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Anchorage of stirrups in prestressed concrete I-girders Hui, Macarious Kin Fung 2016

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  ANCHORAGE OF STIRRUPS IN PRESTRESSED CONCRETE I-GIRDERS by Macarious Kin Fung Hui B.A.Sc., The University of British Columbia, 2009  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Civil Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2016 © Macarious Kin Fung Hui, 2016 ii  Abstract The current research investigates the performance of commonly-used non-code-compliant stirrup detailing in concrete I-girder bridges, specifically when the lower hooks on the stirrups are oriented parallel to the longitudinal prestressing strands and are not bent around any longitudinal bars. Such detailing does not meet the specifications in the Canadian Highway Bridge Design Code CSA S6-06. An experimental investigation was conducted on full-scale partial sections of a concrete I-girder to evaluate the performance of such non-code-compliant stirrup anchorages by comparing their performance to the performance of code-compliant stirrup anchorages. An analysis of an example concrete I-girder bridge was conducted to determine the demands on the stirrup anchorage during the tests. In the tests, the flexural tension force was applied to the prestressing strand while a diagonal force was applied to the web of the test specimens at approximately 30° to the longitudinal axis of the specimen. Two pairs of stirrups were fixed to a support as the diagonal force was applied. The ratio of the slip of the stirrup to the strain along the exposed length of the stirrup, which equals to the debonded length, was monitored in order to observe the performance of the stirrup anchorage. After applying many cycles of the diagonal force, including about 100 cycles after yielding of the stirrups, the non-code-compliant hooks were found to perform adequately. iii  Preface A brief summary of some of the test results reported in this thesis has been published (Adebar P., Hui M., Graham I., “Anchorage of Stirrups in Prestressed Concrete Bridge Girders – An Experimental Investigation,” CSCE 3rd International Structural Specialty Conference, Edmonton, AB, Canada, 2012). I was responsible for undertaking all of the engineering work required to analyze the bridge as well as design the test setup and the test specimens. I conducted the tests, recorded the data, and analyzed the results. Ian Graham of Armtec – Pacific Region was involved in the construction of the test specimens. Dr. Perry Adebar was the research supervisor and provided oversight throughout the project. iv  Table of Contents Abstract ........................................................................................................................................... ii Preface............................................................................................................................................ iii Table of Contents ........................................................................................................................... iv List of Tables ............................................................................................................................... viii List of Figures ................................................................................................................................. x List of Symbols ............................................................................................................................. xx List of Abbreviations ................................................................................................................. xxiv Acknowledgements ..................................................................................................................... xxv Dedication .................................................................................................................................. xxvi 1 Introduction ............................................................................................................................. 1 1.1 Overview .......................................................................................................................... 1 1.2 Background ...................................................................................................................... 1 1.3 Previous Related Research ............................................................................................... 5 1.4 Overview of Current Research ......................................................................................... 7 2 Analysis of Example Bridge .................................................................................................. 10 2.1 Overview ........................................................................................................................ 10 2.2 Properties of Example Bridge ........................................................................................ 11 2.3 Properties of Prestressed Concrete I-Girders ................................................................. 12 2.4 Loads .............................................................................................................................. 14 2.5 Bending Moment and Shear Force Envelopes ............................................................... 17 2.6 Longitudinal Stresses of the Flexural Tension Flange ................................................... 21 2.7 Methods for Calculating Shear Response ...................................................................... 23 2.7.1 2006 Canadian Highway and Bridge Design Code ................................................ 23 2.7.2 Esfandiari and Adebar Evaluation Procedure ......................................................... 27 v  2.7.3 Response-2000 ........................................................................................................ 30 2.8 Results of Shear Analysis ............................................................................................... 34 2.8.1 Average Longitudinal Strains ................................................................................. 34 2.8.2 Shear Angles ........................................................................................................... 36 2.8.3 Shear Strength ......................................................................................................... 39 2.9 Shear Demand Parameters for Anchorage Tests ............................................................ 40 2.9.1 Longitudinal Strains of Flexural Tension Flange ................................................... 41 2.9.2 Stirrup Stresses........................................................................................................ 43 3 Experimental Program ........................................................................................................... 45 3.1 Overview ........................................................................................................................ 45 3.2 Experimental Approach.................................................................................................. 45 3.3 Test Specimens – Variables ........................................................................................... 47 3.4 Test Specimens – Details ............................................................................................... 49 3.5 Construction of Specimen .............................................................................................. 52 3.6 Material Properties ......................................................................................................... 54 3.7 Test Setup ....................................................................................................................... 56 3.8 Instrumentation............................................................................................................... 58 3.9 Testing Procedure ........................................................................................................... 60 3.9.1 Phase 1: Application of Flexural Tension Force..................................................... 60 3.9.2 Phase 2: Diagonal Loading – Elastic Stirrups......................................................... 61 3.9.3 Phase 3: Diagonal Loading – Yielding Stirrups ..................................................... 62 4 Creep and Shrinkage Strains .................................................................................................. 63 4.1 Overview ........................................................................................................................ 63 4.2 Measured Creep and Shrinkage Strains ......................................................................... 63 4.3 Prediction of Creep and Shrinkage Strains .................................................................... 69 vi  5 Anchorage Test Results ......................................................................................................... 76 5.1 Overview ........................................................................................................................ 76 5.2 Longitudinal Strains ....................................................................................................... 76 5.2.1 Phase 1: Application of Flexural Tension Force..................................................... 77 5.2.2 Phase 2 and Phase 3: Diagonal Loading ................................................................. 85 5.2.3 Estimating Stirrup Strains from Cracks .................................................................. 88 5.3 Stirrup Slip ..................................................................................................................... 91 5.3.1 Phase 2: Diagonal Loading – Elastic Stirrups......................................................... 92 5.3.2 Phase 3: Diagonal Loading -Yielding Stirrups ....................................................... 95 6 Conclusion ........................................................................................................................... 100 Bibliography ............................................................................................................................... 104 Appendix A: Data from Example Bridge Analysis .................................................................... 106 Appendix B: Drawings of Test Specimen .................................................................................. 110 Appendix C: Drawings of Test Setup ......................................................................................... 115 Appendix D: Measured and Predicted Values of Creep and Shrinkage Strains ......................... 122 Appendix E: Anchorage Tests Summary .................................................................................... 124 E.1 Summary of Test T1 ..................................................................................................... 124 E.1.1 Pre-Test ................................................................................................................. 124 E.1.2 Phase 1: Application of Flexural Tension Force................................................... 128 E.1.3 Phase 2: Diagonal Loading – Elastic Stirrups....................................................... 138 E.1.4 Phase 3: Diagonal Loading – Yielding Stirrups ................................................... 146 E.1.5 Application of Horizontal Strain with Eight Strands ............................................ 150 E.1.6 Summary of Encountered Problems and Corresponding Solutions ...................... 151 E.2 Summary of Test L1 ..................................................................................................... 152 E.2.1 Phase 1: Application of Flexural Tension Force................................................... 153 vii  E.2.2 Phase 2: Diagonal Loading – Elastic Stirrups....................................................... 161 E.2.3 Phase 3: Diagonal Loading – Yielding Stirrups ................................................... 166 E.3 Summary of Test T2 ..................................................................................................... 168 E.3.1 Phase 1: Application of Horizontal Strain ............................................................ 168 E.3.2 Phase 2: Diagonal Loading within the Elastic Region of Stirrups........................ 179 E.4 Summary of Test L2 ..................................................................................................... 179 E.4.1 Phase 1: Application of Flexural Tension Force................................................... 179 E.4.2 Phase 2: Diagonal Loading – Elastic Stirrups....................................................... 187 E.4.3 Phase 3: Diagonal Loading – Yielding Stirrups ................................................... 191 Appendix F: Measured Values of Crack Widths ........................................................................ 195    viii  List of Tables Table 1: Summary of BCL-625 Truck and BCL-625 lane loads when 𝑽 = 6.6 m. ...................... 16 Table 2: Summary of dead load. ................................................................................................... 17 Table 3: Summary of load factors. ................................................................................................ 18 Table 4: Summary of resistance factors. ....................................................................................... 26 Table 5: Summary of required tension force at each target longitudinal strain. ........................... 48 Table 6: Summary of cylinder compressive strengths in MPa. .................................................... 55 Table 7: Summary of yield and ultimate strengths of reinforcing bars in MPa. ........................... 56 Table 8: Compressive strains at top targets. ................................................................................. 66 Table 9: Compressive strains at bottom targets. ........................................................................... 67 Table 10: Summary of parameters used for shrinkage and creep prediction. ............................... 74 Table 11: Summary of initial longitudinal strains due to prestressing. ........................................ 77 Table 12: Summary of longitudinal strains in Phase 1. ................................................................ 81 Table 13: Summary of parameters calculated from bilinear best fit lines in Phase 1. .................. 84 Table 14: Predicted and experimental total longitudinal strain in Phase 1. .................................. 85 Table 15: Predict and experimental total longitudinal strain at initial yielding of stirrups during first loading cycle up to D = 320 kN. ................................................................... 86 Table 16: Summary of longitudinal strains at the end of Phase 2. ............................................... 87 Table 17: Predicted and experimental total longitudinal strain when first reaching the indicated maximum diagonal force. .............................................................................................. 87 Table 18: Summary of longitudinal strains in Phase 3. ................................................................ 88 Table 19: Summary of debonded length at in Phase 2. ................................................................. 94 Table 20: Summary of debonded length in Phase 3. .................................................................... 99 ix  Table 21: Summary of Mad River Bridge analysis for SLS. ...................................................... 107 Table 22: Summary of Mad River Bridge analysis for ULS. ..................................................... 108 Table 23: Summary of Mad River Bridge analysis for overload. ............................................... 109 Table 24: Summary of measured and predicted creep and shrinkage strains ............................. 123 Table 25: Pre-test summary of horizontal pressure and change in length in prestressing strand. .......................................................................................................................................... 128 Table 26: Test T1 Phase 2: summary of load cycles. ................................................................. 143 Table 27: Test L1 Phase 2: summary of load cycles. ................................................................. 164 Table 28: Test L2 Phase 2: summary of load cycles. ................................................................. 190 Table 29: Crack width data of Test T1. ...................................................................................... 196 Table 30: Crack width data of Test L1. ...................................................................................... 197 Table 31: Crack width data of Test L2. ...................................................................................... 198 x  List of Figures Fig. 1: Typical I-girder bridge: elevation (top) and cross section (bottom).................................... 1 Fig. 2: Cross section of typical Type 5 I-girder. ............................................................................. 2 Fig. 3: Assembly of reinforcement cage at end of I-girder; insert shows code-compliant stirrup anchorage. ............................................................................................................................ 3 Fig. 4: Assembly of reinforcement cage at middle of I-girder: insert shows non-code-compliant stirrup anchorage. ........................................................................................................... 4 Fig. 5: Comparison of stirrup detailing: non-code-compliant (left) and code-compliant (right). ............................................................................................................................................. 5 Fig. 6: Comparison of Type 5 I-girder (left) and test specimen (right). ......................................... 8 Fig. 7: Experimental approach used to test full-scale element. ...................................................... 8 Fig. 8: Elevation of example bridge. ............................................................................................. 11 Fig. 9: Cross section of example bridge........................................................................................ 11 Fig. 10: Cross section used in analysis. ........................................................................................ 12 Fig. 11: Cross section of Type 5 I-girder. ..................................................................................... 13 Fig. 12: Stirrup arrangement Type T (left) and stirrup arrangement Type L (right). ................... 14 Fig. 13: CL-625 truck load (from Canadian Highway Bridge Design Code). .............................. 15 Fig. 14: CL-625 lane load (from Canadian Highway Bridge Design Code). ............................... 16 Fig. 15: Bending moment envelopes for SLS, ULS and overload................................................ 18 Fig. 16: Shear force envelopes for SLS, ULS, and overload. ....................................................... 20 Fig. 17: Stresses of flexural tension flange for SLS. .................................................................... 22 Fig. 18: Response-2000 generated diagram of the cross section at midspan (in mm).................. 30 xi  Fig. 19: Response-2000 generated bending moment-shear force interaction diagram at midspan for overload. ................................................................................................................... 31 Fig. 20: Response-2000 generated longitudinal strain profile at midspan for overload. .............. 32 Fig. 21: Response-2000 generated shear angle profile at midspan for overload. ......................... 33 Fig. 22: Response-2000 generated stirrup stress profiles at midspan for overload; (left) not at crack; (right) at crack. ......................................................................................................... 34 Fig. 23: Average longitudinal strains for CHBDC, E&A and Response-2000: (top) SLS; (middle) ULS; (bottom) overload. ....................................................................................... 35 Fig. 24: Shear angles from CHBDC, E&A, and Response-2000: (top) SLS; (middle) ULS; (bottom) overload. ............................................................................................................... 37 Fig. 25: Factored shear demand and shear resistances from CHBDC, E&A, and Response-2000 for ULS. ............................................................................................................... 39 Fig. 26: Factored shear force demand and shear resistances from CHBDC, E&A, and Response-2000 for overload. ........................................................................................................ 40 Fig. 27: Longitudinal strain of flexural tension flange for CHBDC, E&A and Response-2000: (top) SLS; (middle) ULS; (bottom) overload..................................................... 42 Fig. 28: Interaction of stirrup stress and longitudinal strain of flexural tension flange from Response-2000 for ULS and overload. ................................................................................ 43 Fig. 29: Comparison of Type 5 I-girder (left) and test specimen (right). ..................................... 46 Fig. 30: Schematic of test setup. ................................................................................................... 46 Fig. 31: Details of Type T specimen: (top) plan view, (bottom) sections. ................................... 49 Fig. 32: Details of Type L specimen: (top) plan view, (bottom) sections. ................................... 50 Fig. 33: Wooden form: (left) flange piece, (right) web piece. ...................................................... 52 xii  Fig. 34: Sixteen holes at one end of the flange piece of the wooden form. .................................. 53 Fig. 35: Wooden form in prestressing bay with prestressing strands partially fed through. ......................................................................................................................................... 53 Fig. 36: Compressive strength versus age of concrete cylinders. ................................................. 55 Fig. 37: Plan view of test setup: (top) schematic, (bottom) photograph. ...................................... 56 Fig. 38: Location of Invar strain targets........................................................................................ 58 Fig. 39: LVDT setup on individual stirrup: (left) schematic (right) photograph. ......................... 59 Fig. 40: Locations of Invar pins on test specimen. ....................................................................... 63 Fig. 41: Compressive strains: (top) top targets; (bottom) bottom targets. .................................... 65 Fig. 42: Average compressive strains of top targets and bottom targets. ..................................... 68 Fig. 43: (Left) end cross section; (right) middle cross section. .................................................... 69 Fig. 44: Lengths of idealized cross sections used for shrinkage and creep strains calculations. .................................................................................................................................. 70 Fig. 45: Predicted compressive strains: (top) top targets; (bottom) bottom targets. ..................... 72 Fig. 46: Comparison of shrinkage and creep strain from CHDBC and CAC Handbook........................................................................................................................................................ 73 Fig. 47: Phase 1 horizontal applied tension force versus measured additional longitudinal strain: (top) Test T1; (middle) Test L1; (bottom) Test L2. ...................................... 79 Fig. 48: Phase 1 horizontal force versus measured total longitudinal strain with bilinear best fit lines: (top) Test T1; (middle) Test L1; (bottom) Test L2. ................................................ 83 Fig. 49: Longitudinal strain based on crack widths in Test T1 at diagonal compression force of (top) 0 kN, (middle) 160 kN, and (bottom) 320 kN. ....................................................... 90 Fig. 50: Locations of stirrups and LVDTs. ................................................................................... 91 xiii  Fig. 51: Slip-strain interaction of Phase 2: (top) Test T1; (middle) Test L1; (bottom) Test L2. ......................................................................................................................................... 93 Fig. 52: Slip-strain interaction in Phase 3 of Test T1 at diagonal compression force of (top) 320 kN and (bottom) 420 kN. .............................................................................................. 96 Fig. 53: Slip-strain interaction in Phase 3 of Test L1 at diagonal compression force of (top) 400 kN and (bottom) 500 kN. .............................................................................................. 97 Fig. 54: Slip-strain interaction in Phase 3 of Test L2 at diagonal compression force of (top) 400 kN and (bottom) 440 kN. .............................................................................................. 98 Fig. 55: Plan view of Type L test specimen with dimensions. ................................................... 111 Fig. 56: Cross section of Type L test specimen with dimensions. .............................................. 112 Fig. 57: Plan view of Type T test specimen with dimensions. ................................................... 113 Fig. 58: Cross section of Test T test specimen with dimensions. ............................................... 114 Fig. 59: Plan view of test setup. .................................................................................................. 116 Fig. 60: Test setup component A: support-horizontal actuators. ................................................ 117 Fig. 61: Test setup component B: support-stirrups. .................................................................... 118 Fig. 62: Test setup component C1: diagonal actuator-specimen. ............................................... 119 Fig. 63: Test setup component C2: diagonal actuator-support. .................................................. 120 Fig. 64: Test setup component D: prestressing strands-support. ................................................ 121 Fig. 65: Pre-test response. ........................................................................................................... 125 Fig. 66: Pre-test horizontal pressure vs. change in length in prestressing strand. ...................... 126 Fig. 67: Pre-test response at target constant pressure of 1010 psi. ............................................. 127 Fig. 68: Test T1 Phase 1: test specimen at horizontal pressure of 2000 psi; bottom of flange........................................................................................................................................... 130 xiv  Fig. 69: Test T1 Phase 1: test specimen at horizontal pressure of 2000 psi; close-up of crack on side of flange. ............................................................................................................... 131 Fig. 70: Test T1 Phase 1: test specimen at horizontal pressure of 2300 psi; bottom of flange........................................................................................................................................... 131 Fig. 71: Test T1 Phase 1: test specimen at horizontal pressure of 2700 psi (first cycle); bottom of flange. ......................................................................................................................... 132 Fig. 72: Test T1 Phase 1: test specimen at horizontal pressure of 2700 psi (first cycle); side view. .................................................................................................................................... 133 Fig. 73: Test T1 Phase 1: test specimen at horizontal pressure of 2700 psi (15th cycle); bottom of flange. ......................................................................................................................... 134 Fig. 74: Test T1 Phase 1: test specimen at horizontal pressure of 2700 psi (15th cycle); side view. .................................................................................................................................... 134 Fig. 75: Test T1 Phase 1: test specimen at horizontal pressure of 3000 psi (25th cycle); bottom of flange. ......................................................................................................................... 135 Fig. 76: Test T1 Phase 1: test specimen at horizontal pressure of 3000 psi (25th cycle); side view. .................................................................................................................................... 136 Fig. 77: Test T1 Phase 1: horizontal load–concrete strain relationship. ..................................... 137 Fig. 78: Test T1 Phase 2: diagonal load-displacement relationship with load-control system. ........................................................................................................................................ 139 Fig. 79: Test T1 Phase 2: diagonal load-stirrup strain relationship with load-control system. ........................................................................................................................................ 139 Fig. 80: Stirrup and LVDT arrangement..................................................................................... 140 xv  Fig. 81: Test T1 Phase 2: diagonal load-displacement relationship at 80 kN diagonal force. ........................................................................................................................................... 141 Fig. 82: Test T1 Phase 2: diagonal load-stirrup strain relationship at 80 kN diagonal force. ........................................................................................................................................... 142 Fig. 83: Revised stirrup and LVDT arrangement. ...................................................................... 144 Fig. 84: Test T1 Phase 2: diagonal load-stirrup strain relationship at 320 kN diagonal force. ........................................................................................................................................... 144 Fig. 85: Test T1 Phase 2: slip-strain interaction at 320 kN diagonal force. ............................... 146 Fig. 86: Test T1 Phase 3: stirrup stress-strain relationship. ........................................................ 147 Fig. 87: Test T1 Phase 3: stirrup stress- strain relationship (averaged). ..................................... 148 Fig. 88: Test T1 Phase 3: slip-strain interaction at 440 kN diagonal force. ............................... 149 Fig. 89: Test T1 Phase 3: slip-strain interaction at 440 kN diagonal force (averaged). ............. 150 Fig. 90: Test T1: horizontal strain-concrete strain relationship with only eight strands...................................................................................................................................................... 151 Fig. 91: Test L1 Phase 1: test specimen at horizontal pressure of 1000 psi; bottom of flange........................................................................................................................................... 154 Fig. 92: Test L1 Phase 1: test specimen at horizontal pressure of 2000 psi; bottom of flange........................................................................................................................................... 154 Fig. 93: Test L1 Phase 1: test specimen at horizontal pressure of 2000 psi; side view. ............. 155 Fig. 94: Test L1 Phase 1: test specimen at horizontal pressure of 2500 psi; side view. ............. 155 Fig. 95: Test L1 Phase 1: test specimen at horizontal pressure of 2700 psi; diagonal face of web. ................................................................................................................................. 156 xvi  Fig. 96: Test L1 Phase 1: test specimen at horizontal pressure of 2800 psi; bottom of flange........................................................................................................................................... 156 Fig. 97: Test L1 Phase 1: test specimen at horizontal pressure of 2800 psi; side view. ............. 157 Fig. 98: Test L1 Phase 1: test specimen at horizontal pressure of 3000 psi (first cycle); bottom of flange. ......................................................................................................................... 157 Fig. 99: Test L1 Phase 1: specimen at horizontal pressure of 3000 psi (first cycle); side view. ............................................................................................................................................ 158 Fig. 100: Test L1 Phase 1: horizontal load-concrete strain relationship..................................... 160 Fig. 101: Test L1 Phase 2: stirrup stress-strain relationship at 80 kN, 120 kN, 160 kN and 200 kN diagonal force. ......................................................................................................... 162 Fig. 102: Test L1 Phase 2: stirrup slip-stirrup strain relationship at 80 kN and 120 kN diagonal force.............................................................................................................................. 163 Fig. 103: Test L1 Phase 2: stirrup stress-strain relationship at 280 kN and 320 kN diagonal force.............................................................................................................................. 164 Fig. 104: Test L1 Phase 2: stirrup slip-strain interaction at 280 kN and 320 kN diagonal force. ........................................................................................................................................... 165 Fig. 105: Test L1 Phase 3: stirrup stress-strain relationship. ...................................................... 166 Fig. 106: Test L1 Phase 3: slip-strain interaction at 440 kN diagonal force. ............................. 167 Fig. 107: Test T2 Phase 1: test specimen at horizontal pressure of 2000 psi; bottom of flange........................................................................................................................................... 170 Fig. 108: Test T2 Phase 1: test specimen at horizontal pressure of 2000 psi; side view...................................................................................................................................................... 170 xvii  Fig. 109: Test T2 Phase 1: test specimen at horizontal pressure of 2000 psi; top of flange........................................................................................................................................... 171 Fig. 110: Test T2 Phase 1: test specimen at horizontal pressure of 2100 psi; side view...................................................................................................................................................... 172 Fig. 111: Test T2 Phase 1: test specimen at horizontal pressure of 2800 psi; bottom of flange........................................................................................................................................... 172 Fig. 112: Test T2 Phase 1: test specimen at horizontal pressure of 2800 psi; side view...................................................................................................................................................... 173 Fig. 113: Test T2 Phase 1: test specimen at horizontal pressure of 2900 psi; bottom of flange........................................................................................................................................... 174 Fig. 114: Test T2 Phase 1: test specimen at horizontal pressure of 2900 psi; side view...................................................................................................................................................... 174 Fig. 115: Test T2 Phase 1: test specimen at horizontal pressure of 3000 psi; bottom of flange........................................................................................................................................... 175 Fig. 116: Test T2 Phase 1: test specimen at horizontal pressure of 3000 psi; side view...................................................................................................................................................... 175 Fig. 117: Test T2 Phase 1: test specimen at horizontal pressure of 3200 psi; bottom of flange........................................................................................................................................... 176 Fig. 118: Test T2 Phase 1: test specimen at horizontal pressure of 3200 psi; side view...................................................................................................................................................... 176 Fig. 119: Test T2 Phase 1: horizontal load-concrete strain relationship..................................... 178 Fig. 120: Test L2 Phase 1: test specimen at horizontal pressure of 2000 psi; bottom of flange........................................................................................................................................... 181 xviii  Fig. 121: Test L2 Phase 1: test specimen at horizontal pressure of 2000 psi; side view...................................................................................................................................................... 181 Fig. 122: Test L2 Phase 1: test specimen at horizontal pressure of 2500 psi; side view...................................................................................................................................................... 182 Fig. 123: Test L2 Phase 1: test specimen at horizontal pressure of 2700 psi; bottom of flange........................................................................................................................................... 183 Fig. 124: Test L2 Phase 1: test specimen at horizontal pressure of 2900 psi; bottom of flange........................................................................................................................................... 183 Fig. 125: Test L2 Phase 1: test specimen at horizontal pressure of 2900 psi; side view...................................................................................................................................................... 184 Fig. 126: Test L2 Phase 1: test specimen at horizontal pressure of 3200 psi; bottom of flange........................................................................................................................................... 185 Fig. 127: Test L2 Phase 1: test specimen at horizontal pressure of 3200 psi; side view...................................................................................................................................................... 185 Fig. 128: Test L2 Phase 1: horizontal load-concrete strain relationship..................................... 186 Fig. 129: Test L1 Phase 2: stirrup stress-strain relationship at 80 kN, 160 kN, 240 kN and 320 kN diagonal force. ......................................................................................................... 188 Fig. 130: Test L2 Phase 2: stirrup slip-stirrup strain interaction at 80 kN, 160 kN, 240 kN and 320 kN diagonal force. ................................................................................................... 189 Fig. 131: Test L2 Phase 2: stirrup stress-strain relationship at 320 kN diagonal force (cycle 81 to 260). ........................................................................................................................ 190 Fig. 132: Test L2 Phase 2: stirrup slip-strain interaction at 320 kN diagonal force (cycle 81 to 260). ................................................................................................................................... 191 xix  Fig. 133: Test L2 Phase 3: stirrup stress-strain relationship. ...................................................... 192 Fig. 134: Test L2 Phase 3: slip-strain interaction. ...................................................................... 193 Fig. 135: Stirrup D5 and D7 fractured at the end of Test L2 Phase 3. ....................................... 194    xx  List of Symbols 𝐴 = total cross-sectional area of member 𝐴𝑝 = cross-sectional area of prestressing strands in flexural tension 𝐴𝑝1 = cross-sectional area of draped prestressing strands 𝐴𝑝𝑠 = cross-sectional area of prestressing strands in the half-depth on the flexural tension side 𝐴𝑝𝑤 = cross-sectional area of non-prestressed longitudinal reinforcement centred in web 𝐴𝑠 = cross-sectional area of reinforcing steel 𝐴𝑠𝑤 = cross-sectional area of prestressed strands centred in web 𝐴𝑡𝑓 = cross-sectional area of concrete in tension surrounding flexural tension reinforcement 𝐴𝑣 = cross-sectional area of stirrup 𝑏𝑤 = width of shear area, or web 𝐷 = diagonal compression force applied to web of test specimen 𝑑 = depth of cross section 𝑑𝑏 = diameter of prestressing strands 𝑑𝑛𝑣 = depth of uniform compression stress 𝑑𝑣 = shear depth 𝐸𝑠 = elastic modulus of reinforcing steel 𝐸𝑝 = elastic modulus of prestressing strands 𝑒 = vertical distance from strand to neutral axis 𝑓𝑏 = stress at bottom of flexural tension flange 𝑓𝑐′ = specified compressive strength of concrete 𝑓𝑐𝑟 = cracking strength of concrete 𝑓𝑝 = effective stress in prestressing strands xxi  𝑓𝑝0 = decompression stress 𝑓𝑝𝑢 = ultimate strength of prestressing strands 𝑓𝑠 = maximum stress of stirrup 𝑓𝑠𝑐𝑟𝑎𝑐𝑘 = maximum stress of stirrup at crack 𝑓𝑠𝑒 = effective strength of prestressing strands 𝑓𝑦 = yielding strength of reinforcing steel 𝐼 = second moment of inertia of member’s cross section 𝑖 = index representing each draped prestressing strand 𝑗 = ratio of moment arm to depth of cross section 𝐿 = length of bridge 𝐿1 = length of end section of test specimen (without web) 𝐿2 = length of middle section of test specimen (with web) 𝑙𝑡 = transfer length 𝑀 = applied bending moment 𝑀𝐿𝐿 =  maximum live load bending moment 𝑀𝑚𝑎𝑥 = maximum bending moment 𝑁 = applied axial force 𝑛𝑣0 = compressive stress required when average longitudinal strain is zero 𝑠 = stirrup spacing 𝑇 = axial tension force applied to prestressing strands in flange of test specimen 𝑡 = age of test specimen 𝑉 = variable spacing of CL-625 lane load 𝑉𝑐 = shear capacity of concrete xxii  𝑉𝑓 = factored applied shear force 𝑉𝐿𝐿 = maximum live load obtained by BCL-625 lane load 𝑉𝑚𝑎𝑥 = maximum shear force 𝑉𝑝 = shear capacity of prestressing strands 𝑉𝑟 = shear resistance 𝑉𝑠 = shear capacity of stirrups 𝑣 = shear stress 𝑤𝐷𝐿 = uniformly distributed dead load 𝑥 = distance away from support of bridge 𝑦 = distance from neutral axis of section to bottom of flexural tension flange 𝛼𝐷 = dead load factor 𝛼𝐿 = live load factor 𝛽 = concrete shear contribution factor ∆𝑛𝑣 = change in compressive stress per unit change in average longitudinal strain Δ𝜃 = change in shear angle per unit average longitudinal strain 𝜀𝑏𝑜𝑡 = longitudinal strain measured from lower Invar pins 𝜀𝑡𝑜𝑝 = longitudinal strain measured from upper Invar pins 𝜀𝑥 = average longitudinal strain 𝜀𝑥𝑓 = longitudinal strain of flexural tension flange 𝜀𝑦 = yield strain of stirrups 𝜃 = shear angle 𝜃0 = shear angle at zero average longitudinal strain 𝜃𝑝 = angle at which prestressing strands are draped xxiii  𝜆 = ratio of moment arm of prestressing strands in web to the moment arm 𝜌𝑧 = ratio of transverse reinforcement area to concrete area 𝜙 = curvature 𝜙𝑐 = resistance factor of concrete 𝜙𝑝 = resistance factor of prestressing strands 𝜙𝑠 = resistance factor of reinforcing steel xxiv  List of Abbreviations BC = British Columbia, Canada CHBDC = 2006 Canadian Highway Bridge Design Code CSA S6-06 E&A =  Esfandiari and Adebar procedure GU = General use (type of cement) LVDT = Linear variable differential transformers PTFE = Polytetrafluoroethylene SLS = Serviceability limit states Type L = Non-code-compliant anchorage detailing with lower stirrup hooks oriented  parallel to longitudinal axis Type T = Code-compliant anchorage detailing with lower stirrup hooks oriented in  transverse direction bending around longitudinal bars RH = Relative Humidity UBC = University of British Columbia ULS = Ultimate limit state xxv  Acknowledgements I am grateful to all three organizations for their support. Partial funding to conduct this study was provided through a research grant from the Bridge Engineering Section of the Ministry of Transportation and Infrastructure of British Columbia. Additional funding was provided by the Natural Science and Engineering Research Council of Canada through the discovery grant program. Armtec donated the materials and labour to construct the test specimens. I would like to thank my research supervisor Dr. Perry Adebar for his support. I would like to thank him for providing me guidance, answering my questions with his technical knowledge, and sitting through countless meetings with me to make sure that I am on the right track. I would also like to thank him greatly for being the most understanding when I was going through some very tough times in life; I could not have asked for a better supervisor. I would also like to thank Dr. Nemkumar Banthia for being the second reader and spending time with me going through my thesis, offering valuable suggestions, and providing me a different perspective on my research. I would also like to thank the lab technicians who taught me workshop skills, and helped me put together the test setup.  xxvi  Dedication      To my parents   1  1 Introduction 1.1 Overview This chapter introduces the commonly-used non-code-compliant stirrup anchorage detailing found in prestressed concrete I-girder bridges. Section 1.2 explains why this detailing is used by presenting the current construction methods of prestressed concrete I-girders. No previous research has addressed this issue, but two related studies on anchorage of stirrup hooks are summarized in Section 1.3. Section 1.4 provides an overview of the current research and the approach of the experimental program. 1.2 Background In a typical concrete I-girder bridge, the concrete deck is supported by multiple I-girders, and the ends of the I-girders are supported by abutments on both ends as shown in Fig. 1.   Fig. 1: Typical I-girder bridge: elevation (top) and cross section (bottom). 2  Properties, such as dimensions, number of strands, concrete strength, and concrete cover, of the I-girders are specified by the Ministry of Transportation and Infrastructure of British Columbia. For example, in a typical Type 5 I-girder, there are ten draped strands along the web, and the I-girder can have up to 38 straight strands. Stirrups run along the web and they are anchored into the flexural tension flange by bending the free ends into hooks. Reinforcement bars also run longitudinally along the compression flange and the web (see Fig. 2).  Fig. 2: Cross section of typical Type 5 I-girder. When constructing these I-girders at the precast plant, the reinforcement cages are separated into three pre-assembled sections – two end reinforcement cages and one middle reinforcement cage. The two end reinforcement cages are first dropped into the two ends of the metal form. In these cages, the free legs of the stirrups are bent outward to form hooks which are perpendicular to the longitudinal direction of the girder, as shown in the following figure.  3   Fig. 3: Assembly of reinforcement cage at end of I-girder; insert shows code-compliant stirrup anchorage. Prestressing strands are fed through the holes at one end of the metal form. Then, workers feed the strands above the transversely bent stirrup hooks, through the two end reinforcement cages, and eventually to the other end of the metal form. On the other hand, the middle reinforcement cage has stirrup hooks that are bent parallel to the longitudinal strands (see Fig. 4). 4   Fig. 4: Assembly of reinforcement cage at middle of I-girder: insert shows non-code-compliant stirrup anchorage. During fabrication, the middle reinforcement cage is dropped into the metal form when the longitudinal strands are already in place. The stirrups are bent parallel to the longitudinal strands to avoid contact between the prestressing strands and the hooks during assembly. Since the middle reinforcement cage occupies the majority of the length of the I-girder, turning each stirrup, which is tack-welded onto a control bar to form the reinforcement cage, will be very time-consuming. However, the 2006 Canadian Highway Bridge Design Code CSA S6-06 (CHBDC) states in Part (a) of Clause 8.15.1.5 that “transverse reinforcement provided for shear shall be anchored at both ends by… for No. 15 and smaller bars and MD200 and smaller wire, a standard hook, as specified in Clause 8.14.1.1, around longitudinal reinforcement.” With current practice, the lower hooks of the stirrups (except for those near the ends of the girders) are not bent around longitudinal bars, but instead run alongside the longitudinal bars at the bottom flange. On the other hand, the hooks of the stirrups near the two ends of the girder are hooked around the longitudinal bars. Here, the shear demands are larger and stirrup spacing is required to be small. The non-code-compliant 5  detailing is widely employed because it greatly reduces fabrication time. The following diagram compares the code-compliant stirrup detailing with the non-code-compliant stirrup detailing.  Fig. 5: Comparison of stirrup detailing: non-code-compliant (left) and code-compliant (right). To assess this issue, an experimental program, which involves full-scale testing of a partial section of an I-girder has been developed to compare the performance of the non-code-compliant stirrup detailing to the CHBDC-compliant stirrup detailing. 1.3 Previous Related Research Previous work that addressed the issue of non-code-compliant stirrup anchorage in prestressed concrete I-girders was not found. However, two related studies regarding orientation of stirrup hooks in concrete are discussed in this section. A report by James O. Jirsa and Jose L.G. Marques (1975) on pull-out tests regarding beam-column joints reviewed different types of hooked anchorage and observed slip behaviour of the anchorage hooks. Another report by Neal S. Anderson and Julio A. Ramirez (1995) addresses the detailing of stirrup with truss models. In “A Study of Hooked Bar Anchorages in Beam-Column Joints” (1975), Jirsa and Marques evaluated the capacity of anchored beam reinforcement of standard 90° and 180° hooked bars. Twenty-two full-scale specimens were built to simulate typical exterior beam-column joints. Each 6  specimen consisted of small concrete blocks with short bars embedded to ensure that bond failure would occur before steel yields. Sufficient side cover was provided to simulate anchorage in mass concrete. Hydraulic actuators were used against the column to simulate a compression zone in the beam. The authors concluded that hooked anchorages allowed for greater stresses given that the cover, ties, and straight embedment length before the hook were all sufficient. They also concluded that 90° hooks appeared to be stiffer than 180°, yet their behaviours were similar. Slip was noted to be greater with shorter lead embedment and little difference was observed in slip behaviour when varying the lateral confinement. In “Detailing of Stirrup Reinforcement” (1995), Anderson and Ramirez evaluated the performance of various stirrup detailing and their effect on the ultimate strength of the member under large shear stresses with truss models. The authors’ specimens included 16 reinforced concrete beams separated into two series: narrow beams and wide beams. In the series of narrow beams, stirrup detailing was the main variable. Close, U-, and singled-legged stirrups were all tested with 90°, 135°, and 180° standard hooks anchored in the flexural tension and/or compression zones. On the other hand, for the series of wide beams, transverse spacing of the stirrup legs was the main variable. The specimens were loaded at three points in a simple span. Anderson and Ramirez concluded that U- and closed stirrups performed better than single-legged stirrups, and more importantly, they suggested that the anchorage depends primarily on hook and embedment length. They state that with grade 60 steel, it is normally impossible to bend anchorage tightly around longitudinal bars. Thus, even though the anchorage of a bar is known to improve when it is bent around a transverse bar, but in practice, this is only true if direct contact exists between the bars. 7  1.4 Overview of Current Research The purpose of the current research is to evaluate the performance of non-code-compliant stirrup detailing commonly used in prestressed concrete I-girder by comparing the performance of non-code-compliant stirrup anchorages to the performance of code-compliant stirrup anchorages. The research program consists of an analysis of an example concrete I-girder bridge, the monitoring of the effect of creep and shrinkage, and an experimental program consisting of full-scale testing of a partial section of an I-girder. The analysis of an example bridge in Chapter 2 provides information that shaped the design of various parameters in the experimental program. In the analysis, longitudinal strain, bending moment, shear strength, and shear angle were analyzed based on three different load scenarios. The experimental program, presented in Chapter 3, involves a stirrup anchorage pull-out test to compare the performance of the two stirrup anchorage detailings under two levels of longitudinal strain simulated at the flange of the concrete specimens. The experimental program includes six specimens and three were fully tested. The full-scale specimens are composed of a portion of the flexural tension flange and a portion of the web of a typical full-scale Type 5 I-girder, as shown in the following figure. 8   Fig. 6: Comparison of Type 5 I-girder (left) and test specimen (right). Two types of specimens were tested: Type T and Type L. Type T specimens (with transverse stirrup hooks) represent code-compliant stirrup design where the stirrup hooks at the flexural tension flange are hooked around longitudinal bars. Contrarily, Type L specimens (with longitudinal stirrup hooks) represent non-code-compliant design. The experimental approach is shown schematically in Fig. 7.  Fig. 7: Experimental approach used to test full-scale element. 9  In the anchorage tests, the 16 (four rows of four) prestressing strands were pulled on one end using two hydraulic actuators, while the other end of the prestressing strands were fixed to a support. The two actuators were set to provide a constant tension force (𝑇) in order to simulate different levels of longitudinal strain at the flexural tension flange. A diagonal compression force (𝐷) was applied on the web of the specimen using another hydraulic actuator at approximately 30° to the longitudinal axis, and this force simulated diagonal shear. Each specimen contained four pairs of stirrups, but only the middle two pairs were fixed and tested; the two outer pairs provided a boundary condition. The section of the stirrups along the web of the specimen was debonded to allow the stirrup hooks to slip under large demands. Chapter 3 presents in further details the properties of the test specimens, the various components of the test setup, and the test procedure. Chapter 4 examines the effects of prestressing, creep, and shrinkage on the longitudinal strain of the specimen prior to the anchorage tests. In Chapter 5, the longitudinal strain of the flange and the pull-outs of the stirrups during the anchorage test are analyzed.  10  2 Analysis of Example Bridge 2.1 Overview An example prestressed concrete I-girder bridge was analyzed under different load scenarios in order to determine the demands on I-girders and establish parameters for the anchorage tests. Section 2.2 introduces the example bridge and presented some fundamental dimensions of the overall example bridge. In Section 2.3, the properties of the associated prestressed concrete I-girder (including size, arrangement of reinforcement, and some material properties of the reinforcing steel) in the example bridge are presented. Three load scenarios (SLS, ULS, and overload) were analyzed, and the corresponding live and dead loads are presented in Section 2.4. The resulting bending moment and shear force envelopes are presented and discussed in Section 2.5. Section 2.6 discusses the longitudinal stresses of the flexural tension flange under SLS loads. This was a quick analysis to check that no concrete cracking was present during the service life of the example bridge. Section 2.7 evaluates the shear strengths of the example bridge using three different methods: 2006 Canadian Highway Bridge Design Code CSA S6-06 (CHBDC), Esfandiari and Adebar procedure (E&A), and Response-2000. This section outlines the procedure for calculating the shear angles, longitudinal strains, and also, for Response-2000, the stresses in the stirrups. The results of these three analyses are compared in Section 2.8. The numbers obtained from these analyses were incorporated in the design of the anchorage tests to ensure a realistic simulation, explained in Section 2.9. The numbers obtained in the analysis are available in Appendix A. 11  2.2 Properties of Example Bridge The Mad River Bridge, located in Clearwater, British Columbia (2005), was used as an example bridge in the analyses. This bridge was modelled as a simply supported beam member spanning a length of 34.9 m (see Fig. 8). The slight incline of the I-girder was ignored for simplification.  Fig. 8: Elevation of example bridge. The concrete deck is supported by five prestressed concrete I-girders, as shown in the cross section in Fig. 9.  Fig. 9: Cross section of example bridge. The geometry of some components of the example bridge was simplified. The concrete deck is 250 mm thick and 11.5 m wide, and it is supported by five Type 5 concrete I-girders with a concrete haunch between each girder and the deck. Each haunch was simplified as 600 mm wide 12  and 100 mm deep. There are two concrete parapets on the two sides of the bridge. The slight inclination of the cross section was ignored. The cross section used for the purpose of the analyses included only one Type 5 I-girder, a haunch, and a 2.3 m section of the concrete deck (see Fig. 10). The corresponding loads were assumed to be one-fifth of the total load and the loads were distributed evenly amongst all five I-girders.  Fig. 10: Cross section used in analysis. 2.3 Properties of Prestressed Concrete I-Girders There are seven standard types of I-girders designated by the Ministry of Transportation and Infrastructure of British Columbia, and each type is specialized for bridges of different spans. The example bridge in the analyses was comprised of the common Type 5 I-girders, and its cross section is shown in the following figure. 13   Fig. 11: Cross section of Type 5 I-girder. Specified by the Ministry, the number of prestressing strands in a Type-5 I-girders can vary, but with a maximum limit of 38; in the example bridge, thirty-eight 12.7-diameter 7-wire straight strands run along the flexural tension flange. Ten draped strands are located in the web and these strands are held down along the middle third of the span. In addition, six 10M transverse bars of Grade 400W run along the web of the I-girder. The specified concrete compressive strength during release and the strength at 28 days are 40 MPa and 55 MPa, respectively. Note that a high compressive strength provides durability, but also makes the concrete more prone to splitting. The minimum ultimate tensile strength and the tension force immediately before release are 184 kN per strand and 136 kN per strand, respectively. Two stirrup arrangements (Type T and Type L; see Fig. 12) with 10M bars are present along different spans in the I-girder. 14    Fig. 12: Stirrup arrangement Type T (left) and stirrup arrangement Type L (right). Stirrup arrangement Type T consists of two 90° legs that were bent around the straight prestressing strands along the flexural tension flange. Twelve of these arrangements were installed at each end of the I-girder where the stirrups are closely spaced. Stirrup arrangement Type L also consists of two 90° legs, but they were bent so that the free legs were oriented longitudinally (parallel to the prestressing strands). This arrangement was used throughout the remaining span in the middle of the I-girder with three different spacings: 150 mm, 200 mm, and 300 mm. For quicker installation, these legs were not bent around any bars, thus they do not comply with the CHBDC specifications. 2.4 Loads Three load scenarios were analyzed: serviceability limit state (SLS), ultimate limit state (ULS), and overload. In SLS, unfactored loads were used. The stresses in the flexural tension flange were analyzed to verify that no flexural cracks would form during its service life. In ULS, the loads and the strength of the materials were multiplied by specified factors to account for extreme loads and material uncertainties. The resulting bending moment envelopes and the shear force envelopes were compared with the capacity of the bridge to ensure that the bridge will not fail structurally. 15  Thirdly, the overload analysis examined the critical scenario when the shear demand reached the shear capacity of the bridge. The numbers obtained from these analyses were incorporated in the design of the anchorage tests to ensure a realistic simulation. The loads on the example bridge were separated into two types: live loads and dead loads. Live loads on the bridge were generated mainly by moving trucks and the dead loads were generated by the self-weight of the bridge. The live loads were governed by the larger of these two types of loads: BCL-625 truck and BCL-625 lane. The BCL-625 truck load was generated by a moving CL-625 truck running along the entire span of the bridge, and the CL-625 is a five-axel truck with the load distribution as shown in the figure below.  Fig. 13: CL-625 truck load (from Canadian Highway Bridge Design Code). On the other hand, the BCL-625 lane load (Fig. 14) is a combination of a uniformly distributed load of 9 kN/m and 80% of the loads from a moving CL-625 truck. 16   Fig. 14: CL-625 lane load (from Canadian Highway Bridge Design Code). For the example bridge, as shown in Table 1, the BCL-625 lane load produced the largest live load bending moments and shear forces at all locations when 𝑉 = 6.6 m. Table 1: Summary of BCL-625 Truck and BCL-625 lane loads when 𝑽 = 6.6 m.   Distance from the Support (mm) Maximum Bending Moments (kNm) Maximum Shear Force (kN) BCL-625 Truck BCL-635 Lane BCL-625 Truck BCL-635 Lane 0 0 0 481 542 1730 784 886 453 505 3494 1482 1680 424 467 6989 2698 3038 362 390 10483 3482 3940 299 317 13987 3901 4440 237 246 17472 (midspan) 3887 4483 174 179  The dead load, on the other hand, consisted of the self-weight of the various components of the bridge. The uniformly distributed loads were calculated by estimating the cross-sectional area of each section and multiplying it by the corresponding unit weight; the dead load for each component as well as the total weight per unit length are shown in Table 2. 17  Table 2: Summary of dead load. Component Load (kN/m) Deck 13.1 Haunch 0.9 Parapet 2.2 I-Girder 10.9 Total 27.1  2.5 Bending Moment and Shear Force Envelopes The bending moment envelopes were developed by superimposing the maximum bending moments produced by the BCL-625 lane loads with ones produced by the dead loads. Assuming that the bridge is simply supported, the maximum bending moment (𝑀𝑚𝑎𝑥) along the bridge was calculated using the following equation:  𝑴𝒎𝒂𝒙 = 𝜶𝑳𝑴𝑳𝑳 + 𝜶𝑫 [𝒘𝑫𝑳 ∙ 𝒙 ∙ (𝑳 − 𝒙)𝟐] (1) where 𝛼𝐿 = live load factor, 𝑀𝐿𝐿 = maximum live load bending moment obtained from live load bending moment envelopes generated by BCL-625 lane load; 𝛼𝐷  = dead load factor, 𝑤𝐷𝐿  = uniformly distributed dead load, 𝐿 = length of bridge, 𝑥 = distance away from support. The dead load factors and live load factors specified in the CHBDC were used for the SLS and ULS analyses (see Table 3). For the overload analysis, the same 𝛼𝐷 as the one specified for ULS was used, and 𝛼𝐿  was set to the critical value of 2.81; this value of 𝛼𝐿  was obtained through iteration by amplifying the live loads until shear demand reached the shear capacity at any one point along the bridge. 18  Table 3: Summary of load factors. Load Case 𝜶𝑫 𝜶𝑳 SLS 1.00 0.90 ULS 1.10 1.70 Overload 1.10 2.81  The bending moment envelopes of the three analyses are plotted on the tension side in Fig. 15 below.   Fig. 15: Bending moment envelopes for SLS, ULS and overload. Because the bridge was modelled as a simply-supported member, the bending moment envelopes were symmetrical. Thus, only one half of the span was plotted (from 𝑥 = 0 to 𝑥 = 17472 mm). The envelopes were not parabolic because the live load was composed of the maximum bending moment from a moving truck load instead of a distributed load. The maximum bending moments at midspan for SLS, ULS, and overload were 8600 kNm, 12200 kNm, and 15100 kNm, respectively. 02000400060008000100001200014000160000 2000 4000 6000 8000 10000 12000 14000 16000Bending Moment (kNm)Distance Away from Support (mm)SLSULSOverload19  Similarly, the maximum shear forces corresponding to the live load (𝑉𝐿𝐿) were superimposed with the shear forces generated from the dead load to generate the three shear force envelopes, shown in Eq. 2. 𝑽𝒎𝒂𝒙 = 𝜶𝑳 ∙ 𝑽𝑳𝑳 + 𝜶𝑫 ∙ [𝒘𝑫𝑳 (𝑳𝟐− 𝒙)] (2) where 𝑉𝑚𝑎𝑥 = maximum shear force, 𝛼𝐿 = live load factor, 𝑉𝐿𝐿 = maximum live load obtained by BCL-625 lane loads, 𝛼𝐷 = dead load factor, 𝑤𝐷𝐿 = uniformly distributed dead load, 𝐿 = length of bridge, and 𝑥 = distance away from bridge. The same load factors in Table 3 were used to determine the shear force envelopes. The shear force values from the same BCL-625 lane load were also used in the calculation. Note that the position of the moving truck at which the maximum bending moment was produced does not correspond to the position of the moving truck at which the maximum shear force was generated. The shear force envelopes are plotted in the following figure. 20   Fig. 16: Shear force envelopes for SLS, ULS, and overload. The maximum shear forces were located at the support of the bridge, and their values were 930 kN, 1330 kN, and 1660 kN for SLS, ULS, and overload, respectively. At locations near the supports, shear forces were directly transferred to the supports of the bridge, thus the shear forces from 𝑥 = 0 to 𝑥 = 1730 mm remain constant and the shear force was taken as the value at 𝑥 = 1730 mm, which represented a distance equal to the shear depth of the bridge section. The shear forces at midspan were minimal and they are only contributed by the moving truck load, since the uniformly distributed dead load on a simply-supported member resulted in no shear forces at midspan. The shear forces at midspan were 180 kN, 300 kN, and 420 kN for SLS, ULS, and overload, respectively. 0200400600800100012001400160018000 2000 4000 6000 8000 10000 12000 14000 16000Shear Force (kN)Distance Away from Support (mm)SLSULSOverload21  2.6 Longitudinal Stresses of the Flexural Tension Flange The stresses of the flexural tension flange at various sections along the example bridge were analyzed under SLS loads. The longitudinal stresses of the flexural tension flange (𝑓𝑏 ) are a resultant of (1) the flexural stresses induced by the applied loads, (2) the axial stresses in the prestressing strands, and (3) the flexural stresses as a result of the eccentricity of the prestressing forces from the centroid of the section, as shown respectively by the three terms in Eq. 3. 𝒇𝒃 = ±𝑴 ∙ 𝒚𝑰−𝒇𝒔𝒆 ∙ 𝑨𝒑𝑨± ∑𝒇𝒔𝒆 ∙ 𝑨𝒑𝒊 ∙ 𝒆𝒊 ∙ 𝒚𝒊𝑰𝟏𝟎𝐢=𝟏 (3) where 𝑀 = bending moment produced by applied loads, 𝑦 = distance from neutral axis of section to bottom of flexural tension flange, 𝐼 = second moment of inertia of the member’s cross section, 𝑓𝑠𝑒  = effective strength of prestressing strands, 𝐴𝑝  = total cross-sectional area of the 48 prestressing strands, 𝐴 = total cross-sectional area of the section, 𝑒 = vertical distance from the strand to neutral axis, and 𝑖 = index representing each draped prestressing strand numbered from 1 to 10. The first term in Eq. 3 was used to convert the applied bending moments into longitudinal stresses based on the geometry of the cross section (see Fig. 10) where 𝑦 = 1.47 m and 𝐼 = 0.521 m4. In the second term, the axial stresses generated by the straight prestressing strands were calculated by dividing the total axial force from the prestressing strands by the total cross-sectional area (𝐴) of the section. The effective strength of the prestressing strands (𝑓𝑠𝑒) is 1116 MPa, which was taken as 60% of the ultimate strength. The total cross-sectional area of the 48 prestressing strands 22  (𝐴𝑝) is 4752 mm2, and the cross-sectional area of the section is 1.067 m2. The resulting axial stresses were calculated to be -4.96 MPa, where the negative sign indicates compressive stress. The eccentricity of the draped prestressing strands produced additional bending moment and stresses. Because of the varying height along the section, draped strands generated positive bending moments near the two ends of the girder and negative bending moments in the middle. These bending moments were converted into stresses using the flexure formula, and the distance from the neutral axis to the bottom of the flange (𝑦𝑖) varied along the span depending on the height of the draped strands at each section. By summing up the three components, the stresses at the bottom of the flexural tension flange are plotted at various locations along the span of the bridge in Fig. 17.   Fig. 17: Stresses of flexural tension flange for SLS. 0510152025300 2000 4000 6000 8000 10000 12000 14000 16000Compressive Stress (MPa)Distance Away from Support (mm)23  Only compressive stresses were present in the flexural tension flange thus cracking was not expected to occur under service loads. 2.7 Methods for Calculating Shear Response The shear strength of the bridge was computed using three methods: (1) Clause 8.9.3 in the 2006 CHBDC, (2) evaluation procedure proposed by Esfandiari and Adebar (2009), and (3) analysis program Response-2000. The shear strength of prestressed concrete elements is influenced by the axial longitudinal strain and the shear angle of the compressive stresses. In both methods (1) and (2), the shear strength was calculated based on beam theory using the average longitudinal strain, shear angle, and physical properties of the cross section. The two methods differ by the ways the average longitudinal strains are calculated. The 2006 CHBDC uses simplified equations that ignore the shear stress ratio, and the method proposed by Esfandiari and Adebar (E&A) uses more refined equations without the need of a trial-and-error process. In method (3), a computer software outputted the shear angle, longitudinal strain, and shear strength of the section based on the physical properties and load scenarios inputted. In addition, the stresses on the stirrup were also examined using this method. The resulting longitudinal strains were simulated in the anchorage tests. 2.7.1 2006 Canadian Highway and Bridge Design Code From Clause 8.9.3.8 in the 2006 CHBDC, the average longitudinal strain (𝜀𝑥) in a bridge section was first calculated by the following equation. 24  𝜺𝒙 =𝑴𝒋𝒅 + 𝑽𝒇 − 𝝓𝒑𝑽𝒑 + 𝟎. 𝟓𝑵 − 𝑨𝒑𝒔𝒇𝒑𝟎𝟐(𝑬𝒔𝑨𝒔 + 𝑬𝒑𝑨𝒑) (4)  where 𝑀 = applied bending moment, 𝑗𝑑 = moment arm, 𝑉𝑓 = factored applied shear force, 𝜙𝑝 = resistance factor of prestressing strands, 𝑉𝑝 = shear capacity of prestressing strands, 𝑁 = applied axial force, 𝐴𝑝𝑠 = cross-sectional area of prestressing strands in the half-depth on flexural tension side, 𝑓𝑝0 = decompression stress, 𝐸𝑠 = elastic modulus of reinforcing steel, 𝐴𝑠 = cross-sectional area of reinforcing steel,  𝐸𝑝 = elastic modulus of prestressing strands, and 𝐴𝑝 = cross-sectional area of prestressing strands. Dividing the applied bending moment (𝑀) by the moment arm (𝑗𝑑) approximates an equivalent axial tension force acting on the flexural tension flange. The nominal shear force is represented by the difference between the applied shear force (𝑉𝑓) and the shear capacity of the prestressing strands (𝜙𝑝𝑉𝑝). The longitudinal component of the shear force (0.5𝑉𝑓 cot 𝜃, where 𝜃 = shear angle) is simplified to 𝑉𝑓 assuming that 0.5 cot 𝜃 ≅ 1 (Bentz et al. 2006). Half of the total applied axial force (𝑁) is estimated to contribute to the axial force acting on the flange, but 𝑁 = 0 in the example bridge. The decompression force is represented by multiplying the cross-sectional area of prestressing strands in the half-depth on the flexural tension side (𝐴𝑝𝑠) with 𝑓𝑝0. Dividing the total axial force acting on the flexural tension flange (𝑀𝑗𝑑+ 𝑉𝑓 − 𝜙𝑝𝑉𝑝 + 0.5𝑁 − 𝐴𝑝𝑠𝑓𝑝0) by the total axial stiffness of the reinforcing steel and prestressing strands ( 𝐸𝑠𝐴𝑠 + 𝐸𝑝𝐴𝑝 ) yields the longitudinal strain of the flexural tension flange (𝜀𝑥𝑓). The factor of 2 in the denominator assumes that the average longitudinal strain is approximately half of the longitudinal strain of the flexural 25  tension flange. Using the same equation, 𝜀𝑥𝑓 can also be computed by excluding the factor of 2 in the denominator in Eq. 4. The average longitudinal strain (𝜀𝑥), along with the concrete shear contribution factor (𝛽), and the shear angle ( 𝜃 ) were used in calculating the shear strengths. Using the value of average longitudinal strain calculated from Eq. 4, 𝛽 and 𝜃 were calculated by the following equations: 𝜷 =𝟎. 𝟒𝟏 + 𝟏𝟓𝟎𝟎𝜺𝒙 (5)  𝜽 = 𝟐𝟗 + 𝟕𝟎𝟎𝟎𝜺𝒙 (6)  When using these equations, for design purposes, 𝜀𝑥  must not exceed 0.002. These equations assume that 𝛽 and 𝜃 are independent of the shear stress ratio (𝑣𝑓𝑐′). The variable 𝛽 was developed assuming no transverse reinforcement, and the variable 𝜃 assumes a maximum shear stress ratio of 0.25 (Bentz et al. 2006). The shear resistance (𝑉𝑟) of the bridge is contributed by the shear capacity of the concrete (𝑉𝑐), the stirrups (𝑉𝑠), and the vertical component of the draped strands (𝑉𝑝), as shown in the following equation: 𝑽𝒓 = 𝟐. 𝟓𝜷𝝓𝒄𝒇𝒄𝒓𝒃𝒘𝒅𝒗 +𝑨𝒗𝝓𝒔𝒇𝒚𝒅𝒗 𝒄𝒐𝒕 𝜽𝒔+ 𝝓𝒑𝒇𝒑𝒖𝑨𝒑𝟏 𝒔𝒊𝒏 𝜽𝒑 (7) where 𝛽  = concrete contribution factor (see Eq. 5), 𝜙𝑐  = resistance factor of concrete, 𝑓𝑐𝑟  = cracking strength of concrete, 𝑏𝑤 = width of web, 𝑑𝑣 = shear depth, 𝐴𝑣 = cross-sectional area of 26  the stirrup, 𝜙𝑠 = resistance factor of reinforcing steel, 𝑓𝑦 = yielding strength of reinforcing steel, 𝜃 = shear angle (see Eq. 6), 𝑠 = stirrup spacing, 𝜙𝑝 = resistance factor of prestressing strands, 𝑓𝑝𝑢 = ultimate strength of prestressing strands, 𝐴𝑝1 = cross-sectional area of draped prestressing strands, and 𝜃𝑝 = angle at which prestressing strands are draped. The resistance factors (𝜙𝑐, 𝜙𝑠, and 𝜙𝑝) used in each of the three analyses (SLS, ULS, and overload) are summarized in the following table: Table 4: Summary of resistance factors. Load Case 𝜙c 𝜙s 𝜙p SLS 1.00 1.00 1.00 ULS 0.75 0.95 0.90 Overload 1.00 1.00 1.00  The concrete shear strength (𝑉𝑐) is approximated as 2.5 times the axial compression of concrete (𝛽𝜙𝑐𝑓𝑐𝑟𝑏𝑤𝑑𝑣). Because the area of the concrete stress block and 𝛽 are inversely proportion to 𝜀𝑥 (see Eq. 4), the concrete shear strengths are largest near the supports where 𝜀𝑥 is the smallest. The shear resistance of the stirrups (𝑉𝑠) is simply a function of the cross-sectional area of the stirrup, the yield strength of steel, the shear depth, the stirrup spacing, and the shear angle, factored by the corresponding resistance factor. The stirrup contributions along the span vary due to (1) the changing stirrup spacings from 150 mm near the end, 200 mm further away from the support, to 300 mm for the majority of midspan, and (2) the changing 𝜃 which depends on 𝜀𝑥 from Eq. 4. The strength of the draped strands is the product of the ultimate strength of the prestressing strands (𝑓𝑝𝑢) and the area of these stands (𝐴𝑝1). Because only the vertical component of the axial strength 27  is able to resist the shear force, the strength of the prestressing strands is multiplied by sin 𝜃𝑝. Within the span where the prestressing strands are held down, the draped strands do not contribute to the shear strength; 𝑉𝑝 was calculated to be constant elsewhere at 135 kN for SLS and overload, and 135 kN for ULS. 2.7.2 Esfandiari and Adebar Evaluation Procedure The evaluation procedure proposed by Esfandiari and Adebar (2009) uses more refined equations without requiring a trial-and-error process. Also, three failure modes (stirrups yielding, diagonal crushing of concrete before the stirrup yields, and the yielding of longitudinal reinforcement) are analyzed separately in this method; this method provides additional information about the member’s shear failure mode. In this method, 𝜀𝑥 and 𝜃 are computed using formulas validated with strength tests on concrete beams with at least minimum transverse reinforcement. The average longitudinal strain is calculated using Eq. 8.  𝜺𝒙 =𝑴𝒋𝒅 + 𝟎. 𝟓𝒏𝒗𝟎𝒃𝒘𝒅𝒏𝒗 − 𝜶√𝒇𝒄′ 𝑨𝒕𝒇 − 𝒇𝒑(𝑨𝒑 + 𝝀𝑨𝒑𝒘)𝟐[𝑬𝒔(𝑨𝒔 + 𝟎. 𝟐𝟓𝑨𝒔𝒘) + 𝑬𝒑(𝑨𝒑 + 𝝀𝟐𝑨𝒑𝒘)] − 𝟎. 𝟓𝚫𝒏𝒗𝒃𝒘𝒅𝒏𝒗 (8)  where 𝑀 = applied bending moment, 𝑗𝑑 = moment arm, 𝑛𝑣0 = compressive stress required when average longitudinal strain is zero, 𝑏𝑤 = width of shear area, 𝑑𝑛𝑣 = depth of uniform compression stress, 𝛼 = concrete tension strength factor, 𝑓𝑐′ = specified compressive strength of concrete, 𝐴𝑡𝑓 = cross-sectional area of concrete in tension surrounding flexural tension reinforcement, 𝑓𝑝  = effective stress in prestressing strands, 𝐴𝑝 = cross-sectional area of prestressing strands, 𝜆 = ratio of moment arm of prestressing strands in web to the moment arm (𝑗𝑑), 𝐴𝑝𝑤 = cross-sectional area of non-prestressed longitudinal reinforcement centred in web, 𝐸𝑠 = elastic modulus of reinforcing 28  steel, 𝐴𝑠  = cross-sectional area of reinforcing steel, 𝐴𝑠𝑤  = cross-sectional area of prestressed strands centred in web, 𝐸𝑝 = elastic modulus of prestressing strands, 𝐴𝑝 = cross-sectional area of prestressed strands in flexural tension, 𝐴𝑝𝑤 = cross-sectional area of non-prestressed longitudinal reinforcement in flexural tension, and ∆𝑛𝑣 = change in compressive stress per unit change in 𝜀𝑥. The longitudinal strain was calculated by including the forces from these various components: applied bending moment, longitudinal compressive stresses of concrete, tensile stresses in the flange, and the stresses from the prestressing strands. Similar to Eq. 4 in the 2006 CHBDC procedure, the factor of 2 in the denominator in Eq. 8 assumes that 𝜀𝑥 is approximately half of 𝜀𝑥𝑓. Therefore, 𝜀𝑥𝑓 can also be computed using Eq. 8 with the factor of 2 in the denominator excluded. In this method, 𝜃 is calculated using Eq. 9. 𝜽 = 𝜽𝟎 + 𝚫𝜽𝜺𝒙 (9)  where 𝜃0 = shear angle at zero average longitudinal strain, and Δ𝜃 = change in shear angle per unit 𝜀𝑥. Based on the governing failure mode (yielding of transverse reinforcement and concrete crushing), different equations are used to determine 𝜃0 and Δ𝜃. For the case which yielding of transverse reinforcement governs, the following equations are used: 𝜽𝟎 = (𝟖𝟓𝝆𝒛𝒇𝒚𝒇𝒄′+ 𝟏𝟗. 𝟑) (−𝟓𝟎𝜺𝒚 + 𝟏. 𝟏) (10)  29  𝚫𝜽 = 𝟏𝟎𝟎𝟎[𝟑𝟕. 𝟓(−𝟐𝟎𝟎𝜺𝒚 + 𝟏. 𝟒) − 𝜽𝟎] (11)  where 𝜌𝑧  = ratio of transverse reinforcement area to concrete area, 𝑓𝑦  = yield strength of reinforcing steel, 𝑓𝑐′ = specified compressive strength of concrete, and 𝜀𝑦 = yield strain of stirrups. When concrete crushing governs, the following equations are used to determine 𝜃0and Δ𝜃 instead: 𝜽 = 𝟏𝟏𝟗𝝆𝒛𝒇𝒚𝒇′𝒄+ 𝟏𝟓. 𝟔 (12)  𝚫𝜽 = 𝟏𝟓𝟎𝟎𝟎𝝆𝒛𝒇𝒚𝒇′𝒄+ 𝟐𝟎𝟎𝟎 (13)  where 𝜌𝑧  = ratio of transverse reinforcement area to concrete area, 𝑓𝑦  = yield strength of reinforcing steel, and 𝑓𝑐′ = specified compressive strength of concrete. The concrete contribution factor 𝛽 is also calculated differently depending on the governing failure mode. For the case which yielding of transverse reinforcement governs, 𝛽 = 0.18. When concrete crushing governs, the following equation is used: 𝜷 = 𝟎. 𝟔𝟓𝝆𝒛𝒇𝒚𝒇𝒄′+ 𝟎. 𝟎𝟑 (14)  Similar to the 2006 CHBDC procedure, the shear resistance was computed using Eq. 7 but with a different set of 𝜀𝑥, 𝛽, and 𝜃. 30  2.7.3 Response-2000 Response-2000 Reinforced Concrete Section Analysis is a computer program developed by Evan C. Bentz at the University of Toronto. The program is based on modified compression field theory and it is used to calculate the strength of reinforced concrete beams and columns. For the analyses, material properties, dimensions of the cross section, location of reinforcement and prestressing strands, and loads were inputted in the program. The same resistance factors and load factors as the previous two methods were applied. Through a sectional analysis, the average longitudinal strain (𝜀𝑥), longitudinal strain of the flexural tension flange (𝜀𝑥𝑓), shear strength (𝑉𝑟), and the stresses of the stirrups were obtained. The locations of the prestressing strands and the spacing of the reinforcement change along the span of the example bridge, thus different properties were inputted separately for each analyzed section. The following figure shows the diagram of the cross section at midspan generated by Response-2000 after inputting the corresponding dimensions and reinforcement arrangement.  Fig. 18: Response-2000 generated diagram of the cross section at midspan (in mm). 31  The shear resistance and the bending moment resistance were obtained by examining the bending moment-shear force interaction diagram outputted from Response-2000. An example bending moment-shear force interaction diagram for the overload scenario at midspan is shown in Fig. 19.  Fig. 19: Response-2000 generated bending moment-shear force interaction diagram at midspan for overload. The longitudinal strains along the entire height of the section were obtained through the strain profile ouputted by the “One Load” analysis in Response-2000 after inputting the specified loads. The following figure is an example of the longitudinal strain profile outputted by Response-2000 at midspan for overload. 32   Fig. 20: Response-2000 generated longitudinal strain profile at midspan for overload. Fig. 20 shows the curvature, the minimum longitudinal strain, and the maximum longitudinal strain. The average longitudinal strain (𝜀𝑥) was calculated by averaging the longitudinal strains at the top and the bottom of the section, which computed to +0.00087 in this example. The longitudinal strain of the flexural tension flange (𝜀𝑥𝑓) is the longitudinal strain at 119 mm from the base of the cross section; this height corresponds to the centroid of the flexural tension flange. In this example, 𝜀𝑥𝑓 = +0.00219. As oppose to a single value of 𝜃  computed from the previous two methods, Response-2000 outputted a profile of shear angles along each cross section. Fig. 21 shows the shear angle profile for the same example. Beam Depth (mm)x Strain (mm/m)Longitudinal Strain-300-600-900-12000300600-0.4 0.0 0.4 0.8 1.2 1.6 2.033   Fig. 21: Response-2000 generated shear angle profile at midspan for overload. In Fig. 21, Response-2000 demonstrated that 𝜃 was not uniform along the cross section. In order to compare the shear angles from Response-2000 with the previous two methods (where only a single value of 𝜃 for each cross section was computed), the shear angle profile was assumed to be linear along the web as shown by the dashed line (𝐴𝐵̅̅ ̅̅ ) in Fig. 21. The shear angles near the top and the one near the bottom of the web were used to provide a representation of the range of 𝜃. These values were taken at the height of the cross section where the abrupt change in 𝜃 occurred, near the boundary between the web and the flanges (see point A and B in Fig. 21). In addition, Response-2000 also outputted the stirrup stresses under the specified loads. This provided information on the demands specifically along the stirrups, instead of the shear demands along the entire cross section. Response-2000 also provided values for the increased stress experienced by the stirrups at the cracks. Similar to the longitudinal strain profile, Response-2000 outputted stirrup stress profile along the cross section. Fig. 22 shows an example of the stirrup stress profile outputted by Response-2000 at midspan for overload. A B 34    Fig. 22: Response-2000 generated stirrup stress profiles at midspan for overload; (left) not at crack; (right) at crack. As shown in Fig. 22, stirrup stresses varied along its length, and the stirrup stresses could reach the theoretical yield stress at the cracks in the flexural tension flange. The outputted values along the span of the member were summarized along with the other two methods, 2006 CHBDC and the E&A, in the next section. 2.8 Results of Shear Analysis The average longitudinal strains ( 𝜀𝑥 ) and the shear angle ( 𝜃 ) computed with the three aforementioned methods were compared under all three load scenarios (SLS, ULS, and overload). The shear strengths (𝑉𝑟) computed from the three methods were compared only for ULS, where load and resistance factors were applied. 2.8.1 Average Longitudinal Strains The average longitudinal strains under SLS, ULS, and overload were analyzed using three methods: 2006 CHBDC, E&A, and Response-2000. The following figure compares the average longitudinal strains along half the span of the example bridge. Beam Depth (mm)Stress (MPa)Stirrup Stress-300-600-900-120003006000 30 60 90 120 150Beam Depth (mm)Stress (MPa)Stirrup Stress at Crack-300-600-900-120003006000 60 120 180 240 300 36035   Fig. 23: Average longitudinal strains for CHBDC, E&A and Response-2000: (top) SLS; (middle) ULS; (bottom) overload. -0.0015-0.0010-0.00050.00000.00050.00100.00150.00200.00250 2000 4000 6000 8000 10000 12000 14000 16000Average Longitudinal StrainDistance Away from Support (mm)E&ACHBDCResponse-2000-0.0015-0.0010-0.00050.00000.00050.00100.00150.00200.00250 2000 4000 6000 8000 10000 12000 14000 16000Average Longitudinal StrainDistance Away from Support (mm)-0.0015-0.0010-0.00050.00000.00050.00100.00150.00200.00250 2000 4000 6000 8000 10000 12000 14000 16000Average Longitudinal StrainDistance Away from Support (mm)36  For SLS, the entire girder was under compression since the girder was designed to not crack under service conditions, and all three methods predicted similar compressive longitudinal strains. For ULS, the flexural stress near midspan caused the bridge to experience tensile longitudinal strain, and for overload, a greater section of the girder was under tensile longitudinal strain. The CHBDC estimated smaller 𝜀𝑥  than the other two methods. At midspan, for overload, both E&A and Response-2000 estimated a 𝜀𝑥 which is 52% larger than the one predicted with CHBDC. 2.8.2 Shear Angles A single value of shear angle (𝜃) was calculated at each cross section using the CHBDC procedure and E&A. These were compared with the 𝜃 near the top of the web and the 𝜃  near the bottom of the web from Response-2000. The shear angles for each of the three load scenarios (SLS, ULS, and overload) are compared in the following figure. 37    Fig. 24: Shear angles from CHBDC, E&A, and Response-2000: (top) SLS; (middle) ULS; (bottom) overload. 01020304050600 2000 4000 6000 8000 10000 12000 14000 16000Shear Angle (degree)Distance Away from Support (mm)shear angle (E & A)shear angle (CHBDC)shear angle near top of web (Response-2000)shear angle near bottom of web (Response-2000)01020304050600 2000 4000 6000 8000 10000 12000 14000 16000Shear Angle (degree)Distance Away from Support (mm)01020304050600 2000 4000 6000 8000 10000 12000 14000 16000Shear Angle (degree)Distance Away from Support (mm)38  For SLS, CHBDC predicted the largest shear angle at 27.6°. The angle was constant throughout the span because the minimum longitudinal strain of -0.0002 was used in the calculation. The shear angles calculated from E&A ranged from 21.0° to 23.4°, and thus the CHBDC gave the more conservative results. For ULS, similar to SLS, CHBDC computed larger shear angles than E&A. The shear angles computed from CHBDC ranged from 27.6° to 28.6°, whereas the shear angles computed from E&A ranged from 21.5° to 23.8°. These values were similar to the SLS scenario. For overload, the shear angles computed from both the E&A and the CHBDC showed much larger values at midspan, at 38.9° and 39.1°, respectively. This corresponded to the large bending moment demand and larger average longitudinal strains at midspan. The shear angles near the support remained similar to the values for the ULS analysis even with larger applied loads. The shear angles calculated near the top and bottom of the web by Response-2000 behaved differently for each load scenario. When the load demands were low for SLS, the shear angles were much smaller, and at midspan, the shear angles were calculated to be 7.1° and 6.9° near the top and bottom of the web, respectively. Shown in the plots for ULS and overload, when the bending moment demand was large, the shear angles near bottom of the web surpassed the shear angles near the top of the web, and the shear angle profile became more non-uniform (as the difference between the two shear angles increased). For ULS and overload, the shear angles near the bottom of the web at midspan have increased to 49.5° and 58.5°, respectively. This shows that the shear angle near the flexural tension flange at midspan, under large loads, could be larger than the single values predicted from the other methods. 39  2.8.3 Shear Strength The shear resistance is contributed mostly by the stirrups in the I-girder. Based on the average longitudinal strains and shear angles obtained by the CHBDC, E&A, and Response-2000, the resulting shear resistances, using the load and resistance factors from ULS, are shown in the following figure.  Fig. 25: Factored shear demand and shear resistances from CHBDC, E&A, and Response-2000 for ULS. The factored shear demand is plotted with the three shear resistances in Fig. 25. Surprisingly, the shear resistances at midspan calculated from both CHBDC and E&A were less conservative than the shear strength from Response-2000. However, all three methods validated that the example bridge would not fail under ULS loads. Similarly, Fig. 26 shows the shear demand and resistance from the three methods for overload. 0500100015002000250030000 2000 4000 6000 8000 10000 12000 14000 16000Shear Force (kN)Distance Away from Support (mm)factored shearshear resistance (E & A)shear resistance (CHBDC)shear resistance (Response-2000)40   Fig. 26: Factored shear force demand and shear resistances from CHBDC, E&A, and Response-2000 for overload. Fig. 26 shows a larger shear demand than the demand for ULS because the overload scenario used a live load factor of 2.82 instead of 1.10, in the case of ULS. The amplified shear demand greatly increased the longitudinal average strain at midspan, and thus significantly decreased the shear resistances for both E&A and CHBDC. At 𝑥 = 13978 mm, the shear demand equalled the shear resistance computed by E&A. 2.9 Shear Demand Parameters for Anchorage Tests To design the anchorage tests, the longitudinal strains of the flexural tension flange (𝜀𝑥𝑓), the stirrup stresses, and the shear angles (𝜃) were examined. The 𝜀𝑥𝑓 was calculated using the three methods and these values were used in designing the longitudinal strains for the anchorage tests. The stirrup demand was also examined with Response-2000. 0500100015002000250030000 2000 4000 6000 8000 10000 12000 14000 16000Shear Force (kN)Distance Away from Support (mm)factored shearshear resistance (E & A)shear resistance (CHBDC)shear resistance (Response-2000)41  2.9.1 Longitudinal Strains of Flexural Tension Flange In the CHBDC and E&A, 𝜀𝑥𝑓 was calculated assuming that the average longitudinal strain (𝜀𝑥) was approximately half of 𝜀𝑥𝑓. In Response-2000, the values of 𝜀𝑥𝑓 were read from the outputted strain profile. The following figure shows a plot of 𝜀𝑥𝑓 for SLS, ULS, and overload along half the span of the bridge. 42    Fig. 27: Longitudinal strain of flexural tension flange for CHBDC, E&A and Response-2000: (top) SLS; (middle) ULS; (bottom) overload. -0.0015-0.0010-0.00050.00000.00050.00100.00150.00200.00250 2000 4000 6000 8000 10000 12000 14000 16000Longitudinal Strain of FlangeDistance Away from Support (mm)E&ACHBDCResponse-2000-0.0015-0.0010-0.00050.00000.00050.00100.00150.00200.00250 2000 4000 6000 8000 10000 12000 14000 16000Longitudinal Strain of FlangeDistance Away from Support (mm)-0.0015-0.0010-0.00050.00000.00050.00100.00150.00200.00250 2000 4000 6000 8000 10000 12000 14000 16000Longitudinal Strain of FlangeDistance Away from Support (mm)43  In Fig. 27, the longitudinal strains of the flexural tension flange showed very similar trends to the average longitudinal strains plotted in Fig. 23. The largest 𝜀𝑥𝑓 calculated was +0.0022 at midspan from Response-2000 for overload. 2.9.2 Stirrup Stresses The interaction between stirrup stresses and the longitudinal strain of the flexural tension flange were examined using Response-2000; the results are plotted as interaction diagrams with the longitudinal strain of the flexural tension flange. Each data point represented a different location along the span of the bridge. The data from SLS analysis are not plotted because the applied loads were too small to generate stresses on the stirrups.   Fig. 28: Interaction of stirrup stress and longitudinal strain of flexural tension flange from Response-2000 for ULS and overload. ϕsfy(ULS)ϕsfy (Overload)0100200300400500-0.001 0.000 0.001 0.002 0.003Stirrup Stress (MPa)Longitudinal Strain of Flangemaximum stirrup stress (ULS) maximum stirrup stress at crack (ULS)maximum stirrup stress (Overload) maximum stirrup stress at crack (Overload)44  Two sets of data points are shown for both the ULS and the overload analysis in Fig. 28. “Maximum stirrup stress” refers to the maximum stirrup stress experienced at that section. In Response-2000, the variation in stresses along the length of the stirrups was presented, and only the maximum values of these stresses are plotted on the interaction diagram. “Maximum stirrup stresses at the crack” refers to the increased stresses experienced by the stirrups at a crack. The results from Response-2000 showed that when concrete cracks, it loses its shear capacity and the stirrup must pick up the shear loads at the cracks. In addition, even if the bottom flange were under compressive strain, the stirrups might still experience stresses because cracks might form in the web forcing parts of the stirrups in the web to carry shear forces that the cracked concrete were unable to pick up. Therefore, large stirrup stresses can occur throughout the span of the example bridge – not just near the support where the shear demand is large. Fig. 28 shows that at large strains, the stirrups can also experience large tensile demand. For example, at a strain of +0.0001 at midspan for ULS, the stirrup stress had reached the factored yield strength of 360 MPa (𝜙𝑠 = 0.9) at the crack. This observation was more apparent in the interaction plot for overload; the stirrups have yielded at 400 MPa (𝜙𝑠 = 1.0) at values of  𝜀𝑥𝑓 ranging from as small as -0.0003 to as large as +0.0022. Through an analysis of an example bridge, the calculations and the computer simulation provided information for the design of the anchorage tests. In particular, the example bridge was found to have large stirrup stresses at midspan where shear demand was thought to be low. When the longitudinal strain of the flexural tension flange reached a value as large as +0.0022, the stirrups were also experiencing large shear demands.  45  3 Experimental Program 3.1 Overview This chapter presents an overview of the experimental program. The experimental approach used in the research is explained in Sections 3.2. This includes a brief overview of the design of the test specimens and the test setup. Section 3.3 discusses the two variables in the experimental program – orientation of stirrup hooks and longitudinal strain of the flange. Section 3.4 presents the detail design of the test specimens, which includes the dimensions and the arrangement of steel reinforcement. The construction process of the test specimens is outlined in Section 3.5. The properties of the concrete, reinforcing steel, and prestressing strands used to construct the test specimens are presented in Section 3.6. A detail overview of the various components in the test setup is presented in Sections 3.7. The instrumentations, including LVDTs (linear variable differential transformers), pressure gauges, and Invar bars, are discussed in Section 3.8. Finally, Section 3.9 outlines the testing procedure of the experimental program. 3.2 Experimental Approach The experimental program evaluates and compares the performances of non-code-compliant stirrup arrangement and code-compliant stirrup arrangement. The test specimens were designed to simulate a portion of a full-scale Type 5 prestressed I-girder as shown in Fig. 29. 46   Fig. 29: Comparison of Type 5 I-girder (left) and test specimen (right). In each test, the 16 prestressing strands were held in tension by a horizontal force (𝑇) while a compression force (𝐷) was applied on the web to simulate a diagonal compression force. The two middle stirrups were fixed, while stirrup pull-out was monitored. The two outer stirrups provided a more realistic boundary condition. Fig. 30 shows a simple schematic of the anchorage tests.  Fig. 30: Schematic of test setup. 47  3.3 Test Specimens – Variables Six specimens (T1, L1, T2, L2, T3, and L3) were constructed for the anchorage tests. Three of them consist of Type T (transverse hooks; code compliant) stirrup arrangement, and the other three consist of Type L (longitudinal hooks; not code compliant) stirrup arrangement. For each type of specimen (T and L), the three specimens (1, 2, and 3) were designed to be tested at different longitudinal strains, controlled by the horizontal axial force (𝑇) applied on the prestressing strands at the flange. The two test variables in the anchorage tests were the orientation of the stirrup hooks and the longitudinal strain of the flange (𝜀𝑥𝑓). The values of +0.0011 and +0.0022 were chosen as the target longitudinal strain based on the example bridge analysis in Chapter 2, which demonstrated that an I-girder bridge can experience large stirrup stresses even when the longitudinal strain of the flexural tension flange was as large as +0.0022. To achieve the target longitudinal strain levels, an axial tension force (𝑇) was applied to one end of the prestressing strands. To achieve the target longitudinal strain value, 𝑇 was predicted by the following equation: 𝑻 = 𝜺𝒙𝒇𝑬𝒑𝑨𝒑 − (𝑫 ∙ 𝐜𝐨𝐬 𝜽 − 𝒇𝒔𝒆𝑨𝒑) (15) where 𝜀𝑥𝑓 = longitudinal strain of the flange, 𝐸𝑝 = elastic modulus of prestressing strands, 𝐴𝑝 = total cross-sectional area of prestressing strands, 𝐷 = diagonal compression force acting on the web, 𝜃 = angle, from the longitudinal direction, at which the compression force 𝐷 is applied, and 𝑓𝑠𝑒 = effective stress of prestressing strands. 48  The applied tension force (𝑇) was the difference between the equivalent force required to achieve the target longitudinal strain and the horizontal components of the existing forces acting on the specimen. The existing force comprised of the horizontal component of the diagonal compression force (𝐷) applied to the specimen at angle (𝜃) and the compression force from the prestressing strands (𝑓𝑠𝑒𝐴𝑝). The prestressing strands were stressed to 40% of the ultimate strength, and thus 𝑓𝑠𝑒 = 744 MPa. Eq. 15, however, does not account for concrete strength after concrete cracking (tension stiffening), and the effect of creep and shrinkage on the decompression force. Therefore, this equation was only used to provide a preliminary estimate of the tension force for the design of the test setup. More accurate predictions were made in Chapter 5 with experimental data obtained from the Phase 1 of the anchorage tests (before the application of the diagonal compression force). The estimated tension forces required to achieve up to the target longitudinal strains, along with the corresponding stresses of the prestressing strands, are shown in Table 5. Table 5: Summary of required tension force at each target longitudinal strain. 𝜺𝒙𝒇 𝑻 (kN) 𝑻 𝑨𝒑⁄  (MPa) +0.0011 1198 756 +0.0022 1538 971  To achieve a maximum 𝜀𝑥𝑓 of +0.0022, the test setup would require two hydraulic actuators. Each of them would provide an axial force of 785 kN. Also, the stress on the 16 prestressing strands would reach up to approximately 52% of the ultimate strength of 1860 MPa. 49  3.4 Test Specimens – Details The design of the test specimens was based on a standard Type 5 I-girder specified by the British Columbia Ministry of Transportation and Infrastructure. Each test specimen was a full-scale replica of a bottom section of the Type 5 I-girder. The plan view and the cross sections of both types of specimens (T and L) are shown in the following figures.    Fig. 31: Details of Type T specimen: (top) plan view, (bottom) sections. 50    Fig. 32: Details of Type L specimen: (top) plan view, (bottom) sections. Each specimen comprised of two sections: a rectangular bottom flange and a trapezoidal web protruding from the flange. In a standard Type 5 I-girder, there are two types of prestressing strands: 10 draped strands, and up to 38 straight strands (12.7 diameter – 7 wire). The ends of the draped strands are fixed near the top flange, and they extend and drape along the web. The middle third length of the prestressing strands is held down horizontally in the center of the bottom flange. 51  In the test specimens, however, the height of the specimen restricted the installment of draped strands, and a much smaller concrete area limited the number of straight strands. Therefore, sixteen straight strands, and no draped strands, were embedded within the bottom flange of each test specimen. These prestressing strands were prestressed to 744 MPa, 40% of the ultimate strength to enable the relatively smaller cross section of the test specimens to withstand the compression force generated by the release of the prestressed strands. The overall height of each test specimen was 584 mm and the overall length was 1450 mm long. The web was 127 mm wide and 317 mm tall, and the two sides of the web were bevelled with a pitch of 60° on both sides so that the top of the web was 882 mm long and the bottom of the web was 1236 mm long. The bevelled section of the web enabled a diagonal compression force to be applied. The bottom flange was a rectangular prism which was 1450 mm long, 267 mm tall and 350 mm wide. The specimen was designed to have a sufficient transfer length (𝑙𝑡) from the location of the testing stirrups to the end of the specimen, and the transfer length was calculated from the equation: 𝒍𝒕 = 𝟓𝟎 ∙ 𝒅𝒃 (1) where 𝑑𝑏  = diameter of prestressing strands. Given 𝑑𝑏  = 12.7 mm, the transfer length was calculated to be 635 mm. Four pairs of 10M stirrups were installed in each specimen with a 150 mm centre-to-centre spacing. Only the free ends of the middle two pairs of stirrups (testing stirrups) were connected to a fixed support in the test setup whereas the other two pairs of stirrups (dummy stirrups) were present only to provide an accurate boundary condition. A concrete cover of 26 mm, which was 52  the same as the concrete cover in the example bridge in Chapter 2, was provided at the web of the test specimens. The embedded ends of the stirrups were anchored in the flange by 90° hooks; the hooks of the stirrups in the Type T specimens were bent transversely towards the face of the concrete, while the hooks of the three Type L specimens were bent longitudinally parallel to the prestressing strands. Three 10M ties were looped around the 16 strands on each end of the specimen to prevent concrete spalling. Furthermore, two 10M reinforcing bars were placed along the upper face of the web with a concrete cover of 25 mm. Other horizontal bars and controls bars were also included to hold the reinforcement cage together during construction. 3.5 Construction of Specimen The wooden forms of the test specimens were built at UBC and the concrete specimens were cast and prestressed at Armtec, Richmond, BC. Six identical wooden forms were constructed, and each form consisted of a flange piece and a web piece (see Fig. 33). The two components can be separated and reassembled to allow for easy installment of reinforcement.  Fig. 33: Wooden form: (left) flange piece, (right) web piece. 53  The web piece was to be assembled on top of the flange piece after the prestressing strands were fed through the web piece at the prestressing bay at Armtec. Sixteen holes with a diameter of 13 mm each were drilled on each end of the form to allow the prestressing strands to be fed across (see Fig. 34).  Fig. 34: Sixteen holes at one end of the flange piece of the wooden form. After the six wooden forms were built, they were delivered to Armtec and placed in one long prestressing bed with a spacing of 3.5 m between each form (see Fig. 35).  Fig. 35: Wooden form in prestressing bay with prestressing strands partially fed through. 54  The 16 strands were anchored onto one abutment, and then fed through the holes of each of the six forms. The strands were then anchored at the other abutment, and then stressed to a prestressing level of 0.4𝑓𝑝𝑢 = 744 MPa by a hydraulic actuator. Invar pins were installed on the flange to monitor the longitudinal strain of the flange. The distances between the pins were measured periodically to examine the effect of prestressing, creep, and shrinkage. The detail locations of the Invar pins are presented in Section 3.8. Fresh cement was poured into the wooden forms, and 67 hours later, the specimens were stripped. The lengths between the Invar pins were measured before and after the release of the strands. These strain values were discussed and compared in Chapter 4. After stripping, the specimens were removed from the prestressing bay and placed in an open field at Armtec with other I-girders cast at the plant. 3.6 Material Properties Tests were performed to determine the material properties of the test specimens. Cylinder tests were (compressive strength tests) performed at Armtec and UBC, and the properties of the steel reinforcement were provided by the manufacturers. Cement of Type GU (general use) used in the test specimens was supplied by Lehigh Hanson Canada in Delta, BC. The same mix of cement used in typical I-girders were used to cast the test specimens. The cement content was given as 330 kg/m3 and the maximum aggregate size was 14 mm. The density of the concrete was 2334 kg/m3. A series of concrete tests had been performed with moist cured cylinders at Armtec. The slump was tested to be 220 mm and the air content was 55  4.3%. Cylinder tests were also performed at the UBC on the first day of testing (Day 194). The strengths at various days from these tests are summarized in Table 6, and plotted in Fig. 36: Table 6: Summary of cylinder compressive strengths in MPa. Age Individual Cylinder Results Mean 67 hours 33.0, 32.0 32.5 7 days 44.1, 44.9 44.5 14 days 53.4, 54.5 54.0 28 days 59.7, 57.7 58.7 194 days 78.9, 78.1, 78.8, 77.2 78.3   Fig. 36: Compressive strength versus age of concrete cylinders. Note that high compressive strength (58.7 MPa at 28 days) provides durability but also makes the concrete more prone to splitting. The yield strengths and ultimate strengths of the 10M W400 reinforcing bars (stirrups in the test specimens) are summarized in Table 7. 304050607080900 50 100 150 200Compressive Strength (MPa)Age of Cylinder (days)56  Table 7: Summary of yield and ultimate strengths of reinforcing bars in MPa.  Yield Ultimate Sample 1 470 690 Sample 2 478 700 Sample 3 467 685 Mean 473 693  The ultimate strength of prestressing strands was assumed to be 1860 MPa, and the strands were prestressed to 40% of the ultimate strength. 3.7 Test Setup The following figure shows the plan view of the overall test setup:  Fig. 37: Plan view of test setup: (top) schematic, (bottom) photograph. 57  Apart from the test specimen itself, there were four main components in the test setup: (1) double hydraulic actuators on one side of the prestressing strands, (2) a fixed support on the other end of the prestressing strands, (3) a fixed support fastening the stirrups, and (4) a single actuator on the web at approximately 30° to the longitudinal axis of the specimen. Detail drawings of all components are included in the Appendix C. In the test setup, the prestressing strands were attached to a pair of hydraulic actuators mounted onto a support on one end, while the other end was attached to a fixed support. The hydraulic actuators applied a tension force (𝑇) to the prestressing strands in order to achieve the target longitudinal strain. This force was kept constant throughout each test, but the longitudinal strain of the flange would increase with the additional application of the diagonal compression force (𝐷). The fixed support on the other side of the prestressing strands provided the reaction force, which equalled to the sum of the tension force (𝑇 ) and the horizontal component of the diagonal compression force (𝐷). A diagonal compression forces were applied by a hydraulic actuator on the diagonal face of the web at approximately 30° to the longitudinal axis of the specimen. The compression forces were increased throughout the test and stirrup pull-out was monitored. The stirrups were expected to yield when the diagonal compression force reaches approximately 378 kN. The actuator was mounted on a steel bracket on the diagonal face of the web to prevent the actuator from slipping off the specimen. On the other end, the hydraulic actuator was attached onto a steel plate and an I-beam column fixed to the floor. 58  The vertical component of the diagonal compression force was carried by the middle two pairs of 10M stirrups (testing stirrups). These stirrups were welded onto a steel box, which was mounted onto a fixed support by two steel L-brackets (yellow; see Fig. 37 (bottom)). Between the box and the two L-brackets, a layer of PTFE (Polytetrafluoroethylene) were inserted to minimize friction between the two components. This allowed the fixed end of the testing stirrups to move horizontally to account for the possible slight horizontal movement of the test specimen caused by the application of the diagonal compression force during the anchorage tests. The other two pairs of stirrups (dummy stirrups) provided a realistic boundary condition. 3.8 Instrumentation Before the anchorage tests, to monitor the prestressing, creep, and shrinkage of the test specimens, four pairs of Invar pins were installed near the top and bottom of both sides of the flange for each test specimen before the specimens were cast. The location of the Invar strain targets are shown in Fig. 38.   Fig. 38: Location of Invar strain targets Each pair of targets was set approximately 1295 mm apart and the distance between each pair of targets was measured at various specimen age with the same vernier caliper. 59  During the anchorage tests, eleven linear variable differential transformers (LVDT) and one pressure gauge were installed for each test. The pressure gauge was installed on one of the double actuators to measure the pressure exerted by the system. Two of the LVDTs were installed on the two sides of the flange on each specimen to measure the longitudinal strain in the flange. The strain was measured over a 750 mm length at the centre of the flange. One LVDT was installed along one of the prestressing strands on the reaction side of the setup. The elongation of the prestressing strands was measured so that stresses and the total force in the strand could be monitored and checked with the pressures and forces exerted by the horizontal and diagonal actuators. The remaining eight LVDTs were installed on the four fixed stirrups to measure the strain of the stirrups and the slip of the bar away from the specimen. They were installed on the stirrup as shown in the following figures.  Fig. 39: LVDT setup on individual stirrup: (left) schematic (right) photograph. 60  Two readings were made on each stirrup – one LVDT measured the strain along a 300 mm length of stirrup while the other LVDT measured the change in distance from a point on the stirrup to the face of the web. The change in distance measured by the latter LVDT, defined as “slip” in the anchorage tests, was used to monitor the change in debonded length of the stirrup within the specimen. When the bars began to debond or when the hooks began to pull out, the measure of slip would increase at a higher rate than the strain in the stirrup. An equivalent debonded length could also be calculated based on the amount of slip and the measured strain on the corresponding stirrup. The increase in the debonded length would be used as an indicator for observing the pull-out of the stirrup hooks. This is further explained in Chapter 5. 3.9 Testing Procedure The anchorage tests included three phases: Phase 1 – gradual application of horizontal strain, Phase 2 – repeated application of diagonal compression force within the elastic range of the stirrups, and Phase 3 – repeated application of diagonal compression force after yielding of the stirrups. At the end, pull-outs of the stirrup hooks were examined and compared amongst the tests. 3.9.1 Phase 1: Application of Flexural Tension Force In this phase, two hydraulic actuators were connected to the 16 prestressing strands of the specimen, and the prestressing strands on the other end of the specimen were attached to a fixed support. As the pressure in the actuators increased, the concrete specimens were pulled in tension. This tension force acting on the test specimen simulated the flexural tensile behaviour of the tension flange of a typical prestressed concrete I-girder. When the concrete was under large tension strain, the bonding between the stirrups and concrete would weaken. The pull-out of the stirrup hooks would be monitored later in Phase 2. 61  The target tension strains in the test specimens were achieved by increasing the pressure in both actuators to 3000 psi (20 MPa) in Test T1 and Test L1, and to 3200 psi (22 MPa) in Test L2. The equivalent tension forces are 1570 kN and 1675 kN, respectively. During this phase, the pressure in the horizontal actuators was increased to the target pressure for approximately 20 cycles for each specimen. Between each cycle, the pressure was decreased to 800 psi (5.5 MPa) before gradually increasing to the target pressure again.  In the first cycle, the pressure was increased in gradual steps, which allowed the cracks in the concrete and the loads in the prestressing strands to develop more fully. The pressure was maintained at each step to record observations and capture photographs. 3.9.2 Phase 2: Diagonal Loading – Elastic Stirrups In this phase, a diagonal compression force was applied on the bevelled face of the web of the specimen while maintaining the constant axial tension force introduced in Phase 1. The concrete specimen was first loaded axially by increasing the pressure in the horizontal actuators (identical to Phase 1 of the test). The diagonal actuator was then set at 30° to the longitudinal axis of the specimen. The diagonal actuator applied an axial compression force onto the web of the specimen at approximately 30° to simulate a shear force in a typical I-girder. The diagonal actuator applied the compression force at a constant rate to various loads up to 320 kN, and the number of cycles executed for each load level varied from test to test, depending on the behaviour of the test specimen. During the application of the compression force, the length of prestressing strands from the test specimens to the fixed support picked up the horizontal component of the diagonal compression force, while the four testing stirrups, which were 62  connected to a fixed support, picked up the vertical component of the diagonal force. One end of the flange would experience a longitudinal strain larger than the target longitudinal strain established in Phase 1, while the other end would experience a longitudinal strain of at least the target longitudinal strain. The strains and the slips of the stirrups were also monitored. The strain was measured by LVDTs installed on the exposed section of each of the four testing stirrups. Initially, the rate at which the measured slip (the distance from a fixed point on the stirrup to the surface of the concrete specimen) should increase proportionally with the strain of the stirrups (measured separately along each stirrups). If the stirrup hooks began to pull-out, the rate at which the slip increases with strain would also increase. Pull-outs can then be monitored by observing the ratio of the change in slip to the change in strain on each stirrup. 3.9.3 Phase 3: Diagonal Loading – Yielding Stirrups In Phase 3, the horizontal forces were applied to the prestressing strands similar to Phase 1 and Phase 2. Moreover, the load in the diagonal compression force was further increased to allow the stirrups to yield. The same procedure as Phase 2 was used, and the number of cycles executed varied from each test based on the behaviour of the test specimen. 63  4 Creep and Shrinkage Strains 4.1 Overview Creep and shrinkage were monitored, and measurements were taken by recording the distances between Invar pins installed on each of the six test specimens (L1, L2, L3, T1, T2, and T3) before they were cast, and at various time during the experimental program. The data were analyzed and compared with the numbers calculated by the methods in the 2006 CHBDC and the 2006 CAC Concrete Handbook (Design of Concrete Structure CSA A23.3-04). Section 4.2 presents the measured creep and shrinkage strains and these are compared with the predictions in Section 4.3. 4.2 Measured Creep and Shrinkage Strains On each of the six test specimens, eight Invar pins were installed on each specimen. On both sides of the specimen, the pins were positioned as shown in Fig. 40.  Fig. 40: Locations of Invar pins on test specimen. The bottom set of pins were located 76 mm above the base of the test specimen while the top set of pins were located 191 mm above the base. Each pair of pins was installed approximately 64  1295 mm apart, and a more precise measurement was recorded using a vernier caliper for each pair of pins. Measurement readings, using the same vernier caliper, were taken on day 1 (before the application of the prestressing), day 4 (after the release of the prestressing force), day 7, day 41, day 95, day 108 (after the transfer of the test specimens from Armtec to the UBC Structures Laboratory), day 115, day 122, day 182, day 193 (before the first anchorage test), and day 439. Because the Invar pins were installed on both sides of the specimens, each specimen provided two sets of data. However, during the transfer of the specimens from the prestressing plant to the laboratory, a pair of Invar pins broke off in specimen T1, thus some data points were missing. On day 435, only 2 specimens remained as the other 4 specimens were destroyed during the anchorage tests. Based on the collected data, the compressive strains calculated from the top targets and the bottom targets are plotted separately in Fig. 41. Each test specimen had two data points (one on each side of the test specimens) for each day. The average compressive strains amongst the specimens are summarized in Table 8 and Table 9 for top targets and bottom targets, respectively.  65   Fig. 41: Compressive strains: (top) top targets; (bottom) bottom targets. 0.00000.00020.00040.00060.00080.00100.00120.0014L1 L2 L3 T1 T2 T3Compressive StrainTest SpecimensAfter Release Day 7 Day 41 Day 95 Day 108Day 115 Day 122 Day 182 Day 193 Day 4390.00000.00020.00040.00060.00080.00100.00120.0014L1 L2 L3 T1 T2 T3Compressive StrainTest Specimens66  Table 8: Compressive strains at top targets. Age (day) Test Specimen Average L1 L2 L3 T1 T2 T3 3 0.00033 0.00033 0.00034 0.00031 0.00030 0.00032 0.00025 0.00020 0.00035 0.00029 0.00040 0.00039 0.00032 7 0.00044 0.00039 0.00047 0.00038 0.00044 0.00040 0.00037 0.00035 0.00049 0.00042 0.00057 0.00047 0.00043 41 0.00055 0.00049 0.00071 0.00048 0.00054 0.00059 0.00050 0.00049 0.00054 0.00045 0.00063 0.00056 0.00054 95 0.00055 0.00053 0.00069 0.00059 0.00056 0.00061 0.00050 0.00051 0.00051 0.00062 0.00061 0.00056 0.00057 108 0.00069   0.00067 0.00072 0.00073 0.00071 0.00066 0.00070 0.00074 0.00079 0.00082 0.00072 115 0.00075   0.00079 0.00083 0.00092 0.00079 0.00082 0.00078 0.00093 0.00087 0.00093 0.00084 122 0.00083   0.00081 0.00083 0.00092 0.00081 0.00086 0.00082 0.00089 0.00087 0.00093 0.00086 182 0.00087   0.00089 0.00093 0.00110 0.00095 0.00103 0.00091 0.00101  0.00097 0.00096 193 0.00090   0.00089 0.00093 0.00110 0.00093 0.00097 0.00099 0.00099  0.00105 0.00097 439    0.00126   0.00095 0.00105     0.00108  67  Table 9: Compressive strains at bottom targets. Age (day) Test Specimen Average L1 L2 L3 T1 T2 T3 3 0.00041 0.00042 0.00043 0.00043 0.00042 0.00050 0.00044 0.00036 0.00043 0.00040 0.00057 0.00053 0.00044 7 0.00053 0.00058 0.00054 0.00052 0.00059 0.00064 0.00066 0.00053 0.00054 0.00051 0.00074 0.00063 0.00059 41 0.00068 0.00069 0.00085 0.00067 0.00073 0.00076 0.00073 0.00058 0.00062 0.00054 0.00084 0.00070 0.00070 95 0.00070 0.00073 0.00089 0.00073 0.00073 0.00076 0.00081 0.00066 0.00078 0.00074 0.00082 0.00080 0.00076 108 0.00076 0.00091 0.00089 0.00085 0.00075 0.00088 0.00087 0.00103 0.00089 0.00091 0.00096 0.00099 0.00089 115 0.00092 0.00106 0.00091 0.00093 0.00104 0.00097 0.00104 0.00117 0.00099 0.00099 0.00113 0.00117 0.00103 122 0.00092 0.00104 0.00099 0.00102 0.00104 0.00109 0.00104 0.00117 0.00099 0.00101 0.00113 0.00117 0.00105 182 0.00099 0.00116 0.00108 0.00126 0.00114 0.00125 0.00114 0.00123 0.00113 0.00115  0.00124 0.00116 193 0.00103 0.00116 0.00108 0.00132 0.00110 0.00125 0.00112 0.00119 0.00113 0.00117  0.00124 0.00116 439   0.00122 0.00132    0.00119     0.00124  68    The following figure compares the average compressive strains from the top targets with the average compressive strains from the bottom targets.  Fig. 42: Average compressive strains of top targets and bottom targets. The compressive strains from the top targets and the ones from the bottom targets followed a similar trend. The lower section of the flange experienced larger compressive strains because the axial prestressing force was applied eccentrically from the neutral axis of the cross section. From day 95 to day 108, an abrupt increase in the compressive strains was observed in both the top and the bottom targets. The measurement recorded at day 108 was done after the test specimens were delivered to the structures lab. The difference in the temperature, humidity, and the overall environment (from outdoor to indoor) might have contributed to the sudden change in shrinkage rate. After the prestressing force was released from the specimens, the specimens were placed 0.00000.00020.00040.00060.00080.00100.00120.00140 100 200 300 400 500Compressive StrainTime After Casting (days)Top TargetsBottom Targetsspecimens moved from field to lab69  outside in the field at Armtec throughout the rainy winter under humid conditions. On the other hand, the UBC Structures Laboratory provided the specimens a much drier conditions allowing the specimens to undergo higher rate of shrinkage. 4.3 Prediction of Creep and Shrinkage Strains Using the methods in the 2006 CHDBC, the creep and shrinkage strains were predicted and compared with the measured average compressive strains, which were calculated by dividing the total change in length by the initial total length of 1298 mm between the set of Invar pins. The 1300 mm long segment of the concrete specimen over which the concrete strains were measured did not have a constant cross section; therefore, the compressive strains were calculated separately for two different cross sections, named the “end cross section” and the “middle cross section” as shown in Fig. 43.    Fig. 43: (Left) end cross section; (right) middle cross section. The 1300 mm long test specimen was assumed to be made up of a 1058 mm long segment of “middle cross section” and two 120 mm long segments of “end cross section.” (see Fig. 44)  70   Fig. 44: Lengths of idealized cross sections used for shrinkage and creep strains calculations. The specimens were stored outside at Armtec for the first 107 days. The relative humidity (RH) for the winter months in Richmond, BC, was estimated to be 83% based on climatic data for that location at that period of time. The specimens were then transported to UBC and stored within the UBC Structures Laboratory. The lower RH in an indoor environment can be estimated by using a psychrometric chart. Using the difference in the indoor (16°C) and outdoor temperatures (8°C), the RH at the laboratory was estimated to be 50%. These values were used in the predictions of the longitudinal strains. Two different methods were used to predict the creep and shrinkage strains: the procedure given in the 2006 Canadian Highway Bridge Design Code (CHBDC), and the procedure given in the 2006 CAC (Cement Association of Canada) Handbook. The predictions from CHBDC were found to be much closer to the measured strains and therefore will be compared with the measured 71  longitudinal strains. The differences in the two methods (CHBDC and CAC Handbook) were also discussed. Using the CHBDC method, two predictions were made, one for the creep and shrinkage strains corresponding to 83% relative humidity (RH) (outside condition), and one for 50% RH (inside condition). The results are compared with the measured strains in Fig. 45. 72     Fig. 45: Predicted compressive strains: (top) top targets; (bottom) bottom targets. The measured strains were bounded perfectly by the two predictions. While the test specimens were outside, the measured strains showed a trend very similar to the prediction using an RH of 83%. After the specimens were relocated to the structures laboratory, the measured strains 0.00000.00020.00040.00060.00080.00100.00120.00140.00160 100 200 300 400 500Compression StrainTime after Casting (days)RH = 83% (CHBDC)RH = 50% (CHBDC)Measured Strainsspecimens moved from field to lab0.00000.00020.00040.00060.00080.00100.00120.00140.00160 100 200 300 400 500Compression StrainTime after Casting (days)specimens moved from field to lab73  increased at a higher rate, and approached the prediction for an RH of 50%. Note that the prediction using RH = 50% assumed the concrete is at 50% RH during the entire time, so the measured creep and shrinkage strains were expected to be less than the prediction since the specimen spent the first 100 days in an environment with higher RH. The predictions from the CAC Handbook were compared with the predictions from the CHBDC in Fig. 46.   Fig. 46: Comparison of shrinkage and creep strain from CHDBC and CAC Handbook. The CAC Handbook predicted larger shrinkage and creep strains than the CHBDC method at both 50% RH and 83% RH. The difference between the two methods was more apparent at higher RH (83%). Different parameters were used in the two methods. In the CAC Handbook, seven modification factors were used (age at loading the type of curing, RH, ratio of fine to total aggregates, volume-to-surface area ratio, slump, air content, and cement content). On the other 0.00000.00020.00040.00060.00080.00100.00120.00140.00160 100 200 300 400 500Compression StrainDays After CastingRH = 50% (CHBDC)RH = 50% (CAC Handbook)RH = 83% (CHBDC)RH = 83% (CAC Handbook)74  hand, the CHBDC only took into account the RH and the volume-to-surface area ratio. Both methods did not present clear procedure to account for changes in RH during the life of the concrete member. The parameters used in the two methods for predicting the longitudinal strains of the test specimens are summarized in Table 10. Table 10: Summary of parameters used for shrinkage and creep prediction.  CHDBC CAC Strength of Concrete at 28 days 58.7 MPa Elastic Modulus of Concrete 30550 MPa Ultimate Strength of Strands 1860 MPa Effective Strength of Strands 744 MPa Elastic Modulus of Strands 195000 MPa Volume-to-Surface Area – Middle 71.6 mm Volume-to-Surface Area – End 75.7 mm RH – Outdoor 83% RH – Indoor 50% Slump  220 mm Air Content  4.3% Cement Content  330 kg/m3 Fine to Total Aggregates  0.50  The time function also varied in both methods. In the CAC Handbook, the time function predicted the percentage of an ultimate strain based solely on time and curing methods. On the other hand, the time function used in the CHBDC was based on RH, volume-to-surface area ratio, and time. The CHBDC suggested that when the RH and the volume-to-surface area ratio are high, creep and shrinkage strains developed slower along with a lower ultimate strain. 75  Even though the CHBDC method considered fewer parameters than the CAC Handbook, the CHBDC method applied a more complicated time function to capture the effect of RH and volume-to-surface area ratio. In the case of the test specimens, the CHBDC generated an almost perfect prediction of the creep and shrinkage strains. The predicted values for both methods are available in Appendix D. 76  5 Anchorage Test Results 5.1 Overview This chapter presents the results from the anchorage tests. The test specimens were separated into two types: Type T specimens (with transverse stirrup hooks) and Type L (with longitudinal stirrup hooks). The first set of specimens (T1 and L1) was tested at a target longitudinal strain of +0.0011, and the second set of specimens (T2 and L2) was tested at a target longitudinal strain of +0.0022. Specimen T2 was accidentally destroyed near the end of Phase 1 and therefore no useful data was available from that test. Section 5.2 summarizes the measured longitudinal strains of each of the three phases of the tests: Phase 1 – application of flexural tension force, Phase 2 – repeated application of diagonal compression force within the elastic range of the stirrups, and Phase 3 – repeated application of diagonal force after yielding of the stirrups. Section 5.3 summarizes the measured stirrup strains and stirrup slip (including any stirrup anchorage slip) that occurred during the tests. A detail summary of the procedure and observations during each test is documented in Appendix E. 5.2 Longitudinal Strains The change in longitudinal strain of the flange was monitored from the time the concrete specimens were cast to the end of the experiments. When the prestressing strands were released during construction, a compressive strain of about -0.0004 was experienced by the specimens (see Table 1). Over the 14 months that the specimens were stored before testing, creep and shrinkage strain developed as described in Chapter 4. At the time of testing, the total longitudinal compressive strain due to prestressing, creep, and shrinkage was approximately -0.0011 in all the specimens. Normally when an engineer evaluates a bridge, they do not include the additional compressive 77  strain due to creep and shrinkage in their estimate of the longitudinal strain. Thus in this chapter, only the initial strain generated by the release of the prestressing strands will be included in the reported longitudinal strains. The longitudinal strain measured during the anchorage tests will be referred to as the “additional longitudinal strain” while the longitudinal strain including the initial strains, shown in Table 11, will be referred to as the “total longitudinal strain.” Table 11: Summary of initial longitudinal strains due to prestressing. Test Initial Long. Strain T1 -0.00036 L1 -0.00039 L2 -0.00040  In Phase 1 of the anchorage tests, the longitudinal strain of the specimens was increased by applying an axial tension force to the 16 prestressing strands. Subsequently, the test specimen experienced additional longitudinal strain as a diagonal compression force was applied to the specimen during Phase 2 (prior to stirrup yielding) and Phase 3 (after stirrup yielding). The longitudinal strain was measured over a gauge length of 750 mm along the middle of the flange of the specimen. As the increase in longitudinal strain due to the diagonal compression force was not uniform along the specimen, the measured crack widths were also used to estimate the variation of longitudinal strain along the flange in Phase 2.  5.2.1 Phase 1: Application of Flexural Tension Force In this phase, the specimens were pulled by two hydraulic actuators to simulate a flexural tension force. The forces exerted by the hydraulic actuators were kept constant for the subsequent phases and the additional longitudinal strain of the flange was measured. 78  The horizontal tension force in Test T1 and L1 was limited to 1570 kN, while the horizontal tension force in Test L2 was increased to 1675 kN to achieve a larger longitudinal strain in the specimen. Fig. 47 shows the relationship between the horizontal axial forces and the longitudinal strains measured on the flange for tests T1, L1, and L2; the longitudinal strains presented were the averages measured on the two sides of the flange in each specimen. 79     Fig. 47: Phase 1 horizontal applied tension force versus measured additional longitudinal strain: (top) Test T1; (middle) Test L1; (bottom) Test L2. 0200400600800100012001400160018000.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030Horizontal Force (kN)Additional Longitudinal StrainTest T10200400600800100012001400160018000.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030Horizontal Force (kN)Additional Longitudinal StrainTest L10200400600800100012001400160018000.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030Horizontal Force (kN)Additional Longitudinal StrainTest L280  From the axial force versus additional longitudinal strain plot shown in Fig. 47 (top), it can be seen that the concrete in Specimen T1 cracked at an additional longitudinal strain of approximately +0.0003. Some residual strain was observed after unloading the specimen due to the fact that the concrete cracks did not fully close up after unloading. After the initial cycle, the concrete cracked opened at a lower longitudinal strain of approximately +0.0002. During the final (25th), the additional longitudinal strains of the specimen on the two faces of the flange were recorded as +0.0017 and +0.0016. Thus the maximum average longitudinal strain recorded during Phase 1 was +0.0017. In Test L1, the specimen was loaded for 20 cycles, and the target horizontal force was kept the same as Test T1 (1570 kN). The additional longitudinal strain when concrete first cracked during the initial cycle was observed to be +0.0002. The residual strain after unloading was larger than Test T1. It is believed that the uneven stressing (using wedge anchors) of the 16 prestressing strands on to the steel plates might have caused some of the prestressing strands to experience larger loads, causing them to go into the nonlinear range. This resulted in larger residual strain as well as some bending of the specimen. After the initial 10 cycles, the difference in stiffness on both sides of the specimen became less noticeable. It is believed that this was due to the forces in the prestressing strands becoming more uniform. The expected bilinear behaviour can be observed in the last 10 cycles. The maximum additional longitudinal strains measured during the 20th cycle were +0.0014 and +0.0015, on each face of the specimen. However, the maximum average additional longitudinal strain was recorded as +0.0016 during the 15th cycle. In Test L2, the target horizontal force was increased to 1675 kN, and the specimen was loaded for 20 cycles. The additional longitudinal strain when the concrete first cracked was observed in the 81  initial cycle at approximately +0.0002. Significant nonlinear behaviour of the prestressing strands was indicated by the residual strain, which was larger than the previous two tests. Similar to Test L1, the specimen eventually showed the expected bilinear behaviour as the specimen was subjected to more cycles. During the final cycle, the additional longitudinal strains on both sides of the flange had increased to +0.0026 and +0.0025. After unloading at the end of the 20th cycle, the residual additional longitudinal strains were +0.0001 and +0.0004 on the two sides of the flange. The maximum average additional longitudinal strain was recorded to be +0.0026 during the 10th cycle. The following table summarizes the initial longitudinal strain (due to the release of the prestressing), the maximum measured additional longitudinal strain, and the maximum total longitudinal strain of each test. Table 12: Summary of longitudinal strains in Phase 1. Test Initial Long. Strain Maximum Measured Additional Long. Strain Maximum Total Long. Strain T1 -0.00036 0.00164 0.00128 L1 -0.00039 0.00161 0.00122 L2 -0.00040 0.00262 0.00222  The total longitudinal strain (𝜀𝑥 ) of the concrete specimen subjected to axial tension can be estimated from: 𝜺𝒙 =𝑻 − 𝒇𝒑𝟎𝑨𝒑𝑬𝒑𝑨𝒑 + 𝜶𝑬𝒄𝑨𝒄 (16) 82  where 𝑇  = the applied axial tension force, 𝑓𝑝0  = prestressing stress when the strain in the surrounding concrete is zero, 𝐴𝑝  = cross-sectional area of prestressing strands, 𝐸𝑝  = elastic modulus of prestressing strands, 𝛼 = ratio of the concrete contribution to the axial stiffness to the theoretical uncracked concrete stiffness, 𝐸𝑐  = elastic modulus of concrete, 𝐴𝑐  = cross-sectional area of concrete. When the concrete is uncracked, 𝛼 = 1.0, while after cracking 𝛼 would be less than 1.0. Eq. 16 can be rearranged into the slope-intercept form of 𝑦 = 𝑚𝑥 + 𝑏, where 𝑚 is the slope and 𝑏 is the y intercept as follows: 𝑻 = (𝑬𝒑𝑨𝒑 + 𝜶𝑬𝒄𝑨𝒄) ∙ 𝜺𝒙 + 𝒇𝒑𝟎𝑨𝒑 (17) By relating Eq. 17 to the plots of horizontal force versus total longitudinal strain in Fig. 48, the prestressing force when the strain in the surrounding concrete was zero ( 𝑓𝑝0𝐴𝑝 ), and the experimentally measured axial stiffness which included the effect of tension stiffening (𝐸𝑝𝐴𝑝 +𝛼𝐸𝑐𝐴𝑐) were determined by drawing a best fit line along the loading curve after cracking; they are represented respectively by the y-intercept and the slope of this best fit line. 83     Fig. 48: Phase 1 horizontal force versus measured total longitudinal strain with bilinear best fit lines: (top) Test T1; (middle) Test L1; (bottom) Test L2. 020040060080010001200140016001800-0.0005 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025Horizontal Force (kN)Total Longitudinal StrainTest T1EcAc+EpApEpAp+αEcAc020040060080010001200140016001800-0.00050 0.00000 0.00050 0.00100 0.00150 0.00200 0.00250Horizontal Force (kN)Total Longitudinal StrainTest L1EcAc+EpApEpAp+αEcAc020040060080010001200140016001800-0.00050 0.00000 0.00050 0.00100 0.00150 0.00200 0.00250Horizontal Force (kN)Total Longitudinal StrainTest L2EcAc+EpApEpAp+αEcAc84   The variable 𝛼  represents the ratio of the concrete contribution to the axial stiffness to the theoretical uncracked concrete stiffness. Similarly, the axial stiffness of the specimen before cracking (𝐸𝑝𝐴𝑝 + 𝐸𝑐𝐴𝑐) can be determined by examining the slope of the uncracked loading curve. The two best fit lines of each test were drawn on the last cycle of each test to ensure that the forces amongst the prestressing strands were then distributed evenly. Noise in the data was also removed in these plots (see Fig. 48). The 𝑓𝑝0𝐴𝑝 in Test L2 might be larger than the value determined by the best fit line because this analysis excluded the presence of residual strain due to the nonlinear behaviour of the prestressing strands. Table 13 summarizes the calculated (Theo.) parameters and the parameters determined from the best fit lines in each test (Exp.).  Table 13: Summary of parameters calculated from bilinear best fit lines in Phase 1. Test EpAp+αEcAc (kN) EpAp (kN) α fp0Ap (kN) fpiAp (kN) Residual Strain Exp. Theo. Exp Exp. Theo. T1 464000 309000 0.05 988 1178 0.00002 L1 555000 309000 0.08 1018 1178 0.00006 L2 410000 309000 0.03 930 1178 0.00032  The value of 𝛼 was found to vary between 0.03 and 0.08, while in practice 𝛼 is normally neglected for simplicity (assumed to be zero). The prestressing force (𝑓𝑝0𝐴𝑝) determined by the best fit line was lower than the initial decompression force 0.4 𝑓𝑝𝑢𝐴𝑝 due to creep and shrinkage of concrete. 85  Using the experimental value of 𝑓𝑝0𝐴𝑝 and 𝐸𝑝𝐴𝑝 + 𝛼𝐸𝑐𝐴𝑐, the total longitudinal strain 𝜀𝑥 can be predicted using Eq. 16, and the results are shown in the following table.  Table 14: Predicted and experimental total longitudinal strain in Phase 1. Test Total Long. Strain Pred. Exp. T1 0.00125 0.00128 L1 0.00100 0.00119 L2 0.00182 0.00219  It is believed that the measured longitudinal strains were somewhat larger than predicted in specimens L1 and L2 because the prestressing strands went into the nonlinear range. 5.2.2 Phase 2 and Phase 3: Diagonal Loading Phase 2 and Phase 3 involves the application of an axial compression force on the diagonal face of the web of the specimen. This force was applied at an angle of about 30° to the longitudinal axis of the member. The axial tension on one end of the specimen was held constant, while the axial tension on the other end increased to balance the longitudinal component of the diagonal force. Phase 2 includes the cycles of loading up to about the stirrup yielding, while Phase 3 involves additional cycles beyond stirrup yielding. As the diagonal force was increased, the longitudinal component of the diagonal force increased the longitudinal strain of the flange. The total longitudinal strain at any level of applied diagonal force 𝐷 can be estimated from the following: 86  𝜺𝒙 =𝑻 + 𝑫 𝐜𝐨𝐬 𝟑𝟎° − 𝒇𝒑𝟎𝑨𝒑𝑬𝒑𝑨𝒑 + 𝜶𝑬𝒄𝑨𝒄 (18) where cos 30° is the estimate of the horizontal component of the diagonal force. The longitudinal strain was predicted at stirrup yielding with Eq. 18 using the experimentally determined values for 𝑓𝑝0𝐴𝑝 and 𝐸𝑝𝐴𝑝 + 𝛼𝐸𝑐𝐴𝑐. The results are compared with the measured total longitudinal strain when the stirrup first reached the predicted yielding force in Table 15. Table 15: Predict and experimental total longitudinal strain at initial yielding of stirrups during first loading cycle up to D = 320 kN. Test Total Long. Strain Pred. Exp. T1 0.00185 0.00175 L1 0.00149 0.00162 L2 0.00224 0.00242  In Test T1, the experimental longitudinal strain was 5.4% lower than the predicted value. However, in Test L1 and L2, the experimental values were larger than the predicted values by 8.7% and 8.0%, respectively. The tendency for the prestressing strands to go into the nonlinear range due to an uneven distribution of force in the prestressing strands, previously shown in the force-strain plots for Test L1 and L2 in Fig. 47, produced larger longitudinal strain than predicted. Table 16 summarizes the maximum measured longitudinal strains during Phase 2 of the tests.  87  Table 16: Summary of longitudinal strains at the end of Phase 2. Test Initial Long. Strain Maximum Measured Additional Long. Strain Maximum Total Long. Strain T1 -0.00036 0.00217 0.00181 L1 -0.00039 0.00206 0.00167 L2 -0.00040 0.00302 0.00262  As the applied diagonal force was increased in Phase 3 (after yielding of stirrups), the longitudinal strains increased further as shown in Table 17. Table 17: Predicted and experimental total longitudinal strain when first reaching the indicated maximum diagonal force. Test Max. Diagonal Force (kN) Total Long. Strain Pred. Acc. Resid.*  Exp. T1 480 0.00215 0.00156 0.00311 L1 500 0.00178 0.00056 0.00222 L2 440 0.00243 0.00030 0.00283 *Accumulated residual strain prior to the start of the last testing day. In Phase 3, the specimens were loaded up to a different maximum diagonal force. Along with the parameters predicted from the best-fit lines, the predicted total longitudinal strain was calculated using Eq. 18. These values were compared with the experimental total longitudinal strains from the initial cycle at the maximum diagonal force. The experimental values were much larger than the predicted values because the experimental values included the total residual longitudinal strains from previous test days. As shown in Table 17, the residual longitudinal strain accumulated at the end of each test day, which was added to the longitudinal strain on the next test day. However, these residual longitudinal strains may have reduced between each test day (i.e., due to strain recovery at night). Therefore, the overall longitudinal strains might be lower than the values 88  reported above. Generally, the experimental longitudinal strains were larger than the predicted values. The residual longitudinal strain in Test T1 was much larger than the other tests because Test T1, being the first test, was completed over 15 separate days and any reduction of the residual strain between test days were unaccounted for. The maximum measured longitudinal strains at the end of Phase 3 are summarized in Table 18. Table 18: Summary of longitudinal strains in Phase 3. Test Initial Long. Strain Maximum Measured Additional Long. Strain Maximum Total Long. Strain T1 -0.00036 0.00355 0.00319 L1 -0.00039 0.00282 0.00243 L2 -0.00040 0.00338 0.00298 5.2.3 Estimating Stirrup Strains from Cracks The longitudinal strain recorded throughout the experiment was a measure of the average longitudinal strain along a gauge length of 750 mm in the centre of each of the two faces of each specimen. However, because only the reaction end of the prestressing strands could carry the additional horizontal force from the diagonal compression force, the specimen experienced an increase in axial force only on one end. The maximum longitudinal strains measured in Phase 2 and Phase 3, which was an average value along the gauge length, did not give information about the aforementioned variation in longitudinal strain along this length. Crack width measurements were used to investigate the variation in longitudinal strain along the flange of the specimen. The crack widths were measured on one side of the flange throughout the 89  experimental program. The widths were measured at the top and bottom edge of the flange and their locations were recorded. The longitudinal strains at the top edge, bottom edge on each face of the specimen were estimated by dividing the crack width by a length based on the distances between the cracks. This distance was taken as the sum of half the distance from the crack on the left to half the distance to the crack on the right. The resulted longitudinal strains did not account for the strain in the concrete between the cracks. The values of these longitudinal strains are presented in Appendix F. The resulting estimated strains in Test T1 are plotted in Fig. 49 at three levels of diagonal compression force (0, 160 kN, and 320 kN). Most apparent at 320 kN, the figure shows that a strain larger than the measured average value was achieved on one end of the specimen where the horizontal component of the diagonal compression force was transferred to the fixed support through the prestressing strands. 90     Fig. 49: Longitudinal strain based on crack widths in Test T1 at diagonal compression force of (top) 0 kN, (middle) 160 kN, and (bottom) 320 kN. -0.00050.00000.00050.00100.00150.00200.00250.00300.00350.00400 200 400 600 800 1000 1200 1400Longitudinal StrainPosition along the specimen (mm)TopBottomMeasuredD = 0 kN-0.00050.00000.00050.00100.00150.00200.00250.00300.00350.00400 200 400 600 800 1000 1200 1400Longitudinal StrainPosition along the specimen (mm)D = 160 kN0.00000.00050.00100.00150.00200.00250.00300.00350.00400 200 400 600 800 1000 1200 1400Longitudinal StrainPosition along the specimen (mm)D = 320 kN91  5.3 Stirrup Slip Slip and strain were recorded and plotted to monitor any pull-out behaviour of the stirrups. Slip, in this experiment refers to the change in distance from a point on the stirrup 50 mm away from the surface of the web to the surface of the web, or the change in distance ∆𝐵𝐶̅̅ ̅̅  (see Fig. 50); the surface acts as a reference point and as the stirrups are elongated or pulled-out, the point on the stirrup will move away from the surface of the specimen. The strain of the stirrup was simultaneously recorded by measuring the change in distance between two points A and B (see Fig. 50) along each of the four fixed stirrups.  Fig. 50: Locations of stirrups and LVDTs. Shown in Fig. 50, the stirrups were debonded along the height of the web (𝐶𝐷̅̅ ̅̅ = 317𝑚𝑚). Theoretically, the rate at which the slip increases with the measured strain on the stirrup will be proportional to the debonded length. In other words, when there is no pull-out, the strain measured along the exposed section of the stirrups will equal to the strain measured from the bottom of the D 92  web to Point B. This can be determined by dividing the slip ∆𝐵𝐶̅̅ ̅̅  by the initial distance 𝐵𝐷̅̅ ̅̅  of 367 mm. The strain of the stirrups (𝜀𝑦) can be represented by the following equation. 𝜺𝒚 =∆𝑨𝑩̅̅ ̅̅𝑨𝑩̅̅ ̅̅=∆𝑩𝑪̅̅ ̅̅𝑩𝑫̅̅̅̅̅ (19) where ∆𝐴𝐵̅̅ ̅̅𝐴𝐵̅̅ ̅̅ = the stirrup strain measured along the exposed section of the stirrups, ∆𝐵𝐶̅̅ ̅̅  = slip, and 𝐵𝐷̅̅ ̅̅  = the debonded length in the specimen, which also includes the 50 mm of stirrup extruding from the surface of the web to point B (see Fig. 50). From here, Eq. 19 can be arranged as follows. 𝒅𝒆𝒃𝒐𝒏𝒅𝒆𝒅 𝒍𝒆𝒏𝒈𝒕𝒉 =𝒔𝒍𝒊𝒑𝒔𝒕𝒓𝒂𝒊𝒏 (20) When the hooks of the stirrups begin to pull-out, the debonded length of the stirrup will increase, thus slip will increase at a higher rate than the strain in the stirrups. The new debonded length can be determined with the recorded values of slip and strain on each stirrup using Eq. 20. 5.3.1 Phase 2: Diagonal Loading – Elastic Stirrups Slip was plotted against the stirrup strain for each of the tests. Fig. 51 shows the slip-strain interaction in Phase 2 for Test T1, L1, and L2. The theoretical initial debonded length of 367 mm is represented as the slope of the diagonal black line “Theo. Initial Debonded Length”. The slopes of the initial cycle and the final cycle of each test are represented by a bolded black line and a dashed black line, respectively. 93     Fig. 51: Slip-strain interaction of Phase 2: (top) Test T1; (middle) Test L1; (bottom) Test L2. 0.00.20.40.60.81.01.21.41.61.82.00.0000 0.0010 0.0020 0.0030 0.0040 0.0050Slip (mm)Strain of StirrupTest T1Final Cycle (Phase 2)Initial Cycle (Phase 2)0.00.20.40.60.81.01.21.41.61.82.00.0000 0.0010 0.0020 0.0030 0.0040 0.0050Slip (mm)Strain of StirrupTest L10.00.20.40.60.81.01.21.41.61.82.00.0000 0.0010 0.0020 0.0030 0.0040 0.0050Slip (mm)Strain of StirrupTest L294      The maximum slips and strains measured from each test varied due to differing amount of yielding of the stirrups at the end of Phase 2. However, only the amount of slip per strain was needed to monitor the pull-outs of the stirrup hooks. During the initial cycle, at a diagonal compression force of 80 kN, the debonded lengths was calculated using Eq. 20. During the final cycle of Phase 2, because the stirrups had begun to yield, the slip-strain relationship began to behave non-linearly and accumulate residual slip and strain. At this point, since the beginning of each cycle did not begin at the origin (zero slip and zero strain), Eq. 20 was altered as follows to account for the accumulated residual slip and strain from previous cycles. 𝒅𝒆𝒃𝒐𝒏𝒅𝒆𝒅 𝒍𝒆𝒏𝒈𝒕𝒉 =𝒔𝒍𝒊𝒑 − 𝒂𝒄𝒄𝒖. 𝒓𝒆𝒔𝒊𝒅. 𝒔𝒍𝒊𝒑𝒔𝒕𝒓𝒂𝒊𝒏 − 𝒂𝒄𝒄. 𝒓𝒆𝒔𝒊𝒅. 𝒔𝒕𝒓𝒂𝒊𝒏 (21) Table 19 summarizes the calculated debonded lengths at the initial cycle (at a diagonal compression force of 80 kN) and the final cycle (at a diagonal compression force of 320 kN) during Phase 2. Table 19: Summary of debonded length at in Phase 2. Test Debonded Length (mm) Initial Cycle Final Cycle T1 370 403 L1 206 379 L2 289 395 Theo. 367  The debonded length during the initial cycle observed during Test T1 agreed with the theoretical debonded length of 367 mm. However, the debonded length during the initial cycle in Test L1 and L2 were smaller than the theoretical debonded length. During the final cycle of Phase 2, the 95  debonded lengths calculated from the three tests had increased to approximately match the expected theoretical debonded length. During the final cycle in Phase 2, the experimental debonded lengths for Test T1, L1, and L2 are 9.8%, 3.3%, and 7.6%, respectively, larger than the theoretical debonded length of 367 mm. 5.3.2 Phase 3: Diagonal Loading -Yielding Stirrups In Phase 3, the longitudinal forces were applied to the prestressing strands similar to Phase 1 and Phase 2. In addition, the diagonal compression force was further increased to load the stirrups beyond yielding point. The corresponding slip-strain interactions are shown in the following figures. Each figure represents one of the three tests, and each figure is separated into two plots: one for the initial set of cycles, and one for the final set of recordable cycles during Phase 3. If all the cycles during Phase 3 are shown in one plot, the detail of each cycle will be obscured by the large amount of strains and slips caused by the yielding of the stirrups. In these plots, the additional strain and additional slip of the stirrups were plotted on the x-axis and y-axis, respectively, instead of the actual accumulated stirrup strains and slips. The theoretical initial debonded length is represented by the slope of the black line on each plot, and the initial and final cycle during Phase 3 are also represented by a bolded black line and a dashed black line, respectively. 96    Fig. 52: Slip-strain interaction in Phase 3 of Test T1 at diagonal compression force of (top) 320 kN and (bottom) 420 kN. 0.00.10.20.30.40.50.60.70.80.90.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030Additional Slip (mm)Additional Strain in Stirrup at T = 320 kNT = 320 kNInitial Cycle (Phase 3)0.01.02.03.04.05.06.00.0000 0.0050 0.0100 0.0150 0.0200Additional Slip (mm)Additional Strain in Stirrup at T = 420 kNT = 420 kNFinal Cycle (Phase 3)97    Fig. 53: Slip-strain interaction in Phase 3 of Test L1 at diagonal compression force of (top) 400 kN and (bottom) 500 kN. 0.01.02.03.04.05.06.00.000 0.005 0.010 0.015 0.020Additional Slip (mm)Additional Strain in Stirrup at T = 400 kNT = 400 kNInitial Cycle (Phase 3)0.01.02.03.04.05.06.00.000 0.005 0.010 0.015 0.020Additional Slip (mm)Additional Strain in Stirrup at T  = 500 kNT = 500 kNFinal Cycle (Phase 3)98    Fig. 54: Slip-strain interaction in Phase 3 of Test L2 at diagonal compression force of (top) 400 kN and (bottom) 440 kN. In Test L2, due to large displacements and the limitation of the recording instruments, the LVDTs were recalibrated several times throughout Phase 3. Therefore, some data were not recorded, and the remaining data were connected by estimating the slopes from the preceding data points. This 0.01.02.03.04.05.06.00.000 0.005 0.010 0.015 0.020Additional Slip (mm)Additional Strain in Stirrup at T = 400 kNT = 400 kNInitial Cycle (Phase 3)0.01.02.03.04.05.06.00.000 0.005 0.010 0.015 0.020Additional Slip (mm)Additional Strain in Stirrup at T = 440 kNT = 440 kNFinal Cycle (Phase 3)99  is shown in Fig. 54 (top) by the straight lines connecting different parts of the data. However, the changes in slopes can still be observed before and after each recalibration. By examining the slopes, the debonded lengths of the initial and final cycle of Phase 3 are summarized in the following table. Table 20: Summary of debonded length in Phase 3. Test Debonded Length (mm) Initial Cycle Final Cycle T1 415 490 L1 479 481 L2 406 413 Theo. 367  At the end of Phase 3, according to Table 20, the debonded lengths remained approximately the same from the first to the last cycle. The experimental debonded length during the final cycle of Test T1, L1, and L2 are 33%, 31%, and 13%, respectively, larger than the theoretical debonded length. In conclusion, based on the debonded length estimated during the final cycle of each of the three anchorage tests, non-code-compliant hooks perform similarly to code-compliant hooks. 100  6 Conclusion A non-code-compliant stirrup anchorage detailing is commonly used to reduce construction time of concrete I-girder bridges. In this detailing, the lower hooks of the stirrups are oriented parallel to the longitudinal prestressing strands, and thus do not meet the specifications in the Canadian Highway Bridge Design Code CSA S6-06 (CHBDC) which states that “transverse reinforcement provided for shear shall be anchored at both ends by… for No. 15 and smaller bars … a standard hook, as specified in Clause 8.14.1.1., around longitudinal reinforcement.” A few previous studies have compared different stirrup hook arrangements, but none of these have addressed the specific issue of the effect of stirrup hooks that are bent around the longitudinal reinforcing bars rather than being oriented parallel to the bars. In the current study, the performance of stirrup hooks parallel to the longitudinal reinforcement were investigated by conducting full-scale tests of partial sections of concrete I-girders. An analysis of an example bridge, i.e., the “Mad River Bridge,” was done to determine the demands on typical concrete I-girders and establish testing parameters such as the longitudinal strain of the flexural tension flange. The example bridge has five simply supported Type 5 I-girders. Three load scenarios were used in the analysis: serviceability limit states (SLS), ultimate limit state (ULS), and overload (at which the I-girder bridge is expected to fail in shear). Three different methods of shear analysis were used: 2006 CHBDC, Esfandiari and Adebar procedure, and Response-2000. The analysis of the example bridge demonstrated that large stirrup stress can occur throughout the span of the example bridge – not just near the support where the longitudinal strain of the flexural tension flange is small. The example bridge was found to have large stirrup 101  stresses at midspan where shear demand was thought to be low and the longitudinal strain of the flexural tension flange was as large as +0.0022. The experimental program involved specimens that simulated a small portion of full-scale Type 5 prestressed concrete I-girders. Each specimen consisted of a 1.4 m long portion of the flexural tension flange, with 16 prestressing strands, and a 300 mm high portion of the web with four pairs of stirrups. The test specimens were separated into two groups based on the orientation of the stirrup hooks: Type T (transverse hooks; code compliant) and Type L (longitudinal hooks; not code compliant). Six test specimens were constructed; however, only three tests were successfully completed: one Type T and two Type L specimens (T1, L1, and L2). In the test setup, the 16 prestressing strands were fixed at one end while the other end was pulled using two hydraulic actuators. The applied tension force simulated the flexural tension due to the bending moments applied to an I-girder. The diagonal force was applied by another hydraulic actuator pushing against the web at approximately 30° to the longitudinal axis of the specimen. The longitudinal component of the diagonal force was balanced by the prestressing strands connecting the fixed support, while the transverse component of the diagonal force was balanced by two pairs of stirrups that were also connected to a fixed support. The diagonal force generated additional longitudinal strain on one end of the flexural tension flange. Before the concrete specimens were cast, four pairs of Invar pins were installed on each of the specimens. The distance between each pair of pins were measured to determine the elastic strain due to prestressing (-0.0004) as well as the change in strain due to creep and shrinkage. The average longitudinal strain of the flexural tension flange prior to the anchorage test was -0.0011. 102  The anchorage tests include three phases: Phase 1 – gradual application of horizontal strain, Phase 2 – repeated application of diagonal force within the elastic range of the stirrups, and Phase 3 – repeated application of diagonal force after yielding of the stirrups. In Phase 1, an axial tension force of 1570 kN was applied in Test T1 and L1, and 1675 kN was applied in Test L2. The maximum measured longitudinal strains due to this tension force was +0.0016 for T1 and L1, and +0.0026 for L2.  These measured strains do not include the initial compressive strain from prestressing. Normally, the additional compressive strain due to creep and shrinkage is not included when estimating the axial strain of prestressed I-girder. Therefore, only the initial compressive strain of -0.0004 was added to the strains to determine the total strains of the flexural tension flange, which was +0.0012 for T1 and L1, and +0.0022 for L2. Note that in the example bridge, the maximum longitudinal strain of the tension flange in the regions where the stirrups were yielding was +0.0022. Phase 2 and Phase 3 involved the application of a diagonal compression force. At the end of Phase 2, the maximum measured total longitudinal strains of the flexural tension flange were +0.0018, +0.0017, and +0.0026 for Test T1, L1, and L2, respectively. At the end of Phase 3, these strains increased to +0.0032, +0.0024, and +0.0030. Test T1 had a much larger total longitudinal strain because as the first test, it was completed over 15 separate days of testing during which significant residual strain accumulated and any reduction of the residual strain between the test days (i.e., at night) were unaccounted for. The strain of the stirrups and the movement (slip) of the stirrups relative to the concrete web were measured during Phase 2 and 3 of the anchorage tests. If the debonded length of the stirrup did not 103  change, the increase in measured slip would be proportional to the increase in measured stirrup strain. Thus, debonding of the stirrups could be detected by observing the ratio of the change in slip to the change in strain of each stirrup, which is also equal to the debonded length. Based on the position of the slip measurement and the length of the stirrup initially debonded during construction, the initial debonded length was estimated to be 367 mm. After applying many cycles of the diagonal force, including about 100 cycles after yielding of the stirrups, the debonded lengths were measured to be 490 mm, 481 mm, and 413 mm for Test T1, L1, and L2, respectively. Note that the code compliant specimen T1 had the longest debonded length. Also, if the reinforcing bars were fully debonded to the corner of the hook, the debonded length would be 630 mm. Based on this result, it can be concluded that the non-code-compliant stirrup anchorage performed satisfactorily. It is speculated that the non-code-compliant anchorage performed slightly better than the code-compliant anchorage because there was a larger amount of contiguous concrete around the non-code-compliant hooks. Since the hooks of the code-compliant anchorage were located right underneath the longitudinal bars, and along with the higher ratio of steel to concrete, the concrete in this zone was thinner and more irregular (as oppose to the non-code-compliant anchorage where the hooks were oriented longitudinally). This is analogous to an insufficient concrete cover or a member that is too thin, and the concrete might split more easily. The brittleness of high strength concrete can also exacerbate this effect. Therefore, the weakened concrete in this zone might have allowed the code-compliant hooks to move more easily than the non-code-compliant design.   104  Bibliography [1]  A. Esfandiari and P. Adebar, "Shear Strength Evaluation of Concrete Bridge Girders," ACI Structural Journal, pp. 416-426, July-August 2009.  [2]  E. C. Bentz and M. P. Collins, "Development of the 2004 Canadian Standards Association (CSA) A23.3 shear provisions for reinforced concrete," Canadian Journal of Civil Engineering, 33(5), pp. 521-534, 2006.  [3]  J. L. G. Marques and J. O. Jirsa, "A Study of Hooked Bar Anchorages in Beam-Column Joints," ACI Journal, 72(5), pp. 198-209, 1975.  [4]  N. S. Anderson and J. A. Ramirez, "Detailing of Stirrup Reinforcement," ACI Journal, 86(5), pp. 507-515, 1989.  [5]  Bridge Mad River Clearwater, B.C., Con-Force, 2005.  [6]  Ministry of Transportation Southern Interior Region, Mad River Bridge Deck - Sheet 1, British Columbia: Ministry of Transportation and Infrastructure, 2005.  [7]  Ministry of Transportation and Highways Bridge Engineering Branch, Standard Pretressed Concrete I Beams, British Columbia: Ministry of Transportation and Infrastructure, 2006.  [8]  Canadian Standards Association, Design of Concrete Structures, CSA A23.3-04 ed., A23.2-04, Ed., Mississauga, Ontario: Canadian Standards Association, 2004.  [9]  Canadian Standards Association, Canadian Highway Bridge Design Code, CAN/CSA-S6-06 ed., Missisauga, Ontario: Canadian Standards Association, 2006.  105  [10]  Cement Association of Canada, CAC Concrete Design Handbook, Ottawa, Ontario: Cement Association of Canada, 2006.  [11]  E. Bentz, "Welcome to Response-2000," October 2011. [Online]. Available: http://www.ecf.utoronto.ca/~bentz/r2k.htm. [Accessed 31 October 2011].    106  Appendix A: Data from Example Bridge Analysis The results of the example bridge analysis in Chapter 2 are presented in these tables: 1. Table 21: Summary of Mad River Bridge analysis for SLS 2. Table 22: Summary of Mad River Bridge analysis for ULS 3. Table 23: Summary of Mad River Bridge analysis for overload. The methods for obtaining these numbers are present in Chapter 2, and the following figures in Chapter 2 are plotted based on these data: Fig. 15, Fig. 16, Fig. 17, Fig. 23, Fig. 24, Fig. 25, Fig. 26, Fig. 27, and Fig. 28. 107  Table 21: Summary of Mad River Bridge analysis for SLS. distance away from left support (mm)  x 0 1730 3494 6989 10483 13978 17472 Bending Moment (kNm)                 factored moment Mf 0 1666 3172 5690 7421 8418 8627 moment resistance (calculated) Mr 13318 13605 13898 14479 15060 15641 15723 moment resistance (Response-2000) Mr 14334 14694 14984 15558 16282 16931 17003 Longitudinal Stress (MPa)                 flexural stress of concrete at the bottom fbot -24.11 -20.02 -16.39 -10.52 -6.87 -5.30 -4.89 stress in prestress strands fp 1231 1256 1277 1312 1333 1342 1345 Shear Force (kN)                 factored shear Vf 932 932 846 675 506 341 179 shear resistance (E & A) Vr 2616 2616 2236 2236 2111 1668 1526 shear resistance (CHBDC) Vr 2898 2898 2446 2446 2446 1994 1859 shear resistance (Response-2000) Vr 2541 2541 2211 2346 2148 1715 1655 Shear Angle (degree)                 shear angle (E & A) θ 23.4 23.4 21.5 21.5 22.9 21.0 21.1 shear angle (CHBDC) θ 27.6 27.6 27.6 27.6 27.6 27.6 27.6 shear angle near top of web (Response-2000) θ 28.5 27.9 25.9 21.2 15.6 9.2 7.9 shear angle near bottom of web (Response-2000) θ 8.6 11.1 10.4 11.0 10.9 6.7 6.1 average shear angle in web (Response-2000) θ 18.5 19.5 18.2 16.1 13.2 8.0 7.0 Longitudinal and Stirrup Strain                 average longitudinal strain (E&A) εx -0.00056 -0.00044 -0.00038 -0.00020 -0.00009 -0.00010 -0.00010 average longitudinal strain (CHBDC) εx -0.00050 -0.00053 -0.00046 -0.00034 -0.00026 -0.00023 -0.00023 average longitudinal strain (Response-2000) εx -0.00035 -0.00031 -0.00028 -0.00024 -0.00021 -0.00019 -0.00020 longitudinal strain at flange (E&A) εxf -0.00112 -0.00088 -0.00076 -0.00040 -0.00018 -0.00021 -0.00019 longitudinal strain at flange (CHBDC) εxf -0.00100 -0.00107 -0.00092 -0.00067 -0.00052 -0.00047 -0.00045 longitudinal strain at flange (Response-2000) εxf -0.00070 -0.00059 -0.00050 -0.00034 -0.00025 -0.00021 -0.00020 maximum transverse strain (Response-2000) εz 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Curvature (rad/km)                 curvature ф -0.388 -0.306 -0.233 -0.116 -0.044 -0.014 -0.006 Stirrup Stress (MPa)                 maximum stirrup stress (Response-2000) fs 0.0 0.0 0.0 0.0 0.0 0.0 0.0 maximum stirrup stress at crack (Response-2000) fscrack 0.0 0.0 0.0 0.0 0.0 0.0 0.0 108  Table 22: Summary of Mad River Bridge analysis for ULS. distance away from left support (mm) x  0 1730 3494 6989 10483 13978 17472 Bending Moment (kNm)                 factored moment Mf 0 2364 4497 8082 10527 11826 11980 moment resistance (calculated) Mr 13177 13465 13758 14339 14920 15501 15583 moment resistance (Response-2000) Mr 13785 14083 14383 14950 15615 16224 16338 Longitudinal Stress (MPa)                 flexural stress of concrete at the bottom fbot -24.11 -18.04 -12.64 -3.75 1.91 4.61 5.16 stress in prestress strands fp 1231 1267 1299 1352 1385 1401 1404 Shear Force (kN)                 factored shear Vf 1328 1328 1211 976 747 523 304 shear resistance (E & A) Vr 2316 2316 1974 1799 1653 1209 1043 shear resistance (CHBDC) Vr 2472 2472 2065 2065 1942 1463 1332 shear resistance (Response-2000) Vr 2204 2204 1893 2058 1864 1497 1389 Shear Angle (degree)                 shear angle (E & A) θ 23.4 23.4 21.5 23.8 23.4 21.6 21.6 shear angle (CHBDC) θ 27.6 27.6 27.6 27.6 28.1 28.6 28.6 shear angle near top of web (Response-2000) θ 25.8 26.4 24.6 22.9 19.8 13.8 12.3 shear angle near bottom of web (Response-2000) θ 13.1 15.6 18.8 26.7 35.8 39.9 49.5 average shear angle in web (Response-2000) θ 19.5 21.0 21.7 24.8 27.8 26.8 30.9 Longitudinal and Stirrup Strain                 average longitudinal strain (E&A) εx -0.00060 -0.00041 -0.00030 -0.00003 0.00033 0.00055 0.00057 average longitudinal strain (CHBDC) εx -0.00046 -0.00046 -0.00035 -0.00017 -0.00006 -0.00003 -0.00003 average longitudinal strain (Response-2000) εx -0.00038 -0.00032 -0.00027 -0.00019 -0.00015 -0.00012 -0.00012 longitudinal strain at flange (E&A) εxf -0.00120 -0.00083 -0.00059 -0.00005 0.00066 0.00109 0.00113 longitudinal strain at flange (CHBDC) εxf -0.00091 -0.00091 -0.00070 -0.00035 -0.00013 -0.00006 -0.00006 longitudinal strain at flange (Response-2000) εxf -0.00077 -0.00060 -0.00042 -0.00016 -0.00001 0.00008 0.00007 maximum transverse strain (Response-2000) εz 0.00080 0.00076 0.00087 0.00039 0.00000 0.00010 0.00010 Curvature (rad/km)                 curvature ф -0.429 -0.288 -0.165 0.031 0.149 0.202 0.208 Stirrup Stress (MPa)                 maximum stirrup stress (Response-2000) fs 160.0 151.3 173.3 77.0 0.0 0.1 0.1 maximum stirrup stress at crack (Response-2000) fscrack 290.1 269.6 228.2 210.4 0.0 360.0 360.0 109  Table 23: Summary of Mad River Bridge analysis for overload. distance away from left support (mm)  x 0 1730 3494 6989 10483 13978 17472 Bending Moment (kNm)                 factored moment Mf 0 2940 5590 10056 13087 14675 14817 moment resistance (calculated) Mr 13318 13605 13898 14479 15060 15641 15723 moment resistance (Response-2000) Mr 13047 13357 13650 14721 15856 16674 16788 Longitudinal Stress (MPa)                 flexural stress of concrete at the bottom fbot -24.11 -16.42 -9.55 1.83 9.15 12.78 13.40 stress in prestress strands fp 1231 1277 1317 1385 1428 1449 1453 Shear Force (kN)                 factored shear Vf 1656 1656 1514 1230 953 683 420 shear resistance (E & A) Vr 2616 2616 2207 1822 1275 684 449 shear resistance (CHBDC) Vr 2898 2898 2446 2210 1353 921 793 shear resistance (Response-2000) Vr 2364 2531 2157 2210 1959 1584 1462 Shear Angle (degree)                 shear angle (E & A) θ 23.4 23.4 21.8 24.2 36.9 38.8 38.9 shear angle (CHBDC) θ 27.6 27.6 27.6 28.4 36.4 39.3 39.1 shear angle near top of web (Response-2000) θ 26.0 26.6 25.0 23.5 28.8 36.3 41.6 shear angle near bottom of web (Response-2000) θ 15.9 19.9 22.4 29.5 50.9 55.4 58.5 average shear angle in web (Response-2000) θ 20.9 23.2 23.7 26.5 39.9 45.9 50.0 Longitudinal and Stirrup Strain                 average longitudinal strain (E&A) εx -0.00056 -0.00033 -0.00018 0.00064 0.00095 0.00109 0.00110 average longitudinal strain (CHBDC) εx -0.00042 -0.00039 -0.00026 -0.00004 0.00053 0.00073 0.00072 average longitudinal strain (Response-2000) εx -0.00032 -0.00025 -0.00019 -0.00009 0.00005 0.00089 0.00087 longitudinal strain at flange (E&A) εxf -0.00112 -0.00066 -0.00035 0.00128 0.00191 0.00217 0.00219 longitudinal strain at flange (CHBDC) εxf -0.00085 -0.00078 -0.00052 -0.00008 0.00106 0.00147 0.00144 longitudinal strain at flange (Response-2000) εxf -0.00067 -0.00045 -0.00025 0.00007 0.00138 0.00221 0.00219 maximum transverse strain (Response-2000) εz 0.00112 0.00110 0.00129 0.00082 0.00111 0.00109 0.00087 Curvature (rad/km)                 curvature ф -0.376 -0.213 -0.067 0.172 0.953 1.433 1.415 Stirrup Stress (MPa)                 maximum stirrup stress (Response-2000) fs 224.1 224.6 259.0 175.1 221.9 217.4 174.0 maximum stirrup stress at crack (Response-2000) fscrack 378.4 377.9 400.0 400.0 400.0 400.0 400.0 110  Appendix B: Drawings of Test Specimen Appendix B presents the drawings of the test specimens with dimensions, shown in the following figures: 1. Fig. 55: Plan view of Type L test specimen with dimensions 2. Fig. 56: Cross section of Type L test specimen with dimensions 3. Fig. 57: Plan view of Type T test specimen with dimensions 4. Fig. 58: Cross section of Test T test specimen with dimensions.111   Fig. 55: Plan view of Type L test specimen with dimensions. 112   Fig. 56: Cross section of Type L test specimen with dimensions. 113   Fig. 57: Plan view of Type T test specimen with dimensions. 114   Fig. 58: Cross section of Test T test specimen with dimensions.115  Appendix C: Drawings of Test Setup The detail drawings of the anchorage test setup are presented in this Appendix in these following figures: 1. Fig. 59: Plan view of test setup 2. Fig. 60: Test setup component A: support-horizontal actuators 3. Fig. 61: Test setup component B: support-stirrups 4. Fig. 62: Test setup component C1: diagonal actuator-specimen 5. Fig. 63: Test setup component C2: diagonal actuator-support 6. Fig. 64: Test setup component D: prestressing strands-support. 116   Fig. 59: Plan view of test setup. 117   Fig. 60: Test setup component A: support-horizontal actuators.  118   Fig. 61: Test setup component B: support-stirrups. 119   Fig. 62: Test setup component C1: diagonal actuator-specimen.  120   Fig. 63: Test setup component C2: diagonal actuator-support. 121   Fig. 64: Test setup component D: prestressing strands-support.122  Appendix D: Measured and Predicted Values of Creep and Shrinkage Strains The following table shows all the predicted values of longitudinal strains due to prestressing, creep, and shrinkage. Two methods (CHBDC and CAC Handbook) were used, and the strains from each of the two cross sections (end cross section and middle cross section) are presented for each method at two different RH (50% and 83%). The measured strains for individual specimens are presented in Table 8 and Table 9 in Chapter 4. 123  Table 24: Summary of measured and predicted creep and shrinkage strains length of end section 1 (mm) L1 1059          length of middle section 2 (mm) L2 239                   age of test specimen (day) t 4 7 41 95 108 115 122 182 193 439 Average Measured Strains   strain at top target εtop 0.00032 0.00043 0.00054 0.00057 0.00072 0.00084 0.00086 0.00096 0.00097 0.00108 strain at bottom target εbot 0.00044 0.00059 0.00070 0.00076 0.00089 0.00103 0.00105 0.00116 0.00116 0.00124 Estimated Strains (83% RH)              CHDBC section 1 strain at top target εtop 0.00030 0.00043 0.00051 0.00054 0.00055 0.00055 0.00056 0.00059 0.00060 0.00065 CHDBC section 1 strain at bottom target εbot 0.00042 0.00061 0.00071 0.00074 0.00076 0.00076 0.00077 0.00081 0.00083 0.00089 CHDBC section 2 strain at top target εtop 0.00035 0.00051 0.00059 0.00062 0.00063 0.00064 0.00065 0.00068 0.00070 0.00075 CHDBC section 2 strain at bottom target εbot 0.00041 0.00059 0.00069 0.00073 0.00074 0.00075 0.00075 0.00079 0.00081 0.00087 RH = 83% (CHBDC) εtop 0.00031 0.00045 0.00052 0.00055 0.00056 0.00057 0.00058 0.00061 0.00062 0.00067 RH = 83% (CHBDC) εbot 0.00041 0.00060 0.00071 0.00074 0.00075 0.00076 0.00077 0.00081 0.00083 0.00089 CAC section 1 strain at top target εtop 0.00030 0.00042 0.00072 0.00085 0.00087 0.00088 0.00088 0.00093 0.00094 0.00100 CAC section 1 strain at bottom target εbot 0.00042 0.00057 0.00093 0.00108 0.00110 0.00111 0.00112 0.00117 0.00118 0.00126 CAC section 2 strain at top target εtop 0.00035 0.00048 0.00080 0.00093 0.00095 0.00096 0.00097 0.00102 0.00102 0.00109 CAC section 2 strain at bottom target εbot 0.00041 0.00056 0.00090 0.00105 0.00107 0.00108 0.00109 0.00114 0.00115 0.00122 RH = 83% (CAC Handbook) εtop 0.00031 0.00043 0.00073 0.00087 0.00088 0.00089 0.00090 0.00095 0.00095 0.00102 RH = 83% (CAC Handbook) εbot 0.00041 0.00057 0.00092 0.00107 0.00109 0.00110 0.00111 0.00117 0.00117 0.00125 Estimated Strains (50% RH)                       CHDBC section 1 strain at top target εtop 0.00030 0.00052 0.00075 0.00088 0.00091 0.00092 0.00094 0.00098 0.00099 0.00110 CHDBC section 1 strain at bottom target εbot 0.00042 0.00071 0.00100 0.00115 0.00118 0.00120 0.00122 0.00127 0.00128 0.00140 CHDBC section 2 strain at top target εtop 0.00035 0.00058 0.00084 0.00098 0.00100 0.00102 0.00103 0.00108 0.00109 0.00121 CHDBC section 2 strain at bottom target εbot 0.00041 0.00068 0.00096 0.00111 0.00114 0.00116 0.00118 0.00122 0.00124 0.00136 RH = 50% (CHBDC) εtop 0.00031 0.00053 0.00077 0.00090 0.00092 0.00094 0.00095 0.00100 0.00101 0.00112 RH = 50% (CHBDC) εbot 0.00041 0.00070 0.00099 0.00115 0.00118 0.00119 0.00121 0.00126 0.00127 0.00140 CAC section 1 strain at top target εtop 0.00030 0.00046 0.00091 0.00111 0.00113 0.00115 0.00116 0.00122 0.00123 0.00132 CAC section 1 strain at bottom target εbot 0.00042 0.00063 0.00114 0.00135 0.00138 0.00139 0.00141 0.00148 0.00149 0.00159 CAC section 2 strain at top target εtop 0.00035 0.00053 0.00099 0.00119 0.00122 0.00123 0.00124 0.00131 0.00132 0.00142 CAC section2 strain at bottom target εbot 0.00041 0.00062 0.00111 0.00132 0.00135 0.00136 0.00137 0.00144 0.00145 0.00155 RH = 50% (CAC Handbook) εtop 0.00031 0.00048 0.00093 0.00112 0.00115 0.00116 0.00117 0.00124 0.00125 0.00134 RH = 50% (CAC Handbook) εbot 0.00041 0.00063 0.00113 0.00135 0.00137 0.00139 0.00140 0.00147 0.00148 0.00159 124  Appendix E: Anchorage Tests Summary This appendix summarizes the procedures and observations of Test T1, L1, T2, and L2. Test T1, L1, and L2 were fully completed, and Test T2 was not completed because the test specimen was destroyed by accident during the test. Discussion on the data and observations are present in Chapter 5. E.1 Summary of Test T1 Specimen T1 was the first of the six specimens to be tested. In this specimen, since the stirrups hooks are bent around longitudinal bars, specimen T1 simulates a code-compliant I-girder. Three phases were conducted: (1) gradual application of horizontal strain, (2) repeated application of diagonal force within the elastic range of stirrup strength, and (3) repeated application of diagonal force after the stirrups have yielded. After the test was completed, eight of the prestressing strands were cut, and the same specimen (with half the number of prestressing strands) was tested with the horizontal actuators (similar to Phase 1) to find out if a larger longitudinal strain can be achieved with fewer strands. This was done to see if it is viable to test some of the other specimens (which were already built) at a much greater longitudinal in future tests. However, the test had proved that decreasing the number of strands from the current specimens was not viable. In this test, various problems were encountered. Some problems were addressed immediately during the test, while other problems were attended to after this test and before subsequent tests. E.1.1 Pre-Test Prior to the preliminary test, a pre-test was conducted to check the response of the pressure system (two longitudinal hydraulic actuators), and to observe how well the load maintainer can sustain a 125  constant pressure in the pair of horizontal actuators. No specimens were placed in the test setup, and instead, four strands were connected to the test setup between the reaction support and the actuator support. The four strands were attached at the four corner slots at both supports to retain symmetry in the system. The pressure in the two horizontal hydraulic actuators was increased to 1010 psi, and this pressure was maintained by the load maintainer for five hours. Data was recorded by a digital pressure gauge, a linear variable differential transformer (LVDT) on one of the four strands, and a data acquisition system connected to a computer. The digital pressure gauge measured the pressure in the horizontal actuators, and the LVDT measured the change in length along a one-meter length in one of the four strands. The following figure shows the pressure in the actuators and the change in length in the strand throughout the five-hour period.  Fig. 65: Pre-test response. The pressure in the actuators is also plotted on a secondary scale on the right of the plot. The “predicted pressure” is the pressure required to produce the change in length in the strand at a given time, which is related by the following equation: -2000200400600800100012000.02.04.06.08.010.012.00 5,000 10,000 15,000 20,000Pressure (psi)Change in Length (mm)Time (s)Change in LengthMeasured PressurePredicted Pressure126  𝒑𝒓𝒆𝒅𝒊𝒄𝒕𝒆𝒅 𝒑𝒓𝒆𝒔𝒔𝒖𝒓𝒆 [𝒑𝒔𝒊] =𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒍𝒆𝒏𝒈𝒕𝒉 [𝒎𝒎]𝟏𝟎𝟎𝟎 𝒎𝒎∙ 𝑬𝒑 ∙ 𝑨𝒑 ∙𝟑𝟎𝟎𝟎 𝒑𝒔𝒊𝟏𝟓𝟕𝟎 𝒌𝑵 (22) where 𝐸𝑝  = elastic modulus of prestressing strands, and 𝐴𝑝  = total cross-sectional area of prestressing strands. The elastic modulus of the strand (𝐸𝑝) is 195000 MPa and the total nominal area (𝐴𝑝) of the strands is 396 mm2. The maximum capacity of the horizontal actuator is 3000 psi and the equivalent maximum tensile force exerted together by the two horizontal actuators is 1570 kN. The following figure compares the two measured response in the pre-test: pressure in the horizontal actuators and the change in length over a one-meter length of strand.  Fig. 66: Pre-test horizontal pressure vs. change in length in prestressing strand. During the loading stage of the test, the horizontal pressure was increased in five steps to 1010 psi. Between each loading step, the pressure was held constant for approximately 1 to 2 minutes. As shown in the above figure, the change in length in the one-meter length of strand did not increase 0200400600800100012000.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0Pressure (psi)Change in Length (mm)Measured PressurePredicted Pressure127  linearly with increasing horizontal pressure in the actuator. At the beginning of each loading step, the increase in the change in length was delayed, which was apparent when it is compared with the linear trend of the “predicted pressure”. There were two reasons for the delay. Firstly, the axial tensile force exerted by the pressure in the horizontal actuators required some time before it could be distributed along the entire length of the strand. Secondly, at the beginning of the initial step, the lag in the change in length was accounting for the fact that the four strands in the setup might not have been fastened to the support with the exact equal forces. Only visual inspection was possible when checking to see if each strand had the same amount of tautness. Therefore, when the pressure increased, one strand might pick up more forces than the others until all four strands were taut identically thus eliminating the uneven rate of strain amongst the four strands. Fig. 67 shows the response of the change in length and the horizontal pressure throughout the five-hour period where the pressure was kept constant at 1010 psi by the load maintainer.   Fig. 67: Pre-test response at target constant pressure of 1010 psi. 9009209409609801000102010401060108011006.856.906.957.007.050 5,000 10,000 15,000 20,000Pressure (psi)Change in Length (mm)Time (s)Change in LengthMeasured Pressure128  As shown, the pressure decreased slightly overtime; however, at approximately 16000 s, the pressure picked up again and remained constant. At that point, the change in length increased abruptly resulting in a large spike in the figure. There were also other notable spikes in the graph during the five-hour period, but the deviation is relatively insignificant. The following table summarizes the consistency of the pressure maintained by the load maintainer. Table 25: Pre-test summary of horizontal pressure and change in length in prestressing strand.  Change in Length (mm) Pressure (psi) Mean 6.9 1010 Standard Deviation 0.013 2.5 Coefficient of Variance 0.18% 0.25%  The small coefficient of variance in the horizontal pressure demonstrated that in subsequent tests, the pressure which produces the strain in the concrete specimen will remain relatively constant for at least a five-hour period. E.1.2 Phase 1: Application of Flexural Tension Force Phase 1 of the test was carried out over three days. In this phase, two hydraulic actuators were connected to the 16 prestressing strands of the specimen, and the prestressing strands on the other end of the specimen were attached to the reaction-support. As the pressure in the actuators increased, the concrete specimens were pulled in tension. This tension in the concrete simulated the flexural behaviour of the lower flange of a typical prestressed concrete I-girder under loads. When the concrete is under high tensile strain, the bonding between the stirrups and concrete will weaken. Pull-out of the stirrups will then be attempted in Phase 2 as the concrete specimen is under tensile strain. 129  The tensile strain is achieved by increasing the pressure in both actuators to their maximum capacity of 3000 psi (20.7 MPa). Based on the geometry of the actuators, a pressure of 3000 psi can produce a total tensile force of 1570 kN on the 16 prestressing strands. At this point, the strands were at an equivalent stress of 991 MPa, which is 53% of their ultimate strength. The pressure in the actuators was increased slowly in steps, and observations and photographs were recorded between each step. Increasing the pressure in steps allowed the cracks in the concrete and the loads in the strands to develop more fully. There were 42 cycles executed in total and only the first cycle was done in steps. In the initial cycle, detail observations had been recorded. On the first day, the pressure in the two horizontal actuators which were connected to the specimen was increased gradually from 0 to 2700 psi in steps. The equivalent axial tensile force exerted by the hydraulic actuators can be determined using the ratio of maximum tensile force to maximum pressure as follows: 𝒆𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝒇𝒐𝒓𝒄𝒆 [𝒌𝑵] = 𝒑𝒓𝒆𝒔𝒔𝒖𝒓𝒆[𝒑𝒔𝒊] ×𝟏𝟓𝟕𝟎 𝒌𝑵𝟑𝟎𝟎𝟎 𝒑𝒔𝒊 (23) Therefore, at 2700 psi, the hydraulic actuators were exerted an equivalent force of 1400 kN. When the pressure was increased to 490 psi (260 kN) and the prestressing strands tautened, the concrete specimen lifted off the wooden blocks on which the specimen were sat. When the pressure reached 500 psi, the pressure was held constant and the specimen was inspected. No apparent cracks were observed. The pressure was then increased in increments of 250 psi before reaching 1250 psi, and in increments of 50 psi thereafter. Between each step, the pressure was held constant 130  and the crack patterns were documented. The cracks were marked by black fault markers drawn next to the cracks (to not mask the cracks with a marker) and photographs were taken. At 500 psi (262 kN), no cracks were apparent. At 750 psi (393 kN), cracks were formed near the two ends of the bottom side of the flange. As the pressure increased, cracks propagated but no new cracks were observed. At 1750 psi (916 kN), concrete spalling was observed at the two ends of the specimen from where the prestressing strands were protruding. At 2000 psi (1047 kN), a new crack was formed on the bottom side of the flange, as shown in red in the following figure. The cyan lines refer to the cracks formed at 1750 psi.  Fig. 68: Test T1 Phase 1: test specimen at horizontal pressure of 2000 psi; bottom of flange. Also, cracks began to propagate to the side of the flange. The following figure shows that the new crack formed at 2000 psi (shown in red in Fig. 69) had propagated from the bottom of the flange to the side of the flange. 131   Fig. 69: Test T1 Phase 1: test specimen at horizontal pressure of 2000 psi; close-up of crack on side of flange. At 2250 psi (1180 kN), cracks began to form on the top face of the flange near the two ends of the specimen, and at 2300 psi (1200 kN), another crack was formed on the bottom side of the flange. This crack is shown in red in the following figure.  Fig. 70: Test T1 Phase 1: test specimen at horizontal pressure of 2300 psi; bottom of flange. 132   At 2400 psi (1256 kN), more cracks were formed along the bottom and top faces of the flange, and at 2550 psi (1335 kN), cracks began to propagate into the web of the specimen. At the final step of 2700 psi (1413 kN), the measured additional strain in the specimen on the two side faces of the flange were +0.00122 and +0.00131, respectively, and the corresponding crack pattern is shown in the following figures.  Fig. 71: Test T1 Phase 1: test specimen at horizontal pressure of 2700 psi (first cycle); bottom of flange. 133   Fig. 72: Test T1 Phase 1: test specimen at horizontal pressure of 2700 psi (first cycle); side view. The specimen was unloaded to a pressure of 0 psi after documenting the observations at 2700 psi. After the specimen was unloaded, residual concrete strains were recorded on the two sides of the flange as +0.00004 and +0.00008, caused by the opening up of the cracks. On the second day, the specimen was loaded to 2700 psi for 14 times (cycle 2-15). As oppose to the initial cycle, these cycles were not done in steps. The pressure was increased to 2700 psi and then held constant in order to observe the presence of possible new cracks. The specimen was unloaded to 800 psi between each cycle to prevent the specimen from resting on the wood between each load cycle. The largest tensile strain at 2700 psi was observed in the fourth cycle; the strain in the specimen on the two side faces of the flange were recorded to be +0.00130 and +0.00126. During the eighth load cycle, the spluttering sound of interrupted flow of hydraulic fluids assumed that air has possibly entered the system and the pressure might have not been uniform throughout the system. The concrete strains at 2700 psi in the 15th cycle, which is the last cycle of the day, 134  were +0.00107 and +0.00117. The pressure in the actuators was then unloaded. The crack pattern at 2700 psi during the 15th cycle is shown in the following figures.  Fig. 73: Test T1 Phase 1: test specimen at horizontal pressure of 2700 psi (15th cycle); bottom of flange.  Fig. 74: Test T1 Phase 1: test specimen at horizontal pressure of 2700 psi (15th cycle); side view. 135  After the 15th cycle, existing cracks propagated and only two small cracks were formed, which are shown as red lines in Fig. 73. As shown in Fig. 74, two new cracks were formed in the web. The four middle cracks in the web were situated where the four pairs of stirrups are located, thus, this shows that the location of the reinforcement creates a weaker zone in the concrete. Since most cracks were formed initially during the initial cycle (shown by cyan lines in Fig. 73 and Fig. 74), the residual concrete strains were recorded to be much smaller than the previous day at 0.00000 and -0.00001. On the third day, the pressure in the horizontal actuators was loaded to the maximum capacity of 3000 psi for 10 times and unloaded to 800 psi between each cycle (cycle 16-25). More cracks and crack propagations were observed, and during the final cycle (25th cycle), the crack patterns at 3000 psi are shown in the following figures.  Fig. 75: Test T1 Phase 1: test specimen at horizontal pressure of 3000 psi (25th cycle); bottom of flange. 136   Fig. 76: Test T1 Phase 1: test specimen at horizontal pressure of 3000 psi (25th cycle); side view. After 15 cycles at 2700 psi and 10 more cycles at 3000 psi, more cracks were created on the bottom of the flange. As observed in Fig. 75, these new cracks were all located in the weaker region where the stirrups are located. Fig. 76 shows that the existing cracks in the web have propagated further along the whereabouts of the stirrups. The crack widths were recorded at this point at 16 locations; a measurement was taken at each end of the eight cracks on the side of the flange.  At 3000 psi, the concrete strains in the specimen on the two faces of the flange were recorded as +0.00165 and +0.00164. After unloading to a pressure of 0 psi, the residual concrete strains were +0.00005 and -0.00001. The entire load-strain relationship in Phase 1 is plotted in the following figure. 137   Fig. 77: Test T1 Phase 1: horizontal load–concrete strain relationship. The three colours in the diagram represent the three days of testing in Phase 1. The force applied by the actuators are plotted against the measured strain in the middle of the flange, and two strain readings were recorded; one for each side of the flange. The strain in the figure is the average of the two readings. A bi-linear relationship is observed on the figure, where the turning point of the two slopes represents the cracking strain. At the target force (1570 kN), the average strain in the concrete was +0.00170. The cracking strain of concrete was observed in the initial cycle, and is demonstrated to be +0.00030 (ignoring the elastic strain from prestressing) by the figure. Residual strain was observed after unloading due to the inability for the concrete cracks to fully close up after unloading. Therefore, the strain in concrete did not return to zero. After the initial cycle, concrete cracks at a lower strain in subsequent cycles, at +0.00022. 0200400600800100012001400160018000.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018Force Applied from Actuator (kN)Average Concrete Strain of FlangeCycle 1Cycle 2-15Cycle 16-25138  E.1.3 Phase 2: Diagonal Loading – Elastic Stirrups This phase involves the application of a diagonal axial force on the web of the specimen under an axial strain. This phase was completed in 13 non-continuous days. The concrete specimen was first loaded axially by increasing the pressure in the horizontal actuators. This procedure is identical to Phase 1 of the test. The diagonal actuator was then set at 30° to the longitudinal axis. The diagonal actuator applied a compression force onto the web of the specimen to simulate a diagonal shear force in a typical I-girder. The reaction support took up the horizontal component of the diagonal force, whereas the four stirrups took up the vertical component of the diagonal force. Firstly, a load-control system was used to control the diagonal force (as opposed to a displacement-control system). With this control system, three cycles were carried out. In the first cycle, the diagonal force was set at 40 kN, while the diagonal force in the other two cycles were set at 80 kN.  Assuming that the stirrups would yield at 400 MPa, the required diagonal force to cause the stirrups to yield would be 320 kN; thus, setting the diagonal force to 80 kN will not cause the stirrups to yield. During the third cycle, the response in the system was oscillating during the third cycle before reaching 80 kN. The diagonal actuator was physically vibrating and emitting loud noises. Therefore, the test was terminated. The corresponding diagonal load-displacement relationship is plotted as follow. 139   Fig. 78: Test T1 Phase 2: diagonal load-displacement relationship with load-control system. The diagonal load-displacement relationship is shown to be non-linear. In the third cycle, the diagonal actuator did not reach the target load of 80 kN as the vibration of the actuator caused the test to terminate. The following figure shows the strain readings in the four stirrups (D4, D5, D6, and D7).  Fig. 79: Test T1 Phase 2: diagonal load-stirrup strain relationship with load-control system. 0.010.020.030.040.050.060.070.080.090.00 2 4 6 8 10 12Force Applied from Diagonal Actuator (kN)Diagonal Displacement (mm)0.010.020.030.040.050.060.070.080.090.0-0.0012 -0.0010 -0.0008 -0.0006 -0.0004 -0.0002 0.0000 0.0002 0.0004Force  Applied from Diagonal Actuator (kN)Strain of StirrupD4D5D6D7140  Stirrups D4 and D6 are located closer to the diagonal actuator and will be referred to as “left stirrups.” Stirrups D5 and D7 are on the side closer to the pairs of horizontal actuators and will be referred to as “right stirrups.” The reading on D7 was rounded off to two decimal places instead of three decimal places as in other readings during this test. The data logging system was adjusted afterwards so that all future readings will be recorded with three decimal places. Bending in the stirrups was observed as the left stirrups experience tensile strain while the right stirrups experience compressive strain. The LVDTs which measured the strain on the stirrups were located at a short distance away from the stirrups shown in the following figure.  Fig. 80: Stirrup and LVDT arrangement. The LVDTs put on different sides of the stirrups enabled the recorded strain data to detect the bending of the stirrups. The bending behaviour occurred as the diagonal actuator pushed the specimen horizontally towards the horizontal actuators while the fixed support where the stirrups are connected to prevents the end of the stirrups from moving. After switching to the displacement-control system in the diagonal actuator, the same procedures were carried out again. However, with this system, a target displacement instead of a load was inputted into the system for each cycle. Therefore, the trial-and-error procedures were involved 141  initially thus not occur in every cycle in this process. The following figure shows the diagonal load-displacement relationship of the 20 loading cycles with a target load of 80 kN with the displacement-control system.  Fig. 81: Test T1 Phase 2: diagonal load-displacement relationship at 80 kN diagonal force. This relationship between the diagonal load and the jack displacement is non-linear, similar to the one in Fig. 78. However, the displacements in the diagonal jack measured here are much smaller than the displacements measured in the three load-control cycles. The difference might have been caused by the vibration and unsteadiness of the diagonal jack with the load-control system. The load in the diagonal actuator is plotted against the strain in the four stirrups in Fig. 82. 01020304050607080900.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50Force Applied from Diagonal Actuator (kN)Displacement of Diagonal Jack (mm)Cycle 1Cycle 2 - 20142   Fig. 82: Test T1 Phase 2: diagonal load-stirrup strain relationship at 80 kN diagonal force. As shown, the same bending behaviour shown in Fig. 79 was observed initially. As the diagonal force increased, the increase in the tensile strain in the stirrups increased at an almost constant rate. More loading cycles were carried out at increasing diagonal loads afterwards. The following table summarizes the number of cycles performed during this phase of the test. 0102030405060708090-0.0002 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012Force Applied from Diagonal Actuator (kN)Strain of StirrupD4D5D6D7143  Table 26: Test T1 Phase 2: summary of load cycles. Diagonal Force (kN) Number of Cycles Notes 80 42  120 22  160 20  200 20  240 20  280 20  320 10  200 8 LVDT showed that stirrups were yielding, but the sum of the stirrup forces did not add up to the corresponding component of the diagonal force. 140 16 LVDT showed that stirrups were yielding, but the sum of the stirrup forces do not add up to the corresponding component of the diagonal force.  Load cell on the diagonal actuator was re-calibrated. 320 507   During cycle 155 to cycle 178, the LVDTs on the stirrups showed that the stirrups were yielding. However, the load cell recorded load values of 200 kN and later 140 kN, which were much lower than the nominal diagonal yielding load of 320 kN. The load cell had been re-calibrated before continuing on to cycle 179, where yielding of stirrups was no longer observed even during a larger load of 320 kN. Over 500 loading cycles were carried out at 320 kN. 144  To avoid the bending behaviour in the strain data, the LVDTs on the stirrups had been repositioned as follow.  Fig. 83: Revised stirrup and LVDT arrangement. The diagonal load-displacement relationship for the last 75 loading cycles (at a target diagonal load of 320 kN) in Phase 2 is plotted in Fig. 84.  Fig. 84: Test T1 Phase 2: diagonal load-stirrup strain relationship at 320 kN diagonal force. 050100150200250300350400-0.0005 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030Applied Force from Diagonal Actuator (kN)Strain of StirrupD4D5D6D7145  In this plot, the diagonal force-strain relationship is shown to be mostly linear. Slight non-linearity is observed at lower diagonal loads. Because the displacement of the actuator was manually controlled, as oppose to a load-control loading system, during one cycle, the diagonal load had unexpectedly exceeded the target load of 320 kN and reached a load of 365 kN. At this load, the stirrups began to yield, which was shown by a shifted unloading curve in each of the four load-strain relationships. The bending behaviour was also observed with the revised LVDT arrangement as D6 and D7 (bottom stirrups) pick up compressive strain readings at low diagonal loads. This bending in the vertical direction might be caused by the altitudinal misalignment of the specimen with the fixed support, as well as the slant of the specimen due to the self-weight of the concrete web. On each stirrup, a LVDT was installed to measure the change in distance between the concrete surface at the top of the web and a point on the stirrup just away from the concrete surface. This value, defined here as “slip” is plotted against the strain for each stirrup. By comparing the slip and the strain in a stirrup, the degree of pull-out of the stirrups, and the debonded length (see Chapter 5), from the specimen can be evaluated. 146   Fig. 85: Test T1 Phase 2: slip-strain interaction at 320 kN diagonal force. Given that the strain in the debonded section of the stirrup within the specimen is the same as the strain measured by the LVDT along the exposed length, the equivalent debonded length can be represented by the slope of the slip-strain relationship. E.1.4 Phase 3: Diagonal Loading – Yielding Stirrups In Phase 3, the horizontal forces were applied to the strands similar to Phase 1 and Phase 2. However, the load in the diagonal compression force was further increased to allow the stirrups to yield. The stress-strain relationship for the four stirrups D4, D5, D6, and D7 in the first cycle are plotted by combining the loading curve of the initial cycle, the maximum point for the following 60 cycles and the unloading curve of the last cycle. -0.50.00.51.01.52.02.5-0.0010 -0.0005 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030Additional Slip of Stirrup (mm)Additional Strain of StirrupD4D5D6D7147   Fig. 86: Test T1 Phase 3: stirrup stress-strain relationship. The “theoretical stress in stirrups” was computed by dividing the horizontal component of the applied diagonal compressive force by the total area of the stirrups. During these cycles, the diagonal actuator was exerting a compressive force of 440 kN. As shown in Fig. 86, the theoretical stress in the stirrups had exceeded the actual yielding stress of 470 MPa and the shifting of the unloading curves demonstrate that the stirrups had yielded in this phase of the test. The maximum theoretical stirrup stress in the 60 cycles was 549 MPa (117% of actual yielding stress). The vertical bending behaviour of the stirrups was also observed in the stress-strain relationship. Assuming that the strain readings caused by the bending behaviour were complete opposite in direction but same in magnitude, the strain readings in the left stirrups and the right stirrups are averaged separately and plotted in Fig. 87. 0100200300400500600-0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012Theoretical Stress of Stirrups (MPa)Strain of StirrupsD4D5D6D7148   Fig. 87: Test T1 Phase 3: stirrup stress- strain relationship (averaged). In this figure, the initial compressive strain readings are no longer observable. This shows that the effect of bending in the strain readings in the top and bottom stirrups was the same in magnitude. In addition to the strain reading due to the actual elongation of the stirrup, the top stirrups experienced compressive strains while the bottom stirrups experienced the same magnitude of tensile strains. Both the left and right stirrup strains agree with the computed yielding strain of +0.00235, where both curves began to experience yielding deformation. The maximum averaged strain in the left and right stirrups were +0.00932 and +0.00754, respectively (4.0 and 3.2 times the yielding strain, respectively). The left stirrups are located closer to the diagonal actuator where the compressive force was applied, thus, they may experience higher loads and deformation. Note that the theoretical stress in the plot was computed based on the applied diagonal load and not the measured stirrup stresses. 01002003004005006000.000 0.002 0.004 0.006 0.008 0.010Theoretical Stress of Stirrups (MPa)Strain of StirrupsLeftRight149  The slip-strain relationship is plotted for the same 60 cycles at 440 kN. Again, the following two figures are composed only of the loading curve of the first cycle and data taken at each maximum load. D8, D9, D10, and D11 are the “slip” measurements corresponding to the strain measurements of D4, D5, D6, and D7, respectively.  Fig. 88: Test T1 Phase 3: slip-strain interaction at 440 kN diagonal force. The data in stirrup D4 and D6 were averaged to form the data series “left stirrups” and the data in stirrup D5 and D7 were averaged to become the data series “right stirrups” in the following figure. 0.00.51.01.52.02.53.03.54.04.50.000 0.002 0.004 0.006 0.008 0.010Slip (mm)Strain in StirrupD4/D8D5/D9D6/D10D7/D11150   Fig. 89: Test T1 Phase 3: slip-strain interaction at 440 kN diagonal force (averaged). E.1.5 Application of Horizontal Strain with Eight Strands An additional phase was conducted in Test T1 where only eight out of the 16 strands were connected to the horizontal actuators. This phase evaluated the possibility of simulating a larger longitudinal strain in the specimen with the same load applied with the horizontal actuators. Three cycles were performed with only the eight strands closest to the bottom of the flange; the other eight were cut off from the test specimen. The horizontal load-strain relationship is plotted in the following figure. 0.00.51.01.52.02.53.03.54.04.50.000 0.002 0.004 0.006 0.008 0.010Slip (mm)Strain in StirrupLeftRight151   Fig. 90: Test T1: horizontal strain-concrete strain relationship with only eight strands. The maximum longitudinal strain, averaged from the two sides of the flange, was recorded to be +0.00137. However, during this test, the eccentricity in the system had caused the specimen to rotate causing the measurement to be inaccurate. The possibility of connecting only eight out of 16 strands was determined to be unviable. Also, the rotation of the specimen caused the stirrups to fracture as the specimen pushed the stirrups towards the fixed support. E.1.6 Summary of Encountered Problems and Corresponding Solutions The following list summarizes the problems encountered in Test T1 and their corresponding solutions for future tests: 1. The reaction support for the 16 prestressing strands had yielded during Phase 1 because the bending strength of the individual flanges had been neglected. A new reaction support was fabricated with multiple stiffener plates. 02004006008001000120014000.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016Force Applied from Actuator (kN)Average Concrete Strain of FlangeCycle 1Cycle 2Cycle 3152  2. The load-control system for the diagonal actuator had failed to work consistently. A displacement-control system was used instead afterwards. However, it had become more difficult to monitor the target load, since a target displacement value must be estimated and inputted into the system instead of the load. 3. Data acquisition system had failed to keep a consistent number of decimal places among all data. Program had been changed and all data after had been recorded with three decimal places. 4. Bending had been observed in the stirrups when the diagonal actuator pushed the specimen horizontally as the fixed support held back the other end of the stirrups. This fixed support was re-designed to allow for free horizontal movement of the stirrups by minimizing friction with a layer of PTFE within the contact surface in the support. E.2 Summary of Test L1 Specimen L1 was the second of the 6 specimens to be tested. In this specimen, the stirrups were not hooked around longitudinal bars, and thus Test L1 simulates a non-code compliant section of an I-girder. There were three phases to this test (similar to Test T1): (1) gradual application of horizontal strain, (2) repeated application of diagonal force within the elastic range of stirrup strength, and (3) repeated application of diagonal force after the stirrups have yielded. In this test, various changes were made to the test set-up.  153  E.2.1 Phase 1: Application of Flexural Tension Force Phase 1 of Test L1 was carried out in two days. In this phase, two hydraulic actuators were connected to the 16 prestressing strands of the specimen, and the prestressing strands on the other end of the specimen were attached to the reaction support. As the pressure in the actuators increased, the concrete specimen was pulled in tension. This tension in the concrete simulated the flexural tensile behaviour of the flexural tension flange of a typical prestressed concrete I-girder under bending moment loads. When the concrete was under large tensile strain, the bonding between the stirrups and concrete would weaken. The pull-out of stirrups would be tested in Phase 2 as the concrete specimen would be experiencing a tensile strain. The tensile strain was achieved by increasing the pressure in both actuators to 3000 psi. Based on the geometry of the actuators, a pressure of 3000 psi can produce a total tensile force of 1570 kN distributed in the 16 prestressing strands. At this point, the strands were at an equivalent stress of 991 MPa, which is 53% of their ultimate strength of 1860 MPa. There were 20 loading cycles performed in total and only the first cycle was done in steps. In the initial cycle, the pressure in the actuators was increased slowly in steps from zero, and observations and photographs were recorded at each step. Increasing the pressure in steps allowed the cracks in the concrete and the loads in the strands to develop more fully.  In the initial cycle, the pressure in the two horizontal actuators was increased from 0 to 3000 psi in gradual steps. At 1000 psi, concrete spalling was observed at the two ends of the specimen from where the prestressing strands are protruding, and larger cracks were observed on the actuator end. When the pressure had increased to 2100 psi, a crack was formed on the bottom of the flange. This crack was located near the actuator-end as shown in Fig. 91. 154   Fig. 91: Test L1 Phase 1: test specimen at horizontal pressure of 1000 psi; bottom of flange. At 2200 psi, two new cracks were formed. These cracks are represented by the two red lines in the following figure.  Fig. 92: Test L1 Phase 1: test specimen at horizontal pressure of 2000 psi; bottom of flange. Also, at this point, the two new cracks, along with the existing crack had propagated to the side of the flange as shown in Fig. 93. 155   Fig. 93: Test L1 Phase 1: test specimen at horizontal pressure of 2000 psi; side view. At 2500 psi, a crack had formed at the LVDT mount. Also, cracks were formed in the web, as shown in the following figure.   Fig. 94: Test L1 Phase 1: test specimen at horizontal pressure of 2500 psi; side view.  At 2700 psi, a crack was formed in the 30° face in the web as shown in Fig. 95. 156   Fig. 95: Test L1 Phase 1: test specimen at horizontal pressure of 2700 psi; diagonal face of web. At 2800 psi, a new crack was formed in the web along one of the stirrups. Also, more cracks were formed in the flange. The cracks on the bottom side of the flange were concentrated on one side as shown in Fig. 96.  Fig. 96: Test L1 Phase 1: test specimen at horizontal pressure of 2800 psi; bottom of flange.  157   Fig. 97: Test L1 Phase 1: test specimen at horizontal pressure of 2800 psi; side view. At 3000 psi, many more cracks were formed on the bottom side of the flange, the side of the flange, and the side of the web.  Fig. 98: Test L1 Phase 1: test specimen at horizontal pressure of 3000 psi (first cycle); bottom of flange. 158    Fig. 99: Test L1 Phase 1: specimen at horizontal pressure of 3000 psi (first cycle); side view. At 3000 psi, most cracks on the bottom side of the flange had propagated to the other side of flange and this indicated that both sides of the flange had surpassed the cracking strain. In the web, one of the new cracks was formed along one of the stirrups, which highlighted the weak zone of the concrete, which the presence of the stirrups had created. At this point, the longitudinal strain on the two sides of the flange were recorded to be +0.00178 and +0.00017. The significant difference between the two strains showed that the specimen was misaligned or the stresses were not uniformly distributed on the two sides of the flange. This was also suggested by the concentration of cracks on one side of the flange at lower pressure. Afterwards, the specimen was unloaded to a pressure of 0 psi. In the next nine cycles, the pressure was increased steadily to 3000 psi at once and unloaded to 800 psi in between each cycle. At the tenth cycle, the two strains were recorded to be +0.00187 and +0.00045. These strains are 5.06% and 165% higher than the two strains recorded after the first cycle at 3000 psi, respectively. The significant increase in the strain on the bottom side of the flange suggested that the test set-up had 159  begun to realign the specimen so that the axial force on the sides of the flange will be distributed more evenly. However, despite the increase in strain on the bottom side of the flange, no new cracks were formed. After unloading the pressure to 0 psi at the end of the tenth cycle, the residual strain readings were +0.00001 and +0.00014. On the second day, the specimen was loaded to 3000 psi for 10 more cycles (cycle 11-20). These cycles were also not done in steps. In addition, the specimen was manually realigned before beginning the test. The pressure was increased to 3000 psi and then held constant in order to observe the presence of possible new cracks. The specimen was unloaded to 800 psi between each cycle to prevent the specimen from resting on the steel bracket holding up the specimen. The longitudinal concrete strains measured at 3000 psi in the 20th cycle, which was the last cycle of the day, were +0.00127 and +0.00133. These values demonstrated that the strains in the specimen were distributed more evenly than the first day. Also, no new cracks were formed. However, new cracks might have formed on the side of the flange which was not observable when the specimen was being tested. Also, significant amount of concrete had spalled at the two ends of the specimen where the prestressing strands are protruding. The residual strains measured at the end of the 20th cycle were -0.00011 and -0.00002. In addition to the concrete strain in the specimen, the crack widths were also recorded at 16 locations; a measurement was taken at both ends of the eight cracks on the side of the flange. These 16 measurements were taken on only one side of the flange because the other side of the flange was inaccessible when the specimen was too close to the floor in the test set-up. Based on the distance between the cracks, the tensile strains at each of the 16 measured crack locations were estimated. 160  The load-strain relationship in Phase 1 is plotted in the following figure.  Fig. 100: Test L1 Phase 1: horizontal load-concrete strain relationship. The three colours in the plot represent the initial cycle, the 9 additional cycles on the same day, and the 10 cycles on the second day, respectively. The forces applied by the actuators are plotted against the strains in the middle of the flange. Two strain readings were recorded: one for each side of the flange. The strains in the figure represent the average of the two readings. Evident in the figure, a bi-linear relationship was observed, where the turning point of the two slopes represents the cracking strain. The bi-linear behaviour was more apparent in later cycles. At the target pressure (3000 psi), the average strain in the concrete increased as the number of cycles increased, and the maximum strain was recorded to be +0.00158. The cracking strain of concrete was observed in the initial cycle, and was found to be +0.00018 in the figure. This value was much lower than subsequent cycles because the concrete had not cracked at this stage. The cracking strain was found to be approximately +0.00040 in the subsequent cycles. Residual strain was 0200400600800100012001400160018000.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018Force Applied in Actuator (kN)Average Concrete Strain in FlangeCycle 1Cycle 2-10Cycle 11-20161  observed after unloading due to the inability for the concrete cracks to fully close up after unloading. Therefore, the strain in concrete does not return to zero. E.2.2 Phase 2: Diagonal Loading – Elastic Stirrups The second phase involves the application of a diagonal axial force on the 30° face of the web of the specimen while maintaining a constant longitudinal axial force. This phase was completed in four non-continuous days. The concrete specimen was first loaded axially by increasing the pressure in the horizontal actuators; this procedure was identical to Phase 1 of the test. The diagonal actuator was then set at 30° to the longitudinal axis. The diagonal actuator applied a compression force onto the web of the specimen at 30° to simulate a shear force in a typical I-girder. The reaction-support took up the horizontal component of the diagonal force, while the four stirrups, which were connected to a fixed support, took up the vertical component of the diagonal force. On the first day, the specimen was loaded five times to 80 kN with the diagonal actuators, five times to 120 kN, five times to 160 kN, and ten times to 200 kN. At each load cycle, the loading rate and the unloading rate were constant and identical; the period was kept at 1 minute per each load cycle for all target loads on this day. 162   Fig. 101: Test L1 Phase 2: stirrup stress-strain relationship at 80 kN, 120 kN, 160 kN and 200 kN diagonal force. The vertical axis “Theoretical Stress in Stirrups” refers to the equivalent stress each stirrup was experiencing under the applied diagonal load assuming that the corresponding component of the diagonal load was perfectly distributed amongst the four stirrups. As shown, the stress-strain relationship amongst the four stirrups varied. The offset of the origin on each curve suggested that (1) the specimen might have moved from its original position, (2) the fixed stirrup support might not have fastened properly, and/or (3) the stirrups were bending. Also, stirrup D5 showed larger strain values than the other three stirrups. This strain of +0.00279 exceeded the strain at yielding of +0.00235, which was calculated from a yielding stress of 470 MPa. Slip, here, refers to the distance from a fixed point on the stirrup close to the surface of the concrete specimen to the surface of the web of the concrete specimen; the concrete surface acted as a reference point and as the stirrups were elongated, the fixed point on the stirrup would move away 050100150200250300-0.0005 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030Theoretical Stress in Stirrups (MPa)Strain in StirrupsD4D5D6D7163  from it. Slip is plotted against the strain (along the exposed section of the stirrups) in each of the four stirrups in the following figure with the slope of the plot representing the debonded length.  Fig. 102: Test L1 Phase 2: stirrup slip-stirrup strain relationship at 80 kN and 120 kN diagonal force. Readings D8, D9, D10, and D11 are the slip measurements corresponding to stirrups D4, D5, D6, and D7 respectively. As shown in Fig. , the behaviors of the four stirrups differ significantly. In stirrup D4, the origin of the slip-strain curve has moved which shows that the support which holds stirrup D4 might have been loose causing movement every time the force was unloaded. Reading D10 failed to measure the slip for stirrup D6 because the LVDT was improperly placed. More loading cycles are carried out at increasing diagonal loads afterwards. The following table summarizes the number of loading cycles performed during this phase of the test. -0.200.000.200.400.600.801.00-0.0005 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030Slip (mm)Strain in StirrupsD4/D8D5/D9D6/D10D7/D11164  Table 27: Test L1 Phase 2: summary of load cycles. Diagonal Force (kN) Number of Cycles Notes 80 5  120 5  160 5  200 20  240 20 Period of loading was increased from 1 min to 1.5 min. 280 30  320 20   The diagonal load-displacement relationship for the last 40 loading cycles (20 cycles at 280 kN and 20 cycles at 320 kN) in Phase 2 is plotted in the following figure.   Fig. 103: Test L1 Phase 2: stirrup stress-strain relationship at 280 kN and 320 kN diagonal force. 050100150200250300350400450500-0.0005 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 0.0040Theoretical Stress in Stirrups (MPa)Strain in StirrupsD4D5D6D7165  During this phase of the test, yielding was observed in the right stirrups (D5 and D7) which are shown by the shifting of the unloading curves. Also, the strains in these two stirrups were larger than the other two stirrups. This might be caused by the increasing displacement of the diagonal actuator. As the specimen rotated due to the physical displacement on one side, the right stirrups, which are located further from the diagonal actuator, would have to elongate more than the other two stirrups and take more forces. The corresponding slip-strain relationship is shown in the following figure.  Fig. 104: Test L1 Phase 2: stirrup slip-strain interaction at 280 kN and 320 kN diagonal force. In this figure, the slopes of the slip-strain relationship refer to the debonded length of the corresponding stirrup. At low strain, the bending behaviour of the stirrups was apparent, as the right stirrups behaved differently than the left stirrups. However, at larger strain, the axial strain of -0.200.000.200.400.600.801.001.201.401.601.800.000 0.001 0.002 0.003 0.004 0.005 0.006Slip (mm)Strain in StirrupsD4/D8D5/D9D6/D10D7/D11166  the stirrups became more significant and the debonded length of stirrups D4, D5, and D6 are very similar. E.2.3 Phase 3: Diagonal Loading – Yielding Stirrups In Phase 3, the horizontal forces were applied to the strands similar to Phase 1 and Phase 2. On top of that, the load in the diagonal compression force was further increased to allow the stirrups to yield. The stress-strain relationship for the four stirrups D4, D5, D6, and D7 in the first cycle are plotted by combining the loading curve of the initial cycle, the maximum point for the following 80 cycles and the unloading curve of the last cycle.  Fig. 105: Test L1 Phase 3: stirrup stress-strain relationship. During these cycles, the diagonal actuator was exerting a target compressive force of 400 kN.  However, in the last five cycles, the diagonal actuator was only able to apply a diagonal force of 370 kN. As shown in Fig. 86, the theoretical stress in the stirrups had exceeded the actual yielding 01002003004005006000.0000 0.0050 0.0100 0.0150 0.0200 0.0250Theoretical Stress in Stirrups (MPa)Strain in StirrupsD4D5D6D7167  stress of 470 MPa and the shifting of the unloading curves demonstrated that the stirrups had yielded significantly in this phase of the test. The maximum theoretical stirrup stress in the 40 cycles was 504 MPa (107% of actual yielding stress). On the stress-strain plot, the vertical bending behaviour in the stirrups is less noticeable than in Test T1. Stirrups D5 and D7, which were located furthest away from the diagonal actuator had reached higher strains than the other two stirrups which might be caused by the rotation of the specimen with the increase in displacement induced by the diagonal actuator. The slip-strain relationship is plotted for the same 60 cycles at 440 kN. Again, the following two figures are composed only of the loading curve of the first cycle, data taken at each maximum load, and the unloading curve of the last cycle.   Fig. 106: Test L1 Phase 3: slip-strain interaction at 440 kN diagonal force. 0.001.002.003.004.005.006.000.0000 0.0050 0.0100 0.0150 0.0200 0.0250Slip (mm)Strain in StirrupsD4/D8D5/D9D6/D10D7/D11168  There are three apparent slopes (debonded length) observed with each of the four stirrups. In the initial section, when the strain was less than +0.0023, the slips in the left stirrups (D4 and D6) increased at a higher rate than the right stirrups (D5 and D7); this was possibly due to the slight bending behaviour in the stirrups. In the midsection, where the stirrup strains ranged from +0.0023 to +0.0100, the slope of the curves for stirrups D4, D5 and D6 are very similar as the axial strain of the stirrups began to overshadow the effect of the stirrup bending. Stirrup D7, however, showed a slower rate of increase in slip. In the remaining section, all four stirrups showed a slight increase in slope, demonstrating pull-outs of the stirrups. However, the increase in slope was less apparent than in Test T1. E.3 Summary of Test T2 Specimen T2 was the third of the 6 specimens to be tested. In this specimen, which is identical to specimen T1 in Test T1, the stirrups were hooked around longitudinal bars, and thus Test T2 simulates a code compliant section of the I-girder. There were three planned phases in this test: (1) gradual application of horizontal strain, (2) repeated application of diagonal force within the elastic range of stirrup strength, and (3) repeated application of diagonal force after the stirrups have yielded. In this test, the horizontal force applied in the flange of the specimen was increased from 1570 kN to 1675 kN.  However, because of unexpected circumstances which destroyed the specimen, Phase 2 and Phase 3 were not performed in this test. E.3.1 Phase 1: Application of Horizontal Strain Phase 1 of Test T2 was carried out in three non-continuous days. In this phase, two hydraulic actuators were connected to the 16 prestressing strands of the specimen, and the prestressing 169  strands on the other end of the specimen were attached to the reaction-support. As the pressure in the actuators increased, the concrete specimens were pulled in tension. This tension in the concrete simulated the flexural tensile behaviour of the lower flange of a typical prestressed concrete I-girder under loads. The target tensile strain was achieved by increasing the pressure in both actuators to 3200 psi (3000 psi in the two previous tests). Based on the geometry of the actuators, a pressure of 3200 psi produces a total tensile force of 1670 kN, which would be distributed amongst the 16 prestressing strands. At this pressure, the strands were at an equivalent stress of 1057 MPa, which is 57% of their ultimate strength of 1860 MPa. There were 20 loading cycles performed in total and only the first cycle was done step-wise at increasing target loads. At each target load, observations and photographs were recorded. Increasing the pressure in steps allowed the cracks in the concrete and the loads in the strands to develop more fully.  When the pressure in the horizontal actuators was increased to 2000 psi, a crack was formed on the edge of the bottom of the flange as shown. 170   Fig. 107: Test T2 Phase 1: test specimen at horizontal pressure of 2000 psi; bottom of flange. This crack was located near the reaction end (away from where the horizontal force was applied). In addition, this crack also propagated to the side of the flange and to the top of the flange, shown in the following two figures.  Fig. 108: Test T2 Phase 1: test specimen at horizontal pressure of 2000 psi; side view. 171   Fig. 109: Test T2 Phase 1: test specimen at horizontal pressure of 2000 psi; top of flange. Shown in Fig. 91, the specimen cracked only on one side (away from the floor), and this crack had propagated all the way around the side of the flange. This demonstrated that the axial load was concentrated on this side of the specimen causing only one side to crack. At this point, the concrete strain on the cracked side of the flange was +0.00022, and the concrete strain on the other side of the flange was +0.00016. At 2100 psi, the same crack had propagated to the web, shown in Fig. 110. The blue line represents existing crack and the red line represents the crack which was newly observed at 2100 psi.  172   Fig. 110: Test T2 Phase 1: test specimen at horizontal pressure of 2100 psi; side view. At 2800, a new crack was formed on the bottom and the side of the flange. In addition, the crack on the bottom side of the flange had propagated towards other side of the flange. These are shown in the following figures.  Fig. 111: Test T2 Phase 1: test specimen at horizontal pressure of 2800 psi; bottom of flange. 173    Fig. 112: Test T2 Phase 1: test specimen at horizontal pressure of 2800 psi; side view. At 2800 psi, the concrete strains on the side shown in Fig. 112 and on the opposite side of the flange were +0.00053 and +0.00017, respectively. Similar to Test L1, the strain in the specimen was concentrated on one side of the flange. At 2900 psi, a new crack was formed near the reaction-end of the specimen. In addition, an existing crack had propagated into the web. This is shown in the following two figures. 174   Fig. 113: Test T2 Phase 1: test specimen at horizontal pressure of 2900 psi; bottom of flange.  Fig. 114: Test T2 Phase 1: test specimen at horizontal pressure of 2900 psi; side view. Similar to Test T1 and L1, many more cracks were formed at 3000 psi. The concrete strains on the two sides of the flange were +0.00247 and +0.00138. A significant difference between the strains on the two sides was apparent – one side has 79% more strain than the other side. The crack pattern is shown in the following two figures. 175   Fig. 115: Test T2 Phase 1: test specimen at horizontal pressure of 3000 psi; bottom of flange.   Fig. 116: Test T2 Phase 1: test specimen at horizontal pressure of 3000 psi; side view. At this pressure, existing cracks propagated and new cracks were formed on the actuator end (the end closer to the hydraulic actuators), showing a more evenly distributed crack pattern. Similar to the two previous tests, the cracks in the web also travelled along the location of the stirrup. 176  Different from the two tests earlier, the pressure in the hydraulic actuators was increased to 3200 psi in this test. As the pressure increased, the strain increased at a faster rate since the concrete was cracked. At 3200 psi, the concrete strains were +0.00298 and +0.00183. The following figures show the location of the cracks.  Fig. 117: Test T2 Phase 1: test specimen at horizontal pressure of 3200 psi; bottom of flange.   Fig. 118: Test T2 Phase 1: test specimen at horizontal pressure of 3200 psi; side view. 177  Afterwards, the specimen was unloaded to a pressure of 0 psi. In all remaining cycles, the pressure was increased steadily to 3200 psi and unloaded to 800 psi between each cycle. On the 20th cycle, the concrete strains on both sides of the flange increased to +0.00348 and +0.00198, which are 17% and 8.2%, respectively, higher than the concrete strain measured at the same pressure in the first cycle. After unloading the pressure to 0 psi at the end of the tenth cycle, the residual strain readings were +0.0010 and +0.0002, since the cracks do not close up completely after unloading. In addition to the concrete strain in the specimen, the crack widths were also recorded at 16 locations; a measurement was taken at each end of the eight cracks on the side of the flange. These 16 measurements were taken on only one side of the flange because the other side of the flange was inaccessible, being very close to the floor. Based on the distance between the cracks, the tensile strains at each of the 16 measured crack locations were estimated. The entire load-strain relationship in Phase 1 is plotted in the following figure, where the average concrete strains between the two sides of the flange were used. 178   Fig. 119: Test T2 Phase 1: horizontal load-concrete strain relationship. The three colours in the diagram represent the initial cycle, the 9 additional cycles on the second day, and the 10 cycles on the last day. The forces applied by the actuators were plotted against the strain in the middle of the flange. Two strain readings were recorded; one for each side of the flange. The strain in the figure is the average of the two readings. Evident in the figure, a bi-linear relationship was observed, where the turning point of the two slopes represents the cracking strain. At the target pressure of 3200 psi, the maximum average strain in each cycle increased as the number of cycles increase; the maximum average strain was recorded to be +0.00273. The cracking strain of concrete was observed in the initial cycle, and was found to be +0.00036. The cracking strain was found to be approximately +0.00100 in the subsequent cycles. Residual strain was observed after unloading due to the inability for the concrete cracks to fully close up after unloading. Therefore, the strain in concrete did not return to zero. 05001000150020002500300035000.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035Pressure in Horizontal Actuators (psi)Average Concrete Strain in FlangeCycle 1Cycle 2 - 10Cycle 11 - 20179  E.3.2 Phase 2: Diagonal Loading within the Elastic Region of Stirrups At the beginning of Phase 2, before the horizontal actuators re-applied the axial stress in the flange of the specimen, the diagonal actuator unexpectedly began to apply a force on the diagonal face of the web due to programming error by the technician. The abrupt diagonal force on the specimen caused the stirrups to experience high stresses and two of the stirrups have eventually snapped and failed.  Therefore, Phase 2 and Phase 3 of this test cannot be completed. To prevent this incident from happening again, during the subsequent tests, the diagonal actuator had been rotated away from the specimen during the loading of the horizontal tension force.  The diagonal actuator would be realigned with the diagonal face of the web after the horizontal axial stress is applied in the flange of the specimen. E.4 Summary of Test L2 Specimen L2 was the fourth of the 6 specimens to be tested. In this specimen, which was identical to specimen L1 in Test L1, the stirrups were not hooked around longitudinal bars thus Test L2 simulated a non-code compliant section of the I-girder. There were three phases to this test: (1) gradual application of horizontal strain, (2) repeated application of diagonal force within the elastic range of stirrup strength, and (3) repeated application of diagonal force post-yielding. Similar to Test L1, the horizontal force applied in the flange of the specimen was set to 1675 kN. At the end of the third phase, two of the stirrups in the specimen were fractured. E.4.1 Phase 1: Application of Flexural Tension Force Phase 1 of Test L2 was carried out in two days. In this phase, two hydraulic actuators were connected to the 16 prestressing strands of the specimen, and the prestressing strands on the other 180  end of the specimen were attached to the reaction-support. As the pressure in the actuators increased, the concrete specimens were pulled in tension. This tension in the concrete simulated the flexural tensile behaviour of the lower flange of a typical prestressed concrete I-girder under loads. When the concrete was under tensile strain, the bonding between the stirrups and concrete would weaken. The pull-out of stirrups would then be tested in Phase 2 as the concrete specimen experienced high tensile strain. Similar to Test T2, the target axial tensile load was increased to 1675 kN to achieve a higher tensile strain than Test T1 and Test L1. The tensile strain was achieved by increasing the pressure in both actuators to 3200 psi. Based on the geometry of the actuators, a pressure of 3200 psi produces a total tensile force of 1675 kN, which was distributed amongst the 16 prestressing strands in the test. At this pressure, the strands experienced an equivalent stress of 1057 MPa, which is 57% of their ultimate strength of 1860 MPa. There were 20 loading cycles performed and only the first cycle was done step-wise at various intermediate loads. At each intermediate load, observations and photographs were recorded. Increasing the pressure in steps allowed the cracks in the concrete and the loads in the strands to develop more fully.  When the pressure in the horizontal actuators increased to 2000 psi, a crack was formed on the edge of the bottom of the flange as shown. 181   Fig. 120: Test L2 Phase 1: test specimen at horizontal pressure of 2000 psi; bottom of flange. This crack was located near the reaction end (away from where the horizontal force is applied). In addition, this crack also propagated to the side of the flange, shown in the following figure.  Fig. 121: Test L2 Phase 1: test specimen at horizontal pressure of 2000 psi; side view. Shown in Fig. 121, the specimen only cracked on one side (away from the floor), and this crack propagated all the way around the side of the flange. This demonstrated that the axial load is 182  concentrated on this side of the specimen. At this point, the concrete strain on the cracked side of the flange was +0.00027, and the concrete strain on the other side of the flange was +0.00018. At 2500 psi, the same crack had propagated to the web, shown in the following figure.  Fig. 122: Test L2 Phase 1: test specimen at horizontal pressure of 2500 psi; side view. The blue line represents the existing crack and the red line represents the crack newly observed at 2500 psi. The axial strains on the upper face (shown in the picture) and the lower face were +0.00032 and +0.00020, respectively.  At 2700 psi, the crack on the bottom side of the flange had also propagated to the lower face of the flange. This is shown in Fig. 123. 183   Fig. 123: Test L2 Phase 1: test specimen at horizontal pressure of 2700 psi; bottom of flange.  At 2900 psi, many cracks formed, and they concentrated near the upper face of the flange. This is shown in the following two figures.  Fig. 124: Test L2 Phase 1: test specimen at horizontal pressure of 2900 psi; bottom of flange. 184   Fig. 125: Test L2 Phase 1: test specimen at horizontal pressure of 2900 psi; side view. The concrete strains on the two sides of the flange were +0.00182 and +0.00097. There was a significant difference between the strains on the two faces of the flange. One face had 88% larger strain than the other face. At the target pressure of 3200 psi, the axial strains were +0.00232 and +0.00189 for the upper and lower faces, respectively.  The following figures show the crack pattern of the bottom of the flange and the upper face of the flange. 185   Fig. 126: Test L2 Phase 1: test specimen at horizontal pressure of 3200 psi; bottom of flange.   Fig. 127: Test L2 Phase 1: test specimen at horizontal pressure of 3200 psi; side view. At this pressure, existing cracks had propagated, and new cracks were formed on the actuator end (the end closer to the hydraulic actuators) showing a more evenly distributed crack pattern. Similar to the three previous tests, the cracks in the web also travelled along the location of the stirrups. 186  Afterwards, the specimen was then unloaded to a pressure of 0 psi. In all remaining cycles, the pressure was increased steadily to 3200 psi and unloaded to 800 psi between each cycle. On the 20th cycle, the concrete strains on both sides of the flange had increased to +0.00255 and +0.00249, which were 9.9% and 32% larger than the concrete strain measured at the same pressure in the first cycle. The strains recorded on the two faces of the flange varied only by 2.4% at the end of the 20th cycle. After unloading the pressure to 0 psi at the end of the 20th cycle, the residual strain readings were +0.00011 and +0.00040, since the cracks did not close up completely after unloading. The entire load-strain relationship in Phase 1 is plotted in the following figure, where the applied pressure in the horizontal actuators is plotted against the average concrete strain between the two sides of the flange.  Fig. 128: Test L2 Phase 1: horizontal load-concrete strain relationship. 05001000150020002500300035000.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035Pressure in Horizontal Actuators (psi)Average Concrete Strain in FlangeCycle 1Cycle 2 - 20187  The two colours in the diagram represent the initial cycle and the subsequent 19 cycles separately. The force applied by the actuators are plotted against the concrete strain in the flange, and two strain readings are recorded; one for each side of the flange. The strains in the figure are the average of the two readings from the two sides of the flange. Evident in the figure, a bi-linear relationship is observed (which is more apparent in later cycle), and the turning point in the first cycle represents the cracking strain. At the target pressure of 3200 psi, the maximum average strain in each cycle varied, and the maximum strain was recorded to be +0.00259. The cracking strain of concrete was observed in the initial cycle, and was found to be +0.00034. The cracking strain in the following 19 cycles ranged from +0.00059 to +0.00068. Residual strain was observed after unloading due to the inability of the concrete cracks to fully close up after unloading. Therefore, the strain in concrete did not return to zero. E.4.2 Phase 2: Diagonal Loading – Elastic Stirrups This phase involves the application of a diagonal axial force on the 30° face of the web of the specimen while maintaining a constant axial force throughout the specimen. This phase was completed in three non-continuous days. The concrete specimen was first loaded axially by increasing the pressure in the horizontal actuators; this procedure was identical to Phase 1 of the test. The diagonal actuator was then set at 30° to the longitudinal axis. The diagonal actuator applied a compression force onto the web of the specimen at 30° to simulate shear in a typical I-girder. The reaction support took up the horizontal component of the diagonal force, while the four stirrups which were connected to a fixed support took up the vertical component of the diagonal force. 188  On the first day, the specimen was loaded with the diagonal actuators 20 times to 80 kN, 20 times to 160 kN, 20 times to 240 kN, and 20 times to 320 kN. At each load cycle, the loading rate and the unloading rate were constant and identical; however, the period was kept at 1 minute per each load cycle for all target loads on this day. A plot of the stress-strain relationship of the four stirrups is shown.  Fig. 129: Test L1 Phase 2: stirrup stress-strain relationship at 80 kN, 160 kN, 240 kN and 320 kN diagonal force. “Theoretical Stress in Stirrups” refers to the equivalent stress each stirrup was experiencing under the applied diagonal load assuming that the corresponding component of the diagonal load was perfectly distributed amongst the four stirrups. As shown, the stress-strain relationship amongst the four stirrups varied. Stirrups D4 and D6, which were located farthest from the diagonal actuator, showed larger strain values than the other two stirrups. The maximum stirrups strains in D4, D5, D6, and D7 at 320 kN were 0.00258, 0.00227, 0.00258, and 0.00174, respectively. 050100150200250300350400450-0.0005 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030Theoretical Stress in Stirrups (MPa)Strain in StirrupsD4D5D6D7189  Slip, here, refers to the distance from a fixed point on the stirrup close to the surface of the concrete specimen to the surface of the concrete specimen; the surface acts as a reference point and as the stirrups were elongated, the fixed point on the stirrup will move away from it. Theoretically, the rate at which the slip increases with strain in the corresponding stirrup will be constant and this rate represents the debonded length in the specimens during fabrication. However, when the hooks of the stirrups begin to pull-out, the debonded length of the stirrup will increase thus the corresponding rate of slip per unit strain will also increase. Slip is plotted against the strain in each of the four stirrups, and the slope of the plot represents the debonded lengths of the stirrups.  Fig. 130: Test L2 Phase 2: stirrup slip-stirrup strain interaction at 80 kN, 160 kN, 240 kN and 320 kN diagonal force. Readings D8, D9, D10, and D11 are the slip measurements corresponding to stirrups D4, D5, D6, and D7 respectively. The slopes of all four plots are shown to be constant. -0.200.000.200.400.600.801.001.20-0.0005 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030Slip (mm)Strain in StirrupsD4/D8D5/D9D6/D10D7/D11190  More loading cycles were carried out at increasing diagonal loads afterwards. The following table summarizes the number of loading cycles performed during this phase of the test. Table 28: Test L2 Phase 2: summary of load cycles. Diagonal Force (kN) Number of Cycles Notes 80 20  160 20  240 20  320 20  320 180 Extra cycles to further observe the behaviour of the stirrups  The diagonal load-displacement relationship and the slip-strain relationship of the stirrups are plotted for the extra 180 loading cycles in the following two figures.   Fig. 131: Test L2 Phase 2: stirrup stress-strain relationship at 320 kN diagonal force (cycle 81 to 260). 050100150200250300350400450-0.0005 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030Theoretical Stress in Stirrups (MPa)Strain in StirrupsD4D5D6D7191   Fig. 132: Test L2 Phase 2: stirrup slip-strain interaction at 320 kN diagonal force (cycle 81 to 260). No significant increase in the slopes was observed after 180 more cycles at 320 kN were performed. E.4.3 Phase 3: Diagonal Loading – Yielding Stirrups In Phase 3, the horizontal forces were applied to the strands similar to Phase 1 and Phase 2. On top of that, the load in the diagonal compression force was further increased to allow the stirrups to yield. Eighty cycles were performed during this phase at increasing diagonal forces from 360 kN to 500 kN. The stress-strain relationship is plotted. On the 81st cycle, stirrup D5 and D7 failed in tension and the test was then terminated. 0.000.200.400.600.801.001.20-0.0005 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030Slip (mm)Strain in StirrupsD4/D8D5/D9D6/D10D7/D11192   Fig. 133: Test L2 Phase 3: stirrup stress-strain relationship. As shown in Fig. 133, the theoretical stress in the stirrups had exceeded the actual yielding stress of 470 MPa and the shifting of the unloading curves demonstrates that the stirrups had yielded significantly in this phase of the test. The maximum theoretical stirrup stress was measured to be 631 MPa, or 134% of the yield stress. During this phase, the significant strain in the stirrup and the significant slip in the LVDT exceeded the measurement range of the LVDT, thus the test was paused when the LVDT was close to reaching the limit, and the LVDT was recalibrated. The slip-strain relationship is plotted for the same 80 cycles. Because some data was not recorded due to the limitation of the measurement range of the LVDT, the missing data is predicted by assuming that that the slip increased at a constant rate with the strains. 01002003004005006007000.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18Theoretical Stress in Stirrups (MPa)Strain in StirrupsD4D5D6D7193   Fig. 134: Test L2 Phase 3: slip-strain interaction. Shown in Fig. 85, stirrups D5 and D6 have a constant slope, thus no pull-out was observed. Stirrups D4 and D7, however, show a slight change in slope at a strain of +0.065. At the 81st cycle, the test was terminated when stirrup D5 and D7 (located closest to the diagonal actuator) failed and fractured in tension as shown in the following figure. 051015202530354045500.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18Slip (mm)Strain in StirrupsD4/D8D5/D9D6/D10D7/D11194   Fig. 135: Stirrup D5 and D7 fractured at the end of Test L2 Phase 3. 195  Appendix F: Measured Values of Crack Widths This appendix presents the measured crack widths and the corresponding local longitudinal strains estimated in the anchorage tests. The calculations were explained in Chapter 5, and  Fig. 49 in the same Chapter was plotted based on these data. The following tables are included in this Appendix: 1. Table 29: Crack width data of Test T1Table 29: Crack width data of Test T1 2. Table 30: Crack width data of Test L1 3. Table 31: Crack width data of Test L2. 196  Table 29: Crack width data of Test T1.   Load (kN): 0 160 320 Location Relative to LHS (mm) Left Distance (mm) Right Distance (mm) Mean Distance (mm) Width (mm) Average Strain Width (mm) Average Strain Width (mm) Average Strain Top of Flange 165 165 195 180 0.32 0.001778 0.36 0.002000 0.32 0.001778 360 195 130 163 0.20 0.001231 0.20 0.001231 0.22 0.001354 490 130 205 168 0.22 0.001313 0.30 0.001791 0.30 0.001791 695 205 120 163 0.20 0.001231 0.26 0.001600 0.22 0.001354 815 120 170 145 0.20 0.001379 0.24 0.001655 0.28 0.001931 985 170 145 158 0.20 0.001270 0.34 0.002159 0.36 0.002286 1130 145 200 173 0.24 0.001391 0.42 0.002435 0.58 0.003362 1330 200 145 173 0.10 0.000580 0.22 0.001275 0.26 0.001507 Bottom of Flange 175 175 175 175 0.30 0.001714 0.42 0.002400 0.34 0.001943 350 175 125 150 0.22 0.001467 0.22 0.001467 0.18 0.001200 475 125 182 154 0.20 0.001303 0.20 0.001303 0.24 0.001564 657 182 140 161 0.16 0.000994 0.18 0.001118 0.30 0.001863 797 140 145 143 0.20 0.001404 0.26 0.001825 0.32 0.002246 942 145 155 150 0.14 0.000933 0.18 0.001200 0.16 0.001067 1097 155 190 173 0.10 0.000580 0.14 0.000812 0.20 0.001159 1287 190 135 163 0.32 0.001969 0.38 0.002338 0.42 0.002585  197  Table 30: Crack width data of Test L1.     Diagonal Load (kN)     0 180 320 Location Relative to LHS (mm) Left Distance (mm) Right Distance (mm) Mean Distance (mm) Width (mm) Average Strain Width (mm) Average Strain Width (mm) Average Strain Top of Flange 180 180 175 178 0.24 0.001352 0.24 0.001352 0.24 0.001352 355 175 265 220 0.10 0.000455 0.16 0.000727 0.16 0.000727 620 265 240 253 0.20 0.000792 0.24 0.000950 0.24 0.000950 860 240 220 230 0.20 0.000870 0.30 0.001304 0.50 0.002174 1080 220 220 220 0.20 0.000909 0.10 0.000455 0.10 0.000455 1300 220 145 183 0.34 0.001863 0.30 0.001644 0.30 0.001644 Bottom of Flange 155 155 220 188 0.12 0.000640 0.14 0.000747 0.14 0.000747 375 220 200 210 0.26 0.001238 0.26 0.001238 0.26 0.001238 575 200 210 205 0.16 0.000780 0.16 0.000780 0.15 0.000732 785 210 280 245 0.50 0.002041 1.00 0.004082 1.00 0.004082 1065 280 200 240 0.30 0.001250 0.46 0.001917 0.56 0.002333 1265 200 180 190 0.10 0.000526 0.10 0.000526 0.10 0.000526  198  Table 31: Crack width data of Test L2.     Diagonal Load (kN)     0 320 Location Relative to LHS (mm) Left Distance (mm) Right Distance (mm) Mean Distance (mm) Width (mm) Average Strain Width (mm) Average Strain Top of Flange 140 140 215 178 0.40 0.002254 0.40 0.002254 355 215 140 178 0.36 0.002028 0.36 0.002028 495 140 115 128 0.20 0.001569 0.28 0.002196 610 115 155 135 0.12 0.000889 0.24 0.001778 765 155 120 138 0.12 0.000873 0.36 0.002618 885 120 120 120 0.10 0.000833 0.12 0.001000 1005 120 135 128 0.42 0.003294 0.26 0.002039 1140 135 85 110 0.06 0.000545 0.10 0.000909 1225 85 145 115 0.52 0.004522 0.55 0.004783 Bottom of Flange 150 150 80 115 0.20 0.001739 0.20 0.001739 230 80 130 105 0.10 0.000952 0.08 0.000762 360 130 90 110 0.26 0.002364 0.30 0.002727 450 90 150 120 0.30 0.002500 0.34 0.002833 600 150 165 158 0.26 0.001651 0.26 0.001651 765 165 120 143 0.30 0.002105 0.28 0.001965 885 120 150 135 0.34 0.002519 0.44 0.003259 1035 150 120 135 0.30 0.002222 0.86 0.006370 1155 120 130 125 0.34 0.00272 0.22 0.001760 1285 130 135 132.5 0.2 0.001509 0.2 0.001509  

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