aging due to pollution or marine environments which cause corrosion of the embedded reinforcement/2 4 , 2 7' Deterioration also occurs due to physical aging. Physical aging includes abrasion, occasional overloads, and impact damage/ 1 3' 2 7' The degree of deterioration over time is largely dependent on the bridge design, construction, and the durability of the materials used. ( 2 4 , 2 7 ) Constant improvements in concrete technology continue to improve the strength and durability characteristics of concrete. These improvements will increase the life of structures currently under construction, however reinforced concrete bridges built in years past often have durability issues because of the type of concrete used. Some of the problems existing in today's concrete structures are discussed in this section. 2.1 Alkali Aggregate Reaction One cause of concrete deterioration is alkali-aggregate reactivity (AAR). A A R describes a reaction that occurs between active mineral constituents in some aggregates, and sodium and potassium alkalis that are usually present in cement paste. A l l aggregates will react with cement to some extent. Some amount of A A R between aggregates and paste is beneficial to the concrete matrix as it creates bond between the paste and the aggregates. A A R is damaging when the reaction is significant enough to cause excessive expansion within the concrete. A A R to this extent results in cracking/ 3 1' A A R can be controlled through careful selection of aggregates and by restricting the amount of alkalis in the cement. Restriction on aggregates known to participate in A A R was introduced to the Canadian design code for concrete structures (CSA Standard A23.1) in 1960. ( 3 1 ) This code modification strives to limit any excessive expansion and cracking in concrete caused by A A R . 6 Chapter 2 - Literature Review 2.2 Freeze-Thaw and Deicing Chemicals Two common causes of concrete degradation in areas with cold climates are freeze-thaw and deicer scaling. Although these are two different phenomenon, the end result of cracking and spalling is the same. Cycles of freezing and thawing can cause cracking and spalling due to the expansive pressure caused by absorbed water within the concrete.'1 7'3 1' The use of deicer chemicals can cause osmotic and hydraulic pressures build in excess of hydrostatic. If pressures are excessive within the concrete matrix cracking and spalling can occur. Deicing chemicals can also increase the possibility of freeze-thaw damage if moisture absorbed by salts increases the saturation of the concrete.'31' Degradation caused by these two mechanisms can be controlled through the use of appropriately air entrained concrete. A i r entrained concrete was developed in the 1930s.'3 1' Today, almost all concrete mixtures involve the use of air entrainment. A i r entrained concrete contains extremely small air bubbles in the concrete paste, most of which are 10 to 100 micrometres. These very small air spaces are created through the use of an air entraining agent.'31' With air entrained concrete, air bubbles provide space for freezing and migrating water from the capillaries. This relieves pressure within the concrete matrix and thus reduces damage to the concrete. When thawing occurs, the water is pushed back through the capillaries by capillary action and pressure from the air within the bubble. This cycle can continue over several seasons with very limited concrete damage. Entrained air also provides room for salt crystals to grow, thus also relieving stress within the concrete paste.'31' 2.3 Carbonation Causing Corrosion of Reinforcing Bars Another cause of concrete deterioration is carbonation. Carbonation occurs when carbon dioxide from the environment reacts with calcium hydroxide in the cement paste creating calcium carbonate.'31' A drop in pH is associated with this reaction which reduces the alkalinity of the concrete. The normally highly alkaline concrete provides protection against reinforcement corrosion.' 3 1 ' 3 7 ' When the pH decreases the steel components may start to corrode.' 2 8 ' 3 1 ' The amount of carbonation can be significantly reduced by using an appropriate mix design, curing techniques, and depth of concrete cover over reinforcing steel. The mix design should generate a low permeability paste. Concrete permeability can be reduced by using a low water-cement ratio, and through the use of supplementary cementing materials such as fly ash and silica fume. Increasing the curing duration and conditions such as improved consolidation, and controlled placement temperature also reduces the amount of carbonation that will occur in a concrete component.'1 3'3 1' In addition, increasing the thickness of the concrete cover over the internal steel reinforcement also helps to prevent the damage that may occur due to carbonation. 7 Chapter 2 - Literature Review 2.4 Corrosion of Reinforcing Steel Corrosion of the reinforcing steel is another cause of structural deficiency in reinforced concrete structures. In the alkaline cement environment, a protective oxide film on the surface of the reinforcing steel provides protection against corrosion. This oxide layer is destroyed when the alkalinity of the cement paste is reduced due to infusion of chloride ions or by carbonation. In electrochemical corrosion, anodic and cathodic sites exist in the reinforcing steel. At the anode, iron cations are released into the electrolyte solution surrounding the reinforcing steel. These iron cations combine with anions in the electrolyte solution surrounding the reinforcing steel to create corrosion at the cathode. Using sufficient cover over the reinforcing steel can reduce corrosion in reinforced concrete. This provides a physical and chemical barrier against carbonation and infusion of chloride ions, and helps to maintain an alkaline environment. Using a low permeability concrete with appropriate placement and curing procedures can also reduce corrosion of the reinforcing steel. 3.0 Tested Bridges Have More Strength Than Predicted by Analytical Methods Many concrete bridges that are severely deteriorated are able to carry normal traffic loads/8' This load capacity cannot be explained by analytical methods. This additional reserve strength has been verified by proof tests on existing bridges/5'7'8'29' For example, in Ontario over 225 bridges have been field tested by Ontario's Ministry of Transportation and Communications. Many of these bridges have been found to have greater load carrying capacity than predicted by analytical methods.'7'8' As a result, many of the bridges that were judged to be inadequate were found to have sufficient strength to remain in service/7' This indicates that there are several discrepancies between the actual strength of bridges, and the strength found by traditional calculations. There are several reasons why this occurs. Bridges are generally stiffer than assumed during analysis due to the interaction of structural and non-structural elements and bearing restraint. The design of bridges is also generally a very conservative process; therefore there is much reserve strength in the structure. The following parts of this section will outline the reasons why the actual strength of bridges is greater than estimated in more detail. 3.1 Stiffness The stiffhess of a reinforced concrete bridge is affected by several different factors including non-structural elements, bearing restraint, and concrete strength. Non-structural elements have a significant effect on bridge stiffhess. Differences between calculated and actual stiffhess is often attributed to the interaction of bridge girders with secondary components such as curbs and decks/5'813' Discrepancies in bridge stiffness may also be contributed to bearing restraint. Tests have proven that 8 Chapter 2 - Literature Review large bearing restraint forces can stiffen bridge girders enough that the applied load moment at the mid-span is reduced significantly/8 1 Also, the stiffness of a concrete member is related to the ultimate compressive strength ( f c) of the concrete.'8' As a result, if the assumed value for concrete strength is lower than the actual value, the stiffness of the bridge will be underestimated. 3.2 Conservative Design Conservative design procedures also cause the underestimation of a reinforced concrete bridge's load carrying capacity. Several conservative assumptions are made in order to simplify the bridge design process. Bridge design generally uses conservative values for strength of the component materials. Having greater material strength in the actual construction than assumed in the design creates structural members with higher load carrying capacity than predicted. Most load assessments also idealize a bridge as a two-dimensional structure. While this assumption significantly simplifies design calculations, two-dimensional analysis neglects several aspects of bridge behavior.'8' 4.0 Bridge Retrofit Advantages and Options 4.1 Benefits of Repair Compared to Replacement Three options exist for structurally deficient bridges. The alternatives are to: 1. replace the bridge; 2. administer load restrictions on the existing bridge; or 3. repair the bridge to improve its load carrying capacity Bridge replacement is very expensive and maintaining traffic flow for the duration of the removal and replacement of the new structure can create traffic problems.'1 3' As a result, replacing the bridge should be done only i f absolutely necessary. Reducing the allowable live load on a bridge is an inexpensive alternative, but with the trend towards higher bridge loading, this option may be unacceptable. Repairing a bridge to improve its load carrying capacity is much less expensive than replacing a bridge. It is also possible to repair the bridge not only so that its original strength is restored, but that its final strength is in excess of the original design. With successful strengthening no load restrictions need be placed on the structure. With limitations on funding, and the need to carry increased loads, the most popular option is usually to retrofit the existing bridge. 9 Chapter 2 - Literature Review 4.2 Retrofit Options Several options exist for retrofitting aging structures. Some conventional retrofit techniques include shortening the existing spans, increasing sectional area of existing support members, and external post-tensioning. ( 2 4 , 3 6 ) Other strengthening options include adding moment restraint to the ends of simple spans, and providing additional trusses to the bridge. ( 2 6 ) Cathodic protection may also be provided in order to prevent further corrosion of the reinforcing steel. Often, retrofitting a deteriorating bridge wil l involve applying external reinforcement to an existing section. Types of external reinforcement include shotcrete, epoxy bonded steel plate, and glass or carbon fibre reinforced polymer. Bonded external reinforcement increases the strength of bridge members. Also, by covering the member further damage to the existing section can be minimized. 5.0 Retrofit Mater ia ls This research will focus on the use of fibre reinforced polymers (FRP) for retrofitting deteriorating bridges. This section reviews details of the use of different types of FRP including their advantages and disadvantages, their application to concrete members, and their material properties. The use of FRP for structural repair and strengthening is still relatively new in the construction industry. Current industry practice is preferential to the use of steel plate as an external reinforcement: Since these two types of materials have a similar retrofit application, both steel plate and fibre reinforced polymers are discussed and compared in this section. 5.1 Steel Plate The use of steel plates bonded to concrete members is a common technique used for strengthening and stiffening aging structures.'9'14' This retrofitting option is widely accepted by the structural engineering design community, and has been used extensively in the past for structural repair. 5.1.1 Application Steel plates are bonded to the surface of concrete using a combination of an epoxy resin and anchor bolts. The installation procedure first involves sanding or sandblasting the concrete in order to roughen the surface. Aligning holes are then drilled in the concrete and the steel plate. These holes are then filled with an epoxy resin and anchor bolts are inserted. The concrete surface is then coated with an epoxy primer. Once the primer has cured, an epoxy resin is placed over the primed surface. The steel plate is then positioned over the epoxy resin layer in alignment with the anchor bolts. Nuts are 10 Chapter 2 - Literature Review then placed on the anchor bolts and tightened. ( 2 7 ) The combination of the epoxy layers and the tightened nuts on the anchor bolts provides bond between the steel plate and the concrete. 5.1.2 Advantages and Disadvantages An advantage of using steel plates as a retrofit option is that it has gained the acceptance of structural engineers. Structural engineers are accustomed to working with steel. Steel has well defined material properties, and its use is well covered by established codes of practice.'2 4' Although steel plate has been the conventional material for external reinforcement of aging concrete structures for several years, it does have some disadvantages. Durability is a concern because of possible corrosion of the steel plate.' 9 ' 2 7 , 4 2 ' Corrosion reduces the strength of the steel plate and weakens the epoxy bond.'9' Also, steel plate installation can be difficult due to the large size and weight.' 1 4 ' 2 7 ' Other concerns with this type of system include difficulties with forming a butt connection between plates,' 1 4 ' 2 7 ' and the development of only partial composite action.' 2 7 ' 5.2 Fibre Reinforced Polymers Fibre reinforced polymers, or fibre reinforced plastics, are composed of thin diameter reinforcing fibres in a polymer matrix. The matrix is a polymer such as epoxy, polyester, or polyurethane.'24'30' For structural applications the fibres are usually carbon, glass (E-glass), or aramid. During the 1950s and 1960s carbon fibre reinforced plastics were used extensively in the United States military and space program.' 2 4 ' The development of FRP as strengthening for structures first occurred in Switzerland and Germany.' 9 , 4 2 ' FRP has been used in Japan and Europe, and recently in North America for repair and strengthening of concrete structures."8'2 4' 5.2.1 Components of Fibre Reinforced Polymers 5.2.1.1 Polymer Matrix Polymers are the most commonly used matrix materials for fibre composites. This is because of their low cost, good chemical resistance, low specific weight, and high strain capacity. When curing, the thermosetting polymers used in structural repair go through a chemical reaction called polymerization in which monomers link together to form the matrix of polymers. The rate and temperature of this reaction is controlled by the use of an appropriate catalyst.'2' Two commonly used types of polymers are epoxy and polyester. Epoxies have high strength, low shrinkage rates, and low viscosity, which allows full coverage of the fibres. The disadvantages of epoxies are their relatively high cost in comparison to polyester. Polyesters are low in cost, but have high shrinkage during curing which can induce large stresses in the composite matrix.' 3 0 ' Vinyl esters are slowly replacing polyesters due to their improved durability characteristics. 11 Chapter 2 - Literature Review 5.2.1.2 Fibres The fibres used in fibre reinforced polymers are available in three different orientations. Fibre fabrics may contain aligned unidirectional fibres, or bi-directional woven fibres.'18' The third alternative is chopped fibre that forms a random two-dimensional orientation. Unidirectional and woven fibres are available in the form of fabric sheets, or as plates containing the fibres and polymer. Chopped fibres for use in structural retrofits are available as plates of fibre and polymer, or may be created by using FRP spray equipment. Glass fibres are one of the commonly used types of fibres for structural strengthening applications. The type of glass used is E-glass. The E in E-glass stands for electrical as this material was originally designed for electrical applications.'30' Glass filaments are approximately 10 micrometres in diameter. Fiberglass rovings are a spool of filaments that have been drawn into strands of multiple filaments.'2' Unidirectional and woven fibre meshes are composed of multiple filament strands. Glass fibres have the advantage of having relatively low cost and high strength.'2'3 0' In addition glass provides high chemical resistance.'30' The disadvantages of glass fibres compared to carbon fibres are their relatively low elastic modulus, poor adhesion to polymers, high specific gravity, sensitivity to abrasion, and low fatigue strength.'30' 5.2.2 Advantages of FRP Fibre reinforced plastics offer several advantages over the traditional bonded steel plate alternative. FRP offer excellent corrosion resistance. FRP also have high strength and stiffness while having a low specific weight. As a result, the addition of FRP to a structure does not significantly add to dead load or geometry of a section.'2 4' Low weight also means that FRPs are easier to handle and install than steel plates, particularly in enclosed places. ' 2 4 , 4 0 ' 4 2 ' This relative ease in constructability generally translates to a reduced installation cost of FRP in comparison with steel plate.'2 4' Other advantages of FRP are that they can form to almost any shape,'2 4' and are available in very long lengths, thus reducing the requirement for joints.' 4 2 ' 5.2.3 Disadvantages of FRP The use of fibre reinforced polymers as a repair material has some disadvantages. The use of such materials for the purpose of structural repair is relatively new, and thus there are some concerns regarding long-term durability. For example, the bond of the epoxy to the concrete surface may degenerate over time. Also, polymers slowly degrade under prolonged exposure to ultraviolet light.'2'9' Fibre reinforced polymers also have poor fire resistance. In addition, standards or code of practice for FRP are virtually non-existent.'24' As a result, conventional repair materials such as steel are can be more convenient to use. 12 : Chapter 2 - Literature Review 5.3 Fibre Reinforced Plastic Wrap Fibre reinforced plastic wraps include any FRP in which the fibres are available as unidirectional or woven fibre fabric sheets. The wrap may contain fibres only, or may be pre-impregnated with polymer resin. The application procedure described in this section is for a fabric sheet composed of fibres only. 5.3.1 Application Surface preparation is required before applying a fibre reinforced plastic wrap to a concrete structural element in order to achieve a sound bond between the concrete and the FRP. First, any existing reinforcement corrosion must be removed.' 2 2 ' 2 4 ' 2 6 ' A reinforced concrete member that is significantly corroded may require reinforcement replacement, or additional reinforcement such as a bolted or welded section.'2 6' In the case of prestressed members, existing spalls and cracks should be sealed to provide protection for the prestressing steel against possible corrosion.'2 6 ' The concrete surface should be then be prepared by sanding or sandblasting to remove surface dust and expose the coarse aggregate.'4' Once the surface preparation is complete, an epoxy based primer is applied. The surface primer provides a smooth surface for the application of the FRP wrap. The use of an epoxy based primer between the concrete and the epoxy resin also allows a bond to form between almost identical materials. This reduces the interfacial tension between the concrete surface and the layer of FRP wrap and thus reduces the possibility of debonding.'2 4' Once the primer has dried, a layer of mixed polymer and catalyst is applied. A sheet of FRP wrap is then applied. When the wrap is to be used as flexural reinforcement, the fibres are aligned parallel to the axis of the beam. When the wrap is being applied to enhance shear resistance, the fibres are aligned perpendicular to the axis of the beam. The wrap is then pressed using serrated rollers in order to saturate the fibres, and to remove any existing air. A second layer of polymer/catalyst mixture follows the application of the FRP sheet and the rolling procedure is repeated. This process is repeated for each layer of FRP wrap that is applied. 5.4 Fibre Reinforced Plastic Spray Sprayed FRP is a mixture of chopped fiberglass strand together with a polymer such as polyester or vinyl ester. It is called sprayed FRP because of the application process. In applying FRP spray, special equipment is used that projects the chopped fiberglass and polymer onto the concrete surface. By spraying the FRP in this manner a two dimensional random distribution of fibres is created on the surface of the concrete member.'9' 13 Chapter 2 - Literature Review 5.4.1 Application As in the application of a FRP wrap, surface preparation is important for a strong bond between the concrete surface and the sprayed layer of FRP. The same surface preparations used prior to applying FRP wrap are also utilized for the application of sprayed FRP. These surface preparations include the removal of significant corrosion, replacement of steel reinforcement i f necessary, filling of spalls and severe cracks, and sanding or sandblasting the surface of the concrete. Prior to applying the FRP spray, a primer is brushed on to the cleaned concrete surface. Once the primer has attained a sticky consistency, the FRP spray may be applied. The FRP spray is generated using a compressed air powered machine. The machine has three primary parts including the polyester resin pump, the catalyst pump, and the spray or chopper gun unit.' 1 5 ' The gun contains the nozzle and a chopper unit. Polymer and catalyst are conveyed as separate pressurized streams to the nozzle.' 9 ' These two streams merge in the turbulent mixer within the nozzle. The chopper contains a set of circular blades that cut the spool of multi-filament glass fibre strand at a set length. This length may be within the range of 8 to 48 millimetres,' 9 1 5 ' but is set at a constant length for a given application. Chopped fiberglass exits from the chopper unit and merges with the polyester and catalyst mixture exiting the nozzle. The sprayed FRP mixture requires manual pressure in order to remove any existing air, to condense the mixture, and to align the fibres in a two dimensional matrix. This is done using metal serrated rollers. The mixture is rolled after each pass of spray. 5.4.2 Advantages and Disadvantages of Sprayed FRP Compared to FRP Wrap The use of sprayed FRP has some advantages in comparison to FRP wrap. In general, the use of sprayed FRP is faster because thickness of the material can be easily increased without adding extra layers of fabric' 9 1 4 ' . As a result, FRP spray can be less costly than the application of FRP wrap'9'. Also, the equipment is portable and the job could be done by a single worker. Sprayed FRP also has some disadvantages when compared to FRP wrap. The spray-up technique relies on the skill of the operator for a good quality surface'9'. Also, the cost of the spray equipment can be expensive, and thus must be considered relative to the cost benefits in application time and labour. Another disadvantage of the FRP spray in comparison to a FRP wrap is that it is a very new application method. While sprayed FRP has been used extensively for boat repairs, the use of this application technique for structural strengthening is new. FRP wrap has had several field applications while sprayed FRP has had no field applications to date. 14 Chapter 2 - Literature Review 5.5 Comparison of Different Retrofit Materials 5.5.1 Material Behavior Fibre reinforced plastics have significantly different behavior under tensile loading than steel. Steel exhibits ductile behavior under tensile loading while FRP has completely linear elastic properties. When the tensile capacity of a FRP is reached, it wil l fail in a sudden, brittle manner. 5.5.2 Material Properties Table 2.1 gives material properties for various types of fibre reinforced polymers, and structural steel. Material Tensile Modulus [E] Tensile Strength Ultimate Tensile (GPa) (MPa) Elongation (%) Carbon FRP Tow Sheet ( 3 4 ) 235-380 2940-3480 0.8-1.5 E-Glass FRP Tow Sheet ( 3 4 ) 70 1670 2.0 Epoxy Resin ( 3 4 ) 3 54 2.5 Sprayed Glass F R P ( 1 5 ) 12 110 1.25 Steel 200 400 20 Table 2.1: Material Properties Carbon FRP has a greater ultimate tensile strength and tensile modulus than glass FRP. Carbon FRP is used when very high strengths are required. Carbon FRP is also more expensive than glass FRP. Glass FRP wrap has a much larger tensile modulus, strength, and ultimate strain than glass FRP spray. This difference is because of the relative fibre content in the two materials. Glass FRP wrap has a much higher ratio of glass fibre relative to resin than the sprayed FRP. The fibre content of the FRP wrap is 81% by volume, while the fibre content of the FRP spray is 9% by volume. Since the strength of the FRP is provided by the fibres this results in higher values for the mechanical properties of FRP wrap relative to FRP spray. To achieve similar properties using FRP spray, a greater thickness must be applied in order to have a comparable fibre content. 15 Chapter 2 - Literature Review 6.0 Structural Effects of Fibre Reinforced Plastic on Reinforced Concrete Members 6.1 Design and Analysis Using FRP 6.1.1 Flexural Analysis Flexural design and analysis of a reinforced concrete beam strengthened using FRP is an iterative procedure based on the principle of strain compatibility/ 2 7 , 3 5 ' The ultimate flexural capacity is found by first assuming a failure mode. One possible assumption is that is that flexural strength of the beam will be limited by a compression failure in the concrete compression block. For this failure mode, the concrete strain is assumed to be at its maximum allowable value at the top of the beam. The depth of the neutral axis is then assumed and the strains in the longitudinal reinforcing steel and the FRP are found. The stress distribution in the cross section is then found from the stress strain relationships for each material. The forces in the concrete, steel, and FRP are then calculated and summed. This procedure is iterated until the correct neutral axis depth is found based on the sum of the constituent material forces. Once the correct neutral axis depth has been found, the assumed failure mode is verified by comparing the magnitude of strain in the FRP to the maximum allowable for this material. If strain in the FRP exceeds the ultimate strain, then flexural failure of the beam wil l be due to tensile fracture of the FRP. If this is determined to be the governing failure mode, the analysis is repeated with strain in the FRP assumed to be at its maximum value. Depth of the neutral axis is then assumed, and the corresponding strains in the reinforcing steel and the concrete compression block are again found. The stresses and forces in each material then calculated. This procedure once again iterated until the correct neutral axis depth is calculated. The ultimate flexural capacity is found from summing moments about the neutral axis of the beam cross section. The following stress, strain, and force distributions of a typical rectangular reinforced concrete section shown below in Figure 2.1 illustrate this method. This method of calculating the flexural capacity of a reinforced concrete beam repaired with FRP is based on the assumption of strain compatibility. In order to use the strain compatibility method, continuous bond between the FRP and the concrete until failure is assumed.'35' Thus, this calculation is not correct if debonding occurs during loading. 16 Chapter 2 - Literature Review Beam Cross-Section Strain Stress Stress (With Modif ied Stress Block) Forces N A — ; fs ) fs F c F s E F R P f f R P f f R P F R P F R P Figure 2.1: Calculation of Flexural Resistance 6.1.2 Shear Analysis Shear design and analysis o f a reinforced concrete beam strengthened using F R P may be evaluated using the 45 degree truss model for design o f transverse shear reinforcement. ' 4 2 ' B y this method, the contribution to shear resistance made by each different material within the beam is considered separately. The general formulation which accounts for the shear resistance from the F R P , is shown by Equation 1: v R = v c + v s + v F R P (1) The F R P contribution to shear resistance may be found from Equation 2. ( 4 2 ) 0.9 V = PFRP ' ' £FRP,E ' D W ' d FRP Where: YFRP = partial safety factor for F R P ; p F R P = F R P area fraction, (pF R P=2t/bw, t=thickness o f F R P ) ; E F R P = elastic modulus o f F R P ; E F R P , E = effective F R P strain; bw = m i n i m u m effective width o f cross section wi th in effective depth d; and d = effective depth of cross section 17 Chapter 2 - Literature Review The effective strain in the FRP (e F Rp > E) is dependent on the failure mode of the FRP material. Shear failure of the FRP material may occur due to debonding of the FRP from the concrete surface, tensile fracture, or by a combination of these mechanisms. The effective strain in the FRP is has been found to be dependent on the product of P F R P E F R P . As the P F R P E F R P factor increases, the effective strain in the FRP decreases. This indicates that as the FRP layers become thicker and stiffer, debonding starts to govern as a failure mode over tensile fracture of the FRP, and the effective strain in the FRP is reduced/ 4 2 ' Effective strain in the FRP is calculated using Equations 3 and 4 (where D F R P E f r p is in GPa). < 4 2 ) For 0 < p F R P - E F R P <1 s F R P =0.0119-0.0205-(pF R P •E F R P)+0.0104-(p F R P - E F R P ) 2 (3) For p F R P - E F R P >1 8 F R P = -0.00065 • (p F R P • E F R P ) + 0.00245 (4) 6.2 Effect of FRP on Mechanical Properties of Reinforced Concrete Members 6.2.1 Increased Strength and Stiffhess The addition of a layer of FRP increases the load carrying capacity, and stiffhess of a reinforced concrete beam/ 1 4 ' 1 8 ' 2 7 ' 4 0 ' These enhanced mechanical properties are a direct result of the high strength and stiffhess of the reinforcing fibres relative to reinforced concrete. A beam wrapped with FRP has a larger cross sectional area, moment of inertia, and modulus, which increases its stiffhess and reduces its deflection/ 2 7 ' 6.2.2 Reduced Stress and Strain The use of fibre reinforced plastics as external reinforcement reduces the magnitude of stress and strain at a given load level compared to a beam that has not been fixed with FRP. Reduction in stress and strain values is due to composite action/ 2 7 ' Composite action between reinforced concrete and FRP reduces stress and strain by forming a load sharing system. Tensile load that would have originally been supported by the steel reinforcement only is also carried by the FRP. This results in decreased tensile stress in the reinforcing steel/ 2 7 ' A consequence of this is that yielding of the steel reinforcement will occur at a higher load level than in a reinforced concrete beam not repaired with FRP. 18 Chapter 2 - Literature Review Stress and strain values may be further reduced if the FRP material is wrapped around the full cross section of the beam. This configuration of FRP provides confinement, which reduces cracking and volumetric expansion of the concrete.'27' 6.3 Factors Influencing FRP Effectiveness 6.3.1 FRP Thickness The thickness of FRP is an important parameter in defining the reduction in the reinforcing steel stress, the ultimate load carrying capacity, and the failure mode of a reinforced concrete beam. The greater the thickness of FRP under tension, the less tension that is carried by the longitudinal steel and thus the higher the applied load may be when the steel yields. The thickness of the applied FRP also has a direct impact on the failure mode that a beam wil l exhibit.'3 5' In general, the ultimate load of a retrofit specimen wil l increase with increasing FRP thickness.'1 4' However, there exists a limiting FRP thickness, beyond which debonding will occur prior to reaching the ultimate load of the retrofit beam.' 3 5 ' Thus there is an optimum thickness where the ultimate load is maximized, and the beam will still fail in a ductile, flexural mode. 6.3.2 Beam Cross Section The effectiveness of the FRP layer is dependent on the cross section shape. The use of FRP as an external reinforcement is more effective in deep members than in shallow members.'4' In deep members the extreme outer fibres are further from the neutral axis than in shallow members, thus the stresses at the outer edges can be larger than in a shallow beam. The composite action of the FRP and concrete is able to reduce these high magnitude stresses that develop at the extreme top and bottom edges of a deep beam. 6.3.3 Reinforcing Ratio FRP is more effective in beams with lower reinforcement ratios than in beams with a high steel content.'4'27' This is because the steel in lightly reinforced beams will yield at a lower load level than steel in highly reinforced beams. The composite action between the reinforced concrete beam and the FRP serves to increase the load level at which the rebar will yield. This is more appropriate for a beam with a lower reinforcement ratio. 6.4 Failure Mode of Reinforced Concrete Members Strengthened with FRP The failure of a beam externally reinforced with FRP may occur as classical reinforced concrete failure, debonding at the concrete/FRP interface, or due to failure of the FRP material. Reinforced concrete failures include flexural and shear failure. Debonding occurs when the bond 19 Chapter 2 - Literature Review between the concrete and the FRP is compromised. The third type of failure is initiated by a failure within the FRP material. The repair of reinforced concrete members with FRP can lead to significant increases in ultimate strength. Since the strength of the original member has been changed, often the associated failure mode is also altered. FRP has entirely linear elastic properties; thus it can change the failure mode of a reinforced concrete member from ductile to brittle. The possible change in failure mode may be of concern when using FRP as a repair material, and must be given careful consideration in design. 6.4.1 Reinforced Concrete Failure 6.4.1.1 Flexural Failure Flexural failure of a beam retrofit with GFRP can occur by one of two mechanisms. Failure occurs when either the concrete within the compression block crushes, or the maximum tensile strain in the FRP at the bottom of the beam is reached. Flexural failure is ductile in either of these cases if the longitudinal reinforcing steel has yielded. If the reinforcing steel has not yielded, the flexural failure will be brittle. The use of external FRP can cause a beam that was originally under-reinforced to become over-reinforced. The use of FRP on the extreme bottom fibre as tensile reinforcement lowers the c/d ratio of the original beam/ 2 7 ' This creates a more extreme strain condition at the top and bottom of the beam. As a result, concrete crushing or ultimate strength of the FRP may be attained before the longitudinal reinforcing steel yields. A brittle flexural failure can be avoided by ensuring yielding of the longitudinal reinforcing steel in the flexural design of a member retrofit with FRP. Using principles of strain compatibility, the strain profile in the cross section of the beam at the ultimate flexural load can be determined. Yielding of the reinforcing steel may be verified from this strain profile. If the reinforcing steel has not yielded, too much FRP has been added.and the beam has become over-reinforced. In this case the retrofit design strategy should be modified to ensure a ductile failure mode. 6.4.1.2 Shear Failure Shear failure occurs when the shear capacity of a beam retrofit with FRP is exceeded prior to reaching its flexural strength. This type of failure should be avoided because it is brittle and can cause sudden failure. A shear failure mode can be detected through member analysis. In designing a beam retrofit with FRP, both the flexural and shear strength of the member are calculated. These calculation methods are outlined in section 6.1. 20 Chapter 2 - Literature Review If a beam retrofit with FRP is predicted to have a shear failure mode, either the flexural resistance of the beam must be reduced or the shear strength increased to ensure a ductile failure mode. The flexural capacity of the beam may be lowered by reducing the amount of FRP along the underside of the beam contributing to flexural resistance. Additional FRP shear reinforcement may also be added along the edges of the beam to increase the shear resistance of the member. 6.4.2 Debonding at Concrete/FRP Interface Failure of a reinforced concrete beam strengthened with FRP may be initiated by debonding at the concrete/FRP interface/ 4 , 2 7 , 4 0 ' Debonding is defined as the FRP fabric pulling away from the concrete surface under increased loading. When debonding occurs, it may initiate other failure mechanisms such as shear failure, or rupture of the FRP fabric. This can result in a sudden load drop and brittle fai lure. 0 8 , 4 0 ' The amount and locations of debonding in a beam are difficult to predict with design calculations. The possibility of debonding is dependent on anchorage of the F R P , < 4 2 ) thickness of the laminates/ 4 2 ' and the bonding agents. By controlling these factors, the risk of debonding causing beam failure can be reduced. For example, additional anchorage of the FRP may be achieved from wrapping around the entire cross section or from mechanical fastening. The risk of debonding also becomes greater as FRP layers become thicker and stiffer ( 4 2 ), thus only the thickness of FRP required to provide the required increase in strength should be used. 6.4.3 FRP Failure Failure of a reinforced concrete beam strengthened with FRP may be caused by a failure within the FRP material. FRP failure may occur as buckling or rupture of the FRP fabr ic / 4 , 1 8 ' 2 7 , 4 0 ' or as fracture at an area of tensile stress concentration/ 2 7 ' 4 2 ' The actual failure mechanism wil l depend on several factors including the thickness of the applied F R P / 4 , 4 2 ' the bonded length/ 4 , 4 2 ' and the bonding agents. Often the failure mechanism of the FRP is a combination of debonding and fracture at different locations within the F R P / 4 2 ' Tensile stress fracture may occur at an area of stress concentration such as a corner or an area of debonding/ 4 2 ' This can happen at a stress lower than the tensile strength of the FRP material/ 4 2 ' This type of failure is difficult to predict with simple design calculations. Controlling the surface and geometry of the cross section can minimize the risk of this type of FRP failure. Having a smooth concrete surface, and having rounded corners to limit angle changes in the cross section can minimize stress concentrations in the FRP material. 21 CHAPTER 3 EXPERIMENTAL PROGRAM 1.0 Introduction This chapter describes the experimental program for load testing non-retrofit and retrofit channel beams. The channel beam sections used for testing were once a part of the Neil Bridge on Vancouver Island in British Columbia, Canada. This bridge was located on Highway 14 between Victoria and Sooke. The Neil Bridge was recently been taken out of service after approximately forty years of use. This bridge was removed because of excessive deterioration of the channel beam bridge girders. Four channel beams were tested in this experimental program. Two channel beams received no retrofit, and two channel beams were retrofit with glass fibre reinforced polymers (GFRP). One of these beams was retrofit with GFRP spray, and the other was retrofit with GFRP wrap. In this series of experiments, channel beams were tested to failure with two different load configurations. Based on the results of these experiments, information regarding the structural properties of the channel beams was obtained. This chapter explains the channel beams, retrofit procedures, the experimental program, and experimental results. The reinforced concrete channel beam bridge girders are described in terms of their configuration, component materials, and damage state. GFRP application procedures are also presented. This chapter also explains the testing program including load configuration, instrumentation, test procedures, and experimental results. Sections two and three describe the channel beam sections. Section two describes the channel beam specimens in terms of their cross section, reinforcing scheme, and material properties. In section three, the initial damage condition of each of the beams prior to testing is characterized. Differences in damage in each of the beams is described in terms of missing concrete, cracking, exposed reinforcement, and corrosion of the reinforcement. Sections four and five present the experiment configuration and instrumentation details. Section four gives specifics of the experiment set-up. This section includes information on the support conditions and the load configuration used in testing. Section five outlines the electronic equipment used to record load, displacement, and strain data during the experiment. Section six describes the application of a GFRP spray, and a GFRP wrap to two different beams. Section seven explains the test procedures used. A l l four beams were first subjected to flexural and flexural-torsional loading within their elastic range prior to loading to failure. Testing 22 Chapter 3 - Experimental Program within the elastic range was performed to obtain elastic flexural and torsional stiffness properties. Once elastic load range testing was complete, the beams were tested to failure. Details of the retrofit condition and the type of loading used in ultimate strength testing are outlined in this section. Section eight explains the failure of each of the four channel beams during ultimate load testing. Events leading to failure, and the ultimate failure mode are described. Section nine presents the experimental results of the channel beam load testing. Test results for both elastic range testing and ultimate load testing are included. First, initial elastic flexural and torsional stiffness test results for each beam are shown. The results of ultimate flexural and flexural-torsional load testing are also presented. Results include the load-vertical deflection relationship, and the torsion-angle of twist per unit length relationship. Strain and horizontal displacement under increasing load are also given in this section. The applicability and accuracy of experimental results are discussed in the final section of this chapter. 2.0 Channe l Beam Test Specimens 2.1 Channel Beam Cross Section A typical channel beam cross section is shown in Figure 3.1. Figure 3.1: Channel Beam Cross Section (dimensions in millimetres) Chapter 3 - Experimental Program 2.2 Reinforcing Scheme 2.2.1 Longitudinal Steel Reinforcement Four longitudinal steel bars at the bottom of the channel flanges provide the flexural reinforcement in the channel beam. The reinforcement configuration for the channel beams is shown in Figure 3.2. The longitudinal reinforcement at the top of the channel beam is not considered to act in the flexural response of this beam. The reinforcement ratio is 1.3%. 2.2.2 Shear/Torsion Reinforcement Imperial size number three (% of an inch/ten millimeter diameter) reinforcing ties provide shear and torsion reinforcement in this channel beam. The shear/torsion reinforcement is shown in cross section in Figure 3.2. Spacing of the shear/torsion reinforcing ties along the 22 foot (6700 millimetre) length of the channel beam is presented in Figure 3.3. The spacing of the shear/ torsion reinforcement along the length of the beam was determined using a pachometer. I — 1 4 0 — r - H O — i - J 6 0 1 - -J60 1— Figure 3.2: Reinforcement Details (dimensions in millimetres, imperial bar sizes) 8 @ 127mm = 1016mm N—H 8@5"=40" 305 N—• 12" 508 20" 762 30" 762 30" 762 30" 762 30" 508 20" 305 12" 8 @ 127mm = 1016mm 8@5"=40" Figure 3.3: Shear Reinforcement Distribution Along Length of Channel Beam 24 2.3 Material Properties Chapter 3 - Experimental Program 2.3.1 Steel Reinforcement Tensile Properties Tensile testing of the steel reinforcement from the channel beams was performed to determine its yield point, ultimate tensile strength, and ultimate elongation. Samples of reinforcing steel for testing were removed from the end of beam one using a jackhammer after testing was completed. It was assumed that the properties of this reinforcement would be consistent with those from the other channel beams. Tensile testing was performed on the two sizes of bottom longitudinal reinforcement (imperial sizes number ten and number eight), and on the shear ties (imperial size number three). Two samples of each type of reinforcement were tested. Only two samples of each type of reinforcement were tested because of the difficulty in obtaining usable test specimens from the beam. Tensile testing of the longitudinal reinforcement was performed using a Baldwin BTE-120 machine. These samples were tested using a sixteen inch (400 millimetre) gauge length. Testing of the shear ties was performed using a Tinius Olsen Super L-60 machine. In this case a gauge length of four inches (100 millimetres) was used. This is much smaller than the standard gauge length. This gauge length was used because only a limited length of shear tie could be obtained from the channel beam. In both of the tests performed on the shear tie reinforcement, the ultimate failure occurred outside of this four inch gauge length. The results of the tensile testing of the steel reinforcement are summarized in Table 3.1. Imperial Sample Area Yield Ultimate Ultimate Bar Size Number Strength Tensile Strain Strength (mm2) (MPa) (MPa) #10 1 819 305.4 496.4 0.150 #10 2 819 302.7 496.4 0.200 Average for #10 819 304.1 496.4 0.175 #8 1 510 394.4 609.5 0.175 #8 2 510 420.6 604.0 0.145 Average for #8 510 407.5 606.8 0.160 #3 1 71 409.5 574.3 0.170 #3 2 71 348.2 510.9 0.190 Average for #3 71 378.9 542.6 0.180 Table 3.1: Summary of Reinforcement Tensile Properties 2.3.2 Concrete The concrete in the channel beams contained lightweight aggregate. The concrete density was 18.8 kN/m 3 . 25 Chapter 3 - Experimental Program 2.3.2.1 Concrete Compressive Strength Concrete strength tests were performed using three inch and four inch diameter cores. The core samples were taken from the ends of beam one. It was assumed that the strength of concrete from beam one would be representative of the other three beams. Adjustments to the core compressive strength results are required in order to obtain values comparable to a standard six inch diameter cylinder. The calculation of equivalent compressive strength used was based on a method proposed by Bartlett and MacGregor. ( 1 1 ) This formulation of equivalent concrete strength incorporates modification factors for core length to diameter ratio, core diameter, core moisture, and damage due to drilling. The average equivalent concrete compressive strength ( f g) was determined to be 35 MPa. The calculation of equivalent concrete strength may be found in Appendix 1. 3.0 Damage Characterization of Channel Beams Prior to Testing 3.1 Introduction Some of the bridge girders tested were more damaged than others. The response of each beam under increased loading may be dependent on the degree and type of damage in the specimen. By characterizing the damage state of each of the beams, a more effective comparison of experimental results can be achieved. The following part of this section will describe general types of damage that are common to all four of the channel beams. Differences in damage state for each beam are presented in part 3.3. Damage specific to each beam is defined in terms of: 1. amount of concrete section loss; 2. amount of exposed reinforcement; 3. amount, type, and width of cracking; and 4. amount of corrosion 3.2 Damage Common to All Four Channel Beams 3.2.1 General Damage Description A l l four of the beams had some similarities in their damage condition. Each of the four beams was damaged at the ends. The type of end damage was consistent between each of the four beams. Each of the beam webs had regions of spalled concrete along the underside. Photos of end and web damage are presented in Appendix 2. A l l beams showed evidence of alkali aggregate reaction (AAR). A A R was evident by the random crack partem along the surface of the concrete, and by a ring 26 Chapter 3 - Experimental Program of discoloration around the larger aggregates. The concrete contained several air voids. Many of the voids close to the surface were filled with salt particles. A l l of the beams in this testing program also had patchy efflorescence along their underside. 3.2.2 Loss of Section Due to Separation In the original bridge configuration, a shear key connects the channel beams to each other. When the bridge was taken out of service, removing the shear key separated these beams. This beam separation process caused some of the existing damage along the outside of the flanges. Beam separation damage was distinguished from traditional deterioration by the pattern of missing concrete, and the degree of corrosion of the exposed reinforcement. Damage due to separation was indicated by missing concrete at the widest part of the flange, causing loss of cross section. In addition, when the separation process caused the damage, the exposed reinforcing steel was not corroded. The beams were separated in the field approximately one year prior to delivery to the laboratory. In this case, there has not been time for the reinforcing steel to develop significant corrosion. As a result of this separation process, the degree of damage seen in these four beams may not be truly representative of a beam in the field. This type of damage was evident in all of the four beams tested. A photo illustrating this type of damage is shown in Appendix 2. 3.3 Individual Beam Damage Characterization The following parts of this section provide details of the amount and type of damage in each of the four beams used in the testing program. The damage in each of the beams is shown by a series of figures and photographs. The damage to each beam is first shown by a series of photographs of the beam prior to testing. The damage to each of the flanges is also summarized in a schematic diagram. Each diagram shows the outside, bottom, and inside of one flange. These figures indicate the configuration and quantity of missing concrete, exposed reinforcing steel, and cracking in each of the flanges. These figures and photos are presented in Appendix 2. 3.3.1 Summary of Individual Beam Damage In general, beams one and two were more damaged than beams three and four. Beams one and two had larger sections of missing concrete, more cracking, and greater crack widths. Beams one and three had the greatest amount of exposed longitudinal reinforcing steel. A l l four channels had periodic flexural cracking along the bottom of the flanges. The reinforcing steel was most significantly corroded in beam three. 27 Chapter 3 - Experimental Program 3.3.2 Beam One 3.3.2.1 Missing Concrete and Exposed Reinforcing Steel Most of the damage to beam one was in flange one. Flange one had four lengths of exposed reinforcing steel along the bottom of the flange. The total length of exposed longitudinal reinforcing bar in flange one was 18.5 feet (5.6 metres). Flange one also had large regions of missing concrete along its sides. The outside of flange one had two areas in which there was significant section loss along the outside of the flange. Flange two also had regions of missing concrete. Flange two had two areas of exposed reinforcing steel along the bottom of the flange. The total length of exposed reinforcing steel in flange two was 11.75 feet (3.6 metres). The damage on the sides of flange two was mainly limited to missing concrete cover over the reinforcing steel. There was only minor loss of cross section along the outside of flange two. Beam one was unique in that its top is badly damaged. Several sections of concrete were missing along the top. 3.3.2.2 Cracking Flange one had significant flexure-shear cracking along its inside. These cracks initiated mainly from the areas of missing concrete. The diagonal cracks in flange one of this specimen were much wider than in any of the other beams. Flange two showed much smaller crack widths than flange one. Most of the notable cracks on this flange also originated in the regions of missing concrete cover. 3.3.2.3 Corrosion The longitudinal reinforcement in this beam was not highly corroded. In some areas of exposed reinforcement virtually no corrosion was evident. At other locations patchy corrosion extended over the bar deformations and some of the bar surface. There was no apparent loss of section due to corrosion. 3.3.3 Beam Two 3.3.3.1 Missing Concrete and Exposed Reinforcing Steel Flange one of beam two was more damaged than flange two. Flange one had three sections where the concrete cover was missing along the bottom of the flange. In total, 16.5 feet (five metres) of longitudinal steel was exposed in flange one. This flange also had significant concrete loss along its outside. Some of this damage appeared to have been caused by the girder separation process. Flange 28 Chapter 3 - Experimental Program two had one length of spalled concrete cover at the end of the outside of the flange. Eighteen inches (460 millimetres) of longitudinal reinforcing steel was exposed in flange two. 3.3.3.2 Cracking Most of the visible cracks in beam two were located along the inside of the flanges. Flange one had more cracking damage than flange two. Flange one had more cracks, and the cracks were much wider than in flange two. Flange one had a significant amount of flexure-shear and flexural cracking. Many of the cracks on the inside of flange one began at one of the three regions of missing concrete cover. Flange two had mainly flexural cracking along the inside. 3.3.3.3 Corrosion The exposed reinforcing steel in flange one had very little corrosion damage. In general the bar deformations were slightly corroded while the main surface of the bar is clean of corrosion. The exposed shear ties in flange one were more corroded than the longitudinal steel. The small section of exposed reinforcing steel in flange two was corroded along its entire surface. 3.3.4 Beam Three 3.3.4.1 Missing Concrete and Exposed Reinforcing Steel Most of the damage in beam three was in flange one. Flange one had two main lengths of concrete missing along its bottom. The total length of longitudinal steel exposed in these two regions was 25.5 feet (7.8 metres). There was also a minor spall at the end of flange one along the inside. At this location only a small fraction of the longitudinal bar and shear tie were visible. In flange one the concrete was missing over the bottom of the flange only. There was virtually no concrete loss along the sides of the flange. Flange two was essentially intact and has no significant areas of missing concrete. 3.3.4.2 Cracking Beam three had less cracking than beams one and two. Flange one had flexural cracking along its inside and outside. Flange two also showed flexural cracking, primarily along the inside. 3.3.4.3 Corrosion The amount and length of reinforcing steel corrosion in flange one of beam three was more severe than that found the other three beams. This was because corrosion in flange one covered the bar deformations and much of the bar area over the entire length of exposed steel (25.5 feet/7.8 metres). This degree of corrosion was also evident at the end of flange two in beam two. However, in beam two the corroded length was much less than in beam three (eighteen inches/460 millimetres). 29 Chapter 3 - Experimental Program Although corrosion covered much of the exposed steel in beam three, it did not appear to have caused any significant reduction in bar area. 3.3.5 Beam Four 3.3.5.1 Missing Concrete and Exposed Reinforcing Steel Most of the concrete missing in beam four was from the outside of flange one. The configuration of missing concrete indicated that it was probably removed as a consequence of beam separation. Flange one had one small region of missing concrete cover along its bottom. There was 3.5 feet (1.1 metres) of exposed longitudinal reinforcement in flange one. The surface of flange two was intact over most of its length. There was one concrete spall at the end of flange two where the reinforcement was exposed. The amount of uncovered longitudinal steel in this region was two feet (600 millimetres). 3.3.5.2 Cracking Flange one of beam four had both flexural and flexure-shear cracking. Cracking was most prominent along the inside and bottom of the flange. The region of spalled concrete initiated much of the flexure-shear cracking in this flange. Flange two had primarily flexural cracking. This cracking was most visible along the inside and bottom of the flange. The outside of flange two also had one long crack that follows the longitudinal reinforcement almost the entire length of the beam. 3.3.5.3 Corrosion The exposed reinforcing steel in beam four was not significantly corroded. There was patchy corrosion on the bar deformations. In general, this corrosion did not extend over the bar surface. The exposed reinforcement in flange two was more corroded than in flange one. There did not appear to be any loss of bar diameter due to corrosion in this beam. 4.0 Experiment Set-Up The experiment configuration used for testing the reinforced concrete channel beams is shown from in Figures 3.4, 3.5, and 3.6, and in Photo 3.1. Details of the experiment set-up including the end support conditions and the load configuration used are presented in this section. 30 Chapter 3 - Experimental Program 4.1 Supports The channel beams were simply supported at their ends during testing. The supports consisted of a roller or pin connection mounted on a concrete pedestal. Each pedestal was fixed to the strong-floor using two 'tie-down beams'. This was done to ensure fixity of the supports during flexural-torsional loading. In this load case horizontal forces could cause instability. The tie-down beams were each three feet long, and had holes two feet apart. Dywidag bars connected the tie-down beams to the strong-floor. Photo 3.1: Experiment Set-up 31 Chapter 3 - Experimental Program Chapter 3 - Experimental Program Chapter 3 - Experimental Program Figure 3.6: Experiment Set-Up, End View 34 Chapter 3 - Experimental Program Steel plates were positioned on top of the tie down beams to build up height between the channel beam and the tie-down beams. This was done so that the specimen would not touch the tie down beams while deflecting during testing. The bearings were placed on top of the steel plates. Two roller and two pin supports were used at opposite ends of the beam. Two rollers and pins were used because of the large width of the specimen relative to the available length of pin and roller. The pin connection consisted of a steel plate with a 114 inch (38 millimetre) diameter steel bar welded to it. The roller connection was a VA inch diameter steel bar that was allowed to roll freely over a steel plate. Square bars were welded to the plate to prevent the possibility of the steel bar rolling off the plate during testing. The roller and pin supports are shown schematically in Figure 3.7. (a) Pin Support (b) Roller Support Figure 3.7: End Supports 4.2 Load Configuration Load was applied at approximately the third points of the beam. The exact third points could not be used because the actuators had to be aligned with the two foot hole spacings in the strong floor. As a result, the beam's middle section was six feet (1.8 metres) long, and the end sections were eight feet (2.4 metres) long. The load was applied using four low friction hydraulic load actuators. Each load actuator had a twelve inch (305 millimetre) stroke and a load capacity of 1080 kN in compression. The hydraulic actuators were connected to mounting brackets. These mounting brackets were used to connect the actuators to the load beams and the strong-floor. Two load actuators were located at each load point, on opposite sides of the channel beam. Each actuator pair connected to a steel loading beam that rested on the channel beam. Each of the actuators was connected to the strong-floor by Dywidag bar. 35 5.0 Instrumentation Chapter 3 - Experimental Program The test specimens were instrumented in order to record load, hydraulic pressure in the actuators, vertical and horizontal displacement at various locations, and strain values. Details of the instruments used are included in Appendix 1. 5.1 Applied Load The load in each actuator was monitored by two methods. Load was found from a load cell attached to the Dywidag bars that fixed the actuators to the strong-floor. The strain values found during testing were converted to the corresponding load being applied by each actuator. The hydraulic pressure in the actuators was also monitored throughout the test as an indication of applied load. Hydraulic pressure in the actuators was controlled using a 'load maintainer' unit. For flexural testing each of the four actuators were connected to a single set of input/output hydraulic hoses, thus the hydraulic pressure to each actuator was the same. For torsion testing two sets of input/output lines were used. The pressure in the actuators on the west side of the specimen was calibrated to be twice the pressure of the two actuators on the east side of the concrete beam. 5.2 Vertical Displacement Vertical displacement was monitored at six different locations using a combination of displacement transducers (linear motion potentiometers) and dial gauges with scales. All instrumentation for measuring vertical displacement was supported from above the specimen. Four displacement transducers were used to monitor vertical displacement of the beam. The displacement transducers each had a range of six inches (150 millimetres). Displacement transducers were placed in pairs at the centre line, and at approximately 80 inches (two metres) from the end of the beam. Each displacement transducer was set near the outside edge of the beam. This was done in order to determine the effects of twisting that occurred during the flexural-torsional testing. This had the added benefit of providing redundancy during flexural testing. In addition to the four displacement transducers, two dial gauges with scales were also used to measure vertical deflection of the concrete beam. The dial gauges each had a range of one inch (25 millimetres), and the scale was divided into 0.01 inch increments. Scales were read manually periodically during testing. Displacement transducers and dial gauges with scales were each attached to a magnetic base that was connected to steel framing over the experiment set-up. A column beside the test set-up supported this steel framing. The tip of each displacement transducer and dial gauge rested upon a small steel plate mounted to the top of the channel beam in order to provide an even bearing surface. Two displacement transducers and a dial gauge and scale positioned on top of a channel beam are shown in Photo 3.2. 36 Chapter 3 - Experimental Program Dial Displacement Gauge Transducers Photo 3.2: Vertical Displacement Instrumentation on Top of Beam 5.3 Strain Strain in the reinforcing steel was measured using strain gauges. Strain gauges were applied to exposed longitudinal reinforcing steel. Since exposed reinforcing steel was in variable locations in each of the beams, strain gauges were in different positions in each channel beam. Beams one and two each had two strain gauges, and beams three and four each had one. Strain gauges were applied to the imperial sized number ten bar in the flange. Average concrete strain, or average effect concrete cracks opening over a set gauge length, was also measured in the concrete. This was recorded at the top and bottom of the channel beam using two linear variable displacement transducers (LVDTs). The two LVDTs measured the horizontal reduction or extension of the beam length over a 500 millimetre gauge length. This was then converted to an averaged strain measurement by dividing the displacement recorded by the LVDT by the gauge length. A fine threaded rod was attached to the end of the LVDT probe by shrink tubing in order to extend the gauge length to 500 millimetres. A bracket that was fixed to an aluminum plate supported the LVDT. The aluminum plate was attached to the channel beam using epoxy. The end of the threaded rod was supported by a small piece of four inch (100 millimetre) aluminum channel. This LVDT configuration is depicted in Photo 3.3. 37 Chapter 3 - Experimental Program Photo 3.3: Horizontal LVDT on Top of Beam 5.4 Horizontal Displacement Horizontal displacement of the beam was measured at one of the roller supports using a dial gauge and scale. The dial gauge had a range of 10 millimeters, and the scale was divided into 0.01 millimetre increments. The dial gauge and scale were supported on a steel rod attached to a magnetic base. This magnetic base attached to the steel plates beneath the roller. The dial gauge tip rested on the roller. The scale was read manually during testing. Photo 3.4 shows the dial gauge and scale used for measuring beam horizontal displacement. Photo 3.4: Dial Gauge and Scale at Roller Support 38 Chapter 3 - Experimental Program 5.5 Data Acquisition System In total sixteen different quantities were monitored during this test. Each separate measurement required a separate channel on the data acquisition system. Data from each of the instruments was read and recorded to the computer file every second. 6.0 Application of Retrofit Materials 6.1 Introduction Beams three and four were selected for GFRP retrofit. These two beams were chosen because they were the simplest to repair. Beams three and four had the least amount of missing concrete and cracking damage along the insides of the flanges. The cross sectional damage in these two channels was mostly limited to missing concrete cover over the longitudinal reinforcement. Surface preparation for retrofit, and application of retrofit materials was done with the beams upside down so that their undersides were exposed. This was done for increased accessibility, and for ease in application of materials. This would not be the case if the retrofit were to occur on a real bridge. GFRP was applied only to areas that would be exposed i f these girders were still a part of a bridge. The GFRP was applied over the underside of the web, the insides of the flanges, and the bottom of the flanges only. GFRP was not applied to the outsides or top of the beams. The following parts of this section outline the procedures used for surface preparation of the beams, the application of GFRP spray, and the application of GFRP wrap. 6.2 Surface Preparation The first step in the channel beam retrofit process was to prepare the surface for the application of GFRP wrap or spray. In most surface preparations existing corrosion should be cleaned from exposed reinforcement. In this case the corrosion was not removed from the surface of the reinforcing steel. Corrosion should be removed in the case of a real bridge so that it does not continue to propagate in the reinforcement. Since these beams were to be tested immediately, existing steel corrosion was left in place. The beam cross section was restored to its original shape before applying GFRP. This was done by applying grout to areas of missing concrete areas. A section of the restored beam surface is shown in Photo 3.5. The restored cross section was sandblasted prior to the application of the GFRP spray. Sandblasting was not considered a necessary surface preparation for the GFRP wrap. Next, a primer was applied. A primer was used for both the GFRP wrap and spray applications. The primer used on the beam retrofit with GFRP spray was vinyl ester. A n epoxy primer was used on the beam that was to be retrofit with GFRP wrap. The primer application for beam three is depicted in Photo 3.6. 39 Chapter 3 - Experimental Program Chapter 3 - Experimental Program 6.3 Application of GFRP Spray GFRP spray was applied to beam three. The GFRP spray was applied using a machine manufactured by Venus-Gusmer. This equipment is shown in Photo 3.7. In this application, polyester and catalyst were mixed in a ratio of three percent catalyst to polyester. The multi-filament glass fibre was cut into 48 millimetre lengths by the chopper unit. GFRP spray was applied first to the underside of the web, then to the bottoms of the flanges, and finally to the insides of the flanges. The GFRP was first sprayed over the entire length of the web underside. Next, serrated rollers were used to remove air and to condense the fibres into a two dimensional matrix. Once this was completed, a second pass of GFRP was sprayed on the bottom of the web, and the process of rolling the mixture was repeated. In total, this process of spraying and rolling was repeated three times for the underside of the web. This same procedure was followed when applying GFRP spray to the bottoms and insides of the flanges. In total, ten millimetres of GFRP spray was applied to the underside of channel beam three. The GFRP spray cured for approximately forty hours prior to ultimate load testing. The GFRP spray application process is shown in Photos 3.8 and 3.9. Photo 3.7: GFRP Spray Application Machine 41 Chapter 3 - Experimental Program Chapter 3 - Experimental Program 6.4 Application of GFRP Wrap GFRP wrap was applied to beam four. The GFRP wrap used for the retrofit of beam four was the MBrace™ Composite Strengthening System. This system consists of a primer, unidirectional E-glass fabric, and an impregnating resin. The first step in the GFRP wrap application process was to cut fabric pieces to the desired size. Pieces of fabric were cut to fit the underside of the web, the insides of the flanges, and the bottom of the flanges. The MBrace™ GFRP wrap system was applied once the primer had set. First, the impregnating resin was applied to the primed surface using a paintbrush. Then the fabric was set into place, and serrated rollers were used to remove any air existing between the impregnating resin and the fabric. Once this was completed, a final coat of impregnating resin was applied. The product was then condensed a final time using the serrated rollers. The GFRP wrap was applied in sections. First, the wrap was applied to the bottom of the flanges, then to the insides of the flanges, and finally to the underside of the web. The GFRP was allowed to cure for about forty hours prior to testing. The fabric for the underside of the web was positioned such that the unidirectional fibres were parallel to the longitudinal axis of the beam (0° orientation). The fabric on the insides of the flanges was placed so that the fibres were perpendicular to the beam's longitudinal direction (90° orientation). Two layers of unidirectional fabric covered the bottoms of the flanges. One layer was parallel and one layer was perpendicular to the longitudinal axis of the beam (0°-90° orientation). The fabric was placed in two different directions in order to best align the fibres with the direction of the stresses during loading. At the bottom of the web and flanges longitudinal fibres are intended to carry tension forces due to bending. Along the insides of the flanges vertical fibres are best suited to resist shear stresses. The GFRP wrap application process is shown in Photos 3.10 and 3.11. The completed retrofit using GFRP wrap is shown in Photo 3.12. 43 Chapter 3 - Experimental Program Chapter 3 - Experimental Program Photo 3.12: Completed GFRP Wrapped Beam 7.0 Test Procedure Four reinforced concrete channel beams were included in this test program. Each of the four channel beams was first tested within its elastic range in order to obtain initial elastic stiffhess properties in flexure and torsion. Elastic flexural and torsional stiffhess testing was performed a second time on beams three and four after being retrofit. This was done in order to determine the increase in stiffhess relative to the non-retrofit reinforced concrete section. After initial elastic stiffness testing was completed, each channel beam was tested to failure. The load configuration, shear force diagram, bending moment diagram, and torsion diagrams along the length of the span for the two different load conditions are shown in Appendix 1. The load condition used to induce failure, and the retrofit condition of each beam are summarized in Table 3.2. 45 Chapter 3 - Experimental Program Beam Load Retrofit Condition Condition 1 Flexural Not Retrofit 2 Flexural-Torsional Not Retrofit 3 Flexural GFRP Spray 4 Flexural GFRP Wrap Table 3.2: Beam Designation 7.1 Initial Elastic Stiffness In this series of tests the channel beams were loaded within their elastic range in order to determine initial elastic flexural and torsional stiffness. 7.1.1 Initial Elastic Flexural Stiffness During initial elastic flexural stiffness testing, each of the four actuators applied uniform load. This load was controlled using a load maintainer unit to regulate hydraulic pressure in the actuators. The force was increased steadily over two to three minutes from zero to a maximum load ranging from 20 to 25 kN in each actuator. This load was then maintained for five minutes in order to allow the actuators time to stabilize. The applied force was then removed. The system was then allowed five minutes in order to ensure the pressure in the actuators had stabilized to a zero applied load condition. This procedure was repeated five times. The load was cycled multiple times in order to determine the true elastic stiffness of the channel beam. 7.1.2 Initial Elastic Torsional Stiffness Initial elastic torsional stiffness testing was performed after elastic flexural stiffness testing was completed. For this test the actuators on the west side of the channel beam were set to exert twice the pressure of the actuators on the east side. The loading procedure was the same as for initial flexural stiffness testing. Pressure in the actuators was increased steadily over a two to three minute period from zero until the load on the west side ranged from 20 to 25 kN. The actuators were then allowed five minutes to stabilize. After five minutes the system was unloaded. The actuators were then given five minutes to ensure zero load. This procedure was repeated three times. 7.2 Ultimate Load Testing Channel beams were tested to failure after initial elastic flexural and torsional stiffness testing was completed. Beams one, three, and four were tested to their ultimate load under flexural loading. Beam two was tested to failure by torsional-flexural loading. 46 Chapter 3 - Experimental Program 7.2.1 Ultimate Flexural Loading Ultimate flexural loading was performed on channel beams one, three, and four. For each of these three beams, uniform hydraulic pressure in each of the four actuators was increased to create additional downward force on the beam. First, initial measurements from the dial gauges on the top of the beam and at the roller were recorded. The load was then increased from zero to approximately 20 to 25 kN per actuator (100 lb/in 2 / 690 kPa hydraulic pressure) within two to three minutes. The hydraulics were then allowed a few minutes to stabilize. At this point, the readings from the dial gauges were recorded. The load was held constant for thirty minutes. The downward force on the beam was then increased to approximately 32 to 38 kN per actuator (160 lb/in 2 /1100 kPa hydraulic pressure) and then to approximately 43 to 48 k N per actuator (195 lb/in 2 / 1345 kPa hydraulic pressure). At each of these load levels the load was maintained for 30 minutes. After maintaining the hydraulic pressure for 90 minutes over three increasing load levels, the beams were then loaded to failure by increasing the pressure in the hydraulic actuators. Failure was defined by a significant reduction in load carrying capacity of the system. 7.2.2 Ultimate Flexural-Torsional Loading Beam two was loaded to failure under a combined torsion and flexural load condition. This load condition was generated by setting the actuators on the west side of the beam to apply twice the hydraulic pressure of the actuators on the east side. Ultimate flexural-torsional load testing followed a procedure similar to ultimate flexural load testing. After initial dial gauge readings were recorded, the pressure in the actuators was increased steadily until a load of 22 kN was obtained in each of the west side actuators (100 lb/in 2 / 690 kPa hydraulic pressure). The corresponding load in each of the actuators on the east side of the beam at this pressure was 12 kN. The actuators were then allowed a few minutes to stabilize before dial gauge reading were taken. This pressure level was maintained for thirty minutes. The load was then increased to 35 kN per actuator on the west side and 18 kN per actuator on the east side (165 lb/ in 2 / 1140 kPa hydraulic pressure). This pressure was again maintained for thirty minutes. The final constant load interval was 44 kN per actuator on the west side and 22 kN per actuator on the east side (200 lb/ in 2 / 1380 kPa hydraulic pressure). This pressure was also maintained for thirty minutes. After the third load interval, the load on the beam was increased until failure occurred. 47 8.0 Beam Failure Modes Chapter 3 - Experimental Program 8.1 Beam One Beam one was tested to failure under flexural loading. This beam did not receive any retrofit material. Under increased loading a diagonal crack formed within the shear zone of the beam. This crack initiated from a region of missing concrete cover, and progressed upwards towards the top of the beam. The crack was truncated when it reached the compression zone underneath the load beam. At this point, the crack was forced to proceed horizontally under the load beam into the central, flexure zone. This crack is shown in Photo 3.13. Although the instability within this beam started with cracking in the shear zone, the ultimate failure mode of beam one was in flexure. With increasing load the concrete in the top middle third of the beam began to crush. Crushing in the concrete compression block caused the ultimate flexural failure of channel beam one. The longitudinal reinforcing steel had yielded when failure occurred. Crushing of the concrete at the top of the beam is shown in Photos 3.14 and 3.15. Photo 3.16 shows the permanent deflected shape of beam one after the applied load was removed. Photo 3.13: Beam One, Initiating Shear Crack 48 Chapter 3 - Experimental Program Photo 3.14: Concrete Crushing in Failure Zone of Beam One Photo 3.15: Concrete Crushing in Failure Zone of Beam One (Close-up) 49 Chapter 3 - Experimental Program Photo 3.16: Beam One, Final Deflected Shape 8.2 B e a m Two Beam two was tested under flexural-torsional loading. This beam was tested to failure in its original state, without any applied retrofit material. Beam two failed in shear. Under increased loading, diagonal cracks within the shear zones formed and opened. At the failure location, significant shear cracking was evident on the outside of both flanges at approximately the same distance from the load beam. The shear cracking on the most heavily loaded side eventually progressed through the entire depth of the beam and caused the failure. The crack causing the shear failure of beam two is shown in Photo 3.17. The associated cracking on the opposite side of the beam, adjacent to the failure zone is shown in Photo 3.18. The final deflected shape of beam two with the load removed is shown in Photo 3.19. 50 Chapter 3 - Experimental Program Chapter 3 - Experimental Program Photo 3.19: Beam Two, Final Deflected Shape 8.3 Beam Three Beam three was tested to failure under flexural loading. This beam was retrofit using 10 millimetres of GFRP spray. Under increased loading, extension of flexural cracking was evident underneath the GFRP layer in the middle third of the beam. Beam three failed suddenly when the tensile capacity of the sprayed fibre mesh was exceeded. This failure occurred within the middle third of the beam. At failure the GFRP fractured in tension, and a crack formed along the length of the longitudinal reinforcement. This crack began at the failure location and spread to almost the centre of the beam, a length of approximately three feet (900 millimetres). The concrete within the top of the compression zone within the middle third of the beam crushed after the GFRP failed. The longitudinal reinforcing steel had yielded, and the concrete surrounding the reinforcing steel had disintegrated when tensile failure of the GFRP occurred. The failure of beam three is presented in the following photos. Photos 3.20 and 3.21 show the rupture of the GFRP. Photo 3.22 shows the crack that formed along the length of the longitudinal reinforcement during the failure of the GFRP. Photo 3.23 indicates the final deflected shape of beam three. 52 Chapter 3 - Experimental Program Chapter 3 - Experimental Program Chapter 3 - Experimental Program 8.4 Beam Four Beam four was tested to failure under flexural loading. This beam was loaded to failure after having been retrofit with two layers of unidirectional GFRP wrap in a 0°-90° orientation over the flanges, and a single layer of unidirectional GFRP wrap over the bottom of the web. Under increasing load, the formation of flexural cracks in the middle third of the beam was evident by delaminations of the GFRP fabric. This flexural cracking is shown in Photo 3.24. Longitudinal cracking also began along the bottom of the beam. No crack development was evident in the shear regions of the beam. The failure of beam four occurred when the GFRP fabric reached its ultimate tensile capacity. The splitting of the GFRP fabric was initiated by one of the many flexural cracks within the centre third of the beam. This GFRP fabric rupture is shown in Photo 3.25. Concrete within the top middle third of the beam crushed after the failure of the GFRP. The bottom longitudinal reinforcement had yielded when failure occurred. Cracking along the bottom longitudinal reinforcement also opened significantly at failure. This cracking is shown in Photo 3.26. Photo 3.27 shows the final deflected shape of beam four after all applied load was removed. Photo 3.24: Flexural Cracking 55 Chapter 3 - Experimental Program Chapter 3 - Experimental Program 9.0 Results 9.1 Initial Elastic Stiffness Testing Results 9.1.1 Initial Elastic Flexural Stiffhess The initial elastic flexural stiffhess of each of the four channel beams was found from elastic flexural testing as described in Section 7.1.1 of this chapter. An initial elastic flexural test was performed on each of the four channel beams. Beams three and four were tested for elastic flexural stiffhess both before and after GFRP application. Graphs of total load versus average centre deflection for each of the four beams are presented in Figures 3.8 to 3.11. In these figures, total load refers to the sum of the load applied by all four actuators. Average centre deflection corresponds to the averaged results of the two displacement transducers at the centre of the beam. The initial elastic stiffhess for each beam was obtained from the slope of the total load versus average centre deflection relationship. In the calculation of initial elastic deflection data from the first load cycle is neglected because it was not consistent with data from load cycles two through five. A sample calculation of an initial elastic stiffhess value from experimental results may be found in Appendix 1. Initial elastic flexural stiffhess results for each beam are summarized in Table 3.3. Elastic flexural stiffhess values obtained from ultimate load testing are also included in Table 3.3. 57 Chapter 3 - Experimental Program 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Average Centre Deflection (mm) Figure 3.8: Beam One, Initial Flexural Loading, Total Load versus Average Centre Deflection 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Average Centre Deflection (mm) Figure 3.9: Beam Two, Initial Flexural Loading, Total Load versus Average Centre Deflection 58 Chapter 3 - Experimental Program 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Average Centre Deflection (mm) Figure 3.11: Beam Four, Initial Flexural Loading, Total Load versus Average Centre Deflection 59 Chapter 3 - Experimental Program Beam Retrofit Test Flexural Condition Stiffness [EI] (Nmm2) 1 No Retrofit Initial Stiffhess 4.10E+13 1 No Retrofit Ultimate Load 3.52E+13 \ 2 No Retrofit Initial Stiffness 4.66E+13 3 No Retrofit Initial Stiffhess 4.82E+13 3 GFRP Spray Initial Stiffness 6.04E+13 3 GFRP Spray Ultimate Load 4.97E+13 4 No Retrofit Initial Stiffhess 3.40E+13 4 GFRP Wrap Initial Stiffness 4.78E+13 4 GFRP Wrap Ultimate Load 4.16E+13 Table 3.3: Summary of Flexural Stiffhess Values 9.1.2 Initial Elastic Torsional Stiffhess Initial elastic torsional stiffhess of the channel beams is based on results of elastic torsional stiffhess testing as outlined in Section 7.1.2 of this chapter. Elastic torsional stiffhess testing was performed on beams one and two in without any retrofit. Beams three and four were tested twice for elastic torsional stiffness, both before and after being retrofit. Initial elastic torsional stiffhess is based on the relationship between torsion within the channel beam and the angle of twist per unit length. Sample calculations of initial elastic torsional stiffness may be found in Appendix 1. Data from all three load cycles was used in calculating the elastic torsional stiffness, as the data was from each of the load cycles was consistent. Plots of torsion versus angle of twist per unit length 80 inches (2030 millimetres) from the end of the beam for each of the four channel beams are shown in Figures 3.12 to 3.15. Values for initial elastic torsional stiffhess are summarized in Table 3.4. This table also indicates elastic torsional stiffhess values found from ultimate load testing of beam two. 2.50E+O6 2.00E+06 i 1.50E+06 a .2 | 1.00E+06 H 5.00E+05 0.00E+00 0.00E+00 5.00E-07 1.00E-06 1.50E-06 2.00E-06 2.50E-06 3.00E-06 Angle of Twist per Unit Length at Third Point (rad/mm) Figure 3.12: Beam One, Initial Flexural-Torsional Loading, Torsion versus Angle of Twist per Unit Length at Third Point 60 Chapter 3 - Experimental Program 2.5E+06 2.0E+06 1.5E+06 a .o I 1.0E+06 H 5.0E+05 0.0E+00 0.0E+00 5.0E-07 1.0E-06 1.5E-06 2.0E-06 2.5E-06 3.0E-06 Angle of Twist per Unit Length at Third Point (rad/mm) Figure 3.13: Beam Two, Initial Flexural-Torsional Loading, Torsion versus Angle of Twist per Unit Length at Third Point 2.50E+06 1 2.00E+06 1.50E+06 a .g I 1.00E+06 5.00E+05 0.00E+O0 0.00E+00 5.00E-07 1.00E-06 1.50E-06 2.00E-06 2.50E-06 3.00E-06 Angle of Twist per Unit Length at Third Pont (rad/mm) Figure 3.14: Beam Three, Initial Flexural-Torsional Loading, Torsion versus Angle of Twist per Unit Length at Third Point 61 Chapter 3 - Experimental Program 2.50E+O6 i 0.00E+00 5.00E-07 1.00E-06 1.50E-06 2.00E-06 2.50E-06 3.00E-06 Angle of Twist per Unit Length at Third Point (rad/mm) Figure 3.15: Beam Four, Initial Flexural-Torsional Loading, Torsion versus Angle of Twist per Unit Length at Third Point Beam Retrofit Test Torsional Condition Stiffness [GJ] (Nmm2) 1 No Retrofit Initial Stiffness 1.23E+12 2 No Retrofit Initial Stiffness 9.73 E+11 ! 2 No Retrofit Ultimate Load 7.59E+11 3 No Retrofit Initial Stiffness 7.93E+11 3 GFRP Spray Initial Stiffness 1.52E+12 4 No Retrofit Initial Stiffness 7.07E+11 ! 4 GFRP Wrap Initial Stiffness 1.06E+12 Table 3.4: Summary of Torsional Stiffness Values 9.2 Flexural Load Test Results 9.2.1 Total Applied Load Versus Vertical Deflection at Midspan Beams one, three, and four were tested to failure with a flexural load condition. Applied load versus vertical deflection of the beam is shown in Figure 3.16. In this figure, total load corresponds to the sum of the load applied by all four actuators. Average centre deflection represents the averaged vertical displacement between the two linear displacement transducers at the midspan of the beam. The maximum moment and maximum vertical deflection results for each beam are summarized in Table 3.5. 62 Chapter 3 - Experimental Program 0 25 50 75 100 125 150 Average Centre Deflection (mm) Figure 3.16: Beams 1, 3, and 4, Ultimate Flexural Loading, Total Load versus Average Centre Deflection Beam Ultimate Maximum Flexural Vertical Load Deflection (kN) (mm) 1 237 114 3 470 j 128 4 323 143 Table 3.5: Summary of Maximum Load and Vertical Deflection 9.3 Ultimate Flexural-Torsional Load Test Results 9.3.1 Torsion Versus Angle of Twist per Unit Length at Third Point Beam two was tested to failure with a flexural-torsional load condition. Figure 3.17 shows the relationship between torsional forces and angle of twist per unit length 80 inches (2030 millimetres) from the end of the beam. The maximum torsion at the centre of the beam was 4.33 kNm and the maximum angle of twist per unit length was 1.56 x 10"5 rad/mm. 63 Chapter 3 - Experimental Program 5.0E+06 a o B o 0.00E+00 2.50E-06 5.00E-06 7.50E-O6 1.00E-05 1.25E-05 1.50E-05 1.75E-05 Angle of Twist per Unit Length at Third Point (rad/mm) Figure 3.17: Beam Two, Torsion versus Angle of Twist per Unit Length 9.4 Flexural and Flexural-Torsional Test Results 9.4.1 Strain 9.4.1.1 Longitudinal Strain Strain was monitored at three different depths within the beam cross section. Average concrete strain measurements were recorded at the top and bottom of the beam cross section using an LVDT extended over a 500 millimetre gauge length. Strain was also measured in the longitudinal reinforcing steel using strain gauges. The position of each of the strain measurements along the length of each beam is summarized in Table 3.6. Distance From South End of Beam Beam Top and Bottom LVDTs Longitudinal Steel Strain Gauge 1 Strain Gauge 2 (metres) (feet) (metres) (feet) (metres) (feet) j 1 3.60 11.8 2.65 8.7 3.45 11.3 2 3.35 11.0 3.00 9.9 4.60 15.2 3 3.35 11.0 3.40 11.2 — . . . 4 3.35 11.0 1.95 6.5 — . . . Table 3.6: Position of Strain Measurements Along Length of Beam 64 Chapter 3 - Experimental Program Figures 3.18 to 3.21 show the relationship between total load in the four actuators versus strain during ultimate load testing for each of the beams. In these charts, compressive strain considered as negative. Peak values from these charts are summarized in Table 3.7. The results from only one strain gauge are shown for beams one and two. This is because in these beams the two strain gauges recorded similar results. In many cases strain values just prior to failure were not obtained or were disregarded. For example, the LVDT on the bottom of the beam was always removed prior to failure so that it would not be damaged. In some cases, strain gauge measurements became unstable under increasing load and thus this data is not included in the following figures. As a result, values shown in Figures 3.18 to 3.21 and in Table 3.7 represent the maximum recorded values. These are not necessarily the maximum strain values experienced by the beam. 400 - i 350 1 300 j -O Top Long. Steel Bottom -0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004 Strain Figure 3.18: Beam One, Total Load versus Strain 65 Chapter 3 - Experimental Program a -Top -Long. Steel -Bottom i 1—1 1 -0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004 Strain Figure 3.19: Beam Two, Total Load versus Strain -0.004 -0.003 -0.002 -0.001 0.000 0.001 0.002 0.003 0.004 Strain Figure 3.20: Beam Three, Total Load versus Strain 66 Chapter 3 - Experimental Program 400 -0.004 -0.003 -0.002 -0.001 0.000 0.001 0.002 0.003 0.004 Strain Figure 3.21: Beam Four, Total Load versus Strain Beam Maximum Load at Maximum Load at Maximum Load at Recorded Maximum Recorded Maximum Recorded Maximum Strain at Top Strain Strain in Rebar Strain at Bottom Top of Rebar Strain Bottom of Strain Beam Beam (um) (kN) (pm) (kN) (um) (kN) 1 -2600 209 1400 195 1000 146 2 -600 175 1200 171 1600 138 3 -3400 411 2500 398 1800 206 4 -4200 283 1400 235 2700 229 Table 3.7: Summary of Maximum Recorded Strain Values and Corresponding Total Load 9.4.1.2 Strain Distribution The strain distribution through the cross section of the beam for at increasing levels of total applied load are shown in Figures 3.22 to 3.25. 67 Chapter 3 - Experimental Program 40 kN 80 kN 100 kN 130 kN -0.0008 -0.0004 0 0.0004 0.0008 0.0012 0.0016 Strain Figure 3.23: Beam Two, Strain Profiles 6 8 Chapter 3 - Experimental Program 69 Chapter 3 - Experimental Program 9.4.2 Horizontal Displacement Horizontal displacement of the beam with increased flexural loading was monitored through the use of a dial gauge positioned on one of the rollers. Readings for horizontal displacement were taken manually during the test. Results for total load in all four actuators versus horizontal displacement of the channel beam are shown in Figure 3.26. The results shown for horizontal displacement were obtained while the beam was within its elastic range. Manual horizontal displacement recordings were not taken as the beam approached failure. 200 175 150 % 1 2 5 | 100 a e 75 50 25 0 0.0 0.5 1.0 1.5 2.0 2.5 Horizontal Displacement (mm) Figure 3.26: Ultimate Loading, Total Load versus Horizontal Displacement 9.5 Summary of Experimental Results In this section results from the experimental program have been summarized. Elastic flexural and torsional stiffhess values were found from initial elastic stiffness testing. Beam response from ultimate flexural and flexural-torsional load testing was also found. For ultimate flexural loading the total applied load versus vertical midspan deflection response was presented. For flexural-torsional loading the torsion versus the angle of twist per unit length at the third point of the beam was shown. The longitudinal strain and horizontal deflection response under increased loading was also presented for each of the four beams in the test program. 70 10.0 Applicability and Accuracy of Results Chapter 3 - Experimental Program 10.1 Applicability of Results 10.1.1 Differences in Beam Damage States and Comparison of Results Each of the beams tested had a different amount and type of damage. As a result, there is no control specimen in this series of tests in which to reference variations in structural behavior. Experimental results from the different beams may not be directly comparable. This is unavoidable due to the nature of the specimens in this test program. 10.1.2 Damage Due to Beam Separation Process The process of removing the shear key from adjacent beams caused some of the damage to the beams. Damage due to beam separation was evident as concrete missing from the widest part of the section. As a result, the degree of damage evident in these four beams may not be truly representative of the damage state for a beam in an existing bridge. 10.1.3 Load Condition The load condition used in this series of experiments is not representative of the loading that would occur if this were a bridge in service. In these tests, load was applied slowly at approximately the third points of the beams. This load was held constant for three, thirty minute long intervals within the beam's elastic range. In an actual bridge, live load would generally be applied quickly, over the entire beam as vehicles pass over the bridge at high speeds. This type of loading was chosen for its simplicity. This load configuration was easy to set-up, and the results are simple to use in order to obtain mechanical properties for the bridge. The load was maintained for three, thirty minute intervals to check if increased vertical displacement would occur under constant load. Additional vertical deflection will reduce the effective elastic stiffness calculated for a beam. This provides a conservative estimate for the beam's elastic stiffness. 10.1.4 Boundary Conditions In this series of experiments, the beams were simply supported using a pin and roller at opposite ends of the beam. In an actual bridge, these bridge girders would be simply supported using elastomeric bearings. This difference in boundary conditions will have an effect on the stiffness found for the channel beams. A beam will deflect more under a given load when supported by a pin and roller than when elastomeric bearings are used. As a result, the effective stiffness values found from these experiments will be less than might be found for a bridge of this type in the field. A pin and roller type of simple support condition was chosen because it is simple to use and provides a conservative estimate of beam stiffness. 71 10.2 Accuracy ofResults Chapter 3 - Experimental Program 10.2.1 Support Seating Seating of the supports was measured during the ultimate load testing of channel beam four. During this test, the height of the support was measured at maximum load and after unloading. Based on these measurements, it is estimated that seating in the supports accounts for two to three millimetres of the total vertical deflection. This was neglected in the experimental results presented in this chapter, and in calculating effective stiffhess values. 10.2.2 Electrical Interference During some of the tests electrical interference due to other activity in the laboratory was noted in the data. These inconsistencies in the data were limited to single occasional points within the data set. Such irregularities were deleted when processing and analyzing test data. 72 CHAPTER 4 FINITE ELEMENT ANALYSIS 1.0 Introduction This chapter describes the development of three channel beam bridge deck finite element models. Finite element models are created for a non-retrofit reinforced concrete channel beam bridge deck, a channel beam bridge deck retrofit with GFRP spray, and a channel beam bridge deck retrofit with GFRP wrap. Finite element modeling is done using SAP2000® software (version 6.1). First, a finite element model of a single, non-retrofit, reinforced concrete channel beam is developed using solid elements. This model is then checked for accuracy by comparing its output to experimental test results for non-retrofit beams. Details of this reinforced concrete channel beam finite element model are given in section three. Section four describes the creation of two retrofit, channel beam finite element models. One model simulates the reinforced concrete channel beam with a GFRP spray retrofit. The second model corresponds to the channel beam retrofit with GFRP wrap. In these models, shell elements representing the GFRP are added to the reinforced concrete channel beam model developed in section three. The retrofit channel beam models are then checked for accuracy. The increase in flexural and torsional stiffhess, and the reduction in longitudinal stress relative to the non-retrofit model are found for each of the retrofit channel beam models. These results are then compared to experimental results in order to verify model behavior. Section five explains the development of three single span channel beam bridge deck finite element models. Models are produced for a non-retrofit, reinforced concrete bridge deck; a bridge deck retrofit with GFRP spray; and a bridge deck retrofit with GFRP wrap. The bridge deck models are created by joining ten individual channel beam models. The bridge deck finite element models are then used to predict bridge deck behavior. Bridge deck finite element model results are presented in section six. Vertical deflection and longitudinal stress within the bridge deck model flanges are summarized for each of the three bridge deck models. 73 2.0 Limitations of Model Chapter 4 - Finite Element Analysis All of the finite element models in this study exhibit elastic behavior only. This is because the SAP2000® solid and shell elements used to develop the models do not have inelastic capabilities. As a result of this limitation, the finite element models created will not accurately reflect behavior beyond the yield point of the channel beam. In order to assess the applicability of finite element results, it is necessary to determine if the model has been loaded beyond the actual elastic range of the channel beams. Model deflection values are compared to the experimental results from flexural and flexural-torsional load testing in order to determine if beam behavior should be elastic or inelastic. Based on flexural load test results, the non-retrofit beam, the channel beam retrofit with GFRP spray, and the channel beam retrofit with GFRP wrap all yielded when their midspan displacement was approximately 33 millimetres. As a result, the finite element models are considered valid if midspan deflection is less than 33 millimetres. Experimental flexural-torsional load test results showed that a non-retrofit channel beam yielded at approximately 4xl0"6 rad/mm at the third point of the span. Finite element models are considered valid if the curvature at the third point is less than this yield value. The flexural load versus midspan deflection curve based on experimental results is shown in Figure 3.18 of this report. The experimental torsion versus angle of twist per unit length at the third point of the beam span response is presented in Figure 3.19. 3.0 Model of an Individual, Non-Retrofit, Reinforced Concrete Channel Beam This section describes the development of an individual, non-retrofit, reinforced concrete channel beam finite element model. This channel beam model is described in terms of its elements, coordinate system, geometry, material properties, and boundary conditions in section 3.1. The model is then checked for accuracy in section 3.2 by comparing its output to flexural stiffness, torsional stiffness, and longitudinal stress results obtained from the experimental program. 3.1 Finite Element Model Description 3.1.1 Elements The reinforced concrete channel beam was modeled as a series of solid elements. SAP2000® solids are three-dimensional elements with six quadrilateral faces. There is a node with three translational degrees of freedom at each of the eight solid element corners. Stresses are calculated using a 2x2x2 Gauss integration scheme. The results of this stress calculation are extrapolated to the element nodes.(38) 74 Chapter 4 - Finite Element Analysis 3.1.2 Coordinate System A rectangular coordinate system with x, y, and z axes was used for the reinforced concrete channel beam finite element model. The longitudinal axis of the channel beam was aligned with the x-axis, and the cross section of the beam was in the y-z plane. 3.1.3 Geometry The cross section of the non-retrofit, reinforced concrete channel beam was modeled using 35 solid elements. Each of the elements in the cross section was 50 millimetres by 50 millimetres in size. Cross sectional geometry of the channel beam finite element model is shown in Figure 4.1. Seventy-two solid elements were used along the channel beam's 6700 millimetre length. The solids were 50 millimetres in length within 250 millimetres of the span ends. The elements were 100 millimetres in length within the central 6200 millimetres of the span. Shorter length elements were used at the ends of the beam in order to increase the number of different span lengths that could be generated. In total, 2520 solid elements were used in the reinforced concrete channel beam section model. Figure 4.2 shows the three dimensional view of the channel beam finite element model. 950 mm | | Solid Element • Node Figure 4.1: Cross Section of Reinforced Concrete Channel Beam Finite Element Model 75 Chapter 4 - Finite Element Analysis Figure 4.2: Three Dimensional View of Reinforced Concrete Channel Beam Finite Element Model 3.1.4 Material Properties The reinforcing steel and the concrete were modeled as a single material with averaged material properties in this analysis. This was done in order to simplify the finite element model. The solid elements in the reinforced concrete channel beam finite element model were given isotropic material properties. The solid elements were assigned a modulus of elasticity (E) of 26,000 MPa, a torsional modulus of rigidity (G) of 1,000 MPa, a Poisson's ratio (u) of zero, and a mass (m) of zero. The torsional modulus of rigidity value was set lower than would typically be expected for a reinforced concrete structure with a concrete compressive strength of 35 MPa. With a typical modulus of rigidity value (10,000 to 15,000 MPa) the model had much greater torsional stiffhess than found from experimental results. In order to reduce the model's torsional stiffhess, the torsional modulus of rigidity was set to an artificially low value of 1,000 MPa. Mass of the solid elements was set to equal zero. As a result, this channel beam model had no dead load due to its own weight. This was done because deflection values found in the experiment do not include displacement caused by self-weight of the beam. Since output from this model will be compared to experimental results, the dead load of the beam has been neglected. 3.1.5 Boundary Conditions The reinforced concrete channel beam model was fixed at nodes located 200 millimetres from its ends in the lateral (y) and vertical (z) directions. These were the same locations where supports were set during the experiments, thus the span length was the same as was used in the test program. The beam was fixed in the longitudinal direction (x) at the midspan. 76 Chapter 4 - Finite Element Analysis The boundary condition fixity was slightly different from that used in the experiments. In the testing program, the channel beams were supported by a pin connection at one end of the beam, and a roller support at the opposite end. In preliminary model testing, the use of a pin connection at one of the beam's ends was found to generate a model that was too rigid. Boundary conditions were revised to include roller supports at both its ends to reduce this apparent stiffness. The required longitudinal restraint of this beam was provided at the beam's midspan. The midspan was chosen as the location for longitudinal restraint because the load configurations used on this beam are symmetrical about the midspan. As a result, there should theoretically be no longitudinal movement at the centre of the beam. These boundary conditions generated a model that was less rigid, without otherwise changing the behavior of the channel beam model. 3.2 Verification of Model The finite element model of the reinforced concrete channel beam was tested for accuracy by applying loads in the same configuration as used in the experimental program. Model output was then compared to experimental results from elastic range initial stiffness testing. The channel beam finite element model was loaded by point loads placed on nodes along the top surface of the beam. Two lines of point loads were used. A series of point loads was placed 2450 millimetres from each of the ends of the beam. The load distribution within these series of point loads varied depending on whether a flexural or flexural-torsional load condition was being generated. For the flexural load condition each of the point loads applied had a constant magnitude. For the flexural-torsional load condition the magnitude of the individual loads increased from one side of the cross section to the other. The load distribution used for the flexural-torsional load condition was the same as was assumed during the experiments. This flexural-torsional load distribution is shown in Appendix 1. 3.2.1 Flexural Stiffness Flexural stiffness (EI) of the non-retrofit, reinforced concrete model was found from the relationship between total applied load from the flexural load condition, and vertical midspan displacement. Vertical displacement values were found at nodes located at the outside-bottom of the flanges at beam's midspan. The calculation of flexural stiffness from this relationship is described in Appendix 1. The deformed shape of the reinforced concrete channel beam model with 100 kN of total applied load is shown in Appendix 3. The flexural stiffness of the finite element model channel beam was confirmed by comparing it to initial elastic flexural stiffness values from the experimental program. Total applied load versus midspan deflection results for the reinforced concrete channel beam model are shown with experimental initial elastic stiffness relationships in Figure 4.3. These initial flexural stiffness values 77 Chapter 4 - Finite Element Analysis are also summarized and compared in Table 4.1. The average of the error values for all four beams from the test program compared to the finite element model was 9%. 0 5 10 15 20 Average Centre Deflection (mm) Figure 4.3: Total Load versus Average Centre Deflection Beam Initial Flexural Difference Stiffness [EI] (Percent Model Greater (Nmm2) Than Experiment) 1 4.10E+13 7% 2 4.66E+13 18% 3 4.82E+13 21% 4 3.40E+13 -12% Model 3.81E+13 — Table 4.1: Summary of Flexural Stiffness Values 3.2.2 Torsional Stiffness Torsional stiffness (GJ) of the non-retrofit, reinforced concrete channel beam finite element model was found from the relationship between beam torsion and the angle of twist per unit length. Torsion was found from the eccentric load introduced in the channel beam cross section by the flexural-torsional load condition. Angle of twist per unit length values were calculated from vertical displacement output. Vertical deflection was found at a distance of 2050 millimetres from the ends of the beam. This was the same location along the span of the beam where angle of twist per unit length measurements were 78 Chapter 4 - Finite Element Analysis obtained from experimental results. Displacement data was used from nodes along the bottom outsides of the flanges at this location. A sample calculation of torsional stiffness is shown in Appendix 1. The deformed shape of the non-retrofit, reinforced concrete channel beam model with 2 kNm of torsion is shown in Appendix 3. Torsional stiffhess of the reinforced concrete finite element model was verified by comparing it to elastic torsional stiffhess values from the experimental program. Figure 4.4 shows the torsion versus angle of twist per unit length curves for the reinforced concrete channel beam model and the initial elastic torsional stiffhess testing of the four beams in the test program. Torsional stiffhess values are also summarized and compared in Table 4.2. The average error between the reinforced concrete channel beam model and the four beams in the experimental program was 37%. 0.00E+00 1.00E-06 2.00E-06 3.00E-06 Angle of Twist per Unit Length (rad/mm) Figure 4.4: Torsion versus Angle of Twist per Unit Length Beam Initial Torsional Difference Stiffness [GJ] (Nmm2) (Percent Model Greater Than Experiment) 1 1.23E+12 2% 2 9.73E+11 -24% 3 7.93E+11 -53% 4 7.07E+11 -71% Model 1.21E+12 — Table 4.2: Summary of Torsional Stiffhess Values 79 Chapter 4 - Finite Element Analysis 3.2.3 Longitudinal Stress Stress in the longitudinal direction (rjn) of the non-retrofit, reinforced concrete finite element model was also compared to experimental results. Stress results shown in this section are from a flexural load condition. Stress values were compared at two locations at the midspan of the beam: the bottom of the flanges, and the top-centre of the web. These were the same positions where strain measurements were taken in the experimental program. Stress values from the experimental program were found by multiplying strain values from elastic flexural stiffness testing by the modulus of elasticity (E) for concrete. The modulus of elasticity value used for this calculation was 29,600 MPa. Longitudinal stress results are shown in the following figures and tables. Total applied load versus stress for the two cross section locations are shown in Figures 4.5 and 4.6. Stress results are summarized and compared for 100 kN of total applied flexural load in Tables 4.3 and 4.4. The non-retrofit, reinforced concrete channel beam is shown with longitudinal stress contours at 100 kN of applied flexural load in Appendix 3. 0 10 20 30 40 Tensile Stress (MPa) Figure 4.5: Total Applied Load versus Longitudinal Stress in Bottom of Flange at Midspan Beam Tensile Stress at Bottom Difference of Flanges at 100 kN (Percent Model Greater Load (MPa) Than Experiment) 1 20.4 15% 2 26.3 -11% 3 25.9 -9% 4 36.2 -35% Model 23.4 — Table 4.3: Summary of Stress Values at Bottom of Flanges at Midspan (100 kN applied load) 80 Chapter 4 - Finite Element Analysis Compressive Stress (MPa) Figure 4.6: Total Applied Load versus Longitudinal Stress in Top-Centre of Web at Midspan Beam Compressive Stress at Top Difference Centre of Flanges at 100 kN (Percent Model Greater Load (MPa) Than Experiment) 1 17.4 -73% 2 15.5 -70% 3 15.7 -71% 4 21.6 -79% Model 4.6 — Table 4.4: Summary of Stress Values at Top-Centre of Web at Midspan (100 kN applied load) The tensile stress values at the bottom of the flange at the midspan of the beam exceeded the tensile capacity of the concrete. This indicates that the concrete at this location in the cross section was no longer supporting tensile forces. In reality, the longitudinal reinforcing steel carried this tensile stress. Experimental strain results were also obtained for the longitudinal reinforcing steel but these values cannot be compared with channel beam finite element results. In this model, the concrete and the reinforcing steel were not modeled as separate elements with separate material properties. Instead, solid elements have been used to represent the combination of reinforcing steel and concrete. Although the tensile stress results shown in the previous tables were beyond the tensile capacity of the concrete, the comparison of such values still provides some indication of the quality of the reinforced concrete channel beam finite element model. Finite element model stress values from the bottom of the flanges at the midspan of the beam showed good agreement with experimental 8 1 ' Chapter 4 - Finite Element Analysis results. The average error between the finite element model and the experimental results for each of the four beams was 10%. Compressive stress values from the finite element model of the channel beam did not show good agreement with experimental values at the top of the web. The average percent error between the model and the experimental results of the four beams tested was 73%. 4.0 Model of an Individual Channel Beam Retrofit With GFRP This section discusses the development of finite element models of reinforced concrete channel beams retrofit with GFRP. Two separate finite element models are developed in this section. One model represents a channel beam retrofit with GFRP spray; the other model is a channel beam retrofit with GFRP wrap. In both models, the application of GFRP to the channel beam was simulated by the addition of shell elements to the finite element model of the non-retrofit, reinforced concrete channel beam. In section 4.1 the finite element models of reinforced concrete channel beams retrofit with GFRP are described in terms of their elements, coordinate system, geometry, material properties and boundary conditions. The accuracy of the two models is then verified in section 4.2 by comparing model output to flexural stiffness, torsional stiffness, and longitudinal stress results from the testing program. 4.1 Finite Element Model Description 4.1.1 Elements The application of GFRP to the channel beam was simulated by the addition of shell elements to the reinforced concrete channel beam model. The SAP2000® shell elements used were two-dimensional elements with four nodes. Each of the nodes had six degrees of freedom available. For this model full shell behavior was used. The shell elements calculated stresses and internal forces by extrapolating the results of a 2x2 Gauss integration scheme to the element nodes.(38) 4.1.2 Coordinate System The coordinate system used for the finite element models of the channel beams retrofit with GFRP was the same as was used for the model of the non-retrofit, reinforced concrete channel beam. 82 Chapter 4 - Finite Element Analysis 4.1.3 Geometry Shell elements were added to the reinforced concrete channel beam model along the underside of the beam web, and the inside and underside of each flange. This configuration of shell elements is shown on the cross section of the retrofit channel beam finite element model in Figure 4.7. Shells of two different aspect ratios were used in the retrofit channel beam model. This is because the mesh refinement varied along the length of the beam. Within 250 millimetres of the ends of the beam, the shell elements were 50 millimetres by 50 millimetres in size. Within the central 6200 millimetres of the span, the shell elements were 50 millimetres by 100 millimetres in size. In total, 2520 shell elements are used. The thickness of the shell elements varied for the two different GFRP retrofit models. For the model of the channel beam retrofit with GFRP spray, the thickness of the shell elements used was 15 millimetres. A shell element thickness of four millimetres was used when generating the model of the channel beam retrofit with GFRP wrap. 950 mm w 1 1 1 1 1 1 1 1 1 1 1 i i i y < i _ i 450 mm J Solid Element • Node — Shell Element Figure 4.7: Cross Section of Channel Beam Finite Element Model With Applied GFRP 4.1.4 Material Properties The shell elements used in the retrofit channel beam finite element models were assigned material properties including modulus of elasticity (E), Poisson's ratio (u), and mass (m). The GFRP spray was simulated using shell elements that had a modulus of elasticity of 12,000 MPa, and a Poisson's ratio of 0.3. The shell elements representing the GFRP wrap had a modulus of elasticity of 70,000 MPa, and a Poisson's ratio of 0.3. The mass of the GFRP was assumed to be negligible for both the GFRP spray and the GFRP wrap channel beam models. All material properties for the solid elements remained the same as described in the section three. 83 Chapter 4 - Finite Element Analysis 4.1.5 Boundary Conditions The finite element models of the channel beams retrofit with GFRP used the same boundary conditions as used for the model of the non-retrofit, reinforced concrete channel beam. 4.2 Verification of Model In this section increase in flexural stiffness, increase in torsional stiffness, and reduction in longitudinal stress of the model beams retrofit with GFRP compared to the non-retrofit beam model are presented. These values are compared to the increase in stiffness and the reduction in stress found from initial elastic flexural and initial elastic torsional stiffness testing. Only initial elastic stiffness test results for the same beam before and after retrofit were compared. This was done because the initial damage condition of each of the four beams was not the same. As a result, comparing the results of two different beams will not show the true effects of a retrofit with GFRP. 4.2.1 Flexural Stiffness Flexural stiffness (EI) of the channel beam models with simulated GFRP was determined from the total applied load versus vertical midspan displacement relationship as described in section three. The deformed shape of each of the two retrofit channel beam models with 100 kN of applied flexural load is shown in Appendix 3. A summary of flexural stiffness increases for the two GFRP retrofit finite element models and the two retrofit beams in the experimental program are presented in Table 4.5. 1 } Spray Wrap Model Experimental (Beam Three) Model Experimental (Beam Four) Non-Retrofit Flexural Stiffness (Nmm2) 3.81E+13 4.82E+13 3.81E+13 3.40E+13 Retrofit Flexural Stiffness (Nmm2) 5.13E+13 6.04E+13 5.68E+13 4.78E+13 Difference (% Retrofit Less than Non-Retrofit) 35% 25% 49% 41% Table 4.5: Increase in Flexural Stiffness of Retrofit Beams Relative to Non-Retrofit Beams Both the retrofit channel beam finite element models showed good agreement with experimental results. The increase in flexural stiffness of the model channel beam retrofit with GFRP spray compared to the non-retrofit, reinforced concrete model was within 10% of the increase in initial flexural stiffness found from experimental values for beam three. The model of the channel beam with simulated GFRP wrap showed an increase flexural stiffness over the non-retrofit, reinforced concrete 84 Chapter 4 - Finite Element Analysis model that was within 8% of the increase in flexural stiffhess shown from experimental data for beam four. 4.2.2 Torsional Stiffness Initial torsional stiffhess (GJ) for each beam was determined from the slope of the torsion versus angle of twist per unit length curve as discussed in section three. The deformed shapes of the two retrofit channel beam models with 2 kNm of torsion are presented in Appendix 3. Table 4.6 contains a summary of model and experimental torsional stiffhess increases for the GFRP sprayed and GFRP wrapped beams. Spray Wrap Model Experimental (Beam Three) Model Experimental (Beam Four) Non-Retrofit Torsional Stiffhess (Nmm ) 1.21E+12 7.93E+11 1.21E+12 7.07E+11 Retrofit Torsional Stiffness (Nmm2) 1.51E+12 1.52E+12 1.62E+12 1.06E+12 Difference (% Retrofit Less than Non-Retrofit) 25% 92% 34% 50% Table 4.6: Increase in Torsional Stiffness Values of Retrofit Beams Relative to Non-Retrofit Beams The torsional stiffhess of the finite element model of the GFRP wrapped beam showed reasonable agreement with experimental results. The increase in torsional stiffhess of the channel beam model with GFRP wrap compared to the non-retrofit, reinforced concrete model was within 16% of experimental results for beam four. The results for the finite element model of the channel beam repaired with GFRP spray were in poor agreement with experimental results. The model of the channel beam with the GFRP spray had an increase in torsional stiffhess compared to the non-retrofit channel that was within 67% of the increase in torsional stiffhess from beam three experimental data. 4.2.3 Longitudinal Stress The reduction in longitudinal stress (rjn) of the GFRP retrofit channel beam models relative to the non-retrofit, reinforced concrete channel beam model was also compared with experimental results. Percentage reduction in stress was only considered at the bottom of the flanges at the midspan of the beam. Stress values were not compared at the top of the web at the midspan of the beam because there was a large amount of error between experimental and model results at this location for the non-retrofit, reinforced concrete channel beam model. 85 Chapter 4 - Finite Element Analysis Table 4.7 summarizes reduction in stress values at the bottom-midspan of the flanges for 100 kN of total flexural load from experimental and model data for the two retrofit cases. The two retrofit channel beam models are shown with longitudinal stress contours for 100 kN of total applied flexural load in Appendix 3. Spray Wrap Model Experimental (Beam Three) Model Experimental (Beam Four) Non-Retrofit Longitudinal Stress (MPa) 23.4 25.9 23.4 36.2 Retrofit Longitudinal Stress (MPa) 19.0 24.3 17.5 27.4 Difference (% Retrofit Greater than Non-Retrofit) 19% 6% 25% 24% Table 4.7: Reduction in Longitudinal Stress at Bottom of Flanges of Retrofit Beams Relative to Non-Retrofit Beams (100 kN total load) Reduction in stress values for finite element models of the GFRP sprayed and GFRP wrapped beams showed good agreement with experimental results. The reduction in stress from the model of the channel beam retrofit with GFRP spray compared to the non-retrofit channel model was within 13% of the reduction in stress values found from testing beam three. The model of the channel beam retrofit with GFRP wrap showed a reduction in stress compared to the non-retrofit, reinforced concrete channel beam that was 1% different from experimental results for beam four. 5.0 Finite Element Analysis of Channel Beam Bridge Decks This section presents the development and loading of single span channel beam bridge deck finite element models. Three channel beam bridge deck models are created. The first model represents a non-retrofit reinforced concrete channel beam bridge deck. The second model simulates a channel beam bridge deck retrofit with GFRP spray. The third finite element model is of a channel beam bridge deck retrofit with GFRP wrap. Each of the bridge deck models are based on the channel beam finite element models developed in the previous sections. The channel beam bridge deck models are described in terms of their elements, coordinate systems, geometries, material properties, and boundary conditions section 5.1. The load configuration used for testing the three channel beam bridge deck models is presented in section 5.2. 86 5.1 Model Description Chapter 4 - Finite Element Analysis 5.1.1 Elements The same elements that were used in the models of the single channel beams were used for the finite element model of the channel beam bridge decks. The non-retrofit, reinforced concrete bridge deck model used solid elements only. The models of the channel beam bridge spans retrofit with GFRP used a combination of solid and shell elements. 5.1.2 Coordinate System The bridge deck models used the same coordinate system as the individual channel beam models. The span of the beam was aligned with the x-axis. The width of the bridge deck was formed in the y-z plane. 5.1.3 Geometry Ten individual, model channel beams were placed side by side to build the deck width in the finite element bridge deck models. A shear key connection was simulated in the bridge deck finite element models by linking the top 200 millimetres of adjacent flanges. The channel beam bridge deck models were 9500 millimetres wide, and had a span length of 6700 millimetres. The geometry of the finite element bridge decks is shown in Figure 4.8. Figure 4.8: Finite Element Model of Bridge Deck 5.1.4 Material Properties The channel beam bridge deck models included solid element mass. Mass of the solid elements was not considered in the models of the individual channel beams. All of the other material properties described for the individual channel beam models remained the same for the bridge deck models. 87 Chapter 4 - Finite Element Analysis A weight density of 18.8 kN/m3 was used for the solid elements. This relatively low density was used because the channel beams contained lightweight aggregate. Shell element mass was not included because the mass of the GFRP was considered to be negligible compared to the weight of the channel beam. 5.1.5 Boundary Conditions The channel beam bridge deck finite element models were fixed in the vertical (z) and lateral (y) directions at nodes located 0, 50, 100, and 150 millimetres from their ends. This simulated the continuous support at the ends of the bridge spans. The bridge was fixed in the longitudinal (x) direction at the midspans of each of the ten channel beams. 5.2 Load Configuration The load configuration used for the channel beam bridge deck models was from live load specifications in the CAN/CSA-S6-98, Canadian Highway Bridge Design Code (Pre-Ballot Draft).( ,9) Traffic live loading in this code is based on the CL-625 truck load configuration; an idealized five-axle vehicle with a gross load of 625 kN. The configuration of a CL-625 truck is shown in Figure 4.9. 1 2 3 Axle No. 4 5 25 50 62.5 62.5 125 125 I 11 Wheel Loads (kN) Axle Loads (kN) 87.5 175 I 75 150 I 3.6m 1.2m 6.6m 6.6m 18.0m 1.8m Figure 4.9: CL-625 Truck Load Configuration095 (Adapted from Canadian Highway Bridge Design Code) The load configuration used represented the placement of the CL-625 truck in the bridge deck finite element models that induced the greatest moment and torsional effects on the bridge deck. This 88 Chapter 4 - Finite Element Analysis occurred when truck axles two and three were centred about the midspan, and were placed along the width of the bridge deck as shown in Figure 4.11. In this load condition four 62.5 kN point loads were placed on the channel beam bridge deck model. This load condition is shown along the span of the bridge model in Figure 4.10, and along the width of the bridge deck model in Figure 4.11. An additional truck load was not placed in the other lane because the greatest flexural and torsional effects occurred in flange 3. Including an additional truck in the other lane had little effect on the maximum stresses generated in flange 3. 1600 1800 1350 4750 62.5 kN 62.5 kN i—s 1 2 3 4 5 6 7 8 9 10 Figure 4.11: Load Configuration Along Deck Width (dimensions in millimetres) 11 6.0 Channel Beam Bridge Model Results The load configuration was tested with the non-retrofit, reinforced concrete bridge deck model; the bridge deck model with simulated GFRP spray; and the bridge deck model with simulated GFRP wrap. In this section, vertical displacement results and stress results for each of the three different bridge deck models are presented. 6.1 Verification of Elastic Range Results Vertical displacement results from the finite element bridge deck models were found to be within the linear elastic range of the channel beams. A maximum vertical deflection of 11.3 89 Chapter 4 - Finite Element Analysis millimetres occurred within flange 3 of the non-retrofit channel beam bridge model. Yielding in the experimental program occurred at approximately 33 millimetres of midspan deflection. Curvature results at the third point of the bridge deck span were also within the linear range for each of the channel beam bridge deck models with this load configuration. The maximum angle of twist per unit length value found at the third point of the non-retrofit bridge deck model was 2.9X10"6 rad/mm. Based on experimental results, yielding occurred at approximately 4.0xl0"6 rad/mm. 6.2 Vertical Deflection of Bridge Deck Flanges Vertical displacement at the bottom of each of the bridge deck flanges was found for the non-retrofit reinforced concrete channel beam bridge deck model, the bridge deck model with GFRP spray retrofit, and the bridge deck model with GFRP wrap retrofit. Maximum displacement values at each of the flanges for each of the three bridge models are shown in Table 4.8. In this table, bridge deck flanges are referred to as flanges 1 to 11. These flanges are identified in Figure 4.11. Displacement along the length of flange 3 for each of the three bridge models is shown in Figure 4.12. Flange 3 is shown because this is flange that had the maximum vertical displacement with this loading. Vertical Displacement (mm) (Negative Equals Downward Deflection) Flange Reinforced GFRP Sprayed GFRP Wrapped Concrete Deck Deck Deck 1 0.8 0.6 0.6 2 -7.0 -4.7 -4.2 3 -11.3 -7.7 -6.8 4 -10.5 -7.1 -6.3 5 -8.8 -6.0 -5.3 6 -1.8 -1.2 -1.1 7 0.3 0.2 0.2 8 0.3 0.2 0.2 9 0.1 0.0 0.0 10 0.0 0.0 0.0 11 0.0 0.0 0.0 Table 4.8: Maximum Vertical Flange Deflection 90 Chapter 4 - Finite Element Analysis 6.3 Longitudinal Stress at Bottom of Bridge Deck Flanges Longitudinal stress along the bottom of the bridge deck flanges was also found for each of the three finite element channel beam bridge deck models. Stress results were found at the bottom of the flanges only because model stress results for the beam webs were in poor agreement with experimental results for the individual channel beams. Table 4.9 shows the maximum tensile stresses found in each of the bridge deck flanges for the lane in which the truck was situated. Figure 4.13 shows the longitudinal stress distribution along the bottom of flange 3 for each of the three bridge deck models. Stress results shown in this table and figure are the average of the stress values found at the two nodes along the bottom of a channel beam flange. Longitudinal stress contours generated by SAP2000® for each of the three bridge deck models are presented in Appendix 3. Maximum Tensile Stress (MPa) Flange Non-Retrofit GFRP Sprayed GFRP Wrapped Bridge Bridge Bridge 1 0.8 0.1 0.1 2 12.6 9.6 8.8 3 19.8 14.4 13.1 4 18.4 13.8 12.5 5 15.6 11.1 10.0 6 2.6 1.8 1.5 Table 4.9: Maximum Tensile and Compressive Longitudinal Stresses in Flanges 91 Chapter 4 - Finite Element Analysis Non-Retrofit GFRP Spray GFRP Wrap Span Length (mm) Figure 4.13: Longitudinal Stress Distribution At Bottom of Flange 3 92 CHAPTER 5 COMPARISON AND INTERPRETATION OF RESULTS 1.0 Introduction Design calculation values, experimental data, and finite element analysis results are summarized and compared in this chapter. Design calculation values and experimental results are compared in section two. Calculation and experimental results for failure mode, ultimate load capacity, ductility, elastic stiffhess, and longitudinal cross sectional strain are presented in this section. Calculated and experimental results are compared to determine the accuracy of design calculation procedures for retrofit beams. Results for the non-retrofit and retrofit channel beams are also compared in order to determine the effects of a GFRP retrofit on channel beams load behavior. Finite element analysis results from models of channel beam bridge decks with and without GFRP retrofit are compared in section three. Model vertical displacement and longitudinal stress values are presented. Contrasting these results predicts the differences between non-retrofit and retrofit channel beam bridge deck behavior. 2.0 Comparison and Interpretation of Experimental Results and Design Calculations 2.1 Failure Modes In the experimental program channel beams were tested to failure with a flexural or a flexural-torsional load condition. Channel beam failure modes and failure locations along the span for these two load configurations were predicted using design calculations. In this section, predicted failure modes and failure locations are compared to experimental results. 2.1.1 Ultimate Flexural Load Tests Three channel beams were tested to failure under a flexural load condition. Each of these three beams had a different retrofit condition. Beam one received no retrofit, beam three was retrofit using 10 millimetres of GFRP spray, and beam four was retrofit using two layers of unidirectional GFRP wrap in a 0°-90° orientation. 93 Chapter 5 - Comparison and Interpretation of Results Channel beams one, three, and four were predicted to fail within the middle third of the beam span in a flexural failure mode. Design calculations for the flexural load condition indicated both the non-retrofit and retrofit channel beams have less moment resistance than shear resistance for this load configuration. The failure was predicted to occur in the middle third of the span because this is the region with the greatest moment for the flexural load configuration. Flexural failure of both of the retrofit beams was predicted to occur when the strains in the GFRP at the bottom of the beam exceeded the maximum tensile strain values for the GFRP material. Calculated flexural and shear capacities for the non-retrofit, and retrofit channel beams are presented in Appendix 1. The predicted failure mode and failure location were confirmed by experimental testing. Channel beams one, three, and four all failed in flexure within the middle third of the channel beam as predicted by design calculations. The flexural failure of beams three and four was initiated by failure of the GFRP material at the bottom of the beam flanges. Details of the flexural failure modes of channel beams one, three, and four are presented in chapter three, section 8.0 of this report. 2.1.2 Ultimate Flexural-Torsional Load Tests Channel beam two was tested to failure under a flexural-torsional load condition. This beam two did not receive any retrofit. Channel beam two was predicted to fail in torsion, approximately 2440 millimetres from the end of the beam. Design calculations indicated that the channel beam has less torsional resistance than moment resistance for the flexural-torsional load configuration. Failure was predicted to occur at this location within the zone of torsional forces because the shear/torsion reinforcement was at its maximum spacing within this region. Calculated flexural and torsional capacities for the non-retrofit channel beam are shown in Appendix 1. The predicted failure mode and failure location were confirmed by ultimate flexural-torsional load testing of beam two. Channel beam two failed due to shear forces induced by torsional loading. The shear failure extended from approximately 1680 millimetres from the end of the beam, to 2440 millimetres from the end of the beam. Further details of the failure mode of channel beam two may be found in chapter three, section 8.2 of this report. 2.2 Ultimate Load Capacity 2.2.1 Ultimate Flexural Load Capacity Predicted flexural capacity found from design calculations, and the actual moment capacity from experimental results are summarized and compared in Table 5.1. Calculations of ultimate moment capacity for the non-retrofit beam, the beam retrofit with GFRP spray, and the beam retrofit with GFRP wrap are presented in Appendix 1. 94 Chapter 5 - Comparison and Interpretation ofResults Beam Retrofit Calculated Experimental Difference Condition Ultimate Flexural Ultimate Flexural (% Calculated Capacity (kNm) Capacity (kNm) Greater than Experimental) 1 No Retrofit 302 237 27% 3 GFRP Spray 464 470 -1% 4 GFRP Wrap 356 323 10% Table 5.1: Comparison of Ultimate Flexural Capacity Values Calculated and experimental ultimate flexural capacity results for the channel beams retrofit with GFRP show good agreement. This indicates that moment resistance of a channel beam bridge girder retrofit using GFRP may be accurately predicted by design calculations based on strain compatibility principles. Calculated and experimental results for the ultimate flexural capacity of the non-retrofit channel beam are in poor agreement. For the non-retrofit beam, the actual ultimate flexural load capacity found from the experimental program was much less than what was predicted by design calculations. The moment capacity of a non-retrofit beam should be able to be predicted with as much, or even greater accuracy than the moment resistance of a retrofit channel beam. The moment resistance of the non-retrofit beam found from the experimental program was much less than predicted by design calculations because of the initial damage condition of channel beam one. This beam was significantly damaged along its top compared to the other channel beams. This limited the beam's ability to carry longitudinal compressive forces, thus reducing the ultimate flexural load for channel beam one. 2.2.2 Difference in Channel Beam Flexural Load Capacity Due to GFRP Retrofit Experimental and calculation results show that channel beams retrofit with GFRP have greater ultimate flexural strength non-retrofit channel beams. Quantifying the improvement from the experimental program is difficult since it requires a direct comparison between ultimate values of two beams. Each of the beams used in the experimental program had a different amount and type of damage prior to testing, therefore there was no control specimen to reference variations in behavior. Channel beam one had much more damage to its top surface than channel beams three and four. This limited its ultimate flexural capacity. The increase in flexural strength found from design calculations and experimental results for the beam retrofit with GFRP spray, and the beam retrofit with GFRP wrap relative to the non-retrofit beam are shown in Table 5.2. 95 Chapter 5 - Comparison and Interpretation ofResults Beam Retrofit Calculated Increase Experimental Increase Condition Ultimate Flexural (% Retrofit Ultimate Flexural (% Retrofit Capacity (kNm) Greater than Capacity (kNm) Greater than Non-Retrofit) Non-Retrofit) 1 No Retrofit 302 — 237 — 3 GFRP Spray 464 54% 470 98% 4 GFRP Wrap 356 18% 323 36% Table 5.2: Increase in Flexural Capacity of Retrofit Beams Relative to Non-Retrofit Beams 2.2.3 Ultimate Torsional Load Capacity The calculated ultimate torsional capacity of the non-retrofit, reinforced concrete channel beam was 3.3 kNm. The calculation of torsional resistance is shown in Appendix 1. The actual torsional load at the failure of beam two found from the experimental program was 4.3 kNm. This represents a difference of 23% relative to the experimental results. 2.3 Ultimate Ductility Capacity/Ultimate Vertical Deflection Capacity 2.3.1 Ductility Capacity/Vertical Deflection Capacity of Channel Beams in Flexural Load Test Applied flexural load versus vertical midspan deflection from calculations and experimental data are compared for the non-retrofit and retrofit beams in Figures 5.1, 5.2, and 5.3. The calculation of vertical deflection for increasing values of applied load is shown in Appendix 1. Maximum vertical deflection values from design calculations and ultimate load tests deflection results are also summarized and compared for the non-retrofit beam, the beam retrofit with GFRP spray, and the beam retrofit with GFRP wrap in Table 5.3. 450 -Design Calculation -Beam l,Uh. Load Test 0 20 40 60 80 100 120 140 160 180 200 220 240 Vertical Deflection at Midspan (mm) Figure 5.1: Non-Retrofit Beam, Total Load versus Vertical Deflection at Midspan 96 Chapter 5 - Comparison and Interpretation of Results Design Calculation Beam 3, Ult. Load Test 0 20 40 60 80 100 120 140 160 180 200 220 240 Vertical Deflection at Midspan (mm) Figure 5.2: Beam Retrofit With GFRP Spray, Total Load versus Vertical Deflection at Midspan Design Calculation Beam 4, Ult. Load Test 0 20 40 60 80 100 120 140 160 180 200 220 240 Vertical Deflection at Midspan (mm) Figure 5.3: Beam Retrofit With GFRP Wrap, Total Load versus Vertical Deflection at Midspan 97 Chapter 5 - Comparison and Interpretation of Results Beam Maximum Deflection Difference (mm) (% Calculated Calculated Experimental Greater than Experimental) 1 234 114 105% 3 114 128 -11% 4 165 143 15% Table 5.3: Comparison of Maximum Vertical Deflection Values Design calculations values for ultimate ductility capacity of retrofit beams are in good agreement with experimental results. This shows that the ultimate vertical deflection, and the deflection response for increasing applied load may be accurately predicted for channel beams retrofit with GFRP using design calculations. Calculated and experimental results for the ultimate vertical deflection for the non-retrofit beam are in poor agreement. The predicted ultimate vertical deflection value calculated for the non-retrofit beam was greater than the value found from load testing because of the initial damage state of channel beam one prior to testing. Beam one was much more damaged on the top than beams three and four. This damage limited the capability of channel beam one to carry longitudinal compressive stresses compared to the other channel beams. This caused premature failure, thus limiting the ductility capacity of channel beam one. 2.3.2 Difference in Channel Beam Ductility Capacity Due to GFRP Retrofit The difference in the ultimate ductility capacity of a reinforced concrete channel beam due to a retrofit with GFRP found from calculation and experimental results is shown in Table 5.4. Beam Retrofit Maximum Decrease Due Maximum Decrease Due Condition Calculated To Retrofit Experimental To Retrofit Deflection (Relative to Deflection (Relative to (mm) Non-Retrofit) (mm) Non-Retrofit) 1 Non-Retrofit 234 — 114 — 3 GFRP Spray 114 51% 128 -12% 4 GFRP Wrap 165 30% 143 -25% Table 5.4: Difference in Channel Beam Ductility Capacity Due to GFRP Retrofit Experimental and calculation results showed opposite trends for ultimate ductility capacity of channel beams retrofit with GFRP. Design calculations showed that channel beams retrofit with GFRP had less ultimate ductile capacity than a non-retrofit channel beam, while experimental results showed retrofit beams had greater ductility than the non-retrofit beam. The trend of the experimental results is due to the initial damage condition of channel beam one, therefore results are inconclusive with regards to the difference in ultimate ductility capacity of retrofit channel beams compared to non-retrofit. 98 Chapter 5 - Comparison and Interpretation of Results 2.4 Elastic Stiffness 2.4.1 Elastic Flexural Stiffness Predicted elastic flexural stiffness values from design calculations are summarized and compared with elastic flexural stiffness results found from the test program in Table 5.5. Calculations of predicted flexural stiffness based on sectional and material properties, and flexural stiffness values from experimental results may be found in Appendix 1. Beam Retrofit Test Calculated Experimental Difference Condition Flexural Flexural (% Calculated Stiffness [EI] Stiffness [EI] Greater than (Nmm2) (Nmm2) Experimental) 1 No Retrofit Initial Stiffness 4.14E+13 4.10E+13 1% 1 No Retrofit Ultimate Load 4.14E+13 3.52E+13 18% 2 No Retrofit Initial Stiffness 4.14E+13 4.66E+13 -11% 3 No Retrofit Initial Stiffness 4.14E+13 4.82E+13 -14% 3 GFRP Spray Initial Stiffness 4.50E+13 6.04E+13 -25% 3 GFRP Spray Ultimate Load 4.50E+13 4.97E+13 -9% 4 No Retrofit Initial Stiffness 4.14E+13 3.40E+13 22% 4 GFRP Wrap Initial Stiffness 4.23E+13 4.78E+13 -12% 4 GFRP Wrap Ultimate Load 4.23E+13 4.16E+13 2% Table 5.5: Comparison of Flexural Stiffness Values Elastic flexural stiffness predictions from traditional hand calculation methods show good agreement with experimental results. For the non-retrofit beams the average difference between calculated values and experimental results is 3% relative to the experimental results. For the beams retrofit with GFRP spray and GFRP wrap the average difference between calculated and experimental results is 11% relative to the experimental results. 2.4.2 Elastic Torsional Stiffness Elastic torsional stiffness values found from design calculations and experimental results are summarized and compared in Table 5.6. The calculation of torsional stiffness based on beam material and sectional properties, and torsional stiffness values found from experimental results may be found in Appendix 1. 99 Chapter 5 - Comparison and Interpretation ofResults Beam Retrofit Test Calculated Experimental Difference Condtion Torsional Torsional (% Calculated Stiffiiess [GJ] Stiffiiess [GJ] Greater than (Nmm2) (Nmm2) Experimental) 1 No Retrofit Initial Stiffness 9.84E+11 1.23E+12 -20% 2 No Retrofit Initial Stiffhess 9.84E+11 9.73E+11 1% 2 No Retrofit Ultimate Load 9.84E+11 7.59E+11 30% 3 No Retrofit Initial Stiffiiess 9.84E+11 7.93E+11 24% 3 GFRP Spray Initial Stiffhess — 1.52E+12 -4 No Retrofit Initial Stiffhess 9.84E+11 7.07E+11 39% 4 GFRP Wrap Initial Stiffiiess — 1.06E+12 — Table 5.6: Comparison of Torsional Stiffhess Values Elastic torsional stiffhess values based on material and sectional properties show reasonable agreement with experimental results for the non-retrofit channel beams. The average difference between calculated and experimental values is 15% relative to the experimental results. 2.4.3 Difference in Channel Beam Flexural Stiffhess and Torsional Stiffness Due to GFRP Retrofit Experimental results show that channel beams retrofit with GFRP have greater elastic flexural and torsional stiffhess than non-retrofit channel beams. The increase in elastic flexural and torsional stiffhess found from experimental results for channel beams retrofit with GFRP spray and GFRP wrap are shown in Table 5.7. Experimental stiffhess increase results are based on a comparison of initial elastic stiffhess results for the same beam. Only stiffness results from the same beam are compared because each of the different beams had a different initial damage condition. As a result, a comparison between the same beam before and after retrofit is required to determine the true effects the GFRP retrofit on elastic stiffhess. Beam Retrofit Experimental Difference Experimental Difference Condition Flexural (% Retrofit Torsional (% Retrofit Stiffness [EI] Greater than Stiffiiess [GJ] Greater than (Nmm ) Non-Retrofit) (Nmm2) Non-Retrofit) 3 No Retrofit 4.82E+13 7.93E+11 3 GFRP Spray 6.04E+13 25% 1.52E+12 92% 4 No Retrofit 3.40E+13 7.07E+11 4 GFRP Wrap 4.78E+13 41% 1.06E+12 50% Table 5.7: Increase in Elastic Stiffhess of Retrofit Beams Relative to Non-Retrofit Beams 100 2.5 Longitudinal Strain Chapter 5 - Comparison and Interpretation ofResults 2.5.1 Longitudinal Strain in Cross Section Values of cross sectional longitudinal strain at the top of the concrete compression block, and within the longitudinal reinforcing steel found from the design calculations are compared to experimental results for the non-retrofit and retrofit beams in Figures 5.4 to 5.9. In these figures, experimental strain results are represented by a second order parabolic relationship. The calculation of maximum compressive strain at the top of the beam, and tensile strain in the reinforcing steel is shown in Appendix 1. Strain results from design calculations and experimental results for the non-retrofit and retrofit beams are also compared at 150 kN of total applied load in Table 5.8. Figure 5.4: Non-Retrofit Beam, Total Load versus Compressive Strain at Top of Beam 101 Chapter 5 - Comparison and Interpretation of Results 1 0 2 103 Chapter 5 - Comparison and Interpretation of Results Beam Top of Beam Difference Reinforcing Steel Difference (Compression) (% Calculated (Tension) (% Calculated Calculated Experimental Less than Calculated Experimental Less than Experimental) Experimental) 1 4.25E-04 1.01 E-03 58% 1.01 E-03 1.08E-03 6% 3 4.07E-04 6.60E-04 38% 9.92E-04 8.90E-04 -11% 4 4.23E-04 7.45E-04 43% 9.19E-04 9.50E-04 3% Table 5.8: Comparison of Strain Values at 150 kN of Applied Load Strain values calculated for the top of the concrete compression block are in poor agreement with experimental results. Calculated compressive strain values at the top of the beam are much less than shown in the testing program. The strain values found from design calculations provide a good approximation of tensile strain in the longitudinal reinforcing steel for both the non-retrofit and retrofit beams. 2.5.2 Difference in Channel Beam Longitudinal Strain Due to GFRP Retrofit Channel beams retrofit with GFRP show reduced longitudinal strains for a given applied load than the non-retrofit channel beam. Experimental total applied load versus strain data is shown for the top of the concrete compression block in Figure 5.10, and for the tensile longitudinal reinforcing steel in Figure 5.11. A comparison of experimental strain values at 150 kN of load is shown for the non-retrofit beam, the beam retrofit with GFRP spray, and the beam retrofit with GFRP wrap in Table 5.9. 104 Chapter 5 - Comparison and Interpretation of Results -3 C H 0.0005 0.001 0.0015 Compressive Strain at Top of Beam 0.002 -Beam 1, Non-Retrofit -Beam 3, GFRP Spray -Beam 4. GFRP Wrap Figure 5.10: Total Load versus Compressive Strain at Top of Beam, Comparison of Experimental Results _ 3 3 o H - Beam 1, Non-Retrofit -Beam 3, GFRP Spray -Beam 4, GFRP Wrap 0.0005 0.001 0.0015 Tensile Strain in Longitudinal Steel 0.002 Figure 5.11: Total Load versus Tensile Strain in Longitudinal Steel, Comparison of Experimental Results Beam Retrofit Strain at Decrease Due Strain in Decrease Due Condition Top of Beam To Retrofit Reinforcing To Retrofit (Compression) (Relative to Steel (Relative to Non-Retrofit) (Tension) Non-Retrofit) 1 Non-Retrofit 1.05E-03 — 1.08E-03 — 3 GFRP Spray 6.60E-04 37% 8.90E-04 17% 4 GFRP Wrap 7.45E-04 29% 9.50E-04 12% Table 5.9: Decrease in Strain for Retrofit Beams Relative to Non-Retrofit Beams at 150 kN Applied Load 105 Chapter 5 - Comparison and Interpretation ofResults 3.0 Comparison and Interpretation of Finite Element Analysis Results A description and diagram of the load condition used on the channel beam bridge deck models is contained in chapter four, section 5.2 of this report. 3.1 Vertical Displacement at Bottom of Flanges Maximum displacement values along the channel beam bridge deck flanges for the non-retrofit bridge deck model, the bridge deck model with simulated GFRP spray, and the bridge deck model with simulated GFRP wrap are summarized and compared in Table 5.10. Vertical Displacement (mm) Reduction in Vertical Displacement (Negative Equals Downward Deflection) Compared to Non-Retrofit Deck Flange Reinforced GFRP Sprayed GFRP Wrapped GFRP Sprayed GFRP Wrapped Concrete Deck Deck Deck Deck Deck 1 0.8 0.6 0.6 24% 30% 2 -7.0 -4.7 -4.2 33% 40% 3 -11.3 -7.7 -6.8 32% 39% 4 -10.5 -7.1 -6.3 33% 40% 5 -8.8 -6.0 -5.3 32% 39% 6 -1.8 -1.2 -1.1 32% 40% Table 5.10: Comparison of Maximum Vertical Displacement Values A channel beam bridge deck retrofit with GFRP spray has an average of 31% less vertical displacement than the non-retrofit reinforced concrete channel beam bridge model. The bridge deck model with simulated GFRP wrap has an average of 38% less vertical displacement than the non-retrofit bridge model. 3.2 Stresses in Flanges Maximum tensile stress at the bottom of the bridge deck flanges found from finite element analysis of a non-retrofit bridge deck, a bridge deck retrofit with GFRP spray, and a bridge deck retrofit with GFRP wrap are presented in Table 5.11. These values represent the longitudinal tensile stress in the concrete at the bottom of the flanges. The effective stress in the reinforcing steel of a channel beam bridge deck could be found by multiplying these stress values by a modular ratio (Ns) of 6.76. 106 Chapter 5 - Comparison and Interpretation ofResults Maximum Tensile Stress Reduction in Stress (MPa) Compared to Non-Retrofit Bridge Flange Non-Retrofit GFRP Sprayed GFRP Wrapped GFRP Sprayed GFRP Wrapped Bridge Bridge Bridge Bridge Bridge 1 0.8 0.1 0.1 82% 85% 2 12.6 9.6 8.8 23% 30% 3 19.8 14.4 13.1 27% 34% 4 18.4 13.8 12.5 25% 32% 5 15.6 11.1 10.0 29% 36% 6 2.6 1.8 1.5 32% 41% Table 5.11: Comparison of Maximum Tensile Longitudinal Stresses in Flanges Finite element analysis results show that the retrofit bridge deck models have reduced longitudinal tensile stresses at the bottom of the flanges compared to the model of the non-retrofit channel beam bridge deck. The model of the bridge deck retrofit with GFRP spray has an average of 27% less longitudinal tensile stress at the bottom of the flanges than the model of the non-retrofit bridge deck. The channel beam bridge deck with simulated GFRP wrap has an average of 35% less tensile stress at the bottom of the flanges than the non-retrofit bridge deck model. These values represent the average for flanges 2 to 6 only. 107 CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS 1.0 Introduction In this study, design calculations, experimental results, and finite element analysis have been used to determine the structural behavior of non-retrofit reinforced concrete channel beams, channel beams retrofit with GFRP spray, and channel beams retrofit with GFRP wrap. This chapter presents the conclusions from this study, and recommendations for retrofitting channel beam bridges in British Columbia. Each of the channel beams in the experimental program had a different amount and type of damage prior to testing. The effect of this initial damage condition on experimental results is discussed in section two. Conclusions on the effects of a GFRP retrofit on channel beam structural properties are presented in section three. Conclusions are based on a comparison of experimental data from non-retrofit and retrofit channel beams. Conclusions are made regarding the differences in flexural strength, ductility, flexural and torsional stiffhess, and longitudinal cross sectional strains between beams retrofit with GFRP and non-retrofit channel beams. Section four presents conclusions on the effects of a GFRP retrofit on bridge deck structural behavior. Conclusions are based on a comparison of finite element results from non-retrofit and retrofit bridge deck models. Conclusions regarding the differences in vertical deflection and longitudinal stresses for bridge decks retrofit with GFRP and non-retrofit bridge decks are summarized in this section. Results from retrofits with GFRP spray and GFRP wrap are compared in section five. In this section design calculation values, experimental results, and finite element analysis are compared to show the effects of the two types of GFRP material on channel beam and channel beam bridge structural properties. In section six, conclusions are made regarding the accuracy of design calculations for retrofit and non-retrofit reinforced concrete channel beams. Conclusions are based on a comparison of design calculation values and experimental results. Conclusions regarding the accuracy of calculation procedures for moment resistance, ductility, elastic stiffhess, and tensile strain of retrofit channel beams are included. Recommendations regarding retrofitting channel beam bridge decks are made in section seven. Recommendations of whether a GFRP retrofit is appropriate for these structures, the best type 108 Chapter 6 - Conclusions and Recommendations of GFRP material for retrofitting, bridge cross section repair, and retrofit design and implementation strategies are presented. 2.0 Effects of Damage on Structural Behavior of Channel Beams Each of the channel beams in the experimental program had a different initial damage condition prior to testing. Damage was defined in terms of amount of concrete section loss; amount of exposed reinforcement; amount, type and width of cracking; and amount of corrosion to the longitudinal reinforcing steel. The initial damage condition of each of the four beams in the experimental program is described in detail in chapter three, section 3.0 of this report. The effect of the initial damage condition On the experimental results is described in the following parts of this section. 2.1 Concrete Section Loss at Top of Channel Beam One and Ultimate Load and Ductility Capacity Channel beam one was more badly damaged at the top of the cross section than the other beams in the experimental program. Channel beam one had sections of concrete missing along its top surface. This damage limited the longitudinal compressive force resistance of the concrete compression block during bending. As a result, the ultimate flexural capacity and the ultimate ductility capacity of the non-retrofit beam were much less than predicted by design calculations. 2.2 Loss of Concrete Cover From Longitudinal Reinforcing Steel and Failure Initiation Failure in channel beams one and two initiated from regions of missing concrete cover from the longitudinal reinforcing steel. These beams were not repaired and did not receive any retrofit prior to testing. This did not occur with beams three and four because their bottom surfaces were repaired before retrofitting. 2.3 Initial Damage Condition and Initial Stiffness The initial damage condition had little effect on initial stiffness properties of the channel beams. Initial elastic flexural and torsional stiffhess values from the four specimens in the non-retrofit state were found to be comparable. 109 Chapter 6 - Conclusions and Recommendations 3.0 Effects of GFRP Retrofit on Channel Beam Structural Properties Conclusions regarding the effects of a GFRP retrofit on the structural behavior of reinforced concrete channel beams are summarized in this section. These conclusions are based on experimental results and design calculations for the non-retrofit and retrofit channel beams. 3.1 Increase in Flexural Load Carrying Capacity Experimental and design calculation results show that the use of GFRP as an external reinforcement improves the ultimate flexural load carrying capacity of channel beam bridge girders. Conclusions regarding the increase in flexural strength due to a retrofit with GFRP are based on a comparison of retrofit and non-retrofit channel beam results from both design calculations and experimental results. Design calculation results are considered to be more accurate. This is because the channel beam that was tested without any retrofit had more significant damage to its top than any of the other channel beams. This damage limited the ability of this beam to carry longitudinal compressive forces in the compression block. As a result, the ultimate flexural strength of the non-retrofit channel beam in the experimental program was much less than predicted by design calculations. Design calculation results show that a retrofit with 10 millimetres of GFRP spray increased the moment capacity of a reinforced concrete channel beam by 54% relative to the non-retrofit channel beam. Experimental results showed a 98% increase in flexural load carrying capacity due to a retrofit with 10 millimetres of GFRP spray relative to the non-retrofit channel beam. Design calculations show a channel beam retrofit with two layers of GFRP wrap in a 0°-90° orientation increased the flexural load carrying capacity of a channel beam by 18% relative to the non-retrofit channel beam. Experimental results indicated an increase of 36% with the GFRP wrap relative to the non-retrofit channel beam. 3.2 Reduction in Ultimate Ductility Capacity Experimental results are inconclusive regarding the reduction in ultimate ductility capacity of a channel beam due to a retrofit with GFRP. In the experimental program, the channel beams that received a GFRP retrofit had greater ductility than the non-retrofit channel beam. This was opposite to the trend predicted by design calculations. Design calculations predicted that ultimate vertical deflection of the channel beams would be reduced by the application of GFRP. The increase in ultimate ductility capacity of the retrofit beams in the experimental program was not due to the retrofit, but was because the retrofit channel beams had sustained less damage to the tops of their cross sections than the non-retrofit beam prior to testing. As a result, no conclusions regarding the reduction in ultimate ductility capacity can be drawn from the experimental program. 110 Chapter 6 - Conclusions and Recommendations The only other information regarding the reduction in ultimate ductility capacity of channel beams retrofit with GFRP relative to non-retrofit beams is from design calculations. Design calculations predicted a 51% reduction in ultimate vertical deflection for a channel beam retrofit with 10 millimetres of GFRP spray relative to the non-retrofit beam. Design calculations also estimated 30% less ultimate vertical deflection for a channel beam retrofit with two layers of unidirectional GFRP wrap in a 0°-90° orientation relative to the non-retrofit beam. 3.3 Increase in Flexural Stiffness and Torsional Stiffness The use of GFRP as a retrofit material increases the flexural and torsional stiffhess of reinforced concrete channel beams. Experimental results for a channel beam retrofit with 10 millimetres of GFRP spray show the increase in flexural stiffhess was 25%, and the increase in torsional stiffhess was 92% relative to the non-retrofit channel beam. For a channel beam retrofit with two layers of unidirectional GFRP wrap in a 0°-90° orientation the increase in flexural stiffhess was 41%, and the increase in torsional stiffhess was 50% compared to the non-retrofit channel beam. 3.4 Reduction in Longitudinal Strain Reinforced concrete channel beams retrofit with GFRP have reduced longitudinal strains at a given load level than non-retrofit channel beams. For example, experimental results for 150 kN of total load show a beam retrofit with 10 millimetres of GFRP spray had 17% reduced longitudinal tensile strains in the longitudinal reinforcing steel, and 37% less compressive strain at the top of the beam relative to a non-retrofit beam. Results also show a channel beam retrofit with two layers of unidirectional GFRP wrap in a 0°-90° orientation had 12% reduced tensile strain, and 29% less compressive strain at the top of the beam than a non-retrofit beam. 4.0 Effects of GFRP Retrofit on Channel Beam Bridge Deck Structural Properties This section summarizes conclusions regarding the effects of a GFRP retrofit on channel beam bridge deck structural properties. These conclusions are based on finite element analysis results for non-retrofit and retrofit channel beam bridge decks. 4.1 Reduction in Vertical Displacement The use of GFRP as an external reinforcement increases flexural stiffhess of a reinforced concrete channel beam bridge deck by reducing vertical displacement at a given applied load level. Finite element analysis results for the retrofit channel beam bridge deck models show reduced vertical displacement compared to non-retrofit channel beam bridge deck model values. The model of a bridge 111 Chapter 6 - Conclusions and Recommendations deck with 10 millimetres of GFRP spray had an average of 31% less vertical displacement at the flanges than a non-retrofit bridge deck model. The model representing the bridge deck with two layers of unidirectional GFRP wrap in a 0°-90° orientation had an average of 38% less vertical displacement at the flanges than the non-retrofit bridge deck model. 4.2 Reduction in Longitudinal Stress A channel beam bridge deck retrofit with GFRP has reduced longitudinal stresses at a given load level than a non-retrofit channel beam bridge deck. Finite element results for retrofit channel beam bridge decks show reduced longitudinal tensile stresses at the bottom of the cross section. The model of a channel beam bridge deck with GFRP spray had an average of 27% reduced longitudinal tensile stress at the bottom of the flanges relative to a non-retrofit channel beam bridge deck model. The finite element model of a bridge deck with GFRP wrap had an average of 35% reduced tensile stress at the bottom of the flanges compared to the model of a non-retrofit channel beam bridge deck. 5.0 Comparison of G F R P Spray and G F R P Wrap Retrofits The effects of a retrofit with 10 millimetres of GFRP spray, and a retrofit with two layers of unidirectional GFRP wrap in a 0°-90° orientation are compared in Table 5.1. This table summarizes results from channel beam load testing, and finite element analysis of channel beam bridge decks. Design calculation values have been used where experimental values were considered questionable or were inconclusive. In this table a positive value represents that the GFRP retrofit increased the value of the structural parameter. A negative value represents a decrease in the structural property value due to a retrofit with GFRP. All results are relative to a non-retrofit sample. 112 Chapter 6 - Conclusions and Recommendations Structural Property Increase Compared to Non-Retrofit Comments GFRP Spray GFRP Wrap Beam Ultimate Flexural Load Capacity 54% 18% Design Calculation Results Beam Ultimate Ductiltiy Capacity -51% -30% Design Calculation Results Beam Elastic Flexural Stiffiiess 25% 41% Experimental Results Beam Elastic Torsional Stiffiiess 92% 50% Experimental Results Longitudinal Compressive Strain at Top of Beam -37% -29% Experimental Results at 150 kN of Total Applied Load Longitudinal Tensile Strain in Beam Reinforcing Steel -17% -12% Experimental Results at 150 kN of Total Applied Load Vertical Displacement at Bottom of Bridge Flanges -31% -38% Finite Element Analysis Results Tensile Stress at Bottom of Bridge Flanges -27% -35% Finite Element Analysis Results Table 6.1: Comparison of GFRP Spray and GFRP Wrap Retrofits on Channel Beam and Channel Beam Bridge Structural Properties 6.0 Accuracy of Design Calculations Conclusions regarding the accuracy of the different design calculation procedures used to predict structural properties for retrofit and non-retrofit channel beams are summarized in this section. Design calculation values and experimental results are compared in order to assess the accuracy of design equations. 6.1 Flexural Resistance Moment resistance of a channel beam bridge girders retrofit with GFRP may be accurately estimated using principles of strain compatibility for channel beams that do not have significant damage at the top of the section, or to the longitudinal reinforcing steel. In this study, flexural capacity results from design equations show good agreement with experimental values for the retrofit channel beams. Moment resistance predicted by design calculations for a channel beam retrofit with fO millimetres of sprayed GFRP was 1% less than from experimental flexural strength results. The calculated moment resistance for a channel beam with two layers of unidirectional GFRP wrap in a 0°-90° orientation was 10% greater than the flexural strength value found from experimental results. 113 Chapter 6 - Conclusions and Recommendations Ultimate moment resistance cannot be accurately predicted if the channel beam is badly damaged. The ultimate flexural capacity of the non-retrofit channel beam was 27% less than predicted by design calculations. This is because the capacity of the non-retrofit channel beam was reduced by damage to its top prior to testing. This damage limited the compressive forces in the concrete compression block during bending, and thus reduced the ultimate moment capacity of this channel beam. 6.2 Ductility Capacity/Vertical Deflection Capacity Ultimate ductility capacity, and ductile response of retrofit channel beams may be predicted using design calculations for channel beams that are not badly damaged. Estimated ultimate deflection values from design calculations were 11% less for the GFRP spray, and 15% greater for the GFRP wrap than vertical deflection data found from the testing program. If channel beams are badly damaged ultimate ductility capacity, and ductile response cannot be estimated using design calculations. This was shown by a comparison of ultimate ductility capacity values, and the ductile response for the non-retrofit channel beam. The design calculations estimated the ultimate deflection at the centre of the non-retrofit channel beam span to be 105% greater than experimental deflection values. This poor agreement is because channel beam one was damaged at its top surface. This damage limited the capability of the beam resist longitudinal compressive forces induced during bending and caused premature failure. 6.3 Elastic Flexural Stiffness Elastic flexural stiffness of channel beams retrofit with GFRP may be predicted using traditional hand calculation methods. Calculated flexural stiffness values for GFRP retrofit channel beams show good agreement with experimental results. The predicted flexural stiffness values for the beams repaired with GFRP spray and GFRP wrap were 11% less than the average of flexural stiffness results from the experimental program. Elastic flexural stiffness values for non-retrofit channel beams predicted from design equations also showed good agreement with experimental results. The predicted flexural stiffness of the non-retrofit beams was 3% greater than the average of experimental results from flexural stiffness testing of the non-retrofit channel beams. 6.4 Longitudinal Strain Tensile strain in the longitudinal reinforcing steel may be predicted accurately for both retrofit and non-retrofit channel beams using design calculations. Values of strain in the longitudinal reinforcing steel found from calculations were in good agreement with strain values found from the test program. For example, at 150 kN of total applied load, strain results for the retrofit and non-retrofit 114 Chapter 6 - Conclusions and Recommendations channel beams found from design calculations were within 11% of strain values found from experimental data. Compressive strain at the extreme compression fibre was not predicted accurately using design calculations for the retrofit and non-retrofit channel beams. Values of compressive strain at the top of the concrete compression block found from design equations were in poor agreement with experimental results for both the retrofit and non-retrofit beams. For example, at 150 kN of applied load, compressive strains found from design calculations were 38% to 58% less than found from experimental results. 7.0 Recommendations It is recommended that the British Columbia Ministry of Transportation and Highways consider retrofitting its reinforced concrete channel beam bridge decks with GFRP. GFRP should be considered as retrofit option for channel beam bridge decks because: 1. The cost to retrofit a channel beam bridge with GFRP will be much less than the cost of bridge replacement. 2. As shown by this study, retrofitting channel beam bridge decks with external GFRP provides improvements to structural properties including increasing the ultimate strength and elastic stiffhess, and reducing longitudinal stresses and strains at a given load level compared to a non-retrofit channel beam bridge deck. 3. GFRP is relatively simple to install, does not significantly add to dead load, and forms easily to the shape of the bridge. 4. A traditional retrofit with steel plate has disadvantages including being difficult to install and being subject to corrosion. 7.1 Recommended Retrofit Material Both the GFRP spray and the GFRP wrap investigated in this study proved to be effective as retrofit materials for reinforced concrete channel beams. In the both the experimental program and the finite element analysis the channel beams retrofit with GFRP spray and GFRP wrap both had improved structural properties compared to the non-retrofit channel beam. Either of these materials could be used for retrofitting channel beam bridges. GFRP wrap is recommended as the preferred material for the retrofit of reinforced concrete channel beam bridges. The reasons GFRP wrap is recommended are described in more detail in the following parts of this section. 115 Chapter 6 - Conclusions and Recommendations 7.1.1 Application of Retrofit Material The application of GFRP wrap to the channel beam in the experimental program was a simpler, and less labour intensive process than the application of GFRP spray. Application of GFRP spray requires more operator experience than GFRP wrap application. Experience is required with the GFRP spray equipment in order to avoid material overheating, and the formation of hotspots. 7.1.2 Environmental Concerns In this study, the application of the GFRP wrap was a much cleaner process than the application of the GFRP spray. For environmental reasons extraneous GFRP material must be contained during application to the underside of a bridge to ensure it does not come into contact with the water below. With improved machine operator experience, the placement of GFRP spray material could also be controlled so that it does not come into contact with the environment around the bridge. 7.1.3 Durability Concerns The use of GFRP as a retrofit material for structural applications is relatively new. At this point in time there have been relatively few studies done on the long term durability of GFRP as a structural retrofit material. The condition of a GFRP structural retrofit several years after its application is yet not known with certainty. Although both GFRP wrap and GFRP spray are relatively new as retrofit materials for structures, GFRP wrap has a longer history in structural repair and strengthening. GFRP spray has not had any structural field applications to date. Although the durability of the two different materials may prove to be comparable, there is still limited information available on the durability of GFRP spray. 7.2 Channel Beam Bridge Repair Recommendations It is recommended that corroded steel reinforcement and areas of missing concrete be repaired in all existing channel beam bridges. Reinforcement corrosion should be cleaned away, steel reinforcement replaced if necessary, and areas of missing concrete filled with grout. This is recommended for the following reasons: 1. Corrosion will eventually reduce the cross sectional area of the exposed longitudinal reinforcing steel. This could lead to a potentially brittle failure mode. 2. Repairing existing damage will reduce the rate of deterioration. This will improve the durability of these structures and be more cost effective in the long term. 3. Repairing the channel beam cross sections is required as a part of the surface preparation before retrofitting with GFRP. When and if these bridges are retrofit in the future, only minimal preparation work will be required. 116 Chapter 6 - Conclusions and Recommendations 7.3 Channel Beam Bridge Retrofit Design Recommendations Calculation procedures presented in this report may be used to design a retrofit scheme for a channel beam bridge. Comparison of design calculation results and experimental data showed that design calculations used in this study may be used to approximate ultimate flexural strength and ultimate vertical displacement for retrofit channel beams that are not badly damaged. Results also showed that design calculations could be used to predict elastic flexural and torsional stiffhess, and tensile strain at the bottom of the flanges for retrofit channel beams. Design calculations presented in this report may be used to ensure a ductile failure mode of a retrofit reinforced concrete channel beam bridge. Flexural and shear capacities of the retrofit bridge should be determined to ensure a ductile flexural failure mode governs. Only the amount of FRP needed to provide the required increases in flexural and shear strength should be provided. Excessive amounts of FRP could cause the beam to become over-reinforced. Very thick layers of FRP also increase the risk of debonding of the FRP from the concrete surface, thus also creating the possibility of a brittle failure mode. The channel beam bridges will likely have greater strength and stiffhess than found from channel beams in this study. Existing channel beam bridges are supported by elastomeric bearings. A pin and roller type support was used in the experimental program and finite element modeling. Elastomeric bearings provide additional restraint therefore existing bridges will have greater load capacity and stiffhess than what was found from this study. In addition, non-structural elements such as curbs, railings, and the paving surface contribute to the strength and stiffness of the bridge. These factors were not taken into account in the experimental and numerical parts of this study. As a result, strength and stiffhess formulations found from this study should provide conservative results. 7.4 Channel Beam Bridge Retrofit Program Implementation Recommendations It is recommended that the British Columbia Ministry of Transportation and Highways perform a load test program for a single reinforced concrete channel beam bridge before implementing any large scale retrofit program. A channel beam bridge should be load tested using a series of heavy trucks both before and after a retrofit with GFRP in order to determine the effects of a retrofit with GFRP on the structural behavior of a channel beam bridge in the field. By doing a single trial retrofit first, the Ministry will be able to form its own conclusions on the effectiveness of retrofitting its structures with GFRP. Retrofitting a single bridge first provides additional information and experience regarding GFRP retrofits including: 117 Chapter 6 - Conclusions and Recommendations 1. the structural behavior of a bridge retrofit with GFRP under field conditions; 2. the optimal retrofit design scheme; 3. the most effective GFRP retrofit application procedures; 4. an assessment of costs and labour; and 5. an indication of the durability of the GFRP material under field conditions Retrofitting a single bridge will provide valuable experience before initiating a larger scale program for retrofitting British Columbia's reinforced concrete channel beam bridges with GFRP. 118 REFERENCES 1. Ahmed, Ahmed E. "Does Core Size Affect Strength Testing?" Concrete International. Volume 21, Number 8. August 1999. pp. 35-39. 2. Agarwal, Bhagwan D. and Lawrence J. Broutman. Analysis and Performance of Fiber Composites. Second Edition. Copyright 1990 by John Wiley and Sons, Inc. 3. 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Copyright 1987 Department of Civil Engineering College of Engineering, The University of Michigan, Ann Arbor, Michigan, USA. June 1987. pp.465-469. 17. Bridge Inspector's Training Manual. US Department of Transporation, Federal Highway Administration, Bureau of Public Roads. Washington DC. 1970. 18. Buyukozturk, Oral, and Brian Hearing. "Failure Behavior of Precracked Concrete Beams Retrofitted with FRP." ASCE Journal of Composites for Construction. Volume 2, Number 3. August 1998. pp.138-144. 19. CAN/CSA-S6-98, Canadian Highway Bridge Design Code, Pre-Ballot Draft, April 1998. Copyright Canadian Standards Association 1998. 20. Collins, Michael P., and Denis Mitchell. Prestressed Concrete Basics. Copyright 1987 by Canadian Prestressed Concrete Institute. 21. CSA Standard A23.3-94, Design of Concrete Structures. Copyright Canadian Portland Cement Association 1995. 22. Ducrot, B. "Diagnostic and Concrete Repair Systems." Bridge Evaluation, Repair, and Rehabilitation, Proceedings of the First US-European Workshop. Nowak, Andrzej S., and Elie Absi (Editors). Copyright 1987 Department of Civil Engineering College of Engineering, The University of Michigan, Ann Arbor, Michigan, USA. June 1987. pp.416-427. 23. Dunker, Kenneth F., and Basile G. Rabbat. "Assessing Infrastructure Deficiencies: The Case of Highway Bridges." ASCE Journal of Infrastructure Systems. Volume 1, Number 2. June 1995. pp. 100-119. 24. Emmons, Peter H., Jay Thomas, and Alexander M. Vaysburd. "Muscle Made with Carbon Fiber." Civil Engineering. Volume 68, Number 1. January 1998. New York, pp.60-61. 25. Fanson, James, and Edward Cohen. "Lincoln Park Lagoon Bridge Restoration." ACI Concrete International. Volume 13, Number 6. June 1991. pp.50-52. 26. Fisher, John W. and Peter B. Keating. "Repair, Rehabilitation, and Strengthening of Highway Bridges in the United States." Bridge Evaluation, Repair, and Rehabilitation, Proceedings of the First US-European Workshop. Nowak, Andrzej S., and Elie Absi (Editors). Copyright 1987 Department of Civil Engineering College of Engineering, The University of Michigan, Ann Arbor, Michigan, USA. June 1987. pp.185-195. 27. GangaRao, Hota V. S., and P. V. Vijay. "Bending Behavior of Concrete Beams Wrapped with Carbon Fabric." ASCE Journal of Structural Engineering. Volume 124, Number 1. January 1998. pp.3-10. 28. Goins, Veldo M. "Bridge Rehabilitation in Oklahoma." Bridge Evaluation, Repair, and Rehabilitation, Proceedings of the First US-European Workshop. Nowak, Andrzej S., and Elie Absi (Editors). Copyright 1987 Department of Civil Engineering College of Engineering, The University of Michigan, Ann Arbor, Michigan, USA. June 1987. pp.251-262. 29. Jorgenson, James L., and Wayne Larson. "Field Testing of a Reinforced Concrete Bridge to Collapse." Bridge Design. Testing and Evaluation, Transportation Research Record 607. Transportation Research Board Commision on Sociotechnical Systems, National Research Council, National Academy of Sciences. Washington DC. 1976. 120 References 30. Kaw, Autar K. Mechanics of Composite Materials. Copyright 1997 by CRC Press LLC. 31. Kosmatka, Steven H., et al. Design and Control ofConcrete Mixtures. Fifth Canadian Metric Edition, Copyright 1991 by the Canadian Portland Cement Association. Ottawa, Ontario, Canada. 32. Levi, Franco, Paolo Nalpoli, and Giovanni Corona. "Typical Damages of Highway Bridges, Redsign Examples, Diagnostic Techniques." Bridge Evaluation, Repair, and Rehabilitation, Proceedings of the First US-European Workshop. Nowak, Andrzej S., and Elie Absi (Editors). Copyright 1987 Department of Civil Engineering College of Engineering, The University of Michigan, Ann Arbor, Michigan, USA. June 1987. pp. 154-167. 33. Loveall, Clellon L. "Evaluation of Existing Bridges in the United States." Bridge Evaluation, Repair, and Rehabilitation, Proceedings of the First US-European Workshop. Nowak, Andrzej S., and Elie Absi (Editors). Copyright 1987 Department of Civil Engineering College of Engineering, The University of Michigan, Ann Arbor, Michigan, USA. June 1987. pp.58-61. 34. Master Builder Technologies, MBrace™ Fiber Reinforcement Systems for the MBrace™ Composite Strengthening System. (Product Information). TM Trademark of MBT Holding A.G., Master Builders, Inc. Cleveland, Ohio. 1998. 35. Mukhopadhyaya, Phalguni, Narayan Swamy, and Cyril Lynsdale. "Optimizing Structural Response of Beams Strengthened with GFRP Plates." ASCE Journal of Composites for Construction. Volume 2, Number 2. May 1998. pp.87-95. 36. Naaman, Antoine E. "Partial Prestressing in the Rehabilitation of Concrete Bridges." Bridge Evaluation, Repair, and Rehabilitation, Proceedings of the First US-European Workshop. Nowak, Andrzej S., and Elie Absi (Editors). Copyright 1987 Department of Civil Engineering College of Engineering, The University of Michigan, Ann Arbor, Michigan, USA. June 1987. pp.391-406. 37. Salomon, Michel. "Durability of Reinforced Concrete Corrosion Diagnosis." Bridge Evaluation, Repair, and Rehabilitation, Proceedings of the First US-European Workshop. Nowak, Andrzej S., and Elie Absi (Editors). Copyright 1987 Department of Civil Engineering College of Engineering, The University of Michigan, Ann Arbor, Michigan, USA. June 1987. pp.428-437. 38. SAP2000 Integrated Finite Element Analysis and Design of Structures Analysis Reference, Version 6.1, Volume 1. Copyright Computers and Structures, Inc. 1978-1997. 39. SAP2000 Integrated Finite Element Analysis and Design of Structures Analysis Reference, Version 6.1, Volume 2. Copyright Computers and Structures, Inc. 1978-1997. 40. Spadea, G., F Bencardino, and R. N. Swamy. "Structural Behavior of Composite RC Beams with Externally Bonded CFRP." ASCE Journal of Composites for Construction. Volume 2, Number 3. August 1998. pp.132-137. 41. Szypula, Ava, and Jocob S. Grossman. "Cylinder vs. Core Strength". Concrete International. Volume 12, Number 2. February 1990. pp. 55-61. 42. Trantafillou, Thanasis C. "Shear Strengthening of Reinforced Concrete Beams Using Epoxy-Bonded FRP Composites." ACI Structural Journal. Volume 95, Number 2. March-April 1998. pp. 107-115. 43. White, Richard N., Peter Gergley, and Robert G. Sexsmith. Structural Engineering, Volume 3, Behavior of Members and Systems. Copyright 1972 by John Wiley and Sons Inc. 121 APPENDIX 1 CALCULATIONS AND MISCELLANEOUS INFORMATION 1.0 Notation Used in Calculations a = depth of equivalent rectangular stress block (a=B,c) APRP = effective tensile area of glass fibre reinforced plastic, [GFRP spray: A F R P = 3040 mm2, GFRP wrap: A F R P = 107 mm2] Aoh = area enclosed by centerline closed transverse torsion reinforcement in channel beam flanges A r = area of shear reinforcement perpendicular to the axis of a member within a distance s A s = area of steel tension reinforcment, [A s= 2568 mm2] A T = area of one leg of closed transverse torsion reinforcement A v = area of steel shear reinforcement AVFRP = area of GFRP shear reinforcement b = width of compression face of member, [b = 822 mm] bw = minimum effective web width within depth d c = distance from extreme compression fibre to neutral axis c0,C] = arbitrary constants d = distance from extreme compression fibre to centroid of steel tension reinforcement, [d = 349 mm] E = modulus of elasticity E c = modulus of elasticity of concrete, [E c= 29,600 MPa] E F R P = modulus of elasticity of glass fibre reinforced plastic, [GFRP spray: E F R P = 12,000 MPa, GFRP wrap: E F R P = 70,000 MPa] E s = modulus of elasticity of longitudinal reinforcing steel, [E s= 200,000 MPa] f c = concrete compressive strength, [f c= 35 MPa] fyp = equivalent in place concrete strength f;,iP9o = 90 percent limit (one-sided) on confidence interval of mean value f c e q = equivalent concrete compressive strength fFRP = tensile stress in glass fibre reinforced plastic at the bottom of the beam flanges fs = tensile stress in longitudinal steel reinforcement fy = specified yield strength of steel reinforcement [fy = 379 MPa] F c = force in concrete compression block FFRP = force in glass fibre reinforced plastic F s = force in longitudinal steel reinforcement 122 Appendix 1 - Calculations and Miscellaneous Information G = shear modulus of reinforced concrete [G = 12,333 MPa] i = y intercept I = moment of inertia I C R = moment of inertia of cracked section j = slope of trendline J = polar moment of inertia k = length of section k| = constant L = length of beam m = depth of compression block / mass M = moment M R = moment resistance n = number of concrete cores NpRp = ratio of glass fibre reinforced plastic modulus of elasticity to concrete modulus of elasticity, [GFRP spray: N F R P = 0.405, GFRP wrap: N F R P = 2.36] N s = ratio of steel modulus of elasticity to concrete modulus of elasticity, [N s = 6.76] P = total applied load s = spacing of shear or torsion reinforcement measured parallel longitudinal axis of the member sc-ip = samples standard deviation of in-place concrete strength t = thickness of section T = torsion T R = torsional resistance vd = coefficient of variation of strength correction factor for damage due to drilling of concrete core vd i a = coefficient of variation of strength correction factor for concrete core diameter V| / d = coefficient of variation of strength correction factor for length to diameter ratio of concrete cores vm c = coefficient of variation of strength correction factor for moisture condition of concrete core vr = coefficient of variation of strength correction factor for concrete core containing reinforcing steel V c = shear resistance provided by concrete V F R P = shear resistance provided by glass fibre reinforced plastic V R = shear resistance V s = shear resistance provided by longitudinal steel reinforcement w = dead load due to self weight x = distance coordinate along length of beam y = distance coordinate in lateral direction 123 Appendix 1 - Calculations and Miscellaneous Information z = distance coordinate in vertical direction ci] = ratio of average stress in rectangular compression block to the specified concrete strength P] = ratio of depth of rectangular compression block to depth to the neutral axis 8 = differential deflection A = vertical deflection at midspan of beam AMAX = maximum vertical deflection at midspan of beam A 3 / i = deflection at point 3 with respect to tangent at point 1 A 2 / i = deflection at point 2 with respect to tangent at point 1 8c = strain at extreme compression fibre ECMAX = strain corresponding to f c, maximum concrete compressive strain, [ECMAX = 0.00215] EFRP = tensile strain in glass fibre reinforced plastic at the bottom of the beam flanges £FRP,E = effective tensile strain in glass fibre reinforced plastic es = tensile strain in longitudinal steel reinforcement Ey = strain at specified yield strength of steel reinforcement YFRP = partial safety factor for FRP X = factor to account for concrete density [X = 0.85] <j> = curvature (angle of twist per unit length) <t>E = curvature within the elastic range (J>MAX = maximum curvature in curvature distribution <t>MAXE = curvature when longitudinal reinforcing steel yields PFRP = GFRP area fraction v = Poisson's ratio 0 = angle of twist £, = distance between potentiometers 124 Appendix 1 -Calculations and Mscellaneousmformation 2.0 Instrumentation Details Multiple Pressure Hydraulic Load Maintainer and Cycling Unit Manufacturer: by John S. Edison Inc. Dial Gauges (Top of Beam) Manufacturer: Mitsutoyo Range: 0.001 inch to 1.000 inch Serial Numbers: Front (East): 2904, Back (West): 2416 Dial Gauge (Roller) Manufacturer: Exceed Range: 0.01 millimetres to 10 millimetres Linear Displacement Transducers Manufacturer: Duncan Electronics Accuracy: 606 R6K +- 20%, Lin +-12% Low Friction Load Actuators Manufacturer: Sealum Industries Capacity: 3000 pounds per square inch, 1080 kilonewtons in compression, 800 kilonewtons in tension Stroke: twelve inches Strain Gauges Manufacturer: Tokyo Sokki Kenkyuju Co. Ltd. Gauge Length: Six millimetres Type: FLA-6.350-11 Gauge: 350+-1.0 Ohms Gauge Factor: 2.13 LVDTs Manufacturer: Trans-Tek Serial Numbers: Top: A-9, 1993. Bottom: E-9 2030 125 Appendix 1 - Calculations and Miscellaneous Information 3.0 Concrete Parameters CD H E o s C .3 crt it W i l l i i i i i i i i m m 36.642 33.497 34.733 34.820 38.249 37.786 m m § § § § § § _ d d o o o >->« 0.0717 0.0715 0.0716 0.0717 0.0123 0.0098 0.0445 0.1418 0.1107 0.1083 0.0102 0.0444 i -5 I m m 1 s 24.2 24.2 24.2 24.2 24.2 24.2 j r- <N * r- ^ <= i h s 2.13 2.24 2.21 2.21 1.94 2.13 I 1 41.8 54.3 47.1 30.6 40.5 34.6 Jl* 159238 207277 179699 116538 286006 249533 i l * m i l l ! 1 3805.1 3815.5 3812.2 3807.9 7055.4 7217.1 !H 69.605 69.7 69.67 69.63 94.78 95.86 ! 1 69.57 69.72 69.65 69.57 94.57 95.80 I I 69.64 69.68 69.69 69.69 94.99 95.92 I I 148.5 156.0 154.0 153.75 183.5 204.5 »\ ON r-oo oo — o o o — o>" o t t -u a . > l £ <2 "°l O C O T u a g 1 V E J3 > D V 4> £ 2 _ f I C SI " 3 S 1 ca u < 3 £ -2 5 E _£ i O. M V - = U V U j3 a . J3 -e w « w m w •O T 3 -O T 3 -o u n l C C C B C B C a a d a d a a | <U U t> V c B c e O O O O U U U U • m i r-is l !/->«/-> M I N N N OOOO OOOO 1/1 «/"N «/-> CN CS < S <N OOOO OOOO OOOO OOOO > 0 0 I o\ • o I o O oo O T f = 2 5 S OOOO H i ^ T ^ ( S M ( N v i cs r-v£> yQ O ON m <m m in o\ © r-*r m TT \0 — — •o NO r-' O m m f —' — T <S CS ON cs is — O O oo ON oo vo m • M o> M o cs S H vo m o ON I B j ON NO vO M S o H H o o o « 9 O H H O O O B R B O O B B I ^ ' CS cn M w ^ H i o NO H j I n i ^ H T r cs NO i r-- w-i i oo o r- m oo vo NO NO oo ON ON T f • O NO ON ON NO K In ON' ON TT NO NO ON 5 S SN ON ON NO NO ON In °° II IT <u u s_ 4> en as > O 0 0 NO 0 0 —•' o * I cr v ON — O N I ob vd r-1 m ^  | ^ ' - 4j O C n u ca B _ a a 03 v |£ © L. V 1^  126 Appendix 1 -CalculaticnsandMscellaneousMormation 4.0 Free Body Diagrams Free body diagrams neglect the effects of dead load. 4.1 Flexural Load Configuration _ I I 2255 mm (7.4 ft) Figure A l . l : Free Body Diagram for Flexural Load Configuration 1830 mm (6 ft) 2255 mm (7.4 ft) V M A X = 2 P V M A X = 2 P - . .,._!,It'.. u » \* p— 1 2255 mm 1830 mm 2255 mm (7.4 ft) (6 ft) (7.4 ft) Figure A 1.2: Shear Force Diagram for Flexural Load Configuration M v f A v = 2.255 x 2 x P (kNm) 2255 mm 1830 mm (7.4 ft) (6 ft) Figure A 1.3: Bending Moment Diagram for Flexural Load Configuration 2255 mm (7.4 ft) 127 Appendix 1 - Calculations and Miscellaneous Information 4.2 Flexural-Torsional Load Configuration 2255 mm (7.4 ft) 1830 mm (6 ft) 2255 mm (7.4 ft) Figure A1.4: Free Body Diagram for Flexural-Torsional Load Configuration .. *•"-;:". <_._.-' - « * / _ . ';. r% V M A X = 3P/2 V M A x = 3P/2 2255 mm (7.4 ft) 1830 mm (6 ft) 2255 mm (7.4 ft) Figure A1.5: Shear Force Diagram for Flexural-Torsional Load Configuration 128 Appendix 1 - Calculations and Miscellaneous Information M M A X = 2.255 x 3/2 x P (kNm) 2255 mm (7.4 ft) 1830 mm (6 ft) 2255 mm (7.4 ft) Figure A1.6: Bending Moment Diagram for Flexural-Torsional Load Configuration T M A X = 0 - 1 4 4 x p / 2 ( k N m ) T M A X = 0 1 4 4 x p / 2 (kN™) + 2255 mm 1830 mm 2255 mm (7.4 ft) (6 ft) (7.4 ft) Figure A 1.7: Torsion Diagram for Flexural-Torsional Load Configuration 129 Appendix 1 - Calculations and Miscellaneous Information 5.0 Ultimate Flexural Capacity 5.1 Ultimate Flexural Capacity of Non-Retrofit, Reinforced Concrete Channel Beam Calculation of ultimate flexural capacity (MR) for a non-retrofit, reinforced concrete channel beam is based on "CSA Standard A23.3-94, Design of Concrete Structures"(21) Concrete Parameters: f c = 3 5 M P a a, = 0.85 -0 .0015f c ' = 0.80 p, = 0 . 9 7 - 0.0025f c ' = 0.88 Longitudinal Reinforcing Steel Parameters: Yield Strength (fy) (MPa) Area (As) (mm2) #10 Bar 304 819 #8 Bar 408 510 Table A1..3: Properties of Longitudinal Reinforcing Steel Sectional Properties: d = 349 mm b = 822 mm Calculation of Ultimate Flexural Capacity ( M R ) a = A . - f y o,.fc.b a = |(2*819*304)+(2*510*408)} 0.80*35*822 a = 39.7mm M R = A s f y 130 Appendix 1 - Calculations and Miscellaneous Information M R ={(2*819*304)+(2*5i0*408)}* 39.7 349-— V 2 j M =302kN-m <- Ultimate Flexural Capacity of Non-Retrofit Channel Beam R Applied Load From Experimental Load Configuration at Ultimate Moment Resistance P P 1 _. k < 2255 mm w ^ — w 1830 mm 2255 mm Figure A1.8: Experimental Flexural Load Configuration Free Body Diagram M R =P-2255 P = -3Q2xl0 6 2255 P = 134 kN <- Total Applied Flexural Load at Ultimate Flexural Load Capacity 131 Appendix 1 - Calculations and Miscellaneous Information 5.2 Ultimate Flexural Capacity of Reinforced Concrete Channel Beam Retrofit with GFRP Ultimate flexural capacity (MR) of GFRP retrofit channel beams use an iterative procedure based on principles of strain compatibility. The strain (s), stress (f), and force (F) profiles for the cross section of the reinforced concrete channel beam retrofit with GFRP are shown in Figure Al.9. Strain Stress Force s c ccfc F c i s pc < w fs F s r ! 349mm 407mm \ » •+ i r 8 F R P fFRP F F R P Figure A1.9: Strain, Stress, and Force Profiles for Channel Beam Cross Section The sum of the constituent material forces must sum to equal zero. The forces in each of the materials are found using the following equations. F c=a,.f 6 '-c.p i.b F s =f s - A s F = f - A FRP FRP FRP The values used in the calculation of flexural capacity of these two retrofit beams are summarized in Table A 1.4. Values were found using an Excel solver to solve for c. Parameter Units GFRP Sprayed Beam GFRP Wrapped Beam Depth of Neutral Axis c mm 6 7 51 Strain — 2 . 4 8 E - 0 3 2 . 8 7 E - 0 3 E S — 1 .04E-02 1 .68E-02 EFRP — 1 .25E-02 2 . 0 0 E - 0 2 Young's Modulus of GFRP EFRP GPa 12 7 0 Tensile Area of GFRP AFRP i mm 3 0 4 0 107 Tensile Area of Steel AFRP i mm 2 6 5 8 2 6 5 8 Force Fc N - 1 3 7 0 -1065 F s N 9 1 4 9 1 4 FFRP N 4 5 6 150 Table A l .4: Values Used in Moment Capacity Calculation For Retrofit Beams 132 Appendix 1 - Calculations and Miscellaneous Information The ultimate flexural capacities of the beams retrofit with GFRP are found by the equation: M R =F C . ( c - j / ) + F s •(349-c) + F F R P -(407-c) Ultimate Moment Capacities of Retrofit Channel Beams GFRP Sprayed Beam: M R = 464 k N • m <r Ultimate Flexural Capacity of Channel Beam Retrofit with 10 Millimetres of GFRP Spray P = 190 kN <- Total Applied Flexural Load at Ultimate Flexural Capacity of Channel Beam Retrofit with 10 Millimetres of GFRP Spray GFRP Wrapped Beam: M R =356kN -m <- Ultimate Flexural Capacity of Channel Beam Retrofit with Two Layers of Unidirectional GFRP in a 0°-90° orientation P = 146 kN <- Total Applied Flexural Load at Ultimate Flexural Capacity of Channel Beam Retrofit with Two Layers of Unidirectional GFRP in a 0°-90° orientation 133 Appendix 1 - Calculations and Miscellaneous Information 6.0 Ultimate Torsional Capacity 6.1 Ultimate Torsional Capacity of Non-Retrofit. Reinforced Concrete Channel Beam Calculation of torsional capacity (TR) of non-retrofit reinforced concrete channel beams is based on "CSA Standard A23.3-94, Design of Concrete Structures"*21' T = 2 - ( 0 . 8 5 - A o h ) - A T . f y 308 mm Figure ALIO: Dimensions Used in Calculation of A ^ A h = 2-(90-308) = 55,440mm' Critical Location: Failure is predicted to occur at the approximate third point of beam (2440 millimetres from the end of the beam). This location has the maximum shear/torsion tie spacing within the shear zones generated from the experimental load configuration. At this location spacing of the shear/torsion ties is equal to 30 inches, (762 millimetres). T -2-(0.85-55440)-71-379 762 T = 3 . 3 k N - m «- Ultimate Torsional Capacity of Non-Retrofit Channel Beam R 134 Appendix 1 - Calculations and Miscellaneous Information Load configuration in actuators required to induce 3.3 kNm of torsion in cross section 433 288 144 Figure A l . 11: Torsion in Channel Beam 3.3kN-m = - x 0.144m 2 P = 45.8kN 3P = 68.8kN <- Total Applied Flexural-Torsional Load at Ultimate Torsional 2 Capacity of Non-Retrofit Channel Beam 135 Appendix 1 - Calculations and Miscellaneous Information 7.0 Ultimate Shear Capacity 7.1 Ultimate Shear Capacity of Non-Retrofit, Reinforced Concrete Channel Beam Calculation of ultimate shear capacity (VR) for the non-retrofit, reinforced concrete channel beam are based on "CSA Standard A23.3-94, Design of Concrete Structures"'20 V R = V C + V S + V F R P Concrete Contribution to Shear Resistance (V c): V c =0.2- , l-VfVb w -d V c =0.2-0.85-V35-(150-2)-(349) V c =105kN Steel Contribution to Shear Resistance (V s): v = A - ' f ' - d v s S Critical Location: Failure is predicted to occur at the approximate third point of beam (2440 millimetres from the end of the beam). This location has the maximum shear/torsion tie spacing within the shear zones generated from the experimental load configuration. At this location spacing of the shear/torsion ties is equal to 30 inches, (762 millimetres). _ ( 4 -71) -379 -349 s ~ 762 V s = 49kN Shear Resistance of Reinforced Concrete Channel Beam (Without GFRP) Retrofit V R =105kN + 4 9 k N V R = 1 5 4 k N <- Ultimate Shear Capacity of Non-Retrofit Channel Beam 136 Appendix 1 - Calculations and Miscellaneous Information 7.2 Ultimate Shear Capacity of Reinforced Concrete Channel Beam Retrofit with GFRP Calculation of GFRP contribution to shear resistance is based Triantafillou, Thanasis. "Shear Strengthening of Reinforced Concrete Beams Using Epoxy-Bonded FRP Composites"(42) FRP contribution to shear resistance: ^FRP = 0 . 9 - p F R P - E F R P - e F R P E - b w -d _ 2-t PFRP — , Where t= thickness of the GFRP layer e F R P . E = 0.0119-0.0205-(p F R P •E F R P )+0 .0104 - (p F R P - E F R P ) 2 For 0 < p F R P • E F R P <1 Where p F R P - E ^ p is in GPa For the GFRP spray: 2-10 . „ 1 r t _ 2 PFRP = = 6.67x10 2 2-150 PFRP , E F R P = 6 . 6 7 x l 0 " 2 -12GPa = 0 .8GPa £ FRP,E =0.0119-0.0205-(0.8)+0.0104-(0.8) 2 e F R P E =0.00216 V F R P =0.9-0.8-0.00216-(2-150)-349 V F R P = 1 6 3 k N V R = 317 k N <- Ultimate Shear Capacity of Channel Beam Retrofit with 10 Millimetres of GFRP Spray 137 For the GFRP wrap: Appendix 1 - Calculations and Miscellaneous Information 2-0.353 PFRP = - t e n - 2 . 3 5 x 1 0 -3 2-150 \-3 P F R P - E F R P = 2 . 3 5 x l 0 - 3 - 7 0 G P a = 0.165GPa 8 F R P E =0.0119-0.0205-(0.165)+0.0104-(0.165) 2 S P R P E =0.0088 V™, =0.9-0.165-0.0088-(2-150)-349 V ^ p = 1 3 7 k N V R = 291 k N <- Ultimate Shear Capacity of Channel Beam Retrofit with One Layer of Unidirectional GFRP Oriented Perpendicular to the Beam's Longitudinal Axis 138 Appendix 1 - Calculations and Miscellaneous Information 8.0 Elastic Flexural Stiffness 8.1 Elastic Flexural Stiffness (EI) of Non-Retrofit, Reinforced Concrete Channel Beam Based on Material and Sectional Properties Young's Modulus of Concrete (Er) E c = 5 0 0 0 ^ = 5000-v735 E c s 29600 MPa Transformed Moment of Inertia of the Cracked Section (Icr) 822 (349-m) O Q-102 305 d=349 Figure A1.12: Depth of Compression Block (m) for Non-Retrofit Channel Beam (Dimensions in millimetres) Solve for depth of compression block (m): X T A lA \  b ' m 2 N s - A s - ( d - m ) = — — 6.76-2658-(349-m) 822 -m1 m = 103.6 mm (from Excel Solver) 139 Appendix 1 - Calculations and Miscellaneous Information I . = ^ + N s - A s . ( d - m ) 2 I c t = 8 2 2 -O 0 3- 6) 2 + 6.76 • 2658 • (349 -103.6)2 I =1.40xl09mm Elastic Flexural Stiffness of Non-Retrofit Channel Beam E c l ^ = 4.14xl013N-mm2 .\ EI = 4.14 x 1013 N • mm2 <- Elastic Flexural Stiffness of Non-Retrofit Channel Beam Based on Material and Sectional Properties of the Channel Beam 8.2 Elastic Flexural Stiffness of Reinforced Concrete Channel Beam Retrofit with GFRP (Design Calculation) 822 m (407-m) (349-m) * VO O O O Figure A1.13: Depth of Compression Block (m) for Retrofit Channel Beam (Dimensions in millimetres) Solve for depth of compression block (m): N s • A s • (349 - m) + • A ^ p • (407 - m) = b-m' 140 Appendix 1 - Calculations and Miscellaneous faformation For the Channel Beam Retrofit with GFRP Spray: N F R P = 0.405 A F R P = 3040 m m 2 . . m = 107.1 mm (from Excel Solver) For the Channel Beam Retrofit with GFRP Wrap: N P K P - 2 . 3 6 A F R P = 1 0 7 m m 2 .-. m = 1 0 4 . 3 mm (From Excel Solver) Transformed Moment of Inertia of the Cracked Section (L,r) I = - ^ - + N s • A s - ( 3 4 9 - m ) 2 + N F R P • A F R P • (407 — m) 2 For the Channel Beam Retrofit with GFRP Spray: I = 1 . 5 2 x l 0 9 m m 4 For the Channel Beam Retrofit with GFRP Wrap: I C T = 1 . 4 3 x l 0 9 m m 4 Elastic Flexural Stiffhess of Channel Beam Retrofit with GFRP For the Channel Beam Retrofit with GFRP Spray: E C I C R = 4 . 5 0 x l 0 1 3 N - m m 2 . EI = 4.50 x 10 1 3 N - m m 2 «- Elastic Flexural Stiffhess of Channel Beam Retrofit With 10 Millimetres of GFRP Spray Based on Material and Sectional Properties of the Channel Beam 141 Appendix 1 - Calculations and Miscellaneous Information For the Channel Beam Retrofit with GFRP Wrap: E C I C R = 4.23xl0 1 3 N-mm 2 .-. E I = 4.23 x 1013 N • mm 2 <- Elastic Flexural Stiffhess of Channel Beam Retrofit with Two Layers of Unidirectional GFRP Wrap in a 0°-90° Orientation Based on Material and Sectional Properties of the Channel Beam 8.3 Derivation of Flexural Stiffness (ED Based on Experimental Results or Finite Element Analysis 2256 mm 1828 mm . 2256 mm .1. 4 - *y 1 1' 1 1 1 1 1 1 1 + 1 1 , , 1 1 + 1 1 1 „ 1 1 1 AMAX — " 1 P [ 4 . » <— * L/2 = 3170 mm L/2 = 3170 mm Figure A1.14: Free Body Diagram of Channel Beam P w 1 1 1 1 1 1 1 1 I I 1 I L/2 2> M =Pk + wL78 Figure A 1.15: Free Body Diagram of Half of Channel Beam 142 Appendix 1 - Calculations and Miscellaneous Information dA _ r dx ~ EI 8EI dx dA Pkx w L ' x — = + + c. dx E I 8EI A - J l Pkx w L 2 x • + -EI 8EI • + c n dx P k x 2 w L 2 x 2 A = + + c 0 x + c, 2EI 16EI Boundary Conditions: When x = 0, A = 0 When x = L, A = 0 0 = 0 + 0 + 0 + C , . \ C , =0 0 = P k L 2 w L 4 • + -2EI 16EI - P k L w L 3 + c n L c 0 = ' 2EI 16EI P k x 2 w L 4 P k L x w L 3 x A _ 2EI + 1 6 E I 2EI 16EI Pk(L/2) 2 PkL(L/2) w L 2 ( L / 2 ) 2 w L 3 ( L / 2 ) A M A X - 2 H 2 E I + 1 6 M 1 6 H 'MAX P k L 2 P k L 2 w L 4 w L 4 8EI 4EI + 6 4 E I 32EI 'MAX P k L 2 w L 4 • + -8EI 64EI 143 Appendix 1 - Calculations and Miscellaneous Information Prediction of Deflection at Centre of Beam from Experimental Results Based on the trendline fitted to the data from a total load versus average beam centre deflection graph, deflection for the beam is: j Where: 2P = total applied load i = y intercept j = slope of trendline Therefore: A PkL 2 wL 4 2 P - i A = + = 8EI 64EI j • Deflection due to self weight is not measured by LVDTs, therefore the effect of dead load on deflection may be ignored. • The y intercept (i) may be taken as zero if slope is shifted to the origin Therefore, the flexural stiffness equation becomes: PkL 2 _ 2P 8EI " j EI = 1^ 16 144 Appendix 1 - Calculations and Miscellaneous Information 8.4 Elastic Flexural Stiffness Sample Calculation for Beam One 100000 0 2 4 6 8 10 12 14 16 Average Centre Deflection (mm) Figure A 1.16: Beam One, Total Load versus Average Centre Deflection for Initial Flexural Stiffness Testing, Load Cycles Two to Five k L 2 j EI = 16 C T (2256X6340)2(7241.6) E l = 16 EI = 4.10 x 1013 N • mm 2 <- Elastic Flexural Stiffness of Channel Beam One (Non-Retrofit) Based on Experimental Results 145 Appendix 1 - Calculations and Miscellaneous Information 9.0 Elastic Torsional Stiffness 9.1 Elastic Torsional Stiffness (GJ) of Non-Retrofit, Reinforced Concrete Channel Beam Based on Material and Sectional Properties Shear Modulus (G) G = 2 - ( l + v) _ 29,600 ~ 2-(1 + 0.2) G = 12,333 M P a Polar Moment of Inertia (J) Using the Membrane Analogy: j = Y - - k - t 3 ^ 3 710 mm 10 mm 308 mm Figure A1.17: Lengths used in Polar Moment of Inertia Calculation Assume concrete is cracked, therefore assume effective polar moment of inertia due to concrete is 50% of gross polar moment of inertia due to concrete contribution. J = ^ £ ( 0 . 5 - 2 - 3 0 8 - 9 0 3 ) + ( 4 - N s - 3 2 8 - 1 0 3 ) + ( 2 - N s -90-10 3 ) + ( N s -710-10 3 ) 146 Appendix 1 - Calculations and Miscellaneous Information No =• E Q 200,000 E c ~ 29,600 = 6.76 J = 7.98xl0 7 mm 4 GJ = 9 . 8 4 x l 0 u N mm^ Elastic Torsional Stiffness of Non-Retrofit Channel Beam Based on Material and Sectional Properties of the Channel Beam 9.2 Derivation of Torsional Stiffness (C J) Based on Experimental Results or Finite Element Analysis T GJ = - k 0 Where k = length along the beam span between support and approximate third point of channel beam Find Torsional Stiffness from the Slope of a Torsion (T) versus Angle of Twist (G) Plot at the approximate third point of the channel beam span. Torsion (T) at Third Point of the Channel Beam Span from Experimental Program load beam channel beam Figure A1.18: Load Beam and Channel Beam 6 feet, 1829 mm A P/2 ^ „ hi ^ 866 mm I P/866mm, uniform load distribution (P/2) / 866mm, triangluar load distribution Figure A l . 19: Free Body Diagram With Assumed Force Distribution Under Load Beam 147 Appendix 1 - Calculations and Miscellaneous Information P/2 433 288 144 Figure A1.20: Torsion in Channel Beam Torsion at third point of channel beam span T = - x 0 . 1 4 4 m 2 Torsional Load Distribution Used in Finite Element Analysis + t • t ! T (P/2) / 866 mm, triangular load distribution P / 866 mm, uniform load distribution 866 mm Figure A 1.21: Torsional Load Distribution Used in Finite Element Analysis Angle of Twist (9) at third point of channel beam span Distance Between Potentiometers (Q Original Top of • Beam Deflected Top of Beam Figure A1.22: Angle of Twist in Channel Beam 148 Appendix 1 - Calculations and Miscellaneous Information 6 = s i n 9.3 Elastic Torsional Stiffness Sample Calculation for Beam One 2500000 i 2000000 1500000 .g 1 1000000 H 500000 o U O.OOE+00 1.00E-03 2.00E-03 3.00E-03 4.00E-03 5.00E-03 Angle of Twist at Third Point (radians) Figure A1.23: Beam One, Torsion versus Angle of Twist for Initial Torsional Stiffhess Testing T G J = - - k 6 GJ = (6.45 x 1 0 8 N • mm)- (1900 mm) GJ = 1.23 x 101 2 N • mm 2 <- Elastic Torsional Stiffhess of Channel Beam One (Non-Retrofit) Based on Experimental Results 149 Appendix 1 - Calculations and Miscellaneous mformation 10.0 Vertical Deflection and Stress/Strain in Channel Beam Cross Section For Increasing Applied Load Calculation is based an iterative solution technique using strain compatibility principles. Calculation Method • Assume values of strain at the extreme compression fibre (ec) and distance from extreme compression fibre to neutral axis (c) • Calculate tensile strain in the longitudinal reinforcing steel (ss) from similar triangles • Calculate curvature at midspan of beam (<j>) • Calculate tensile stress in longitudinal steel (fs) • Assume curvature distribution along beam length • Calculate deflection at midspan of beam (A) • Calculate stress block factors ( c t i and (50 • Calculate concrete block compression force (Fc), tensile force in longitudinal reinforcing steel (Fs), and tensile force in GFRP (FF R P) if applicable • Sum forces, if sum of forces does not equal zero, choose a new value for c and repeat • Calculate Moment (M) in Cross section • Calculate total applied load (P) required to generate this moment in cross section Sample Calculation for Non-Retrofit Channel Beam For a strain at the extreme compression fibre equal to: 6 C =0.001 c = 80.9 mm . \ e s =3.316x10 -3 Figure A1.24: Strain Distribution in Channel Beam Cross Section 150 " Appendix 1 - Calculations and Miscellaneous Information Curvature at midspan of beam ((j>): * = Vc (0 = 0.001/ 9 / 80 .9 mm 9 = 1 .24xl0" 5 rad/mm Tensile stress in longitudinal steel (fs): s^ — e s f s = 3.316xl0~ 3 -200,000 f. = 663 M P a -> steel has yielded .-. f s = 344 M P a Assumed Curvature Distributions Along Length of Beam: w 1 h rf fc. 4 2440 mm 1830 mm 2440 mm Figure A 1.25: Curvature Distribution Along Beam Span, Elastic Range ^ A X - Found from strain profile at midspan Inelastic Curvature rfj— <I>MAX,E - Curvature when steel yields I lastic Curvature 4 ^ «I 2440 mm w 1830 mm 2440 mm Figure A 1.26: Curvature Distribution Along Beam Span, Inelastic Range 151 Appendix 1 - Calculations and Miscellaneous Information Deflection at midspan of beam (A): Deflection is calculated using the curvature from each strain profile and the moment-area method. Figure Al.27: Beam Deflection £ y ^ M A X . E — , d - c _ 344/200,000 ^PMAX,E 3 4 9 _ 1 0 3 6 P M A ^ E = 7 - 0 0 x 1 ° " 6 rad/mm A 3 / , = |x-(p-dx A 3 / 1 = (7.00x 10" 6 )• [ ( 2 4 4 % • 5083)+ (l 830 • 3355)+ ( 2 4 4 % -1627] + ( l . 24x l0~ 5 -7.00xlO" 6 )-[1830-3355] A , , , =133 mm A 2 / i = (7 .00xl0" 6 ) - [ ( 2 4 4 ^/2-1728)+(915-915^ |+( l .24xl0" 5 -7 .00xl0~ 6 ) - [915-915^] A , , , = 20 mm 152 Appendix 1 - Calculations and Miscellaneous Information A = " ^ - A 2 , I A = 1 3 ^ / - 2 0 A = 47rnm Stress block factors ( a i and pi): Calculation of ax and p, based on Collins and Mitchell. "Prestressed Concrete Basics."(20) 4_£c/ 'CMAX 6 - 2 - 8 c / 'CMAX 4 _ 0.001 0.0035 6 - 2 ,0.001/ "0.0035 p, =0.68 a, -Pi =- E C 1 'CMAX f ~ \ V 8CMAX J n , r t „ 0.001 1 a, -0.697 = 1 0.0035 3 0.001 0.0035 a, =0.38 Sum Forces (F): F c + F s + F F R P = 0 ( e c - E c -c- l /2-b) + (f s • A s ) + ( f F R P - A F R P ) = 0 (-0.001 • 35 • 80.9 • 822) + (344 • 2658) + (0) « 0 153 Appendix 1 - Calculations and Miscellaneous Information Moment in Cross Section (M): M = f s - A s - ( d - ' 3 > - % ' ) M = 344 -2658 349-0.68-75.2 M = 294kN-m Total Applied Load (P): M = P//-2.25 p _ 2 - M / r ~ 72.25 P = 261kN 154 APPENDIX 2 INITIAL DAMAGE CONDITION OF CHANNEL BEAMS 1.0 General Damage Photo A2.1: Typical Beam End Damage Photo A2.2: Typical Beam Web Damage 155 Appendix 2 - Initial Damage Condition of Channel Beams 156 2.0 Beam One Appendix 2 - Initial Damage Condition of Channel Beams Appendix 2 - Initial Damage Condition of Channel Beams Photo A2.6: Beam One - Loss of Section on Outside of Flange One (Example One) Photo A2.7: Beam One - Loss of Section on Outside of Flange One (Example Two) 158 Appendix 2 - Initial Damage Condition of Channel Beams Appendix 2 - Initial Damage Condition of Channel Beams Appendix 2 - Initial Damage Condition of Channel Beams Outside Top \ Length (feet) Outside Outside Bottom Inside I- 1 -m-8 T9" 10r 11 12 13 14 15 20 21 22i Inside Bottom Inside Top 7 Legend r — | Undamaged '—' Concrete Surface i—j Missing/ u Spalled Concrete I Exposed Reinforcing Steel \ Crack Shear Key Hook Figure A2.1: Beam One, Flange One 161 Appendix 2 - Initial Damage Condition of Channel Beams Legend I—I Undamaged '—' Concrete Surface j—I Missing/ u Spalled Concrete I Exposed Reinforcing Steel \ Crack Shear Key Hook Figure A2.2: Beam One, Flange Two 162 Appendix 2 - Initial Damage Condition of Channel Beams 3.0 Beam Two * Beam Two Photo A2.12: Beam Two - Outside of Flange One Beam Two Photo A2.13: Beam Two - Loss of Section on Outside of Flange One 163 Appendix 2 - Initial Damage Condition of Channel Beams Appendix 2 - Initial Damage Condition of Channel Beams Inside Top \ Length (feet) Inside Bottom 17 V 1\ i j I / / i / Ipside Outside Outside / Bottom HjJr J 2 U - S --LTr-- 6 --m-11 432]-14--01} 171 18 19 21 22 1 Outside Top Legend p i Undamaged ' Concrete Surface I—I Missing/ L-1 Spalled Concrete | Exposed Reinforcing Steel \ Crack Shear Key Hook Figure A2.3: Beam Two, Flange One 165 Appendix 2 - Initial Damage Condition of Channel Beams Inside Top \ Length (feet) Inside Bottom Inside Outside -L?> 10 12 13 ^ 4 > 17 m -21 \22 Outside Bottom - X Outside Top Legend i— i Undamaged '—' Concrete Surface j—i Missing/ u Spalled Concrete I Exposed Reinforcing Steel \ Crack • Shear Key Hook Figure A2.4: Beam Two, Flange Two Appendix 2 - Initial Damage Condition of Channel Beams 4.0 Beam Three Photo A2.17: Beam Three - Outside of Flange Two 167 Appendix 2 - Initial Damage Condition of Channel Beams Appendix 2 - Initial Damage Condition of Channel Beams Photo A2.20: Beam Three - Damage at the End of Flange One 169 Appendix 2 - Initial Damage Condition of Channel Beams Outside Top \ Length (feet) Outside Outside Bottom 43-10 11 12 13 14 - m 18 19 20 -m-Inside Inside / Bottom Inside Top / Figure A2.5: Beam Three, Flange One 170 Appendix 2 - Initial Damage Condition of Channel Beams Inside Top Length (feet) Inside Bottom [iside Outside Outside Bottom - X -LH--m--10-m --16--18 19 21 Outside Top / Legend j—i Undamaged '—' Concrete Surface i—i Missing/ u Spalled Concrete I Exposed Reinforcing Steel \ Crack • Shear Key Hook Figure A2.6: Beam Three, Flange Two 171 Appendix 2 - Initial Damage Condition of Channel Beams 5.0 Beam Four Photo A2.21: Beam Four - Outside of Flange One Photo A2.22: Beam Four - Outside of Flange Two 172 Appendix 2 - Initial Damage Condition of Channel Beams Photo A2.23: Underside of Beam Four Photo A2.24: Beam Four - Missing Concrete and Exposed Steel on Outside of Flange One 173 Appendix 2 - Initial Damage Condition of Channel Beams Photo A2.25: Beam Four - Missing Concrete and Exposed Steel on Bottom of Flange One Photo A2.26: Missing Concrete and Exposed Steel at End of Flange Two 174 Appendix 2 - Initial Damage Condition of Channel Beams Outside Outside Inside Bottom 10 11 12 13 14 16 17 18 19 20 21 Inside Inside Bottom Top - 3 k / Legend i—j Undamaged • Concrete Surface i—i Missing/ u Spalled Concrete I Exposed Reinforcing Steel \ Crack Shear Key Hook Figure A2.7: Beam Four, Flange One 175 Appendix 2 - Initial Damage Condition of Channel Beams Inside Top Length (feet) Inside Inside Outside Outside Bottom \ / Bottom - L T m -18[ 20 Outside Top / Legend I—I Undamaged '—' Concrete Surface I—I Missing/ !—1 Spalled Concrete | Exposed Reinforcing Steel \ Crack Shear Key Hook Figure A2.8: Beam Four, Flange Two 176 SAP2UUU Apr i l 17,2UU(J 15:28 APPENDIX 3 S A P 2 0 0 0 ® Output Diagrams Figure A3 .1: Channel Beam Load Configuration, Three Dimensional View S A P 2 0 0 0 v6.11 - F i l e : R C B e a m - Joint L o a d s ( E X P ) - N - m m Uni ts 177 Channel Beam Load Configuration, Side View Figure A3.2 SAP2000 v6.11 - File:RCBeam - Joint Loads (EXP) - N-mm Units 178 S A P 2 0 U 0 April 17,2000 15:22 Appendix 3 - SAP2000® Output Diagrams Figure A3.3: Deflected Shape, Non-Retrofit Reinforced Concrete Channel Beam, Flexural Load Condition (100 kN Total Load), 3D View 179 SAP20UU Apr i l 17 ,2000 15 :35 Appendix 3 - SAJP2000® Output Diagrams Figure A3.4: Deflected Shape, Non-Retrofit Channel Beam, Flexural Load Condition (100 kN Total Load), Side View 1 8 0 SAPZUUU Apr i l 17 ,2000 15 :43 Appendix 3 - SAP2000® Output Diagrams Figure A3.5: Longitudinal Stress Contours, Non-Retrofit Channel Beam, Flexural Load Condition (100 kN Total Load), 3D View -30.0 -20 .0 -10 .0 0.0 10.0 20 .0 3 O 0 40J ) 50.0 S A P 2 0 0 0 v6.11 - F i l e : R C B e a m - S 1 1 C o n t o u r s ( E X P ) - N - m m Uni ts 181 SAP2000 Appendix 3 April 17,2000 15:40 - SAP200Q® Output Diagrams J S A . f ^ U U U Apnna.idUUU i/:t>4 Appendix 3 - SAP2000® Output Diagrams • m m Figure A3.7: Deflected Shape, Non-Retrofit Channel Beam, Flexural-Torsional Load Condition, (2 kNm Torsion), 3D View S A P 2 0 0 0 v6.11 - F i l e : R C B e a m - D e f o r m e d S h a p e ( E X P ) - N - m m Uni ts 183 o/vrz: u v u Appendix 3 - SAP2000® Output Diagrams Figure A3.8: Deflected Shape, Non-Retrofit Channel Beam, Flexural-Torsional Load Condition (2 kNm Torsion), End View S A P 2 0 0 0 v6.11 - F i l e : R C B e a m - D e f o r m e d S h a p e ( E X P ) - N - m m Uni ts 184 SAPZUUU April 18,2000 17:14 Appendix 3 - SAP2000® Output Diagrams Figure A3.9: Longitudinal Stress Contours, Non-Retrofit Channel Beam, Flexural-Torsional Load Condition (2 kNm Torsion), 3D View S A P 2 0 0 0 v6.11 - F i l e : R C B e a m - S 1 1 C o n t o u r s ( E X P ) - N - m m Uni ts SAP2000 April 18,2000 17:11 Appendix 3 - SAP2000® Output Diagrams Figure A3.10: Longitudinal Stress Contours, Non-Retrofit Channel Beam, Flexural-Torsional Load Condition (2 kNm Torsion), Bottom of Beam -30.0 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0 50.0 SAP2000 v6.11 - File:RCBeam - S11 Contours (EXP) - N-mm Units 186 S A f ^ U U U apm I O . Z U U U 1 / Appendix 3 - SAP2000® Output Diagrams Figure A3.11: Deflected Shape, Channel Beam Retrofit With GFRP Spray, Flexural Load Condition (100 kN Total Load), 3D View SAP2000 v6.11 - File:SprayBeam - Deformed Shape (EXP) - N-mm Units Mprn io,<:uuu i / . o u Appendix 3 - SAP2000® Output Diagrams Figure A3.12: Deflected Shape, Channel Beam Retrofit With GFRP Spray, Flexural Load Condition (100 kN Total Load), Side View SAP2000 v6.11 - File:SprayBeam - Deformed Shape (EXP) - N-mm Units S A P 2 U U U Apr i l 18 ,2000 17:40 Appendix 3 - SAP2000® Output Diagrams Figure A3.13: Longitudinal Stress Contours, Channel Beam Retrofit With GFRP Spray, Flexural Load Condition (100 kN Total Load), 3D View -30 .0 -20 .0 ^ 1 0 ^ ^ 0.0 10.0 20 .0 30.0 40 .0 50.0 ^ ^ H l WBBM S A P 2 0 0 0 v6.11 - F i l e : S p r a y B e a m - S 1 1 C o n t o u r s ( E X P ) - N - m m Uni ts 189 SAP2000 April 18,2000 17:44 Appendix 3 - SAP2000® Output Diagrams Figure A3.14: Longitudinal Stress Contours, Channel Beam Retrofit With GFRP Spray, Flexural Load Condition (100 kN Total Load), Bottom of Beam SAP2000 v6.11 - File:SprayBeam - S11 Contours (EXP) - N-mm Units Appendix 3 - SAP2000® Output Diagrams Figure A3.15: Deflected Shape, Channel Beam Retrofit With GFRP Spray, Flexural-Torsional Load Condition, (2 kNm Torsion), 3D View S A P 2 0 0 0 v 6 1 1 - F i l e : S p r a y B e a m - D e f o r m e d S h a p e ( E X P ) - N - m m Uni ts 191 j S U l J t i / A | J I I I l o z u w I U X O Appendix 3 - SAP2000® Output Diagrams r m T T T ~s. V v v V \ \ 11 / / / / / / / / Figure A3.16: Deflected Shape, Channel Beam Retrofit With GFRP Spray, Flexural-Torsional Load Condition (2 kNm Torsion), End View 192 S A P Z U U U April 18,2000 18:21 Appendix 3 - SAP2000® Output Diagrams SAP2000 April 18,2000 18:23 Appendix 3 - SAP2000® Output Diagrams Figure A3.18: Longitudinal Stress Contours, Channel Beam Retrofit With GFRP Spray, Flexural-Torsional Load Condition (2 kNm Torsion), Bottom of Beam SAP2000 v6.11 - File:SprayBeam - S11 Contours (EXP) - N-mm Units apni I O . ^ U U U io:4u Appendix 3 - SAP2000® Output Diagrams Figure A3.19: Deflected Shape, Channel Beam Retrofit With GFRP Wrap, Flexural Load Condition (100 kN Total Load), 3D View SAP2000 v6.11 - File:WrapBeam - Deformed Shape (EXP) - N-mm Units 195 Appendix 3 - SAP2QQ0® Output Diagrams Figure A3.20: Deflected Shape, Channel Beam Retrofit With GFRP Wrap, Flexural Load Condition (100 kN Total Load), Side View SAP2000 v6.11 - File:WrapBeam - Deformed Shape (EXP) - N-mm Units 1 9 6 SAPZUUU Apr i l 18 ,2000 18 :43 Appendix 3 - SAP2000® Output Diagrams Figure A3.21: Longitudinal Stress Contours, Channel Beam Retrofit With GFRP Wrap, Flexural Load Condition (100 kN Total Load), 3 D View -30 .0 -20 .0 -10 .0 OJ) 10_rj 20J ) 3 O 0 40TJ 5 O 0 S A P 2 0 0 0 v6.11 - F i l e : W r a p B e a m - S 1 1 C o n t o u r s ( E X P ) - N - m m Uni ts 197 SAP2000 April 18,2000 18:45 Appendix 3 - SAP2000® Output Diagrams O A . f ^ U U U a p n i i s ^ u u u 10:0 Appendix 3 - SAP2000® Output Diagrams Figure A3.23: Deflected Shape, Channel Beam Retrofit With GFRP Wrap, Flexural-Torsional Load Condition. (2 kNm Torsion), 3D View S A P 2 0 0 0 v6.11 - F i l e : W r a p B e a m - D e f o r m e d S h a p e ( E X P ) - N - m m Uni ts 199 Apr i l 19 ,2000 15:55 Appendix 3 - SAP20Q0® Output Diagrams Figure A3.24: Deflected Shape, Channel Beam Retrofit With GFRP Wrap , Flexural-Torsional Load Condition (2 kNm Torsion), End View S A P 2 0 0 0 v6.11 - F i l e : W r a p B e a m - D e f o r m e d S h a p e ( E X P ) - N - m m Uni ts SAFZUUU Apr i l 19 ,2000 15 :48 Appendix 3 - SAP2000® Output Diagrams S A P 2 0 0 0 v6.11 - F i l e : W r a p B e a m - S 1 1 C o n t o u r s ( E X P ) - N - m m Uni ts S A P 2 0 0 0 Appendix 3 April 19,2000 15:44 - SAP2000® Output Diagrams -30.0 -20.0 -10.0 OTJ 10.0 20.0 Figure A3.26: Longitudinal Stress Contours, Channel Beam Retrofit With GFRP Wrap, Flexural-Torsjpnal Load Condition (2 kNm Torsion), Bottom of Beam 30.0 40.0 50.0 SAP2000 v6.11 - File:WrapBeam - S11 Contours (EXP) - N-mm Units 202 SAPZUUU June 19,2000 21:33 Appendix 3 - SAP2000® Output Diagrams Figure A3.27: Longitudinal Stress Contours, Non-Retrofit Bridge Deck, Load Case One, 3D View -30.0 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0 50.0 | ~~ WBmm SAP2000 v6.11 - File:RCF3ridge10 - S11 Contours (EXP) - N-mm Units SAP2000 June 19,2000 21:05 Appendix 3 - SAP2000® Output Diagrams SAP2000 v6.11 - File:RCBridge10 - S11 Contours (EXP) - N-mm Units 204 SAPZUUU June 20,2000 21:50 Appendix 3 - SAP2000® Output Diagrams Figure A3.29: Longitudinal Stress Contours, Bridge Deck Retrofit With GFRP Spray, Load Case One, 3D View 10.0 20.0 30.0 40.0 50.0 SAP2000 v6.11 - File:SprayBridge10 - S11 Contours (EXP) - N-mm Units SAP2000 June 20,2000 21:37 SAP2000 June 21,2000 11:49 Appendix 3 - SAP2000® Output Diagrams Figure A3.31: Longitudinal Stress Contours, Bridge Deck Retrofit With GFRP Wrap, Load Case One, 3D View -10.0 10.0 20.0 30.0 40.0 50.0 SAP2000 v6.11 - File:WrapBridge10 - S11 Contours (EXP) - N-mm Units 207 SAP2000 June 21,2000 11:36 Appendix 3 - SAP2000® Output Diagrams 

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