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Function and Design of Confinement Reinforcement in Pretensioned Concrete I-Girders

Permanent Link: http://ufdc.ufl.edu/UFE0044574/00001

Material Information

Title: Function and Design of Confinement Reinforcement in Pretensioned Concrete I-Girders
Physical Description: 1 online resource (340 p.)
Language: english
Creator: Ross, Brandon E
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: bridge -- concrete -- confinement -- design -- girder -- pretensioned -- reinforcement -- splitting
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Confinement reinforcement is placed near the end of pretensioned concrete I-girders to enclose prestressing strands in the bottom flange. Experimental and analytical test programs were conducted to investigate the function of confinement reinforcement, and to provide the basis for a confinement reinforcement design model.  Five 54-in. deep Florida I-Beam(FIB-54) girders were fabricated and load tested in the experimental program.  Each end of each girder had a different combination of variables, which resulted in ten unique test specimens.  Variables included: presence or absence of embedded steel bearing plates, quantity and configuration of confinement reinforcement, strand bond pattern, strand quantity, and quantity of horizontal and vertical end region reinforcement.  Data were collected during and after prestress transfer to evaluate the effects of test variables on bottom flange cracking. Load tests were then conducted on each specimen (end) to determine the effects of test variables on girder behavior and capacity.  Specimens were loaded in three-point bending at a shear span-to-depth ratio of 2.0.  Failure modes in the test program included web-shear, bond-shear, and lateral-splitting.  Data from fabrication and load testing were used to validate linear-elastic finite element models.  Validated models were then used to investigate additional variables such as: Bearing pad geometry and stiffness, cross-section geometry, prestress release sequence, and strand transfer length. Building on the experimental and analytical results, serviceability and ultimate strength design models were created for the bottom flange of pretensioned I-girders.  The serviceability model is specific to FIB cross-sections and can be used to evaluate transverse splitting stresses which cause bottom flange cracking.  The ultimate strength model is general for any pretensioned I-girder cross-section and can be used to design bottom flange confinement reinforcement to mitigate lateral-splitting failure.  Both the serviceability and ultimate strength models were found to be in good agreement with experimental data.  Other primary outcomes of the research include an improved understanding of the function of confinement reinforcement during prestress transfer and at ultimate load, and an improved understanding the interaction between confinement reinforcement and the other test variables.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Brandon E Ross.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Hamilton, Homer R.
Local: Co-adviser: Consolazio, Gary R.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044574:00001

Permanent Link: http://ufdc.ufl.edu/UFE0044574/00001

Material Information

Title: Function and Design of Confinement Reinforcement in Pretensioned Concrete I-Girders
Physical Description: 1 online resource (340 p.)
Language: english
Creator: Ross, Brandon E
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: bridge -- concrete -- confinement -- design -- girder -- pretensioned -- reinforcement -- splitting
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Confinement reinforcement is placed near the end of pretensioned concrete I-girders to enclose prestressing strands in the bottom flange. Experimental and analytical test programs were conducted to investigate the function of confinement reinforcement, and to provide the basis for a confinement reinforcement design model.  Five 54-in. deep Florida I-Beam(FIB-54) girders were fabricated and load tested in the experimental program.  Each end of each girder had a different combination of variables, which resulted in ten unique test specimens.  Variables included: presence or absence of embedded steel bearing plates, quantity and configuration of confinement reinforcement, strand bond pattern, strand quantity, and quantity of horizontal and vertical end region reinforcement.  Data were collected during and after prestress transfer to evaluate the effects of test variables on bottom flange cracking. Load tests were then conducted on each specimen (end) to determine the effects of test variables on girder behavior and capacity.  Specimens were loaded in three-point bending at a shear span-to-depth ratio of 2.0.  Failure modes in the test program included web-shear, bond-shear, and lateral-splitting.  Data from fabrication and load testing were used to validate linear-elastic finite element models.  Validated models were then used to investigate additional variables such as: Bearing pad geometry and stiffness, cross-section geometry, prestress release sequence, and strand transfer length. Building on the experimental and analytical results, serviceability and ultimate strength design models were created for the bottom flange of pretensioned I-girders.  The serviceability model is specific to FIB cross-sections and can be used to evaluate transverse splitting stresses which cause bottom flange cracking.  The ultimate strength model is general for any pretensioned I-girder cross-section and can be used to design bottom flange confinement reinforcement to mitigate lateral-splitting failure.  Both the serviceability and ultimate strength models were found to be in good agreement with experimental data.  Other primary outcomes of the research include an improved understanding of the function of confinement reinforcement during prestress transfer and at ultimate load, and an improved understanding the interaction between confinement reinforcement and the other test variables.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Brandon E Ross.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Hamilton, Homer R.
Local: Co-adviser: Consolazio, Gary R.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044574:00001


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1 FUNCTION AND DESIGN OF CONFINEMENT REINFORCEMENT IN PRETENSIONED CONCRETE I GI R DERS By BRANDON E. ROSS A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMEN TS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2012

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2 2012 Brandon E. Ross

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3 To my wife Miche lle and to my children Zane, Annie and Soren

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4 ACKNOWLEDGMENTS I express gratitude to the many individuals and organizations th at have assisted me through the research and writing phases of my dissertation. Foremost I thank my wife Michelle and my children Zane, Annie, and Soren. Their sacrifices and support were and are essential fuel to the pursuit of my personal and profess ional goals. I also thank my advisor Dr. Trey expertise is only surpassed by his exceptional humanity the perfect combination of attributes for a graduate advisor. Dr. Gary Consolazio served as my co advisor Through his encouragement and teaching I was able to lose my fear of finite elements (at least the linear elastic ones). I am appreciative of the comments and support from my other committee members: Dr. Ronald Cook, Dr. Mang Tia, and Dr. Bhavani Sanka r. Technical and financial assistance for my research was provided by the Florida Department of Transportation. The late Marc Ansley served as the FDOT project manager until h is sudden passing in June 2010. I will remember Mr. Ansley for this pearl of w In summer of 2010 Sam Fallaha took over the role as project manager for the has improve d both the quality and the breadth of my research. Mr. Fallaha was also instrumental in seeing that the research schedule did not conflict with the birth of my son, Soren. My wife, son, and I are grateful for this act of kindness. I thank the other FDO T structures research center personnel who assisted in my project: David Allen, Steve Eudy, Tony Hobbs, Will Potter, Paul Tighe, David Wagner

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5 and Chris Weigly Assistance was also given by personnel at the FDOT state material s office: Mark Conley, Alfr ed Camps, Richard DeLorenzo, and Jordan Nelson. Many fellow graduate students and other colleagues at the University of Florida worked on aspects of my research. I thank Abraham Alende, Rafael Asencio, Natassia Brenkus, Kunal Malpani, Scott Maul, Kinsman Pearson, Abhay Singh, and Micha el Willis. Dr. Chris Ferraro of the University of Florida provided tec hni cal assistance to my project, as well as a good laugh when needed. Test specimens we re built by Dura Stress, Inc. of Leesburg, FL and Standard Conc rete Products of Tampa, FL. Ma t er ial for test samples was donated by Erico, Inteel, and CEMEX. My research was funded in part by a University of Florida Alumni Fellowship. I thank the University of Florida for providing me with these funds. Finally, I wish to thank my parents Ann Marie and Dale Ross and my late grandmother Martha (Tilly) Goodrich Johnson. Each has provided me with a love of learning that inspires my work past, present, and future. Go Gators.

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ...... 4 LIST OF TABLES ................................ ................................ ................................ .............. 10 LIST OF FIGURES ................................ ................................ ................................ ............ 12 LIST OF ABBREVIATIONS ................................ ................................ .............................. 21 ABSTRACT ................................ ................................ ................................ ........................ 22 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ ........ 24 Motivation ................................ ................................ ................................ .................... 24 Document Organization ................................ ................................ .............................. 25 Original Contribution ................................ ................................ ................................ ... 26 Background ................................ ................................ ................................ ................. 26 2 REVIEW OF LITERATURE ................................ ................................ ........................ 34 End Region Failure Modes ................................ ................................ ......................... 34 Bond Shear Failure ................................ ................................ .............................. 34 Lateral Splitting Failure ................................ ................................ ........................ 35 Code Requirements ................................ ................................ ................................ .... 35 Confinement Reinforcement during Prestress Transfer ................................ ............ 36 Confinement Reinforcement during Loading ................................ ............................. 37 Shear Capacity ................................ ................................ ................................ ..... 38 Transverse Reinforcement ................................ ................................ .................. 38 Vertical Reinforcement ................................ ................................ ........................ 39 Ductil ity ................................ ................................ ................................ ................. 40 Development Length ................................ ................................ ............................ 40 Shear Friction ................................ ................................ ................................ ....... 41 Hoyer Effect ................................ ................................ ................................ ................ 41 Summary of Literature ................................ ................................ ................................ 42 3 TEST GIRDER DESIGN AND CONSTRUCTION ................................ ..................... 50 Test Girder Classification ................................ ................................ ........................... 50 Test Girder Design ................................ ................................ ................................ ...... 51 Girder Construction ................................ ................................ ................................ ..... 54 Material Properties ................................ ................................ ................................ ...... 58 4 SETUP AND TEST PROCEDURES ................................ ................................ .......... 83

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7 Data Collection during Fabrication ................................ ................................ ............. 83 Load Test Setup and Procedures ................................ ................................ .............. 84 Coordinate System ................................ ................................ ................................ ..... 86 5 INSTRUMENTATION ................................ ................................ ................................ 90 Types and Descriptions ................................ ................................ .............................. 90 Strain Gage Coordinates ................................ ................................ ............................ 92 6 RESULTS AND DISCUSSIO N: FABRICATION ................................ ...................... 108 Strain Data ................................ ................................ ................................ ................ 108 Concrete Strain ................................ ................................ ................................ .. 108 Confineme nt Reinforcement and Bearing Plate Strain ................................ ..... 111 Transfer Length ................................ ................................ ................................ .. 117 Crack Data ................................ ................................ ................................ ................ 120 Girders H and V ................................ ................................ ................................ 122 Girders W, F, and D ................................ ................................ ........................... 124 Variable Comparison and Discussion ................................ ............................... 126 Summary and Conclusions ................................ ................................ ...................... 130 7 RESULTS AND DISCUSSION: LOAD TESTS ................................ ....................... 157 Failure Modes ................................ ................................ ................................ ........... 157 Load Test Results ................................ ................................ ................................ ..... 159 HC ................................ ................................ ................................ ....................... 159 HU ................................ ................................ ................................ ....................... 160 VC ................................ ................................ ................................ ....................... 161 VU ................................ ................................ ................................ ....................... 162 WN ................................ ................................ ................................ ...................... 163 WB ................................ ................................ ................................ ...................... 164 FN ................................ ................................ ................................ ....................... 166 FB ................................ ................................ ................................ ....................... 168 DC ................................ ................................ ................................ ....................... 168 DM ................................ ................................ ................................ ...................... 169 Confinement Reinforcement and Bearing Plates ................................ .................... 171 Girders W and F ................................ ................................ ................................ 171 Girders H and V ................................ ................................ ................................ 174 Bearing Plates ................................ ................................ ................................ .... 175 Variable Comparisons ................................ ................................ .............................. 176 Horizontal Reinforcement ................................ ................................ .................. 177 Embedded Steel Bearing Plate ................................ ................................ ......... 177 Confinement Reinforcement ................................ ................................ .............. 178 Strand Quantity ................................ ................................ ................................ .. 179 Strand Placement ................................ ................................ ............................... 180 Code Comparisons ................................ ................................ ................................ ... 181 Summary and Conclusions ................................ ................................ ...................... 184

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8 8 ANALYTICAL EVALUATION OF GIRDERS UNDER APPLIED LOADS ............... 211 Model Configuration ................................ ................................ ................................ 211 Small Beam Model ................................ ................................ ................................ .... 213 Model Validation and Verification ................................ ................................ ............. 213 Parametric Studies ................................ ................................ ................................ ... 216 Bearing Pad Stiffness ................................ ................................ ........................ 216 Bearing Pad Geometry ................................ ................................ ...................... 216 Effect of Steel Bearing Plate ................................ ................................ .............. 220 Bearing Pad Width Effect on Transverse Force ................................ ............... 221 Par ametric Study Conclusions ................................ ................................ ................. 223 9 ANALYTICAL EVALUATION OF GIRDERS DURING PRESTRESS TRANSFER ................................ ................................ ................................ ............... 247 Model Configuration ................................ ................................ ................................ 247 Model Validation and Verification ................................ ................................ ............. 250 Transverse Force Quantification ................................ ................................ .............. 253 Parametric Studies ................................ ................................ ................................ ... 254 Strand Release Parametric Study ................................ ................................ ..... 254 Bearing Plate Contribution ................................ ................................ ................. 256 Transfer Length Parametric Study ................................ ................................ .... 257 End Stresses due to Prestress Forces ................................ .............................. 258 Transverse Action due t o Self Weight ................................ ............................... 261 Parametric Study Summary and Conclusions ................................ ......................... 263 10 ULTIMATE STRENGTH DESIGN MODEL ................................ ............................. 285 Model Derivation ................................ ................................ ................................ ....... 287 Transverse Tie Force ................................ ................................ ......................... 287 Strand Anchorage Force ................................ ................................ .................... 289 Quantity and Placement ................................ ................................ .................... 292 Model Comparison with Experimental Results ................................ ........................ 294 Summary and Conclusions ................................ ................................ ...................... 296 11 SERVICABILITY MODEL ................................ ................................ ......................... 302 Causes of Bottom Flange Splitting at Prestress Transfer ................................ ....... 303 Hoyer Effect ................................ ................................ ................................ ........ 303 Eccentric Prestress Forces ................................ ................................ ................ 304 Self Weight Reaction ................................ ................................ ......................... 304 Transverse Splitting Stress Model Derivation ................................ .......................... 305 Hoyer Stress ................................ ................................ ................................ ....... 306 Peeling St ress ................................ ................................ ................................ .... 310 Self Weight Reaction Stress ................................ ................................ .............. 312 Superposition of Stresses ................................ ................................ .................. 312 Stress Calculations for Experimental Girders ................................ .......................... 313

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9 Model Comparison with Experimental Crack Data ................................ .................. 316 Summary and Conclusion s ................................ ................................ ...................... 317 12 CONCLUDING REMARKS ................................ ................................ ...................... 330 Experimental Program Summary ................................ ................................ ............. 330 Analytical Program Summary ................................ ................................ ................... 331 Conclusions ................................ ................................ ................................ .............. 332 Function of Confinement Reinforcement ................................ .......................... 332 Interaction of Variables with Confinement Reinforcement ............................... 333 Bottom Flange Serviceability Design Model ................................ ..................... 333 Confinement Reinforcement Ultimate Strength Design Model ......................... 334 Recommendations ................................ ................................ ................................ .... 334 Final Comments ................................ ................................ ................................ ........ 336 LIST OF REFERENCES ................................ ................................ ................................ 337 BIOGRAPHICAL SKETCH ................................ ................................ ............................. 340

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10 LIST OF TABLES Table page 3 1 Test girder and specimen variables ................................ ................................ ....... 78 3 2 Specified material properties ................................ ................................ ................. 78 3 3 Fabrication im portant dates ................................ ................................ ................... 79 3 4 Tested concrete compressive strengths ................................ ................................ 80 3 5 Prestressing steel properties ................................ ................................ ................. 81 3 6 Grout strength for NASP Tests ................................ ................................ .............. 81 3 7 NASP Test Results ................................ ................................ ................................ 81 3 8 Steel reinforcement pr operties ................................ ................................ ............... 82 4 1 Load test dates ................................ ................................ ................................ ....... 89 5 1 Instrumentation types and labels ................................ ................................ ......... 100 5 2 Specimen HC strain gage coordinates ................................ ................................ 101 5 3 Specimen HU strain gage coordinates ................................ ................................ 102 5 4 Specimen VC strain gage coordinates ................................ ................................ 103 5 5 Specimen VU strain gage coordinates ................................ ................................ 104 5 6 Specimen WN strain gage coordinates ................................ ............................... 104 5 7 Specimen WB strain gage coordinates ................................ ............................... 105 5 8 Specimen FN strain gage coordinates ................................ ................................ 105 5 9 Specimen FB strain gage coordinates ................................ ................................ 106 5 10 Specimen DC strain gage coordinates ................................ ................................ 106 5 11 Specimen DM strain gag e coordinates ................................ ............................... 107 6 1 Girders H and V fabrication events and stages ................................ .................. 153 6 2 Tensile strain girders H and V ................................ ................................ ............. 153 6 3 Girders W and F fabrication stages ................................ ................................ ..... 153

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11 6 4 Confinement reinforcement strain after prestress transfer ................................ 154 6 5 Confinement and plate forces ................................ ................................ .............. 154 6 6 Recommended action for web splitting cracks (Tadros et al. 2010) .................. 154 6 7 Girders H and V construction events and inspection dates ................................ 155 6 8 Girders W, F, & D construction events and inspection dates ............................. 156 7 1 Transverse forces in W and F specimens ................................ ........................... 208 7 2 Maximum superimposed shear ................................ ................................ ............ 208 7 3 Variable compariso ns ................................ ................................ ........................... 209 7 4 Material properties for capacity calculations ................................ ....................... 209 7 5 Experimental moments and nominal moment capacities ................................ ... 210 7 6 Experimental shear and nominal shear capacities ................................ ............. 210 8 1 Small beam FE model geometry ................................ ................................ ......... 245 8 2 Bearing stiffness sensitivity study details ................................ ............................ 245 8 3 Model details: parametric study of bearing pad width ................................ ......... 245 8 4 Bearing pad properties ................................ ................................ ......................... 246 9 1 Bearing plate study summary of transverse (x x) stresses and forces .............. 284 9 2 Su mmary of transverse (x x) stress at girder end due to strand cutting ............ 284 9 3 Summary of transverse (x x) stress at girder end due to strand cutting ............ 284 9 4 Transverse (x x) stress due to self weight ................................ .......................... 284 11 1 Strand and concrete properties of experimental girders ................................ ..... 328 11 2 Model vs. FE for maximum peeling stress condition ................................ .......... 328 11 3 Model vs. FE for combined stress condition ................................ ....................... 328 11 4 Hoyer stresses end of specimen WN ................................ ................................ .. 328 11 5 Peeling stresses at end of specimen WN ................................ ........................... 328 11 6 Transverse splitting stresses and splitting crack data ................................ ........ 329

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12 LIST OF FIGURES Figure page 1 1 I Girder highway bridge ................................ ................................ .......................... 29 1 2 Cross section 54 in. deep Florida I Beam ................................ ............................. 29 1 3 End region reinforcement ................................ ................................ ....................... 30 1 4 FIB 54 end region reinforcing det ail ................................ ................................ ...... 30 1 5 Confinement reinforcement ................................ ................................ .................... 31 1 6 End region ................................ ................................ ................................ .............. 31 1 7 End region strut and tie ................................ ................................ ......................... 31 1 8 Shear span ................................ ................................ ................................ ............. 32 1 9 Transfer length ................................ ................................ ................................ ....... 32 1 10 Development length ................................ ................................ ............................... 33 1 11 Strand debonding ................................ ................................ ................................ ... 33 2 1 End region strut and tie behavior ................................ ................................ .......... 44 2 2 Bond shear failure ................................ ................................ ................................ .. 44 2 3 Slitting crack ................................ ................................ ................................ ........... 44 2 4 Confinement reinforcement ................................ ................................ .................... 45 2 5 Splittin g crack at prestress transfer ................................ ................................ ....... 45 2 6 Transverse tie above bearing ................................ ................................ ................ 46 2 7 En d region strut and tie models ................................ ................................ ............. 46 2 8 Flange cracking in girder with debonded s trands concentrated below web ........ 47 2 9 Confinement reinforcement as shear reinforcement ................................ ............. 47 2 10 Shear friction model ................................ ................................ ............................... 48 2 11 Hoyer Effect ................................ ................................ ................................ ............ 49 3 1 Labeling scheme ................................ ................................ ................................ .... 60

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13 3 2 Specimen labels and graphical descriptions ................................ ......................... 61 3 3 Cross section FIB 54 ................................ ................................ ............................. 62 3 4 Strand layout and prestressing details ................................ ................................ .. 62 3 5 Strand bond and shielding patterns ................................ ................................ ....... 63 3 6 Reinforcement for girder H ................................ ................................ ..................... 64 3 7 Reinforcement for girder V ................................ ................................ ..................... 65 3 8 Reinforcement for girders W and F ................................ ................................ ....... 66 3 9 Reinforcement for Girder D ................................ ................................ .................... 67 3 10 Reinforcement and bearing plate details ................................ ............................... 68 3 11 Confinement reinforcement schemes ................................ ................................ .... 69 3 12 Cast in place deck reinforcement ................................ ................................ .......... 69 3 13 Girder orientation during fabrication ................................ ................................ ...... 70 3 14 Tension pattern and wire break locations ................................ ............................. 70 3 15 Reinforceme nt girder H. ................................ ................................ ......................... 71 3 16 Reinforcement girder V ................................ ................................ .......................... 71 3 17 Reinforcement girder W ................................ ................................ ......................... 71 3 18 Reinforcement girder F ................................ ................................ .......................... 7 2 3 19 Reinforcement girder D ................................ ................................ .......................... 72 3 20 Concrete placement and internal consolidat ion phase 1 ................................ ...... 73 3 2 1 Concrete placement phase 2 ................................ ................................ ................. 73 3 22 Girder finished surface ................................ ................................ ........................... 74 3 23 Girders covered with tarps ................................ ................................ ..................... 74 3 24 Strand release patterns ................................ ................................ .......................... 75 3 25 Test girder lifted by crane ................................ ................................ ...................... 75 3 26 Girder resting on dunnage on stressing bed ................................ ......................... 76

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14 3 27 Girder H on truck prior to transit ................................ ................................ ............ 76 3 28 Deck Construction ................................ ................................ ................................ .. 77 3 29 Concrete placement ................................ ................................ ............................... 77 4 1 Test set up ................................ ................................ ................................ .............. 87 4 2 Support conditions ................................ ................................ ................................ .. 87 4 3 Test specimen and load frame ................................ ................................ .............. 88 4 4 Coordinate system relative to load and supports ................................ .................. 88 5 1 MS gage installation ................................ ................................ ............................... 93 5 2 XS gage installation ................................ ................................ ............................... 93 5 3 ES gage installations ................................ ................................ .............................. 94 5 4 V gage installation ................................ ................................ ................................ .. 95 5 5 Wire harness and plywoo d bulkhead ................................ ................................ .... 95 5 6 S gage installation ................................ ................................ ................................ .. 96 5 7 LVDT placement and labels ................................ ................................ ................... 96 5 8 LVDT and support frame ................................ ................................ ........................ 97 5 9 Girder H and V strands monitored by LVDT ................................ ......................... 97 5 1 0 Wood frame and LVDTs ................................ ................................ ........................ 98 5 11 Girder W, F, and D strands monitored by potentiometer ................................ ...... 98 5 12 Aluminum brackets and linear potentiometers on strands ................................ .... 99 5 13 Load cells below hydraulic actuators ................................ ................................ ..... 99 6 1 Girders H and V strand cutting stages ................................ ................................ 133 6 2 Transverse Strain HC ................................ ................................ ........................... 133 6 3 Flange displaced shapes for specimen HC ................................ ......................... 134 6 4 Shear and moment durin g release, lifting, storage ................................ ............. 134 6 5 Girders W and F strand cutting stages ................................ ................................ 135

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15 6 6 Girders W and F strand bond patterns ................................ ................................ 135 6 7 Bearing plate strain ................................ ................................ .............................. 136 6 8 Flange displaced shapes specimens FN and FB ................................ ................ 137 6 9 Displaced shapes specimen WB and WN ................................ ........................... 138 6 10 WB Confinement reinforcement strain at 2 in. and 9 in. from end of girder ....... 139 6 11 WN Confinement reinforcement strain at 2 in. and 9 in. from end of girder ....... 140 6 12 FB confinement reinforcement strain at 2in. and 9in. from end of girder ........... 141 6 13 FN Confinement reinforcement strain at 2in. and 9in. for end of girder ............. 142 6 14 Confinement reinforcement average strain at prestr ess release ....................... 142 6 15 Forces in reinforcement and plates after prestress transfer ............................... 143 6 16 Strain gage s for measuring transfer length ................................ ......................... 144 6 17 Transfer length in girders H and V ................................ ................................ ....... 144 6 18 Transfer length girder F ................................ ................................ ....................... 145 6 19 Web splitting and flange splitting cracks ................................ ............................. 145 6 20 Girder H and V cracks prior to load tests ................................ ............................ 146 6 21 Flange splitting crack intersecting outer strand ................................ ................... 147 6 22 Web splitting cracks specimens H and V ................................ ............................ 147 6 23 Maximum cra ck widths girders H and V ................................ .............................. 148 6 24 Flange splitting crack data girders H and V ................................ ........................ 148 6 25 Girders W, F, & D web and flange split ting cracks ................................ ............. 149 6 26 End of bottom flange covered by portion of steel bulkhead ............................... 150 6 27 Girder F flange splitting cracks ................................ ................................ ............ 150 6 28 Flange splitting cracks girders W, F, and D ................................ ........................ 151 6 29 Maximum crack widths girders W, F, a nd D ................................ ........................ 151 6 30 Web splitting cracks girders W, F, and D ................................ ............................ 152

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16 6 31 Girder D flange splitting cracks ................................ ................................ ............ 152 7 1 Web shear failure ................................ ................................ ................................ 186 7 2 Bond shear failure ................................ ................................ ................................ 186 7 3 Lateral splitting failure ................................ ................................ .......................... 187 7 4 Lateral splitting failure mechanics ................................ ................................ ....... 187 7 5 Specimen HC load test summary ................................ ................................ ........ 188 7 6 Specimen HU load test summary ................................ ................................ ........ 189 7 7 Specimen VC load test summary ................................ ................................ ........ 190 7 8 Specimen VU load test su mmary ................................ ................................ ........ 191 7 9 Specimen WN load test summary ................................ ................................ ....... 192 7 10 Specimen WB load test summary ................................ ................................ ....... 193 7 11 Specimen FN load test summary ................................ ................................ ........ 194 7 12 Strut and tie behavior specimen FN ................................ ................................ .... 195 7 13 Longitudinal splitting cracks on bottom of specimen FN ................................ .. 195 7 14 Confinement reinforcement strain specimen FN ................................ ................. 196 7 15 Spe cimen FB load t est summary ................................ ................................ ......... 197 7 16 Specimen DC load test summary ................................ ................................ ...... 198 7 17 Specimen DM load test summary ................................ ................................ ...... 199 7 18 Strain gage placement girders W, F, and D ................................ ........................ 200 7 19 Confinement stress at shear = 375 kip ................................ ................................ 200 7 20 Confinement stress at ultimate capacity ................................ .............................. 201 7 21 Transverse (x x) stress profiles at bearing plate centerline ................................ 201 7 22 Strain gage placement girders H and V ................................ .............................. 202 7 23 Specimens HC and VC confinement reinforcement and bearing plate transverse (x x) forces due to maximum applied load ................................ ........ 203 7 24 Bearing plate stress due to applied load ................................ ............................. 204

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17 7 25 Bearing plate force due to applied load ................................ ............................... 204 7 26 Percent of transverse force due to applied loads carried by bearing plate ........ 205 7 27 Percent of transverse force carried by bearing plate in WB and FB .................. 205 7 28 Maximum superimposed shear ................................ ................................ ............ 206 7 29 Gi rder D bottom flange cracking ................................ ................................ .......... 206 7 30 Relationship between strand quantity and end region capacity ......................... 207 7 31 Comparison of FB and WB ................................ ................................ ................. 207 8 1 Coordinate sys tem relative to load and supports ................................ ................ 225 8 2 FE Model Configuration ................................ ................................ ....................... 225 8 3 Rigid shell and link elements ................................ ................................ ............... 225 8 4 Bearing Pad ................................ ................................ ................................ .......... 226 8 5 End Region Dimensions ................................ ................................ ...................... 2 26 8 6 FE Model Symmetry ................................ ................................ ............................. 227 8 7 FE Model Top View ................................ ................................ .............................. 227 8 8 Comparison of small beam test set up, FE model details, and FE mesh .......... 228 8 9 Bearing pad axial stiffness ................................ ................................ ................... 229 8 10 Transverse strain (x x) at end of beam for proposed and refined mesh ............ 229 8 11 Small beam transverse (x x) strain profile (V=15kip) ................................ .......... 230 8 12 Small beam load vs deflection at load point ................................ ....................... 230 8 13 Small beam load vs. strain S5 (y y) ................................ ................................ ..... 231 8 14 Small beam load vs. average of strain S11 and S12 (y y) ................................ 231 8 15 Maximum principal tensile (P1) strain location ................................ .................... 232 8 16 Sensitivity study maximum transverse (x x) strain ................................ .............. 232 8 17 FIB and rectangular section FE models ................................ .............................. 233 8 18 Location of maximum flexural strain ................................ ................................ .... 233

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18 8 19 Bursting behavior ................................ ................................ ................................ 234 8 20 Normalized transverse (x x) strain at end of FIB 8 ................................ ............. 234 8 21 Flexural behavior ................................ ................................ ................................ .. 235 8 22 Normalized transverse (x x) strain at end of FIB 16 ................................ ........... 235 8 23 Normalized transverse (x x) strain vs. bearing pad width ................................ ... 236 8 24 Normalized transverse (x x) strain vs. bearing pad width, FIB ........................... 237 8 25 Normalized transverse (x x) strain vs. bearing pad width, Rectangular Section ................................ ................................ ................................ .................. 238 8 26 Normalized transverse (x x) strain vs. bearing pad width, small beam .............. 239 8 27 Steel bearing plate beam and model ................................ ................................ ... 240 8 28 Bearing Plate Discretization ................................ ................................ ................. 241 8 29 Effect of bearing plate and bearing pad width on transverse (x x) strain ........... 241 8 30 Normalized transverse (x x) strain vs. bearing pad width, FIB Section with steel bearing plate ................................ ................................ ................................ 242 8 31 Integration area for transverse force ................................ ................................ ... 243 8 32 Element ( x x ) stress and y z area ................................ ................................ ........ 243 8 33 Transverse (x x) force vs. bearing geometry ................................ ...................... 244 9 1 Coordinate system and free body diagram of girder after prestress transfer .... 264 9 2 FE model details ................................ ................................ ................................ ... 265 9 3 Strand layout and element mesh ................................ ................................ ......... 266 9 4 Verification study mesh densities ................................ ................................ ........ 266 9 5 Verification study principal tensile stresses ................................ ......................... 267 9 6 Displaced shape ................................ ................................ ................................ ... 267 9 7 Comparison of experimental and FE model strains at cracks ............................ 268 9 8 Comparison of experimental and FE model transverse (x x) strain ................... 269 9 9 Comparison experimental and FE model longitudinal (y y) strain ...................... 269

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19 9 10 Comparison experimental and FE model vertical (z z) strain ............................. 270 9 11 Integration area for lateral force ................................ ................................ ........... 270 9 12 Element x x stress and y z area ................................ ................................ .......... 271 9 13 Transverse (x x) stress at stages of prestress transfer ................................ ...... 272 9 14 Transverse force vs. % strands released ................................ ............................ 273 9 15 Transverse (x x) stress distribution at stage 1 ................................ .................... 274 9 16 Transverse (x x) stress distribution at stage 2 ................................ .................... 275 9 17 Transverse force vs. length of prestress transfer ................................ ................ 276 9 18 Transverse stress distribution 17.5in. transfer length ................................ ......... 277 9 19 Transverse stress distribution 42.5in. transfer length ................................ ......... 278 9 20 Length of tension area vs transfer length ................................ ........................... 279 9 21 Transverse (x x) stress at MID section through bottom flange ........................... 279 9 22 Fl ange splitting cracks at girder end ................................ ................................ .... 280 9 23 Lines for stress calculations ................................ ................................ ................. 280 9 24 FE model stresses at girder end ................................ ................................ .......... 281 9 25 Transverse (x x) stress at mid flange line ................................ ........................... 281 9 26 Average transverse (x x) stress at end of girder due to strand cutting .............. 282 9 27 Transverse (x x) stress due to self weight ................................ .......................... 282 9 28 Transverse (x x) stress due to self weight ................................ .......................... 283 10 1 Local and general zones ................................ ................................ ...................... 297 10 2 Illustration of transverse and frictional forces caused by the Hoyer effect ......... 297 10 3 Transverse tie force strut and tie models ................................ ............................ 298 10 4 Node layout ................................ ................................ ................................ .......... 299 10 5 Strand anchora ge force ................................ ................................ ....................... 299 10 6 Design model compared to nominal strength of experimental girders ............... 300

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20 10 7 Design model compared to experime ntal girders at maximum shear ................ 300 10 8 Design model compared to experimental girders at maximum shear ................ 301 11 1 Hoyer Effect ................................ ................................ ................................ .......... 318 11 2 Flange tension due to outer strands ................................ ................................ .... 319 11 3 Camber due to prestress force ................................ ................................ ............ 319 11 4 Self weight reaction effects ................................ ................................ .................. 320 11 5 Flange splitting in experimental girder ................................ ................................ 320 11 6 Strand cu tting conditions ................................ ................................ ...................... 321 11 7 Strand physical analog ................................ ................................ ......................... 321 11 8 Calculated radial stress ( p ) distribution ................................ ............................... 322 11 9 Effect of cover distance on calculated radial stress ( p ) ................................ ...... 322 11 10 Concrete stress distribution due to Hoyer Effect ................................ ................ 323 11 11 Stresses at plane cut through strand and concrete ................................ ............ 323 11 12 Bottom flange free body diagram ................................ ................................ ........ 324 11 13 Analysis sections for FIB bottom flange ................................ .............................. 324 11 14 Strand bond and shielding pattern specimen WN ................................ .............. 325 11 15 Transverse (x x) splitting stress at end of specimen WN ................................ ... 325 11 16 Strand pattern CN, PT, and LB ................................ ................................ ........... 326 11 17 Strand pattern SL ................................ ................................ ................................ 326 11 18 Calculated transverse splitting stress vs. experimental crack length ................ 327 11 19 Calculated transverse splitting s tress vs. experimental crack area ................... 327

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21 LIST OF ABBREVIATION S AASHTO American Association of State Highway and Transportation Officials ACI American Concrete Institute FDOT Florida Department of Transportation FEA Finite Element Analysis FE Finite Element FIB Florida I Beam ES Strain gage placed internally in concrete LRFD Load and resistance factor design LVDT Linear variable differential transformer MCFT Modified Compression Field Theory MS Strain gage placed on mild ste el reinforcement SG Strain gage placed on concrete surface during load testing VWG Vibrating wire strain gage XS Strain gage placed on concrete surface during prestress transfer

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22 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy FUNCTION AND DESIGN OF CONFINEMENT REINFORCEMENT IN PRETENSIONED CONCRETE I GIRDERS By Brandon E. Ross August 2012 Chair: H.R. (Trey) Hamilton III Cochair: Gary R. Consolazio Major: Civil Engineering Confinement reinforcement is placed near the end of pretensioned concrete I girders to enclose prestressing strands in the bottom flange. Experimental and analytical test programs were conducted to investigate the function of confinement reinforcement, and to provide the basis for a confinement reinforcement design model Five 54 in. deep Florida I Beam (FIB 54) girders were fabricated and load tested in the experimental program. Each end of each girder had a different combination of variables which resulted in ten unique test specimens Variables included: presence or absence of embedded steel bearing plates, quantity and configuration of confinement reinforcement, strand bond pattern, strand qu antity, and quantity of horizontal and vertical end region reinforcement. Data were collected during and after prestress transfer to evaluate the effects of test variables on bottom flange cracking. Load tests were then conducted on each specimen (end) t o determine the effects of test variables on girder behavior and capacity. Specimens were loaded in three point bending at a shear span to depth ratio of 2.0. Failure modes in the test program included web shear, bond shear, and lateral splitting. Data from fabrication and load testing were used to

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23 validate linear elastic finite element models. Validated models were then used to investigate additional variables such as: Bearing pad geometry and stiffness, cross section geometry, prestress release seque nce, and strand transfer length. Building on the experimental and analytical results, serviceability and ultimate strength design models were created for the bottom flange of pretensioned I girders. The serviceability model is specific to FIB cross secti ons and can be used to evaluate transverse splitting stresses which cause bottom flange cracking The ultimate strength model is general for any pretensioned I girder cross section and can be used to design bottom flange confinement reinforcement to mitig ate lateral splitting failure. Both the serviceability and ultimate strength model s were found to be in good agreement with experimental data. Other primary outcomes of the research include an improved understanding of the function of c onfinement reinfor cement during prestress transfer and at ultimate load, and an improved understanding the interaction between confinement reinforcement and the other test variables.

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24 CHAPTER 1 INTRODUCTION Motivation oximately half utilize prestressed concrete as the structural system (FHWA, 2010). Simple span pretensioned concrete I girders are the most common type of prestressed concrete system ( Figure 1 1 ). In 2009, the Florida Department of Transportation (FDOT) introduced the Florida I Beam (FIB) ( Figure 1 2 efficient to fabricate, safer to construct, and more cost effect when compared to the [previously] use ). To further improve the efficiency of FIB girders, it is desirable to investigate the feasibility of reducing reinforcement placed in the end region ( Figure 1 3 ). End region reinforcement is specified by FDOT standard details ( Figure 1 4 ), which are based on historic FDOT details, code requirements, and constructability considerations (Nolan 2009; F allaha 2009). There is particular incentive to investigate confinement reinforcement, which is placed in the bottom flange around prestressing strands ( Figure 1 3 ). The current use of confinement reinforcement is limited by the following: Confinement reinforcement approximately doubles the amount of time required to place reinforcement in I girders (Magus 2010). Code provisions governing confinement reinforcement are based on limited experimental data. The interaction of confi nement reinforcement and other end region design variables has not been studied. Code provisions governing confinement reinforcement are prescriptive and do not provide a rational model for design.

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25 Previous research (discussed in the C hapter 2 ) has focus ed on the effec ts of confinement reinforcement but does little to address its function. For purposes of this document and when confinement reinforcement acts in the end region str ucture. R esearch presented in this d ocument ma d e use of analytical and experimental methods to investigate the function of confinement reinforcement. Interaction between confinement reinforcement and other e nd region variables was also considered. One goal of the research wa s to provide a rational model for the design of confinement reinforcement. Experimental results coupled with a rational model may justify a reduction in the quantity of reinforcement in the end region, thereby improving the efficien cy of pretensioned I girders. In addition to having sufficient strength p retensioned I girders must also s ati s fy serviceability requirements. B ottom flange splitting cracks are a particular serviceability concern in girders with relatively slender botto m flanges such as the FIB Accordingly, d evelopment of a serviceability design model for the bottom flange of FIB girders was part of the research program Such a model can improve the efficiency of FIB girders by giving engineers a too l for designing bo ttom flanges that are less prone to splitting cracks D ocument Organization This document begins with a summary of the literature and code provisions germane to confinement reinforcement. Chapters following the literature review describe the experimenta l and analytical research programs and present design models for confinement reinforcement. As relevant chapter s i nclude background information

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26 and conclusions specific to that chapter. The final chapter summarize s the work completed and presents overal l conclusions and recommendations Original Contribution Of the few studies that have been conducted investigating confinement reinforcement, most have focused on the effects of confinement reinforcement and provide little or no information on its funct ion. The first goal of the presented research wa s to understand the function of confinement reinforcement. This means determining how, why, where, and when confinement reinforcement acts in the end region structure. The end region of pretensioned concret e I girders can have many design variations such as: placement and quantity of horizontal and vertical reinforcement, placement and shielding of prestressing strands, magnitude of prestress force, and diameter of prestressing strands; just to name a few. The second goal of this research wa s identification of the ways and means by which confinement reinforcement interacts with other variables in the end region. Building on the outcome of the first two goals, the final goal wa s to create rational procedure s for designing confinement reinforcement. Each of the goals represents an original contribution to the field of structural engineering. Background As with any technical subject, pretensioned concrete has specific jargon. This section discusses some of th e terms, phrases, and concepts germane to the study of pretensioned concrete. Confinement r einforcement Confinement reinforcement is m ild steel reinforcement placed around prestressing strands in the bottom flange of precast pretensioned concrete girders ( Figure 1 5 ).

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27 End r egion T he end region is loosely defined as the portion of a girder located within one and a half member depths from the girder end ( Figure 1 6 ). The end region serves two critical functions: 1) Force transfer between the prestressing strands and concrete, and 2) Delivery of shear forces to the support. Mild reinforcement, including confinement reinforcement, is placed in the end region to aid in these functions. Prestress t rans fer In precast pretensioned concrete construction, concrete is cast around steel strands that have been p reloaded in tension. After conc rete is sufficiently cured tension force in the strands is rel eased, thereby transferring force into the surrounding concrete. This event is referred to as prestress transfer. Flame cutting of the strands is a common method of releasing the prestress force. The effects of prestress transfer are important considerations in the design of end region reinforcement. Stru t and tie b ehavior After cracking, the behavior of concrete members can be modeled by a truss analogy. In this analogy, concrete struts carry compressive forces, and steel ties carry tensile forces ( Figure 1 7 ). B ehavior mode led by the truss analogy is referred to as strut and tie behavior. Strut and tie modeling is one approach for design ing of end region reinforcement. Shear s pan Shear span is the horizontal distance from the support to the point of load application ( Figure 1 8 ). Shear span to depth ratio (or a/d ratio) is often used to describe the lo ading condition of concrete members S hear behavior is, among other factors, a function of the shear span to depth ratio. Strut and tie modeling is generally appropriate for members loaded with relatively small shear span to depth ratios.

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28 Transfer l ength Transfer length is the length over which prestressing force is transferred from prestressing strands into the surrounding concrete ( Figure 1 9 ). Transfer length occurs within the end region. By design the p restress force in a strand is always less than ultimate capacity Hence transfer length is not equivalent to the length required for full strand development. Dev elopment l ength Development length is the length of concrete embedment required to fu lly anchor prestressing strands. Strands with full development length can carry their ultimate tensile capacity ( Figure 1 10 ). Development le ngth is greater than transfer length. Strand debonding (s hielding) Stress in pretensioned concrete girders can be controlled by selectively preventing force transfer between strands and concrete. To prevent force transfer, strands are debonded (also cal led shielding), at the ends of the beam. Debonding is accomplished by placing a sleeve over the strand to prevent bond with the concrete. Debonding moves the transfer length of shielded strands away from the girder end ( Figure 1 11 ). Strand Slip Strand slip is movement of prestressing strands relative to the surrounding concrete due to applied loads. S trand slip generally occur s after the formation of cracks within the strand development length. These cracks reduce the avai lable bond length for developing the strands, thus leading to strand slip once load on the strands exceeds capacity along the reduced embedment length. Strands can still partially develop even after the onset of slip.

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29 Figure 1 1 I Girder highway b ridge (Photos courtesy of B.E. Ross) Figure 1 2 Cross section 54 in. deep Florida I Beam

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30 Figure 1 3 End re gion reinforcement (Photo courtesy of B.E. Ross) Figure 1 4 FIB 54 end region reinforcing detail ( Based on FDOT 2009b)

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31 Figure 1 5 Confinement r einforc ement Figure 1 6 End r egion Figure 1 7 End region strut and t ie

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32 Figure 1 8 Shear s pan Figure 1 9 Transfer l ength

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33 Figure 1 10 Development l ength Figure 1 11 S trand d ebonding

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34 CHAPTER 2 REVIEW OF LITERATURE This cha pter summarizes the work of other researchers regarding confinement reinforcement and other relevant top ics. It is organized topically, beginning with a discussion of end region failure modes. Code requirements regarding confinement reinforcement and end region detailing are also summarized. End Region Failure Mode s Two such failure modes are bond shear failure and lateral splitting failure. Both of these modes have been observed experimentally, and have relevance in the study of confinement reinforcement. Bond Shear Failure After cracks form in the end region, load is carrie d by a strut and tie mechanism ( Figure 2 1 ). If c racks form near the girder end then strand anchorage is interrupted, and the strands may slip ( Figure 2 2 ). Bond shear failure occurs when strands can no longer support load, or when the compression zone crushes due to th e rotation allowed in part by strand slip. This type of failure can be very sudden and has also been called shear failure has been observed during load tests of girders without confinement reinforcem ent (Mar uyama and Rizkalla 1988, Kaufma n and Ramirez 1988, Englekirk and Beres 1994, Llanos et al. 2009), as well as during tests of girders with confinement reinforcement ( Ross et al 2010, Deatherage et al. 1994, Barnes et al. 1999, Kuchma et al. 2008).

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35 Lateral Splitting Failure As with bond shear failure, lateral splitting failure occurs after cracks form in the end region and the girder begins strut and tie behavior. In this failure mode, splitting cracks ( Figure 2 3 ) form due to tran sverse stresses above the support ( Ross et. al. 2010, Llanos et al. 2009, Csagoly 1991). Splitting cracks can lead to strand slip relative to the surrounding concrete. In girders without confinement reinforcement the formation of splitting cracks and th e associated strand slip can lead to sudden girder failure (Ross et al 2010). D evelopment of transverse forces and their relationship to confinement reinforcement ar e primary considerations of the research presented in this document Figure 2 3 shows a splitting crack forming at the centerline of the cross section. Splitting cracks in the outer portion of the bottom flange have also been observed experimentally (Llanos et. al. 2009). Splitting cracks in the flange can also lead to sudden girder failure. Code Requirements Confinement reinforcement is required by AASHTO LRFD article 5.10.10.2 (AASHTO 2009). Figure 2 4 graphically presents the confinement reinforcement requirements. The re quirements are prescriptive, meaning that confinement function of confinement reinforcement is not discussed in the code or in the associated commentary. Strand shielding is addressed by AASHTO LRFD article 5.11.4.3 This article limits shielding to no more than 25% of strands in a girder. Limits are also placed on the percentage of shielded strands in a given row (4 0%) and the quantity strands that

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36 can have sh ielding terminate at the same section (greater of 40% or fo ur strands). Shielding is required to be symmetric about the cross section centerline. Article 5.8.3.5 addresses the amount of longitudinal steel required at any section, including sections near t he supports. Requirements at the support are based on a strut and tie model similar to that shown in Figure 1 7 Sufficient steel must be provided to support the horizontal tie force above the bearing. To prevent bond shear fai lures the Confinement Reinforcement during Prestress Transfer In addition to design for ultimate loads, pretensioned girders must also be designed and detailed for serviceability c riteria arising from fabrication, shipping, deck placement and service Loads from prestress transfer in particular can have negative consequences on performance and durability of girders. Llanos et al (2009) observed splitting cracks at prestress trans fer ( Figure 2 5 ) in the bottom flange of test girders. Splitting cracks formed due to a proble matic strand shielding pattern wherein fully bonded strands were placed in the outer portion of the flange and shielded strands were pl aced below the web. Splitting cracks w ere allowed to propagate because confinement reinforcement was not present. Other researchers (Russell and Burns 1996) recommended the use of confinement reinforcement to prevent splitting at prestress transfer. Rus sell an d Burns (1996) investigated transfer length for 0.5 and 0.6 in. diameter prestressing strands in girders with and without confinement reinforcement. The Overall, confining reinforcement had little or no effect in improving the tran

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37 by mild steel reinforcement were marginally longer than strands where confinement was not provided. Other authors have reported similar findings for 0.7 in. diameter strands (Patzla ff et al. 2010 Akhnoukh 2010). None of the authors investigating transfer length in confined girders reported splitting cracks during prestress transfer. Each concluded that the negligible impact on transfer length was due to the inactivity of confineme nt reinforcement in the absence of cracking. Work regarding confinement reinforcement in the anchorage zone of post tensioned concrete members has been conducted by Breen et al. (1991) and Roberts (1990) The s e work s while useful for post tensioned membe rs, do not apply directly to the design of pretensioned members. In post tensioned concrete prestress force is transferred to the concrete i n a relatively small local zone. I n pretensioned concrete however the prestress force is transferred to the con crete over the relatively large strand transfer length. The local zone in post tensioned members is analogous to an axially loaded column, and confinement reinforcement for the local zone can be designed using an approach similar to columns. As demonstra ted in subsequent chapters of this document, confinement in the bottom flange of pretensioned I girders is used to control cracks and to carry transverse tension forces. These functions are distinct from confinement reinforcement in columns and post tensi oned local zones, which provide confinement to axially loaded concrete. Confinement Reinforcement during Loading Confinement reinforcement has been shown to affect girder performance under applied loads. This section summarizes previous research investig ating the effects of confinement reinforcement on girder strength and behavior during loading.

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38 Shear Capacity Csagoly (1991) tested 16 pretensioned girders, some with confinement reinforcement and some without. Confinement reinforcement improved shear cap acity by an average of 13% relative to girders without confinement. Shahawy et al. (1993) and Ross et al (2010) also tested girders with and without confinement reinforce ment. R esults from Shahawy et al indicate that confinement reinforcement improved shear capacity by 10% to 17%. Ross et al reported an average increase in shear capacity of 25%. Transverse Reinforcement In some cases, equilibrium of strut and tie systems requires the formation of tension ties in bottom flange in the transverse directi on. If confinement reinforcement is not provided to act as the transverse tie, concrete must carry the tension force. This condition is undesirable, and has been found culpable in splitt ing cracks by Csagoly (1991), Llanos et a l. (2009), and Ross et al. (2011a ). ing of the reaction force Figure 2 6 A transverse m as the reaction force is spread from the web to the bearing pad. Splitting cracks form when the transverse force exceeds the concrete tensile capacity. Llanos et al. (2009) also observed splitting failures in load tests of full scale girders, and likewi se attributed these failures to transverse forces above the suppo rt. M echanics leadin g to these transverse forces were different from the Csagoly model, and are described by Figure 2 7 Figure 2 7 a is a model of a girder with bonded strands below the web. Inclined compressive forces travel through the web, arriving at a node

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39 above the support. A tie resists the horizontal component of t he inclined force. Because strands are fully bonded, they can act as the tie, and equilibrium is maintained. In contrast to Figure 2 7 a, Figure 2 7 b models the condition from the Llanos et al. test girders in which fully bonded strands were located at the edges of the flange. Because only the strands in the outside portion of the flange were bonded near the support, they were the only strands able to act as ties ( Figure 2 7 b ) This resulted in a disruption of the node at the support point. Because of the offset between the strut in the web and the two ties (fully bonded strands) in the bottom flange secondary struts formed to transfer the load laterally to the nodes at the ties. Additional secondary struts were essential be tween the support and the nodes at the ties to complete the load path to the support. Both pairs of secondary struts induced horizontal components that acted transverse to the beam. Test beams had no reinforcement (such as confinement reinforcement) to support the transverse force, and edges of the bottom flange peeled or split away at failure ( Figure 2 8 Vertical Reinforcement Another possible function of confinement reinforcement is that of vertical, or orcement. Csagoly (1991) proposed this function and included it in a strut and tie model of the end region. In the model, inclined cracks crossing confinement reinforcement mobilize the confinement steel, thereby generating a vertical force that contributes to the end region shear capacity ( Figure 2 9 ).

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40 Ductility Load tests by Ross et al. (2011a ) demonstrated that c onfinement reinforcement can have a positive effect on girder ductility. Six test girders with confinement reinforcement had an average of 157% more displacement ductility than did the six test girders without confinement. The improvement in ductility is attributed to the mitigation of lateral splitting failure affected by the confinement reinforcement. Morcus et al. (2010) also noted an improvement in ductility in girders with confinement reinforcement. Development Length By restraining cracks, confin ement reinforcement may reduce strand development length. To test this possibility, Patzlaff et al. (2010) load tested (6) pretensioned concrete T beams with varying configurations of confinement reinforcement. In all cases, the girders failed in flexure and at loads sufficient to fully develop the strands. Because the strands reached full development in all tests, no conclusions were made regarding the effect of confinement reinforcement on development length. Akhnoukh (2010) investigated the effects o f confinement reinforcement on development length by conducting pullout tests of 0.7 in diameter strands embedded in 4 ft, 5 ft, and 6 ft long concrete prisms. S pecimens also varied in the quantity and spacing of confinement reinforcement. Pullout tests were terminated when the strand ruptured or when the strand slipped relative to the concrete. The 4 ft specimens with (5) #3 confinement hoops always flailed by strand rupture, whereas the majority of the 4 ft specimens with (3) #3 confinement hoops fail ed by strand slip. The author concluded that confinement reinforcement decreased the development length.

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41 Shear Friction Akhnoukh (2010) proposed a shear friction method for designing confinement reinforcement. Currently this is the only design method in the literature. The Akhnoukh method is based on an assumed crack running through a row of strands, which engages the confinement reinforcement thereby inducing normal and friction forces on the crack plane ( Figure 2 10 ). Equilibr ium is applied in the longitudinal direction to equate the friction force with the force in the strands, resulting in Equation 2 1 Akhnoukh applied this model to design confinement reinforcement for the strand pullout tests discussed previously. It was concluded that the shear friction concept can be used to quantify the effect of confinement reinforcement on strand development. (2 1) Where: A ts = A ps = f tsy = f ps = = Area of transverse (confinement) reinforcement crossing crack (in 2 ) Total area of prestressing strand (in 2 ) Yield strength of transverse (confinement) reinforcement (ksi) Stress in prestressing strands at ultimate capacity (ksi) Coefficient of friction Hoyer Effect The diameter of prestressing strand s decrease s due to the Poisson effect as strands are pretensioned ( Figure 2 11 ). Upon re lease strand tension at the end of the member is relieved, and the strand diamete r increases The surrounding concrete resists the increase in diameter, resulting in tensile forces in the concrete and in mechanical bond between the strand and concrete. R adial strand expansion and concrete tensile stress are greatest at the member end Radial strand expansion and the associate concrete tensile stresses are zero at the end of the transfer length. This

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42 condition is referred to as the Hoyer Effect and is the primary contributor to strand concrete bond capacity. This effect is named for Ewald Hoyer, the German Engineer who first discussed radial expansion of prestressing strands (Hoyer 1939). Oh et al. ( 2006) derived a model for transfer length that accounts for the Hoyer effect. The Oh model is rigorous, utilizing equilibrium, materi al constitutive properties, a nd strain compatibility. The model can be used for calculating stresses at the strand concrete interface and for calculating tensile concrete tensile stresses. Building on the equilibrium compatibility potion of the model, Oh then considers the effects of concrete cracking adjacent to the strands within the transfer length. The full model ( including crack effects ) was compared to experimental tests of transfer length and found to have good correlation Summary of Literature The following conclusions are made based on the aggregate findings of the relevant literature. Results from two or more authors support each conclusion. The presence of confinement reinforcement does not prevent strand slip Confinement reinforcement is in active until engaged by cracks in adjacent concrete Confinement reinforcement has negligible effect on transfer length in uncracked concrete Confinement reinforcement improves shear capacity and ductility of girders Transverse tensile forces forming above the bearing can lead to splitting cracks in concrete girders Transverse tensile forces form due to applied loads and the Hoyer effect Based on limited treatment or complete absence in the literature, the following topics are deserving of additional attenti on:

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43 Function of confinement reinforcement at prestress transfer and ultimate strength Effect of confinement reinforcement on development length Optimal quantity and placement of confinement reinforcement Relationship between confinement reinforcement and s plitting failure Effect of prestress force on bottom flange transverse tensile stress Effect of conf inement reinforcement on strand concrete bond capacity Interaction of confinement reinforcement with other end region variables Rational confinement reinfor cement design methods

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44 Figure 2 1 End region strut and tie b ehavior Figure 2 2 Bond shear f ailure Figure 2 3 Slitting c rack

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45 Figure 2 4 Confinement r einforcement ( Based on AASHTO 2007 ) Figure 2 5 Splitting crack at prestress transfer (Photos courtesy o f B.E. Ross)

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46 Figure 2 6 Transverse tie above bearing ( Based on Csagoly 1991) A B Figure 2 7 End region s trut a nd tie model s. A) G irders w ith fully bonded strands below web B) Girder with debonded strands concentrated below web

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47 A B Figure 2 8 Flange cracking in girder with debonded strands concentrated below web A) Side end v iew, B) Close up of end. (Photos courtesy of B.E. Ross) Figure 2 9 Confinement reinforcement as shear reinforcement

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48 Figure 2 10 Shear friction m odel ( Ba sed on Akhnoukh 2010)

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49 Figure 2 11 Hoyer Effect A) Strand before stressing, B) Strand after prestressing, C) Concrete cast around strand, D) Stresses and forces after transfer.

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50 CHAPTER 3 TEST GIRDER DESIGN A ND CONSTRUCTION Five 54 in. deep Florida I Beam ( FIB 54 ) girders were fabricated and tested to evaluate the effects of end region detailing on girder behavior and capacity Variables in the test program include d : quantity of horizontal and vertical mild rein forcement in the end region, quantity or lack of confinement reinforcement strand debonding pattern, and presence or lack of embedded steel bearing plates This chapter presents details of the girders, construction procedures, and material properti es. Th e labeling convention used to identify the different girders and specimens is also presented. Test Girder Classification Each end of each girder had a un ique combinat ion of variables Because of the unique detailing, each end will be referred to as a sepa document. Figure 3 1 presents the nomenclature used to label specimen s and girders The first letter in the label identifies the girder and the second letter is used to designate the end Both letter s combine to form a specimen label. Letters used in the labels describe the key variable s associated with each girder and specimen. A complete description of variables is contained in Table 3 1 Schematic representa tions of each specimen and the assoicated variables are shown in Figure 3 2 Girders were constructed in two phases. The final column in Table 3 1 notes the construction phase for each test girder. Phas e 1 girders were constructed at Dura Stress Inc. in Leesburg, FL in August of 2010. Phase 2 girders were constructed at Standard Concrete Products in Tampa, FL in February of 2012. Meetings were held with the FDOT, the project sponsor, prior to each const ruciton phase to solicite input on test variables. Variables in phase I include the presence or

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51 lack of confinement rienforcement and quanity of mild steel reinforcement in the end region. Variables tested in phase II include confinement reinofrcement co nfiguration, the presence or lack of steel bearing plates, and the strand bond pattern. Test Girder Design Test girder prototype design was based on girders used in a n existing bridge in Clay County, FL which had the FIB 54 cross section ( Figure 3 3 ) and spanned approximately 120 ft. The strand pattern and reinforcement for the prototype girder were designed based on these conditions. Due to laboratory space restrictions, the test girder length was reduced to 49 .5 ft The s ho rter length however, still allowed for evaluation of the end region detailing which w as the primary focus of the research program The prototype design called for (52) 0. 6 in. diameter prestressing strands in the bottom flange and (4) 3/ 8 in. diameter st rands in the top flange ( Figure 3 4 ) using the Figure 3 5 While strand bond patterns were varied among the specimens as indicated in Figure 3 5 the strand diameter, positions, and total prestress force were constant. The design pattern had six partially shielded strands and seven fully shielded strands. Fully shielded strands in the test girders correspond to locations in t he prototype with shielding l engths of 20 ft or 35 ft. Because test girders were shorter than the prototype, these shielding lengths resulted in fully shielded strands in the test girders. Some strands in Figure 3 5 are denoted designation is not strictly accurate for girders W, F, and D. All strands in these girders were bonded to the concrete for at least 18 in. at the girder center span. This was done for safety reasons so that the strands would be restrained from dangerous whipping

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52 movements during release of prestress forces. Bonding at the center 18 in. did not affect the end regions where load tests were conducted. The web pattern and flange pattern ( Figure 3 5 ) were designed to test the effect of strand placement on end region behavior and capacity. These patterns were created by partially shielding strands in select locations. Both patterns violate current AASHTO LRFD requirements for quantity and pla cement of shielding but we re useful for research purposes The two outermost strands in each pattern were fully bonded so that confinement reinforcement could be secured to these strands during fabrication. M ild reinforcement details ( Figure 3 6 through Figure 3 9 ) were based on the prototype girder and on FDOT Florida I 54 B eam Interim Standard Details (FDOT, 2008 2010 ). Bar labels are similar to those used in FDOT standards. The num er ic portion of e ach label indicates the size of bar (i.e. 5A is a #5 bar). Reinforcement bending and bearing plates details are shown in Figure 3 10 The different type s of bar s will be described in the following paragraphs. 5A B ars placed lo ngitud inally in the top flange and we re continuous for the entire length of the girder. Splices of 5A bars were at least 36 in. long. B P G alvanized s teel bearing plate s with headed studs embedded in the concrete at the girder bearing P lates in girders H and V had eight studs, whereas plates in girders W, F, and D had six studs Changes in stud quantity and width were made to follow the FDOT bearing plate detail which changed after girders H and V were constructed. Changes to the FDOT bearing plate de tail were unrelated to the current research program.

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53 3C, 4C, 3D, 4E & 4F Bars placed in the bottom flange as confinement reinforcement around the prestressing strands. Both FDOT and modified confinement schemes were used in the test program and are show n in Figure 3 11 The FDOT confinement scheme used #3 bars and the modified scheme used #4 bars. Fewer bars were used in modified scheme and all bars were placed directly above the bearing. The D and E bars in the modified sche me did not splice at th e cross section centerline as did the C bars in the FDOT scheme. 7G & 8G Bars placed longitudinally in the top flange. These bars were included to control cracking in the top flange after prestress transf er, and are not specified i n FDOT standards The G bars did not extend into the end regions wher e load testing took place. Girders H and V had #7 G bars. Girders W, F, and D had #8 G bars. 5K & 5Ks B ars were pla ced vertically in the web with hooks top and bottom. These bars p r otruded through the top flange to help develop composite action with the cast in place deck. They also acted as shear reinfor cement. The bottom hook on 5K bars was 16 in. long to assist in constructability. The bottom hook on 5Ks bars was only 6 in. lon g. To eliminate any incidental confinement effects from the bottom hooks, 5Ks bars were used in lieu of 5K bars within the end region. 4L & 4L H B ars were placed horizontally in the end region of girder H. The 2008 FIB details specify that 4L bars ex tend beyond the gird er end and hook into a cast in place end diaphragm. T est gird ers did not have end diaphragms. In the absence of a diaphragm to anchor the 4L bars, 4L H bars with headed anchors were used in the web and bottom flange were development w as critical. The 4L bars did not have headed anchors and were placed in the top flange. For reasons unrelated to the experimental

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54 program t he 2010 FDOT standard detail eliminate d the use of end diaphragms and horizontal bars in the end region. Girders W F, and D were designed using the 2010 detail and did not have 4L or 4L H bars 4M Bars placed transversely in the top flange. N Strands Strands placed in the top flange. These strands are sometimes called to support mild reinforcement during fabrication They also provide a nominal amount of crack control to the top flange at prestress transfer 5Y Vertical b a rs bundled with 5K s and 5Z bars at girder ends. These bars are used to control web splitting cr acks that form due to prestressing. 5Z Bars placed vertically within the end region to control web splitting cracks. Cast in place concrete slabs were built on top of the test girders to mimic a bridge deck. The slab was 8 in. thick, 48 in. wide and was reinforced longitudinally and transversely ( Figure 3 12 ). Specified material properties matched FDOT standards. Specifications are listed in Table 3 2 Tested material properties will be discussed in a later section. Girder Construction Girders H and V were fabricated at Dura Stress, Inc. in Leesburg, FL during the first phase of construction Girders W, F, and D were fabricated in the second phase at Standard Concrete Products in Tampa, FL. The fabri cation process was similar for both phases. Differences are specifically noted in the text in this section. Table 3 3 presents a summary of the construction events and dates for both phases. F abrication began with the placement prestressing strands and form bulkheads Plywood bu lkheads were used during phase one Holes were cut in the plywood for

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55 strands to pass through. S tee l bulkheads were used in phase two The steel bulkheads were installed in segments after the strands were tensioned. A hydraulic jack was used to tension the strands J acki ng force was determined from pressure in the hydraulic line a nd was verified by measuring strand e longation. G irders were oriented on stressing beds as shown in Figure 3 13 D ormant strands in the top flange were tensioned first followed by strands in the bottom flange. The same tensioning pattern ( Figure 3 14 ) was used for both phases. Wire breaks occurred in three different stra nds during phase one ( Figure 3 14 ). The wire breaks did not occur inside the test girders so the strand cross section within the girders was not compromised. The jacking force of the strands with broken wires could not be checke d by the elongation method, however the jac king force as determined by pressure in the hydraulic line was still within the specified range. No wires br oke during the second construction phase After tensioning, mild steel reinforcement was placed. S elect bars were instrumented with strain gages prior to placement in the girders Figure 3 15 through Figure 3 19 show the reinforcement in each specimen Concrete was mixed at on site batch plants. For ph ase one girders concrete was placed in two lifts and was consolidated with internal and external vibrators after each lift ( Figure 3 20 ) The internal vibrator was only used on the north side of the web to keep the vibrator away from internal strain gages which were primarily placed on the south side A self consolidating concrete mix was used for phase two ( Figure 3 21 ) and vibration was not necessary Test cylinders were taken by the fabricator s and by the research team from each batch of concrete. T he top surface of each girder was rake d

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56 to intentional ly roughen the surface ( Figure 3 22 ). G irders were covered with heavy tarps during curing ( Figure 3 23 ). Forms were removed six days afte r casting during phase one and three days after casting during phase two Prestress was transferred to the girders the day after form removal. The time between form removal and prestress transfer was used to instal l bonded foil strain gages and to connect the data acquisition system. Two 4x8 fi eld cured cylinders were tested on the day of prestress transfer The average compressive s trength was 6880 psi for phase one and 7320 psi for phase two Both values are abo ve the specified release strength of 6500 psi. Flame cutting was used in both phases to release the prestressing strands. Individual s trands were cut simultaneously at points shown in Figure 3 13 D ormant strands in the top flan ge were cut first, followed by the bottom strands which were cut from the outside in and from bottom to top ( Figure 3 24 ). This release pat tern was selected because it is relatively easy to execute and because it is typical of p recast girders in Florida. Strand cutting was stopped intermittently at multiple stages to obtain strain readings from the vi brating wire strain gages and to check the girders for cracking. For safety reasons, the fully shielded strands in phase one wer e cut la st and were relea sed by a single cut between girders H and V In some cases the fully shielded strands completed slipped out of the girders upon release. This was not an issue in phase two because each strand was at least partially bonded to each girder. T he girders in both phases shifted slightly (less than 1 in.) along the length of the stressing bed multiple times during prestress transfer M ovement events always

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57 corre sponded to strand cuts. A more pronounced shift occurred during phase one a s the final bonded strand was cut. Just after the fi nal bonded strand was cut, girder s H and V each slid approxim ately 2 ft along the stressing bed. After sliding the g ap between girders was approximately 7 ft 6in. To investigate chang es in strain due to lifting ( Figure 3 25 ) girders H and V were lifted by crane immediately a fter prestress transfer was completed Girders were supported by the crane momentarily and then placed on dunnage on the stressing beds ( Figure 3 26 ) Strain data were coll ected during lifting and as girders were placed on dunnage. Afte r the data were collected the girders were taken to a storage yard to await shipping G irders were examined for cracking periodically while in they were held in storage at th e prestress fabrication facilities. Girders w ere trucked to the Marcus H. Ansely FDOT structures laboratory in Tallahassee, FL for deck construction and load testing Strain gages were used to monitor strain in girder H ( phase one ) during transport. Figure 3 27 shows girder H being transported. The black box on top of the girder in the picture housed the data acquisition system. After unloadin g of the test girders in Tallahassee forms were cons tructed and reinforcement was placed for the concrete deck. Wood f orms were affixed to the top flange of the girders using pipe clamps ( Figure 3 28 ). Concrete was prep ared by a local ready mix plant. C ast in place decks were p oured inside the lab. C oncrete was transported from the mix truck to the girders via a bucket and crane ( Figure 3 29 ). Co ncrete was consolidated using hand held and form mounted vibrators. After consolid ation and

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58 screeding the deck s were troweled to a smooth finish. Cyl inders of the concrete were taken for material testing. Material Properties Concrete, mild steel, and prestressing strand were detailed to m atch FDOT specifications FDOT class VI concrete wa s sp ecified for the girders, and FDOT class II concrete 45 00 psi) for the deck. Concrete compressive strength was tested using both 4x8 and 6x12 cylinders Table 3 4 present s the tested concrete strengths. Prestressing strands were Grade 270 low relaxation conforming to ASTM A416. Tested strand properties are shown in Table 3 5 Bond capacity of phase one prestressing strand s was tested in accordance with the proposed standard recommended by the North American Strand Producers (NASP 2009). This test method consists of pull out tests of strand samples embedded in mortar. The method p laces tight requirements on flow an d strength of the mortar. F low must be between 100 and 124, and the strength at the time of the pull out tests must be between 4500psi and 5000psi. The pull out tests must be conducted between 22 and 26 hours after mixing and placing the grout. In spite of effort s to create a grout that would meet specifications, the grout used in the NASP tests failed to achieve the required strength. Table 3 6 lists the grout strengths. Low grout strength was the only deviat ion from the test method. F low of the grout was 107.5. Table 3 7 lists results of the NASP tests. Because the grout strength was less than the value specified by the method, results from NASP tests are conservative when compared to tests that strictly meet the grout strength requirements.

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59 Table 3 8 presents the tes ted material properties for mild steel reinforcement. All reinforcement was ASTM A615 grade 60 with the exception of the 4L H headed bars placed in girder H The supplier of the headed bars provided reinforcing bar s that met ASTM A706. During phase one t he #3 bars came from two separate suppliers; Table 3 8 presents values from both suppliers.

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60 Figure 3 1 Labeling scheme

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61 Figure 3 2 Specimen labels and graphical descriptions

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62 Figure 3 3 Cross section FIB 54 Figure 3 4 Strand layout an d prestressing details

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63 Figure 3 5 Strand bond and shielding patterns

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64 Figure 3 6 Reinforcement for girder H

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65 Figure 3 7 Reinforcement for girder V

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66 Figure 3 8 Reinforcement for girders W and F

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67 Figure 3 9 Reinforcement for Girder D

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68 Figure 3 10 Reinforcement and bearing plate details

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69 Figure 3 11 Confinement reinforcement schemes Figure 3 12 Cast in place deck r einforcement

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70 Figure 3 13 Girder orientation during fabrication Figure 3 14 Tension pattern and wire break locations

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71 A B Figure 3 15 Reinforcement girder H A) Specimen HC, B) Specimen HU. (Photos courtesy of B.E. Ross) A B Figure 3 16 Reinforcement girder V A) Specimen VC, B) Specimen VU. (Photos courtesy of B.E. Ross) A B Figure 3 17 Reinforcement girder W A) Specimen WN, B) Specimen WB. (Photos courtesy of B.E. Ross)

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72 A B Figure 3 18 Reinforcement girder F A) Specimen FN, B) Specimen FB. (Photos courtesy of B.E. Ross) A B Figure 3 19 Reinforcement girder D A) Specimen DC, B) Specimen DM. (Photos courtesy of B.E. R oss)

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73 Figure 3 20 Concrete placement and internal consolidation phase 1 (Photo courtesy of B.E. Ross) Figure 3 21 Concrete placement phase 2 (Photo c ourtesy of B.E. Ross)

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74 Figure 3 22 Girder finished surface (Photo courtesy of B.E. Ross) Figure 3 23 Girders covered with tarps (Photo courtesy of B. E. Ross)

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75 Figure 3 24 Strand release p attern s Figure 3 25 Test girder lifted by crane (Photo courtesy of B.E. Ross)

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76 Figure 3 26 Girder resting on dunnage on stressing bed (Photo courtesy of B.E. Ross) Figure 3 27 Girder H on truck prior to transit (Photo courtesy of B.E. Ross)

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77 A B Figure 3 28 Deck Construction. A) Reinforcement and formwork, B) Wood formwork. (Photos courtesy of B.E. Ross) A B Figure 3 29 Concrete placement A) Bucket an d chute, B) Bucket lifted by crane. (Photos courtesy of B.E. Ross)

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78 Table 3 1 Test girder and specimen variables Test Girder Specimen Bearing plate Mild reinforcement Strand bond pattern Confinement reinf orcement Phase Vertical Horizontal H HC Yes FDOT Yes Design FDOT 1 HU Yes FDOT Yes Design No 1 V VC Yes Mod No Design FDOT 1 VU Yes Mod No Design No 1 W WN No FDOT No Web Mod 2 WB Yes FDOT No Web Mod 2 F FN No FDOT No Flange Mod 2 FB Yes FDOT No Flange Mod 2 D DC Yes FDOT No Design FDOT 2 DM Yes FDOT No Design Mod 2 FDOT: Detailed per FDOT design standards Mod: Detailed with modifications to FDOT design standards Web: Fully bonded strands placed below web Flange: Fully bonded strands placed in outer portion of flange Design: Strand pattern based on prototype design Table 3 2 Specified material properties Material Specification Girder Concrete FDOT class VI 8500 psi 28 day comp ressive strength 6000 psi compressive strength at prestress transfer Deck Concrete FDOT class II 4500 psi 28 day compressive strength Prestressing Strand ASTM A416 270 ksi ultimate strength Low relaxation Mild Reinforcement ASTM A615 60 ksi yield str ength

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79 Table 3 3 Fabrication important dates Event Phase 1 Date Phase 2 Date Strands tensioned August 30, 2010 February 13, 2012 Concrete poured September 1, 2010 February 17, 2012 Concrete exceeds rel ease strength September 3, 2010 February 20, 2012 Forms removed September 7, 2010 February 20, 2012 Prestress released September 8, 2010 February 21, 2012 Moved to storage September 8, 2010 February 22, 2012 Trucked to FDOT laboratory February 23, 2011 April 30, 2012 Deck c ast April 6, 2011 May 7, 2012 Load testing May 9, 2011 to May 17, 2011 May 23, 2012 to June 1, 2012

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80 Table 3 4 Tested concrete compressive s trength s Material Cast date Test date A verage strength (psi) Sample size Testing agent* Cure Method Phase1 Girder Concrete 8 31 10 9 3 10 6400 (2) 4x8 cylinders 1 Wet 9 8 10 6940 (2) 4x8 cylinders 1 Field 9 8 10 6880 (3) 6x12 cylinders 2 Field 9 29 10 9185 (3) 4x8 cylinders 1 Wet 9 29 10 8235 (3) 6x12 cylinders 2 Field 9 28 10 8790 (3) 4x8 cylinders 3 Wet 5 10 11 10,950 (4) 6x12 cylinders 4 Wet 5 17 11 11,610 (3) 4x7 cores girder FH 4 Core 5 18 11 10,510 (3) 4x7 cores girder MH 4 Core Phase 1 Deck Concrete 4 6 11 5 4 11 6615 (3) 6x12 cylinders 4 Field 5 18 11 6950 (3) 6x12 cylinders 4 Field Phase 2 Girder Concrete 2 17 12 2 20 12 7050 (2) 4x8 cylinders 1 Wet 2 21 12 7330 (2) 4x8 cylinders 1 Field 3 02 12 8790 (2) 4x8 cylinders 1 Wet 3 16 12 8250 (3) 6x12 cyl inders 2 Wet 3 16 12 9210 (3) 4x8 cylinders 1 Wet 5 30 12 10,520 (3) 6x12 cylinders 4 Field Phase 2 Deck Concrete 5 7 12 5 30 12 6400 (9) 6x12 cylinders 4 Field 1. Tested by girder fabricator 2. Tested by FDOT State Materials Office 3. Tes ted by FDOT District Office 4. Tested by FDOT Structures Research Center

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81 Table 3 5 Prestressing steel properties Material Stress at 1% elongation Ultimate stress Elongation at ultimate stress Testing age nt* Phase 1 Prestressing Strand 259 ksi 285 ksi 5.47% 1 271 ksi 284 ksi 4.59% 2 Phase 2 Prestressing Strand 261 ksi 287 ksi 5.38% 1 259 ksi 285 ksi NA 2 1. Strand supplier 2. FDOT State Materials Office (average of 4 samples) Table 3 6 Grout s trength for NASP Tests Time of test (Time zero at mixing of grout) Grout Strength* (average of (3) cubes) 22 hr 4210 psi 23 hr 4380 psi 24 hr 4030 psi 25 hr 4280 psi 26 hr 4340 psi Test method req uires a strength between 4500 and 5000 psi Table 3 7 NASP Test Results Test Number Load at 0.1 in. strand slip 1 22.08 kip 2 22.80 kip 3 24.09 kip 4 22.93 kip 5 22.98 kip 6 22.57 kip Average 22.91 ki p

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82 Table 3 8 Steel reinforcement properties Material Yield Stress Ultimate Stress Elongation at Ultimate Stress Testing agent* Phase 1 #4 Headed rebar 68.8 ksi 90.8 ksi 19% 1 64.6 ksi 89.6 ksi 18% 2 Ph ase 1 #3 confinement rebar 72.9 ksi 114.8 ksi 11% 1 78.6 ksi 121.3 ksi 9% 1 69.5 ksi 106.2 ksi 9% 2 Phase 1 #5 vertical rebar 66.1 ksi 100.7 ksi 17% 1 68.6 ksi 105.7 ksi 9 % 2 Phase 2 #3 confinement rebar 73.6 ksi 113.3 ksi 12% 1 85.2 ksi 1 15.4 ksi 12% 2 Phase 2 #4 confinement rebar 70.0 ksi 109.1 ksi 11% 1 76.4 ksi 106.8 ksi 11% 2 Phase 2 #5 vertical rebar 64.5 ksi 103.2 ksi 11% 1 63.2 ksi 103.5 ksi 13% 2 1. Rebar supplier 2. FDOT State Materials Office (average of 2 samples minimum)

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83 CHAPTER 4 SETUP AND TEST PROCE DURES Data Collection during Fabrication Strain and crack data were collected during various stages of fabrication including: prestress transfer, lifting, storage, trucking and deck construction This section d escribes the procedures used to collect data during each stage of construction. Data from strain gages were monitored and logged using a computerized data acquisition system powered by portable generator s Data from vibrating wire strain gages were moni tored using an electronic readout box and logged manually Crack data were collected through visual obser vation and using a microscope. Instrumentation details are presented in Chapter 5. Pr estress t ransfer Data were collected from each girder during prestress transfer. Prior to transfer g irders were examined for cracks and null readings were taken from all gages. For girders H and V, t he acquisition system and generator were secured to the top of the girders For girders F, W, and D the acquisitio n system was placed in a van adjacent to the stressing bed. Strand cutting was paused a t various times during prestress transfer to allow for visual e valuations and to take readings from the vibrating wire gages. Visual evaluat ions and vibrating wire rea dings were also conducted after prestress transfer was complete. Crack widths were measured by microscope at few locations on each specimen C rack locations were marked with a crayon or marker and documented by photograph. Lifting Data were colle cted during lifting of girders H and V only. Immediately following the conclusion of prestress transfer, girder H and V were lifted by crane, held in place for approximately four minutes, and then place d onto dunnage. Strain data

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84 were collected throughout thi s process. The data acquisition systems and generators were strapped to the top of the girders to secure them during lifting. Vibrating wire gage readings were taken and visual crack evaluations were conducted during each step. Storage All girders rece ived periodic visual e valuations while they were in storage at the precast facilities Cracks were marked then documented by photograph. Crack widths were measured by microscope at few locations on each specimen Dates of visual e valuations are listed in Table 3 3 Vibrating wire gage data were also collected while the girders were in storage. Trucking. Internal and external strain gages were used to monitor concrete strains in girder H during trucking from the precast faci lity to the laboratory. The data acquisition system and generator were strapped to the top of the girder to secure them during transport. Vibrating wire readings were taken before and after trucking. A visual evaluation was given to a ll girders upon arr ival at the laboratory. Deck c onstruction All girders were visually e valuated for cracks before and after construction of the cast in place decks. Vibrating wire gage readings were also taken before and after deck construction. Material p roperties S amples of reinforcement, strand, and concrete were taken during each construction phase and were tested to determine the associated material properties. Documentation regarding material properties was also obtained from the supplier of each material Load Test Setup and Procedures Load tests were conducted at the FDOT M. H. Ansley Structures Research Center in Tallahassee, FL Test dates are listed in Table 4 1 Load tests were conducted on

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85 both ends of ea ch girder. After t he first end was tested, the supports and load point were moved and the opposite end was tested. For purposes of this document each end will be referred to as a separate specimen. Each specimen was loaded at least twice. The first loa ding simulated the service load The simulated service load was approximately 300kip and was determined from the prototype girder that was used as a basis for the test girder designs Once the service load was reached, the load was held constant and cracks were identified and marked. After the cracks were marked the load was removed. The second loading determined the spec oad displacement plot was monitored real time during the ultimate load test. Load was applied until it was apparent from t he load displacement plot that a peak load had been reached. Cracking was documented after the ultimate load test was complete. Load and support geometry are shown in Figure 4 1 Each support consisted of a 10 in. x 32 in reinf orced bearing pad. P ads were constructed according to FDOT design interim design standards (FDOT 2009 d ) The bearing pad at the near support was centered below the embedded steel bearing plate ( Figure 4 2 ) Load wa s applied to the specimen using side by side hydraulic actuators. The load rat e was controlled by adjusting a pump that pressurized the hydraulic system. The combined load rate varied from 0.1 kip/sec to 0.6 kip /sec, with the typical rate being approxima tely 0.4 kip /sec. Load was spread from the actuators to the girders through steel plates and a 10 in. x 30 in. reinforced neoprene bearing pad. A reaction frame was used to transmit load from the actuators to the strong floor ( Figure 4 3 ).

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86 Load, displacement, strand slip, and strain data were continuously collected during the service and ultimate load tests. Strain from the vibrating wires strain gages was collect at discrete points during load testing. Concrete samples were t ested in conjunction with the load tests to determine compressive strength at the time of load testing. Coordinate System A consistent coordinate system is used throughout this document. The system is used to define instrumentation locations and to identi fy the direction of strains, stress, and forces. The origin for the coordinate system is placed at the centerline of the cross section, at the bottom of the girder, and at the girder end ( Figure 4 4 ). The z direction is vertical the x direction is horizontal across the width of the girder, and the y direction is horizontal along the span length. The support nearest the origin is denoted as the near support, and the opposite end is denoted as the far support.

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87 Figure 4 1 Test s et up A B Figure 4 2 Support conditions. A) Bearing, B) L oad point (Photos courtesy of B.E. Ross)

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88 A B Figure 4 3 Test specimen and load frame A) Looking at top of girder, B) Looking at side end of girder. (Photos courtesy of B.E. Ross) Figure 4 4 Coordinate system relative to load and support s

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89 Table 4 1 Load test dates Specimen Service load test Ultimate strength test HC May 11, 2011 May 11, 2011 HU May 9, 2011 May 10, 2011 VC May 13, 2011 May 13, 2011 VU May 17, 2011 May 17,2011 WN May 23 2012 May 23, 2012 WB May 25, 2012 May 25, 2012 FN May 29, 2012 May 29, 2012 FB May 30, 2012 May 30, 2012 DC May 31, 2012 May 31, 2012 DM June 1, 2012 June 1, 2012

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90 CHAPTER 5 INSTRUMENTATION Strain, displacement, force, and crack data were collected durin g fabrication and load testing. This chapter describes the instrumentation used to collect data and the labeling scheme that was used to identify the various instruments Types and Descriptions Data were collected using load cells, LVDTs, linear potenti ometers, variable resistance strain gages and vibrating wire strain gages. Table 5 1 lists the different types of instrumentation and the associated labels. With the exception of the vibrating wire strain gages, all data were lo gged electronically. Vibrating wire gage data were logged manually from an electronic readout box. MS strain gages were attached to select mild reinforcement and to bearing plates prior to placement in the test girders ( Figure 5 1 ) MS gages had a gage length of 5mm and were used to monitor strain during prestress transfer and load testing. XS strain gag es ( Figure 5 2 ) were attached to the surface of test girders immediately after formwork was removed. These gages were used to measure concrete strains during prestress transfer, lifting, and trucking XS gages had a 60mm gage length. ES gages were embedded in the test girders and were used to monitor concrete strain during all phases of fabrication and l oad testing ES gages had a gage length of 60mm. Figure 5 3 shows ES gage installations prior to concrete placement V series gages were vibrating wire strain gages which were embedded in the test girders. Theses gages had a gage length of 152mm and were used to measure concrete strain during all phases of fabrication and load testing Figure 5 3 shows a V

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91 series gage installation prior to concrete placement. Because vibrating wire gages do not e xperience electronic drift over time, they were particularly useful in monitoring long term prestress losses. W ire l eads were collected into harness es a fter all internal instrumentation (MS, ES, and V series gages) had been placed in the girders. H arnesse s in girders F and V were routed to the end s of the girders and exited through holes in the wood bulkhead s ( Figure 5 5 ). Harnesses in girders F, W, and D were routed to the top of the girders. W ire harness es were covered with a rubber sleeve and duct tape to protect the wires during concrete casting. A label was placed at the end of each wire lead for identification purposes. Prior to load testing S and R series strain gages were installed at discrete loca tions on girde r surface s ( Figure 5 6 ) These gages had 60mm gages lengths. R series gages were strain rosettes built up from three individual strain gages. L series instruments were LVDTs used to monitor vertical displacement during load tests. Lab els and locations of the LVDTs measuring vertical displacement are shown in Figure 5 7 LVDTs were mounted to fixed support structures as shown in Figure 5 8 LVDTs were also used to monitor strand slip for girders H and V Monitored strands are shown in Figure 5 9 LVDTs for monitoring strand slip were mounted to a wooden bracket affixed to the girder end ( Figure 5 10 ). This set up was unreliable bec ause cracking in the concrete caused the LVDT frame to shift during load testing. Rather than LVDTs, P series variable resistant potentiometers were used to measure strand slip for girders F, W, and D. Instrumented strands are shown in Figure

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92 5 11 P series instruments were mounted directly to the strands using custom machined aluminum b rackets and set screws ( Figure 5 12 ). This set up did not have the problems associated with the wooden frame used fo r girders H and V. Load cells ( Figure 5 13 ) were used to measure the force applied during the load tests. A hydraulic system was used to apply the loads, and a pressure transducer was used to measure pressure in the hydraulic l ine during testing Both f orce and pressure data were logged electronica lly, along with displacement and strain data from the other instruments. Strain Gage Coordinates Figures in this document that present strain data typically also contain information regarding the location of gage (s) from which the data were collected Information in the figures specific coordinates. Table 5 2 through Table 5 11 give s pecific coordinates of gages referenced in this document C oordinate s are based on the system defined in Figure 4 4 Many gages used in the experimental program are not specifically referred to in this document. Additional information regarding these instruments will be available in a forthcoming report for the FDOT (Ross et al., in preparation ).

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93 A B Figure 5 1 MS gage installation A) G age before protective covering, B) Protective cover and label. (Photos courtesy of B.E. Ross) Figure 5 2 XS gage installation (Photo courtesy of B.E. Ross)

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94 A B Figure 5 3 E S gage installation s A) Gage installed vertically, B) Gage installed transversely. (Photos courtesy of B.E. Ross)

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95 Figure 5 4 V gage installation (looking down) (Photo cou rtesy of B.E. Ross) Figure 5 5 Wire harness and plywood bulkhead (Photo courtesy of B.E. Ross)

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96 A B Figure 5 6 S gage installation A) Gage on top of bottom flange, B) Close up of gage. (Photos courtesy of B.E. Ross) Figure 5 7 LVDT placement and labels

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97 Figure 5 8 LVDT and support frame (Photo courtesy of B.E. Ross) Figure 5 9 Girder H and V strands monitored by LVDT

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98 Figure 5 10 Wood frame and LVDTs (Photo courtesy of B.E. Ross) Figure 5 11 Girder W, F, and D strands monitored by potentiometer

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99 Figure 5 12 Aluminum bracket s and linear potentiometer s on strands (Photo courtesy of B.E. Ross) Figure 5 13 Load cells below hydraulic actuators (Photo courtesy of B.E. Ross)

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100 Table 5 1 Instrumentation types and labels Label Type Placement MS Fo il strain gage Reinforcement & bearing plates XS Foil strain gage Concrete surface ES Embedded strain gage Concrete interior V Vibrating wire strain gage Concrete interior S Foil strain gage Concrete surface R Foil strain rosette Concrete surface L Linear variable displacement transducer (LVDT) Load point, supports, & strands P Linear potentiometer Strands -Load Cell Load point

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101 Table 5 2 Specimen HC strain gage coordinate s Instrument X (in.) Y (in.) Z (in.) Orientation Reference(s) XS1 0.5 0 36 Z Figure 9 10 XS2 0 0 24 Z Figure 9 7 XS3 0 0 12 X Figure 6 2 Figure 9 7 Figure 6 3 Table 6 2 XS5 19 18 6 Y Figure 6 17 Figure 9 9 XS6 19 30 6 Y Figure 6 17 Figure 9 9 XS7 19 36 6 Y Figure 6 17 Figure 9 9 XS8 19 42 6 Y Figure 6 17 Figure 9 9 XS9 19 48 6 Y Figure 6 17 Figure 9 9 XS10 19 54 6 Y Figure 6 17 Figure 9 9 XS11 19 18 6 Y Figure 6 17 Figure 9 9 XS12 19 54 6 Y Figure 6 17 Figure 9 9 ES1 0 5 35 Z Figure 9 10 ES2 3 27 8 X Figure 6 2 Table 6 2 ES3 3 47 8 X Figure 6 2 Table 6 2 MS1 0.5 2 0.5 X Figure 7 22 MS2 0 13 0.5 X Figure 7 22 MS10 0 2 1 0 X Figure 7 22 MS14 0 2 2 X Figure 7 22 MS15 1 2 16 X Z Figure 7 22 MS20 0 8 10 X Figure 7 22 MS24 13 8 2 X Figure 7 22 MS25 1 9 16 X Z Figure 7 22 MS30 0 22 10 X Figure 7 22 MS34 0 22 2 X Figure 7 22 MS35 1 22 16 X Z Figure 7 22 MS40 0 66 10 X Figure 7 22 MS44 0 66 2 X Figure 7 22 MS45 1 67 16 X Z Figure 7 22 MS51 0 2 0 X Figure 7 22 MS52 0 13 0 X Figure 7 22 V2 0 2 8 X Figure 9 8

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102 Table 5 3 Specimen HU strain gage coordinates Instrument X (in.) Y (in.) Z (in.) Orientation Reference(s) XS3 0 0 12 X Figure 6 3 Table 6 2 XS5 19 18 6 Y Figure 6 17 Figure 9 9 XS6 19 30 6 Y Figure 6 17 Figure 9 9 XS7 19 36 6 Y Figure 6 17 Figure 9 9 XS8 19 42 6 Y Figure 6 17 Figure 9 9 XS9 19 48 6 Y Figure 6 17 Figure 9 9 XS10 19 54 6 Y Figure 6 17 Figure 9 9 XS11 19 18 6 Y Figure 6 17 Figure 9 9 XS12 19 54 6 Y Figure 6 17 Figure 9 9 ES1 0 5 35 .5 Z Figure 9 10 ES2 3 27 8 X Figure 6 2 Table 6 2 ES3 3 4 8 8 X Figure 6 2 Table 6 2 MS1 0 2 0.5 X Figure 7 22 MS2 0 13 0.5 X Figure 7 22 MS51 0 2 0 X Figure 7 22 MS52 0 13 0 X Figure 7 22 V2 0 2 8 X Figure 9 8

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103 Table 5 4 Specimen VC strain gage coordinates Instrument X (in.) Y (in.) Z (in.) Orientation Reference(s) XS3 0 0 12 X Figure 6 3 Table 6 2 XS5 19 18 6 Y Figure 6 17 Figure 9 9 XS6 19 30 6 Y Figure 6 17 Figure 9 9 XS7 19 36 6 Y Figure 6 17 Figure 9 9 XS8 19 42 6 Y Figure 6 17 Figure 9 9 XS9 19 48 6 Y Figure 6 17 Figure 9 9 XS10 19 54 6 Y Figure 6 17 Figure 9 9 XS11 19 18 6 Y Figure 6 17 Figure 9 9 XS12 19 54 6 Y Figure 6 17 Figure 9 9 ES1 0 5 35 .5 Z Figure 9 10 ES2 3 29 8 X Figure 6 2 Table 6 2 ES3 3 48 8 X Figure 6 2 Table 6 2 MS1 0.5 2 0.5 X Figure 7 22 MS2 0 13 0.5 X Figure 7 22 MS10 0 2 10 X Figure 7 22 MS14 0 2 2 X Figure 7 22 MS15 1 3 16 X Z Figure 7 22 MS20 0 8 10 X Figure 7 22 MS24 13 8 2 X Figure 7 22 MS25 1 8 16 X Z Figure 7 22 MS30 0 22 10 X Figure 7 22 MS34 0 22 2 X Figure 7 22 MS35 1 22 16 X Z Figure 7 22 MS40 0 6 4 10 X Figure 7 22 MS44 0 6 4 2 X Figure 7 22 MS45 1 6 4 16 X Z Figure 7 22 MS51 0 2 0 X Figure 7 22 MS52 0 13 0 X Figure 7 22 V2 0 2 8 X Figure 9 8

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104 Table 5 5 Specimen VU strain gage coordinates Instrument X (in.) Y (in.) Z (in.) Orientation Reference(s) XS3 0 0 12 X Figure 6 3 Table 6 2 XS5 19 18 6 Y Figure 6 17 Figure 9 9 XS6 19 30 6 Y Figure 6 17 Figure 9 9 XS7 19 36 6 Y Figure 6 17 Figure 9 9 XS8 19 42 6 Y Figure 6 17 Figure 9 9 XS9 19 48 6 Y Figure 6 17 Figure 9 9 XS10 19 54 6 Y Figure 6 17 Figure 9 9 XS11 19 30 6 Y Figure 6 17 Figure 9 9 XS12 19 54 6 Y Figure 6 17 Figure 9 9 ES1 0 5 34.5 Z Figure 9 10 ES2 3 27 8 X Figure 6 2 Table 6 2 ES3 3 48 8 X Figure 6 2 Table 6 2 MS1 0 2 0.5 X Figure 7 22 MS2 0 13 0.5 X Figure 7 22 MS51 0 2 0 X Figure 7 22 MS52 0 13 0 X Figure 7 22 V2 0 2 8 X Figure 9 8 Table 5 6 Specimen WN strain gage coordinates Instrument X (in.) Y (in.) Z (in.) Orientation Reference(s) MS10 1 2.5 17.5 XZ Figure 6 11 Figure 7 18 MS11 0 2.5 10 X Figure 6 11 Figure 7 18 MS12 0 2 2 X Figure 6 11 Figure 7 18 MS20 1 9 18 XZ Figure 6 11 Figure 7 18 MS21 0 9 10 X Figure 6 11 Figure 7 18 MS22 0 10 2 X Figure 6 11 Figure 7 18 MS30 1 16.5 17.5 XZ Figure 6 11 Figure 7 18 MS31 0 16.5 10 X Figure 6 11 Figure 7 18 MS33 0 16 2 X Figure 6 11 Figure 7 18

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105 Table 5 7 Sp ecimen WB strain gage coordinates Instrument X (in.) Y (in.) Z (in.) Orientation Reference(s) MS3 0 0.5 0.5 X Figure 6 9 Figure 7 18 MS4 0 7.5 0.5 X Figure 6 9 Figure 7 18 MS5 0 13.5 0.5 X Figure 6 9 Figure 7 18 MS10 1.5 2.5 18 XZ Figure 6 10 Figure 7 18 MS11 0 2 10.5 X Figure 6 10 Figure 7 18 MS12 0 2 2 X Figure 6 10 Figure 7 18 MS20 1.5 9 18 XZ Figure 6 10 Figure 7 18 MS21 0 9 10.5 X Figure 6 10 Figure 7 18 MS22 0 8 2 X Figure 6 10 Figure 7 18 MS30 1.5 16 18 XZ Figure 6 10 Figure 7 18 MS31 0 15.5 10.5 X Figure 6 10 Figure 7 18 MS33 0 15 2 X Figure 6 10 Figure 7 18 Table 5 8 Specimen FN strain gage coordinates Instrument X (in.) Y (in.) Z (in.) Orientation Reference(s) XS1 19 14.5 6.25 Y Figure 6 18 XS2 19 23 5.25 Y Figure 6 18 XS3 19 30 6.25 Y Figure 6 18 XS4 19 121 6.5 Y Figure 6 18 XS5 19 128 6 Y Figure 6 18 XS6 19 135.5 6.5 Y Figure 6 18 XS7 19 142.5 6.5 Y Figure 6 18 MS10 1 2 18 XZ Figure 6 13 Figure 7 18 MS11 0 2 10.5 X Figure 6 13 Figure 7 18 MS12 0 3 2 X Figure 6 13 Figure 7 18 MS20 1 9 18.5 XZ Figure 6 13 Figure 7 18 MS21 0 9 10.5 X Figure 6 13 Figure 7 18 MS22 0 7 2 X Figure 6 13 Figure 7 18 MS30 1 16 18.5 XZ Figure 6 13 Figure 7 18 MS31 0 15.5 10.5 X Figure 6 13 Figure 7 18 MS33 0 14.5 2 X Figure 6 13 Figure 7 18

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106 Table 5 9 Specimen FB strain gage coordinates Instrument X (in.) Y (in.) Z (in.) Orientation Reference(s) XS1 19 14 5.5 Y Figure 6 18 XS2 19 22 6 Y Figure 6 18 XS3 19 29.5 5.25 Y Figure 6 18 XS4 19 119 6 Y Figure 6 18 XS5 19 127 6.25 Y Figure 6 18 XS6 19 135 6 Y Figure 6 18 XS7 19 142 6.25 Y Figure 6 18 MS3 0 0.5 0.5 X Figure 6 8 MS4 0 7 0.5 X Figure 6 8 MS5 0 13.5 0.5 X Figure 6 8 MS10 0.5 2 17 XZ Figure 6 12 Figure 7 18 MS11 0 2 10 X Figure 6 12 Figure 7 18 MS12 0 1.5 2 X Figure 6 12 Figure 7 18 MS20 1 9 18 XZ Figure 6 12 Figure 7 18 MS21 0 8.5 10 X Figure 6 12 Figure 7 18 MS22 0 7.5 2 X Figure 6 12 Figure 7 18 MS30 0.5 16.5 17.5 XZ Figure 6 12 Figure 7 18 MS31 0 16 10 X Figure 6 12 Figure 7 18 MS 33 0 14 2 X Figure 6 12 Figure 7 18 Table 5 10 Specimen DC strain gage coordinates Instrument X (in.) Y (in.) Z (in.) Orientation Reference(s) MS3 0 3 0. 5 X Figure 7 18 MS4 0 9 0.5 X Figure 7 18 MS5 0 15 0.5 X Figure 7 18 MS10 1 2 18 XZ Figure 7 18 MS11 0 1.5 10.5 X Figure 7 18 MS12 0 2 3 X Figure 7 18 MS20 1 9 18 XZ Figure 7 18 MS21 0 9 10 X Figure 7 18 MS22 0 8.5 3 X Figure 7 18 MS30 2 16 18 XZ Figure 7 18 MS31 0 16.5 10.5 X Figure 7 18 MS33 0 16 3 X Figure 7 18

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107 Table 5 11 Specimen DM strain gage coordinates Instrument X (in .) Y (in.) Z (in.) Orientation Reference(s) MS3 0 2.5 0.5 X Figure 7 18 MS4 0 8 0.5 X Figure 7 18 MS5 0 15 0.5 X Figure 7 18 MS10 3 2.5 18 XZ Figure 7 18 MS11 0 2.5 10 X Figure 7 18 MS12 0 3 2.5 X Figure 7 18 MS20 3 9.5 18 XZ Figure 7 18 MS21 0 9 10.5 X Figure 7 18 MS22 0 8 2.5 X Figure 7 18 MS30 3 16 18.5 XZ Figure 7 18 MS31 0 16 10 X Figure 7 18 MS33 0 15 2.5 X Figure 7 18

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108 CHAPTER 6 RESULTS AND DISCUSSI ON: FABRICATION Strain and crack data were collected during multiple stages of fabrication including: prestress transfer, lifting, storage, tr ucking and deck placement. Data were collected to analyze the effects of fabrication events on end region behavior. The effects of end re gion detailing, particularly confinement reinforcement, were also of interest. Strain data are presented and discussed first followed by crack data. Strain Data Concrete Strain Concrete strain data w ere primarily collected from girders H and V. These gir ders had the same strand shielding pattern, instrumentation scheme, material properties, and timing of construction events. To facilitate review of the strain time history, the strand flame cutting sequence is divided into the stages shown in Table 6 1 Stages A through D listed in Table 6 1 are graphically depicted in Figure 6 1 G eneral trend s in the strain time history for speci men HC ( Figure 6 2 ) are representative of the other specimens in girders H and V. Any differences between the specimens were in the strain magnitudes, which are discussed later. Strands in the top flange were the first to be cut; this stage is denoted A in Figure 6 2 D ata indicate that the transverse strain change was negligible when the top strands were cut. C utting the bottom strands (stages B, C, and D) had significan t impact on transverse tensile strain. The largest measured transverse tensile strain in specimen HC was 406 microstrain reported by gage XS3. This gage was located on the end of the girder at the cross section centerline 3in. above the strands. The m aximum strain occurred at the beginning of stage D after all strands in the outer flange

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109 had been cut and before any of the strands below the web had been cut. For this chapter, s trands in the outer portion of the flange are and strands below the web are T ransverse stra in at gage XS3 decreased as inner strands were cut during stage D. The strain time history from gage XS3 can be understood by considering the strand release pattern ( Figure 6 1 ) and the resulting deformed shapes ( Figure 6 3 ). As the outer strands were cut during stage B, the outside edges of the bottom flange deformed as shown in Figure 6 3 This deformed shape corresponded with the formation of tensile strains at the location of XS3. After the inner strands were cut, deformation of the bottom flange was more uniform and the tensile strain at XS3 was part ially relieved. Once all of the strands were cut (stage E), the reported tensile strains at XS3 settled to approximately 25 microstrain. Concrete strain was monitored for all specimens in girders H and V using gages placed at the same location as XS3 on specimen HC. Results from these gages are summarized in Table 6 2 While the overall behavior of the other specimens in girder H and V were similar to that shown in Figure 6 2 the magnitudes of the reported strains differed. Several observations can be made from the strain data in Table 6 2 First, although cracks were not visually observed during prestress transfer, the strain m agnitudes suggest that cracks had likely formed in each specimen, with the possible exception of specimen VC. Expected rupture strain for the concrete used in the specimens is approximately 132 microstrain. This value of expected rupture strain was derive d from empirical equations for concrete elastic and rupture moduli from ACI 318

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110 (2011). Second, the average maximum tensile strain in the unconfined specimens (HU and VU) w as 3.4 times greater than the average maximum tensile strain in the confined specim ens (HC and VC). Cracks forming in the unconfined ends would not have been impeded by confinement reinforcement, resulting in greater maximum transverse strains than in the confined ends. Finally, the average concrete tensile strain during stage E (all s trands cut ) was 2.6 times greater in the specimens without confinement reinforcement. The presence of confinement reinforcement significantly reduce d the concrete tensile strain at the end of specimens HC and VC relative to specimens HU and VU. Internal c oncrete strain gages (ES2 and ES3 in Figure 6 2 ) reported inc reases in tensile strain as prestress force was transferred. In contrast to gage XS3, the tensile strain reported by these gages increased as the inner strands were cut during stage D. Based on this observation and the location of the internal gages, it is concluded that the bending behavior captured by gage XS3 only occurred at or nea r the end of specimen HC. ES gages in HU, VC, and VU confirmed simila r behavior in those specimens In each specimen s train magnitudes reported by ES gages ( Table 6 2 ) suggest that concrete near the internal gages remained line ar elastic (i.e. no cracking) during prestress transfer Confinement reinforcement did not affect the magnitude of concrete strain at the ES gages. Similar strain magnitudes were reported by specimens with and without confinement reinforcement ( Table 6 2 ). Gages ES 2 and ES3 were placed approximately 2ft and 4ft from the specimen end s respectively. It is concluded that

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111 confinement reinforcement only affected concrete strain at the end of the test specimens. Stage F on Figure 6 2 denotes lifting of girder H. Figure 6 4 shows the supports conditions, loading, shear, and moment diagrams for the girders before, during, and after lifting. The change in support conditio ns had negligible effect on strain in the end region. None of the gages in the end region of girders H or V reported more than a 25 microstrain change during lifting and placement on dunnage. Confinement Reinforcement and Bearing Plate Strain Girders W and F were fabricat ed during phase 2 and had the same material properties, instrumentation scheme, and timing of construction events. Instrumentation was designed to capture confinement reinforcement and bearing plate behavior. To facilitate discu ssion of data strand cutt ing events were broken into the stages listed in Table 6 3 Strand cutting events listed in Table 6 3 are keyed to the strand cutting pattern shown in Figure 6 5 The strand bond patterns in girders W and F ( F igure 6 6 ) had significant influence on the observed strain behavior. Girder W had fully bonded strands placed primarily below the w eb and partially shielded strands placed in the outer portion of the flange. Girder F had fully bonded strands in the outer portion of the flange and partially shielded strands below the web. Three strain gages were placed on the bearing plates in specime ns FB and WB. Gages were oriented to monitor the transverse (x x) strain during prestress transfer. Gage locations and strain data are shown in Figure 6 7 Gage MS3 in specimen FB malfunctioned during prestress transfer and data from this gage is not shown in figure.

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112 Strain at MS4 in specimen FB grew in tension as the outer strands were cut during stage K. Outer strands were fully bonded in specimen FB and caused the flange and plate to bend as shown in Figure 6 8 Strain in the plate was fairly constant after stage K. This is because no strands were cut during stage L and because the strands released during stage M were shielded in specimen FB. The difference in strai n between gages MS4 and MS5 indicates in plane bending of the plate due to the eccentric prestress force. Data from gages on the plate in specimen WB also indicate in plane bending during and after strand cutting. The direction of plate bending in specime n WB changed when the strands below the web were cut during stage M. This behavior is attributed to the strand bond pattern in specimen WB, which placed a few fully bonded strands in the outer portion of the flange and many fully bonded strands below the web. This pattern is thought to have caused the deformations and internal forces shown schematically in Figure 6 9 Release of the outermost strands at the beginning of stage K led to tension in the bearing plate at MS3 and compression in the bearing plate at MS5. The strain sense in the bearing plate reversed after the inner strands were released during stage M. After all strands were released (stage N) the bearing plate was in compression at MS3 and tension at MS5. The net strain in the plate after all strands were cut was approximately 32 microstrain tension, as calculated from the average of gages MS3, MS4, and MS5. The average strain from these gages is also equal to the strain reported at MS4, indicating t hat the strain reported by MS4 is also a reasonable measure of net strain.

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113 Transverse forces in the bearing plates were calculated by multiplying the net bearing plate strain s by the plate cross sectional area and elastic modulus. Assuming that the net be aring plate strain is equal to the strain at MS4 (center of plate) the net plate strain at stage N was 32 microstrain tension for specimen WB and 79 microstrain tension for specimen FB. Accordingly, net tensile stress es in the plates were 0.9ksi and 2.3 ksi, and the net tensile force s in the plates were 5.2kip and 13.6kip for specimens WB and FB, respectively. Select confinement reinforcement assemblies were instrumented with strain gages to monitor confinement reinforcement stra in during prestress tran sfer. A confinement assembly is defined as the reinforcing bars placed together at the same y ordinate ( Figure 6 10 ). One strain gage was placed on each of the three reinforcement layers in each assembly. Figure 6 10 shows confinement reinforcement strain from specimen WB. Reinforcement nearest to the end of the girder (y=2in.) was initially in tension due to release of the outermost strands during stage K. The strain la ter became compressive as the inner strands were released during stage M. This strain behavior is similar to the bearing plate strain in WB and is also attributed to flange bending behavior described in Figure 6 9 Confinement reinforcement placed 9in. from the end had very little strain until the innermost strands were released at the end of stage M. General strain behavior from the confinement assembly at 9 in. is representative of the strain behavior reported by gages on the confinement assembly placed 15 in. from the end (not shown). Specimen WN had the same strand bond pattern as WB. The only significant difference in strain data between WN ( Figure 6 11 ) and WB was t hat the confinement

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114 reinforcement located 2in. from the end of specimen WN did not move all the way into compression during stage M. This difference may have been due to the absence of a bearing plate in specimen WN. Without a bearing plate there was l ess confinement in specimen WN and tensile strains were not relieved during stage M. Specimen FB had fully bonded strands in the outer flange, all of which were cut during stage K. As such, confinement strain in FB ( Figure 6 12 ) increased during stage K. No fully bonded strands were cut after stage K and the strain did not change in the subsequent stages. Confinement reinforcement was in tension throughout and after the strand cutting process. Specimen FN had the same strand bond pattern as FB with fully bonded strands located in the outer portion of the flange. Strain behavior in specimen FN ( Figure 6 13 ) was similar to FB up until the inner strands were released dur ing stage M. During stage M the strain increased rapidly in the bottom (MS12) and middle (MS11) layers of confinement reinforcement. The strain magnitude during stage M suggests that cracking occurred in the nearby concrete. This result is puzzling becau se inner strands in specimen FB were shielded for 10ft from the specimen end. It appears that the shielded strands may have induced stresses in the concrete as they expanded after being cut. T he thin plasti c used to shield the strands may have been insuf ficient to absorb the strand expansion and prevent normal stresses at the strand concrete interface. These stresses could have caused the strain changes at gages MS12 and MS11 that occurred during stage M. Strain data at the end of stage N (all strands cu t) is listed in Table 6 4 for each specimen. Several observations can be made by averaging the stage N strain data

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115 ( Figure 6 14 ). First, strain was greatest in the bottom layer of reinforcement for each test specimen. On average strain in the bottom layer was 1.4 times greater than the middle layer strain and almost 3 times greater than the top layer strain. Second, the largest confinement reinforcement strain occurred in specimens FN and FB in the confinement assemblies 2 in. from the member ends. Confinement reinforcement strain at 2in. from the end of FN and FB was almost 4 times greater on average than confinement strain at 9in. This is due to the bending behavior of the FN and FB described in Figure 6 8 Third, confinement strain in specimen FN was typically larger than in FB. The average confinement strain was over 2 times larger in specimen FN than FB. The difference i n strain magnitude is attributed to the bearing plate in FB which carried transverse forces thereby reducing the strain in the confinement reinforcement. Finally, the maximum confinement strains in FN and FB were larger than the maximum confinement strain s in WN and WB. On average the maximum strain in the F X specimens was 2.6 times greater than the W X specimens Strain data were used to estimate the total force in each confinement reinforcement assembly after all strands had been cut (stage N). Forces we r e calculated by multiplying strains from Table 6 4 by the reinforcement area and steel elastic modulus. Two of five assemblies in specimens WB and FB were not monitored with strain gages. Strains in these assemb lies were determined using linear interpolation. In specimens WN and FN three of five confinement assemblies were not monitored. Strains in the unmonitored assemblies were interpolated using the available strain data, or were extrapolated using the avail able data as well as the relationships between assemblies in specimens WB and FB. Results for each specimen are shown

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116 in Figure 6 15 along with the estimated forces in the bearing plates. Only the x direction forc e component in the inclined top layer of reinforcement was included in the results shown in the figure. T otal transverse force in the confinement reinforcement and bearing plate (where present) was 63% larger on average in specimens FB and FN than in spec imens WB and WN. The additional force is attributed to the strand bond pattern in specimens FB and FN, which placed fully bonded strands in the outer portion of the flange. These fully bonded strands led to additional tension at ends of FN and FB. Most outer strands in specimens WB and WN were partially shielded and did not affect tension at the specimen ends. Transverse forces are compared to the jacking forces in Table 6 5 Combined transverse forces were equ al to 0.6% to 1.7% of the jacking force in the fully bonded strands. Once again, due to the strand bond pattern, the relationship of transverse force to jacking force was larger for FN and FB than for WN and WB. Data were not collected to estimate confine ment reinforcement and bearing plate forces in specimens DC and DM. Strands in these specimens were placed in the design strand bond pattern. Fully bonded strands were evenly distributed throughout the bottom flange in this pattern, placing it somewher e between the W x and F x specimens in terms of transverse tensile behavior. The transverse force in specimens with the design pattern would likely be smaller than F x specimens because inner strands in the design pattern relieved tension due to the outer st rand. Also, specimens with the design pattern likely had greater transverse force than the W x specimens because the design pattern included outside strands.

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117 Transfer Length Longitudinal str ains in the bottom flange of I girder s increase through the tran sfer length as prestres s force is transferred from strands to concrete. At locations beyond the transfer length longitudinal strain is approximately constant. Transfer length in the test girders was experimentally determined by identifying the location a t which longitudinal strain in the bottom flange transitioned to constant strain. This was accomplished using strain gages placed at intervals along the bottom flange ( Figure 6 16 ). When sufficient data are avail able, the 95% Average Maximum Strain (AMS) Method is a well established method for determining transfer length from experimental strain data (Russell and Burns 1993). The available strain data in the current study were insufficient to apply the AMS method but were still sufficient to estimate the transfer length by other means. Figure 6 17 presents strain gage data from the bottom flange of girders H and V immediately after prestress transfer. Blue markers on the figure indicate th e strain values reported by individual gages. Values reported by the gages were effectively constant (with some experimental scatter) for the monitored positions along the specimen lengths This indicates that the gages were placed too far from the end of the girder to capt ure strain in the transfer length. A bi linear curve representing the apparent strain profile is also shown in Figure 6 17 The apparent profile shows that the strain must b e zero at the end of the girder and must increase to the experimental values recorded at 18in. Beyond 18in. the experimental strains and apparent strain were approximately constant. Thus the tran sition to constant strain occurred prior to

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118 18in. and it is concluded that the transfer length is not greater than 18in. for girders H and V. Figure 6 18 shows experimental strain data from girder F. As before, the blue markers on the figure are data points from individua l gages. A piecewise linear curve representing the apparent strain profile is also shown in the figure. Girder F had fully bonded strands in the outer portion of the flange. Strands below the web were shielded for 10ft from the end. Gages were placed near the end of the girder and 10ft from the end in order to evaluate the transfer length of both fully bonded and partially shielded strands. Gages placed near the en ds of girder H reported increasing strain indicative of the transfer length. Beyond 30in the strain was approximately constant until 120in. at which point the partially shielded strands began to transfer prestress force. Thus the change to constant strain occurred approximately 30in. from the girder end indicating that transfer length for t he fully bonded strands was also approximately 30in. Gages placed between 120in. and 144in. from the end reported increasing strain along the girder length This indicates that they were within the transfer length of the partially shielded strands. Dat a were not available beyond 144in. and the transition to constant strain was not observed. As such transfer length of the partially shielded strands cannot be obtained directly from the available data. Transfer length can be estimated by assuming linear elastic behavior of the concrete and strands. The 24 fully bonded strands affected a microstrain of 575 at the end of their transfer length. The 20 partially shielded strands should have added a proportion al amount of strain, resulting in 1054 microstrai n at the end of their transfer length. Slope of the apparent strain profile

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119 is based on the available data points. Extending the strain profile along this slope shows that the apparent strain intersects 1054 microstrain at a distance 22 0in. from the memb er end. Prestress transfer of the partially shielded strands is thus estimated to hav e occurred between 120in. and 22 0in. from the member end T he estima ted strand transfer length is 10 0in. This is significantly longer than the transfer length of the fu lly bonded strands. Additional data are necessary, though unavailable, for making a more accurate determination of transfer length in the partially shielded strands Tr ansfer length was not measured i n the other phase two girders (W and D) due to constrai nts with the data acquisition system. The transfer lengths in girders W and D were likely similar to girder F because the same strand and concrete materia ls were used for all phase two girders Measured transfer length for girders H and V was different fr om girder F. This difference is attributed to the different strand and concrete materials used in phase one (girder H and V) and phase two (girder F). Measured transfer lengths for fully bonded strands in both phases were less than the AASHTO LRFD calcul ated transfer length of 36in. Differences between experimental and code values may partially be due to the fact that strain data collected immediately after prestress transfer were used to determine the experimental transfer lengths Barnes et al. (1999) observed that the transfer length grows by 10% to 20% in the weeks following prestress transfer. Gages used to measure transfer length were placed at the outside edge of the bottom flange. Longitudina l strain at this location occurred due to axial short ening of the girder and due to shear lag from prestressing forces in the outer stands. Because of the s hear lag component the apparent transfer lengths measured by the gages were likely

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120 somewhat longer than the effective transfer length. This effect wo uld be greatest near the end of the girder. Barnes et al. (1999) used finite element modeling to quantify the effect of shear lag on transfer length measurements in AASHTO Type I girders. For fully bonded stands and an apparent transfer length of 18in. B arnes et al. calculated that the effective transfer length would be 16.5 in. For the test girders, the shear lag component of the strain will be affected by the relatively slender and wide bottom flange of th e FIB. Thus the correction due to shear lag in the test girders would likely be slightly larger that calculated by Barnes et al. Crack Data Girders were inspected periodically during the time between form removal and load testing. When observed c rack lengths and widths were measured and docume nted C racks widths were determined using a microscop e that was precise to +/ 0.001 in. Crack lengths were determined by visual inspection with the naked eye. Three types of cracks were observed in the test girders: Top flange flexural cra cks Web splitting crac ks Flange splitting cracks Top flange cracking was due to flexural stresses generated by the vertically eccentric prestressing and is outside the scope of this end region research. Web splitting ( Figure 6 19 ) cra cks we re also due to eccentricity of prestres sing. Vertical tension stress form ed in the web at the end of the specimens as the prestress force wa s distributed to the cross section. Flange splitting cracks are of primary interest in the current investigat ion of confi nement reinforcement and we re caused by horizontal eccentricity of prestressing, Hoye r expansion of strands, and self weight reaction of the

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121 test girders. Transverse tensile stress form ed in the bottom flange as prestressing forces were distr ibuted through the cross section from eccentric strands in the outer portion of the flange. Additional tensile stresses form ed due to the Hoyer effect, in which strand expansion after cutting was restrained by t he concrete. Self weight caused tensile str esses above the support due to Poisson and flange bending effect s Cracks in the top flan ge, web, and bottom flange occurred when the tensile stresses described above exceed ed the concrete strength. Presentation of crack data i s divided according to the two phases of construction. This was done because the materials properties, construction procedures, and curing conditions varied between the construction phases. Within each phase, crack data were further divided between flange splitting cracks and web splitting cracks. Cracking was quantified and compared in terms of total crack length, total crack area, and maximum crack width. Total crack length was calculated by summing the length of individual cracks for a specimen. Total crack area was calcula ted by summing the length of each crack multiplied by its representative width. Representative widths were determined from microscope measurements taken at selected points along cracks. Maximum crack width was determined from the microscope readings. As part of an NCHRP research project, Tadros et al. (2010) recommended criteria for acceptance, repair, and rejection of girders with web splitting cracks. Criteria are based on laboratory data and from field data from Nebraska and Virginia. More stringent criteria may be warranted in aggressive environments such as along Florida coasts. Nevertheless, the recommendations shown in Table 6 6 and were used as a benchmark for evaluating crack widths in the test specimen s.

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122 In general, cracking behavior differed between the two phases of construction. Cracks were first observed in phase one girders (H and V) in the days following prestress transfer, whereas cracks were first observed in phase two girders (W, F, and D) dur ing prestress transfer. Another difference wa s that cracks in the phase one girders typically did not grow after they were first observed. Cracks in the phase two girders continued to grow in length during the weeks after they were first observed. Gird ers H and V Girders H and V were fabricated together during the first phase of construction. Girders were inspected for cracking ten times between form removal and load testing ( Table 6 7 ). Figure 6 20 shows web and fl ange splitting cracks observed during inspections. Flexural cracking in the top flange cracking is not shown in the figure. Cracks were first observed in girders H and V nine days after prestress transfer. Th e day that cracks formed is unknown because girders H and V were not inspected during the days immediately following prestress transfer. Web splitting cracks were observed in each specimen. Flange splitting cracks were only observed in specimens without confinement reinforcement (HU and VU). At the end of these specimens the flange cracks intersected with the outermost strand in the third row ( Figure 6 21 ). Strands at this location had 2.5 in. of clear cover to the top surface of the flange, which was the least amount of top cover for any strand in the test girders. Cracks in specimens H and V changed little after they were first observed. An additional web splitting crack was observed in specimen HC during a n inspection fifteen days after prestress transfer. No other significant changes in crack quantity, width or length were observed during subsequent inspections of girders H and V.

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123 Web splitting cracks in specimens with the greater amount of end region rei nforcement (HC and HU) were an average of 72% longer than the cracks in specimens with less reinforcement (VC and VU)( Figure 6 22 ). One possible reason that web cracks were longer in HC and HU was that horizontal bars at the ends of these specimens created a path where horizontal cracks could form and propagate. Web cracks in HC and HU always occurred at the location of horizontal bars. Although the additional reinforcement increased the total web crack length, i t was also more effective in control ling web crack widths. The maximum web splitting crack width was 0.008 in. in specimens HC and HU, whereas maximum crack widths were 0.012in. and 0.02 in. in VC and VU respectively ( Figure 6 23 ). The additional vertical bars in specimens HC and HU appear to have increased the post crackin g stiffness thereby reducing maximum crack width relative to VC and VU. For girders H and V the m aximum crack widths were typically less than 0 0 12 in., which according to the criteria in Table 6 6 do not require repair. Only specimen VU had a crack with a width greater than 0. 0 12 in. One of the web splitting cracks in this specimen had a maximum width of 0.02 in. A ccording to the criteria in Table 6 6 this crack would require repair by filling with cementitious material and application of a sealant to the girder end. T otal crack area ( Figure 6 22 ) wa s derived from both length and width data, and provides a quantitative comparison of end cracking. Web cracks in specimens HC and HU were longer but narrower than web cracks in VC and VU. Because of this, there is less va riation in total web crack area than was observed in total web crack length and

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124 maximum web crack width. Variation in total web crack area varied by 24% between H X and V X specimens. Flange splitting cracks only occurred in specimens HU and VU, which did n ot have confinement reinforcement. The total length and area of flange cracks were similar between HU and VU ( Figure 6 24 ). The maximum width of flange splitting cracks was 0.004 in ( Figure 6 23 ). Presumably, confinement reinforcement in HC and VC controlled the formation and propagation of flange cracks in those specimens Girders W, F, and D Girders W, F, and D were fabricated together during the second phase of constr uction. Construction events, inspection dates, and notes from girders W, F, and D are listed Table 6 8 Flange and web splitting cracks were first observed in the se girders after the outer strands had been cut du ring prestress transfer. Cracks grew in quantity and length in the days and weeks following prestress transfer. Figure 6 25 shows the web and flange splitting cracks observed prior to load testing. Flexural crac ks in the top flange are not shown. Steel bulkheads were used during construction of girders W, F, and D. A portion of the bulkhead covering the end of the bottom flange ( Figure 6 26 ) remained with each test girde r for approximately two weeks after prestress transfer. Bottom flange ends covered by the bulkheads were inspected for the first time 30 days after transfer. Cracks were observed at the girder ends during this inspection. Because the ends were previou sly covered, it is not known when splitting cracks at the end of the bottom flanges first formed. The location of cracks shown in Figure 6 25 can be understood by considering the strand bond patterns in the test sp ecimens. For example, specimens WN and WB had

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125 flange splitting cracks located 10ft from their ends. These cracks formed within the transfer length of partially shielded strands. Strands in WN and WB were 45% partially shielded, with all shielding locate d in the outer portion of the flange. It is believed that the flange cracks in WN and WB occurred due to Hoyer stresses and lateral splitting stresses associated with the partially shielded strands. Strands in specimens FN and FB were also 45% shielded, with all shielding located below the web and all shielding terminating 10ft from the specimen ends. This pattern placed fully bonded strands in the outer portion of the flange and led to tensile stresses in the bottom flange as illustrated by Figure 6 8 Flange s plitting cracks formed when tension stresses at the end of the flange exceeded the concrete tensile strength. Flange cracks at the ends of FN and FB intersected strands ( Figure 6 27 ) suggesting that the Hoyer effect also contributed to the tensile stresses and crack formation. Flange splitting cracks in FN and FB were greater in total length and in total area than all other specimens ( Figure 6 28 ). The maximum width of flange splitting cracks was also greater for FN and FB ( Figure 6 29 ) than other specimens. Specimens DC and DM had the largest number of fully bonded strands (39) in the phase 2 test girders. As such the web stresses and web splitting cracks were greatest in DC and DM All other specimens had only 24 fully bonded strands. The total length of web splitting cracks in specimens DC and DM were 132 in. and 179 in., re spectively ( Figure 6 30 ). The maximum width of web splitting cracks was 0.008 in. specimens DC and DM ( Figure 6 29 ). Specimens DC and DM had flange splitting cracks ( Figure 6 31 ) in addition to web cracks. At the end of these specimens the flange splitting cracks intersected strands,

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126 suggesting that the Hoyer effect contributed to crack formation. In specimen DC the cracks interse cted the outermost strands in the second and third rows. The maximum crack width in girders W, F, and D was 0.008 in. This width does not warrant repair using the criteria from Table 6 6 Variable Comparison a nd Discussion This section compares crack behavior across specimens and variables. Trends identified in the test specimens will be useful in detailing end regions to prevent and control cracking during and after prestress transfer. Flange splitting crac ks ( Figure 6 24 ) formed in phase one specimens without confinement reinforcement (HU and VU) but not in specimens with confinement (HC and VC). This result suggests that confinement reinforcement controls flange sp litting cracks that form due to prestre ssing. It is presumed that confinement reinforcement in HC and VC prevented flange splitting cracks from opening and propagating. The quantity of bonded strands affected the total length and area of web splitting cra cks. This is evident from Figure 6 30 which compares specimens DC and DM (39 strands each) with specimens WN, WB, FN, and FB (24 strands each). On average the total crack length and total crack area were 78 % and 168 % larger, respectively, in specimens with 39 fully bonded strands than in the specimens with only 24 strands. The maximum web crack width was twice as large in specimens with 39 fully bonded strands as in those with 24. These results indicate that red ucing the quantity of fully bonded strands through partial shielding can successfully control the length, area, and maximum width of web splitting cracks. The location of shielded strands within the bottom flange (inner flange or outer flange) was not a factor in length, area, or maximum width of web splitting cracks. Web

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127 splitting cracks in specimens with shielded stands placed in the outer portion of the flange (WN and WB) had similar total length, total area ( Figure 6 30 ), and maximum width ( Figure 6 29 ) as comparable specimens with shielded strands placed below the web (FN and FB). The effect of confinement reinforcement and bearing plates on web splitting cracks is no t obvious from the test data. Comparing total crack area s for girder H and V ( Figure 6 22 ), it can be seen that specimens with confinement reinforcement had similar crack area but longer lengths that specimens wit hout confinement. Specimens WN and FN without bearing plates had more crack length and area ( Figure 6 29 and Figure 6 30 ) as specimens WB and FB with bearing plates. One possible explanation for the greater amount of cracking in FB and WB is that bottom flange confinement provided by the bearing plates resulted in shorter transverse lengths and higher end stresses than in specimens without bearing plates. Specimens FN an d FB had the worst flange cracking and had all bonded strands placed in the outer portion of the flange. Severity of flange cracking specimens FN and FB is attributed to this strand bond pattern. The total length and total area ( Figure 6 28 ) of flange cracks in F X specimens were both on 2.5 times greater on average than the same metrics in the other phase 2 specimens. Similarly, the maximum flange crack width ( Figure 6 29 ) was twice as large in F X specimens as in the other phase 2 specimens. Based on these results it is recommended that strands be placed as near to the centerline of the bottom flange as practical in order to maximize cover and minimize flange splitting cra cks.

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128 Six of the ten specimens had flange splitting cracks at the member end. In five of the six with flange cracks at the end, flange cracking intersected the outermost strand in the third row ( Figure 6 21 ). Stra nds at this location had only 2.5 in. of clear cover to the t op of the bottom flange. This wa s the least amount of cover of any strand in the test specimens It is recommended that this location be avoided when designing strand patterns. Furthermore it is recommended that strand patterns be designed with the maximum amount of top cover. Flange cracks were observed within the transfer length of the partially shielded strands in specimens WB and WN. Approximately 45% of strands in these specimens were par tially shielded, and all shielding terminated at the same section 10ft from the specimen ends. Both the overall shielding percentage and the termination of shielding violated AASHTO LRFD requirements. Flange cracks were not observed within the transfer l ength of partially shielded strands in specimens that complied with the AASHTO requirement s. Similar to specimens WB and WN, specimens FB and FN also violated the AASHTO requirements for total percentage of shielded strands and quantity of strand shieldin g that terminated at a section. Unlike specimens WB and WN, however, specimens FB and FN had partially shielded strands placed below the web and did not have flange cracks within the transfer length of the partially shielded strands. This demonstrates t hat the overall percentage of shielded strands was not a factor in flange cracking. The location of shielding was more critical to flange cracking than was the percentage of strand shielding that terminated at a given section.

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129 Flange cracking in specimen end regions extended up to 30in. from the member end. This length is 6 in. shorter than the code calculated transfer length of 36in. The similarity between these values suggests that code specified transfer length may be a good estimate of flange splitti ng crack lengths and that the code transfer length is a reasonable guideline for placement of confinement. The correlation between flange splitting crack length and transfer length is attributed in part to the Hoyer effect which cause s tensile splitting s tresses within the transfer length. Embedded steel bearing plates were excluded from specimens WN and FN. Absence of a bearing plate in specimen FN led to 64 % greater total crack flange crack length and 76 % greater total crack area when compared to specim en FB which had a bearing plate. Both specimens had fully bonded strands placed only in the outer portion of the flange. Absence of a steel bearing plate did not adversely affect crack ing in specimen WN relative to WB which had a bearing plate. Neither specimen had flange cracks at the member end. Thus presence of a bearing plate had the beneficial effects of reducing crack length and area, but only in specimens with fully bonded strands placed in the outer portion of the flange. Configuration of conf inement reinforcement can be compared using results from specimens DC and DM. Specimen DC had #3 confinement reinforcement as currently specified by FDOT. DM had #4 confinement reinforcement but had fewer total confinement ba rs than DC. Specimen DC had 1 5 1 % greate r total flange crack length, and 113 % greater total flange crack area than did specimen DM. Average flange crack width was not significantly different between the specimens. These results suggest that

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130 the modified confinement reinforcement pe rformed better at controlling flange splitting cracks than the FDOT configuration. This is attributed to the fact that specimen DM had more reinforcement placed closer to the end than did specimen DC. Summary and Conclusions Cracking and strain data were collected in pretensioned FIB girders during multiple stages of construction including: prestress transfer, lifting, storage, transport, and deck construction. Each end of each girder had a different set of variables. Variables included: the quantity or lack of confinement reinforcement, the presence or lack of a steel bearing plate, and the strand bond pattern. Two of the tested strand bond patterns were intentionally designed to violate current AASHTO LRFD requirements. Strain data from the reinforcem ent and bearing plates were used to estimate the transverse forces developed during prestress transfer. The following conclusions are made based on results from the strain data: Transverse tensile strains were observed in the bottom flange, confinement re inforcement and embedded bearing plates during and after prestress transfer. T ensile strain s are attributed to prestressing forces, the Hoyer effe ct and girder self weight and are thought to have caused flange splitting cracks. Transverse tensile strain s are greatest in sections with fully bonded strands placed only in the outer portions of the bottom flange. Bonded strands in the outer flange are eccentric with the resultant internal force, t hereby inducing bending in the bottom flange and associated t ransverse tension at the girder end. Transverse tensile strains are smaller in sections with fully bonded strands placed below the web than in sections without fully bonded strands below the web. This is because prestress forces from the inner (below the web) strands counteract the transverse tension caused by prestress forces from strands in the outer portions of the flange. Confinement reinforcement can be effective in controlling transverse tensile strain and associated splitting cracks in the bottom flange durin g and after prestress transfer. Specimens without confinement reinforcement had average transverse tensile strains in the bottom flange concrete that were 3.4 times greater than specimens with confinement reinforcement.

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131 The greatest strain i n confinement reinforcement typically occurs in the lowest layer of reinforcement. In the test specimens, the bottom layer of confinement had strains 1.4 times greater on average than the middle layer. C onfinement strains are largest near the end in mem bers with fully bonded strands placed in the outer portion of the flange. In test specimens with fully bonded outer stands the strain was 4 times larger in bars 2in. from the end than in bars 9in. from the end. Transverse tensile forces in confinement rei nforcement and bearing plates were approximately 50% larger on average in members with bonded strands in the outer flange only, as compared to members with bonded strands in the inner flange only. The combined transverse tensile force in confinement reinfo rcement and bearing plate was estimated (based on strain data) to be between 0.6% and 1.7% of the total jacking force in fully bonded stands. These values represent lower and upper bounds for extreme strand bond patterns. Lifting of test girders and pla cement on dunnage had little effect on the transverse and vertical strain in the end region. The maximum change in strain during this process of 25 microstrain. Cracking was monitored in test specimens from the time forms were removed until the time of lo ad testing. The following conclusions are made based on results from the crack data: In some cases w eb and flange splitting cracks occur during and immediately following prestress transfer I n other cases cracking occurs during the days or weeks following transfer. Length and width of web and flange cracks are affected by detailing of the end region, even in specimens having the same cross section. Flange splitting cracks in test specimens had maximum widths between 0.002 in. and 0.008 in. These cracks w idths do not warrant repair according to the criteria set forth by Tadros et al (2010). Flange splitting cracks extended up to 30in. from the test specimens ends. This length is comparable to the code calculated transfer length of 36 in. (30 strand diame ters). This result suggests that the code transfer length is a reasonable extent for the placement of confinement reinforcement to control flange splitting cracks

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132 Confinement reinforcement appears to have effectively controlled flange splitting cracks in specimens HC and VC. Splitting cracks were observed in comparable specimens (HU and VU) without confinement reinforcement. Absence of a steel bearing plate affected the lengths and widths of flange splitting cracks in specimens with fully bonded strands placed only in the outer portion of the flange. For example, the total flange crack length was 64 % greater and total flange crack area 76 % greater in specimen FN (no plate) than in specimen FB (with plate). The total length and area of flange splitting c racks were dependent on the strand bond pattern. Specimens with bonded strands placed only in the outer flange had 2.5 times greater total flange crack length and area than specimens with bonded strands distributed throughout the bottom flange. Splittin g cracks did not occur in the end region in specimens where bonded strands were placed only in the inner portion of the flange. Flange splitting cracks formed within the transfer length of partially shielded strands in two specimens. These cracks were a ffected by the placement of shielded strands in the outer portion of the flange, and the quantity of shielding that terminated at a same section. The total percentage of shielded strands did not affect cracking. Flange splitting cracks were not observed i n the transfer length of shielded strands in specimens complying with AASHTO LRFD requirements for quantity of shielding that can terminate at a given section. Splitting cracks in the bottom flange typically intersected the outermost strand in the third ro w from the bottom. This strand location had the least amount of top cover of any location in the test girders. Length and area of web splitting cracks was a function of the quantity of fully bonded strands. Web splitting cracks in specimens with 39 fully bonded strands were 78 % longer and had 1 68 % more area than web cracks in specimens with 24 fully bonded strands. P osition of fully bonded strands in the bottom flange did not affect the length, area, or width splitting cracks in the web

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133 Figure 6 1 Girders H and V s trand cutting stages Figure 6 2 Transverse Strain HC

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134 Figure 6 3 Flange displaced shapes for specimen HC Figure 6 4 Shear and moment during release, lifting, storage (prestressing not shown)

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135 Figure 6 5 Girders W and F s trand cutting stages F igure 6 6 Girders W and F strand bond patterns

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136 Figure 6 7 Bearing plate strain

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137 Figure 6 8 F lange displace d shapes specimens FN and FB

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138 Figure 6 9 Displaced shapes specimen WB and WN

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139 Figure 6 10 WB Confinement reinforcement strain at 2 in. and 9 in. from end of girder.

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140 Figure 6 11 WN Confinement reinforcement strain at 2 in. and 9 in. from end of girder

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141 Figure 6 12 FB confinement reinforcement strain at 2in. and 9in. from end of girder

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142 Figure 6 13 FN Confinement reinforcement strain at 2in. and 9in. for end of girder Figure 6 14 Confinement reinforcement average strain at prestress release

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143 Figure 6 15 Forces in reinforcement and plates after prestress transfer

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144 Figure 6 16 Strain gages for measuring transfer lengt h (Photo courtesy of B.E. Ross) Figure 6 17 Transfer length in girders H and V

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145 Figure 6 18 Transfer length girder F Figure 6 19 Web splitting and flange splitting cracks (Photo courtesy of B.E. Ross)

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146 Figure 6 20 Girder H and V c racks prior to load tests

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147 Figure 6 21 Flange splitting crack intersecting outer strand Figure 6 22 Web splitting cracks specimens H and V

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148 Figure 6 23 Maximum crack widths girder s H and V Figure 6 24 Flange splitting crack data girders H and V

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149 Figure 6 25 Girders W, F, & D web and flange splitting cracks

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150 Figure 6 26 End of bottom flange covered by portion of steel bulkhead (Photo courtesy of B.E. Ross) A B Figure 6 27 Girder F f lange splitting cracks A) Specimen FN, B) Spec imen FB. ( Photos courtesy of B.E. Ross)

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151 Figure 6 28 Flange splitting cracks girders W, F, and D Figure 6 29 Maximum crack widths girders W, F, and D

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152 Figure 6 30 Web splitting cracks girders W, F, and D A B Figure 6 31 Girder D f lange splitting cracks A) Specimen DC B) Specimen DM (Photos court esy of B.E. Ross)

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153 Table 6 1 Girders H and V fabrication events and stages Stage Event A strands 1 4 cut B strands 5 12 cut C strands 13 32 cut D strands 33 49 cut E All bonded strands cut, girder restin g on bed F Girder held aloft by lifting loops G Girder resting on dunnage Table 6 2 Tensile strain girders H and V Strain in s pecimens with confinement reinforcement (microstrain) Strain is s pecimens wi thout confinement reinforcement (microstrain) Gage HC VC HU VU X3 maximum tensile strain 406 177 724 1258 X3 Stage E (all strands released) 25 15 60 45 ES2 Stage E 109 113 100 135 ES3 Stage E 125 88 111 105 Table 6 3 Girders W and F fabrication stages Stage Event J strands 1 4 cut K strands 5 30 cut L P ause M strands 30 56 cut N a ll strands cut

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154 Table 6 4 Confinement reinforcement s train after prestress transfer Specimen Confinement reinforcement layer C onfinement strain (microstrain) y = 2in. y = 9in. y = 15in. WN T op 7 19 not recorded M iddle 47 28 not recorded B ottom 160 87 not recorded WB T op 37 34 53 M iddle 49 117 15 5 B ottom 106 124 150 FN T op 70 18 not recorded M iddle 358 38 not recorded B ottom 560 155 not recorded FB T op 81 51 5 M iddle 134 30 20 B ottom 184 50 12 Table 6 5 Confinement and plate forces S pecimen Confinement reinforcement transverse force Bearing plate transverse force Combined force in reinforcement and plate Jacking force in fully bonded strands Transverse force / jacking force WN 6.2 kip -6.2 kip 1070 kip 0.6% WB 4.3 kip 5.6 kip 9 .9 kip 1070 kip 0.9% FN 11.1 kip -11.1 kip 1070 kip 1.0% FB 4.9 kip 13.7 kip 18.6 kip 1070 kip 1.7% Table 6 6 Recommended action for web splitting cracks (Tadros et al. 2010) Crack Width (in.) Required Action Less than 0.012 None 0.012 to 0.025 Fill cracks with cementitious material and apply surface sealant to end 4 ft of girder 0.025 to 0.05 Fill cracks with epoxy and apply surface sealant to end 4 ft of girder Greater than 0.05 Reject girder un less shown by detailed analysis that structural capacity and long term durability are sufficient

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155 Table 6 7 Girders H and V construction events and inspection dates Event Date Days after prestress transfer Notes Form Removal September 7, 2010 -No cracks observed Prestress Transfer September 8, 2010 0 No cracks observed Lifting and setting on dunnage September 8, 2010 0 No cracks observed Girders in storage September 17, 2010 9 Splitting cracks observed (all specimens) Girders in storage September 23, 2010 15 Additional web splitting crack observed (HC) Girders in storage October 10, 2010 49 No additional cracks Girders in storage January 7, 2011 121 No additional cracks Trucking February 23, 2011 16 7 No additional cracks Casting deck April 6, 2011 204 No additional cracks Begin load tests May 5, 2011 237 No additional cracks

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156 Table 6 8 Girders W, F, & D construction events and inspection dates Even t Date Days after prestress transfer Notes Form Removal February 20, 2012 -No cracks observed Prestress Transfer February 21, 2012 0 First cracks observed after outer strands released. In storage immediately after lifting February 22, 2012 1 Addit ional splitting cracks and extension of previous cracks observed. In storage February 23, 2012 2 Additional splitting cracks and extension of previous cracks observed. In storage February 24, 2012 3 Additional splitting cracks and extension of previous cracks observed. In storage March 6, 2012 14 Additional splitting cracks and extension of previous cracks observed. In storage March 22, 2012 30 Additional splitting cracks and extension of previous cracks observed. Bottom flange at ends examined for first time. Previously the bulkhead plates were covering the flange end. In storage April 9, 2012 48 Additional splitting cracks and extension of previous cracks observed. Trucking April 30, 2012 69 Additional splitting cracks and extension of previ ous cracks observed. Casting deck May 7, 2012 76 No additional cracking observed. Begin load test ing May 23, 2012 92 Bottom of girder inspected for first time. Flange splitting cracks observed prior to load tests.

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157 CHAPTER 7 RESULTS AND DISCUSSI ON: LOAD TESTS This chapter presents the results o f load testing conducted on ten FIB 54 specimens. T est results are presented in terms of superimposed shear which is referred to as shear in this chapter Superimposed shear is defined as the shear force due to the ap plied load acting at the support nearest the load point. Self weight is not included in the superimposed shear. Displacement results are presented as the vertical displacement occurring at the load point. D isplacement at the load point wa s calculated a s the average of the displacements reported by LVDTs that were placed on either side of the load. The effect of bearing pad displacement has been removed. Strand slip data are presented as the average slip from all monitored fully bonded strands. Displac ement data from partially shielded strands are not included Locations of monitored strands are presented in Chapter 5. Failure Modes Three different modes of failure were observed in the test program: Web sh ear lateral splitting and bond shear This s ection defines each type of failure and discusses the characteristics associated with each failure mode. Web shear failur e i s distinguished by crushing of the concrete web at pe ak load. This type of failure i s co ntrolled by the capacity of the web to ca rry diagonal compression between the top and bottom flange s A post peak characteris tic of web shear failure includes sliding of the top portion of the girder relative to the bottom along a shear plane through the web ( Figure 7 1 ) This type of failure mode is considered in the shear design provisions of AASHTO LRFD and ACI 318.

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158 L ateral splitting failure i s characterized by longitudinal cracks in the bottom flange and by peeling (outward) movement at the edges of the bottom flan ge ( Figure 7 3 .) Peeling movement of the bottom flange i s caused by eccentricity between prestressing force s in the outer flange and the resultant equal and opposite force centered in the web ( Figure 7 4 .) This condition creates a moment which opens bottom flange crack s and peels the edge s of the bottom flange outward. In specimens with sufficient bottom flange confinement peeling mo v ement and longitudinal cracks a re r e strained, and p eeling failure i s mitigated. Strand slip i s observed in some specimens failing in lateral splitting m ode. Flange splitting cracks a re a precursor to strand slip in lateral s plitting failures. Once strands start to slip cracks open wider and capacity is lost in a sudden manner. Longitudinal cracking along the specimen bottom ( Figure 7 3 ) i s also a characteristic of lateral splitting failure. C racks on the bottom a re another manifestation of lateral splitting cracks on the top surface of the bottom flange. Bond shear failure i s c haracterized by strand s lip at peak load. This type of failure i s governed by concrete strand bond capacity and by specimen propensity for cracking within the strand development length. Cracking in the development length i s a lways a precursor to strand slip ( Figure 7 2 ). C racks interrupting strand developm ent re duce the embedment length to the distance between the crack and the girder end. After strands start slipping the c ra cks op ened wider and new cracks form. An abrupt slip event occurs at peak load followed by a subsequent loss of capacity. Lo ngitudinal splitting cracks can also be observed on the bottom of specimens that failure in bond shear ( Figure 7 2 ).

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159 As described above, similar characteristics are associated with lateral splitting and bond shear failures. One subtle differenc e between these failure modes i s the cause of cracking in the bottom flange. In lateral splitting failures bott om flange cracking i s caused by shear forces and transverse tensile forces due to eccentric prestressing Bottom flange cracking in bond shear failures a re caused primarily by shea r forces M agnitude of strand slip i s a more obvious distinction between b ond shear and lateral splitting failures. In the test program, s pecimens failing in bond shea r reported maximum average strand slip over 0.25in. When slip was observed in specimens failing in later splitting maximum the average slip was less than 0.1in. Load Test Results HC Detailing of specimen HC ( Figure 3 6 ) was effectively identical to the 2008 FDOT Interim Design Standards (FDOT, 2008). Variables in specimen HC included FDOT specified confinement reinforcement and bearing p late in the bottom flange horizontal reinforcement in the end region, and the design strand bond pattern ( Figure 3 5 ) which had (39) fully bonded strands. Specimen HC failed in web shear mode. Shear displacement and crack pat tern are shown in Figure 7 5 Cracks in HC were first observ ed during the service load test at a shear of 225 kip. Inclined web cracks between the load point and support were the first to be observed. The service load test rea ched a peak shear of 244kip. C racks partially cl osed during the unloading stage of the service load test W eb crack s in specimen HC had a maximum width of 0.004 in. at a shear of 244kip, and 0.002 in. after load was removed. Following service load test ing specimen HC was loaded to ultimate capacity. Stiffness decreased gradually as load increased beyond the level of the service load

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160 tests. Because flexura l cracks were not observed, loss in stiffness is attributed to formation and growth of diagonal cr acks. Ultimate capacity was signaled by web crushing followed immediately by sliding movement of the portion relative to the bottom. Sliding movement occurred along the inclined cracks in the web This type of failure i s classified as a w eb shear failure. Loss of capacity after the web shear failure was abrupt. Specimen HC supported a maximum shear of 766 kip the most of any specimen in the test program Strand slip data are not presented in Figure 7 5 LVDT d ata indicate that s trand slip was negligible at lower loads. At higher loads cracks caused shifting of the f rame holding the LVDTs thereby comp romising the strand slip data. Specimens DC and DM used the same strand bond pattern as HC, but used different strand slip instrumentation that did not shift during testing. Slip data from the DC and DM suggest that strand slip was not a factor in the failure mode of specimens (such as HC) with the design strand pattern. The lack of slip observed in the specimens with this pattern is attributed to the relatively large quantity of fully bonded strands HU Detailing of specimen HC ( Figure 3 6 ) was effectively identical to the 2008 FDOT Interim Design Standards (FDOT, 2008), with the except ion that no confinement reinforcement was placed in the bottom flange. Specimen HU had a bearing plate in the bottom flange horizontal reinforcement in the end region, and the design strand pattern ( Figure 3 5 ) which included (39) fully bonded strands. Shear displacement and crack pattern are shown in Figure 7 6 Cracks in HU were first observ ed during the service load test at a shear of 215 kip. The first crack to be observed was a web crack incline d betwe en the load point and

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161 support. W eb crack s in specimen HU had a maximum width of 0.004 in. at a shear of 230kip, and partially closed to 0.002 in. after load was removed. Following service load testing specimen HU was loaded to u ltimate capacity. Stiffness decreased gradually as load increased beyond the level of the service load tests. Loss in stiffness is attributed to formation and growth of diagonal cracks. Web cracks that formed at lower loads were observed to spread into the bottom flange during the latter stages of testing. Flexural cracks were not observed P eak load in specimen HU corresponded to lateral splitting failure in the bottom flange, which resulted in an abrupt loss of load. Specimen HU supported a maximum shear of 666 kip. Strand slip data are not shown in Figure 7 6 LVDT data indicate that strand slip was negligible at lower loads. At higher loads cracks caused shifting of the frame holding the LVDTs thereby compromising the strand slip data. Data from specimens with similar strand bond patt erns and better instrumentation suggest that strand slip was not a contributing factor to in the failure of in specimens with the design strand bond pattern. VC Detailing of specimen VC ( Figure 3 7 ) was similar to the 2008 FDOT Interim Design Standards (FDOT, 2008) with the exceptions that fewer vertical bars and no horizontal bars were placed in the end region Other variables in specimen V C included FDOT specified confinement r einforcement and bearing plate in the bottom flange and the design strand bond pattern ( Figure 3 5 ) which included (39) fully bonded strands. Specimen VC failed in a web shear failure mode. Shear displacement and crack patter n are shown in Figure 7 7

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162 Cracking in VC was first observed during service load testing at a shear of 240 kip. An inclined web crack between the load point and support was the first to be observed. C racks in specimen VC parti ally cl osed during the unloading stage of the service load test. W eb crack s in VC had a maximum width of 0.014 in. at a shear of 290 kip, and 0.002 in. after load was removed. Following the s ervice load testing specimen V C was loaded to ultimate capacity Stiffness decreased gradually as load increased beyond the level of the service load tests. Because flexural cracks were not observed, the loss in stiffness is attributed to formation and growth of diagonal cracks. Ultimate capacity was signaled by we b crushing followed immediately by movement of the portion of the specimen above the inclined cracks relative to that below the inclined crack. This type of failure i s classified as a web shear failure. Loss of capacity after the web shear failu re was ab rupt. Specimen V C supported a maximum shear of 698 kip Strand slip data are not shown in Figure 7 7 LVDT data indicate that strand slip was negligible at lower loads. At higher loads cracks caused shifting of the frame holdin g the LVDTs thereby compromising the strand slip data. Data from specimens with similar strand bond patterns and better instrumentation suggest that strand slip was pattern. VU Specimen VU ( Figure 3 7 ) had the least amount of reinforcement of any specimen in the test program. Variables in specimen VU included no confinement reinforcement, no horizontal reinforcement and reduced vertical rein forcement in the end region. Specimen VU had a bearing plate in the bottom flange and had the design strand bond

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163 pattern ( Figure 3 5 ) which included (39) fully bonded strands. Shear displacement and crack pattern are shown in Figure 7 8 Crack s in V U were first observ ed during the service load test at a shear of 243 kip. The first crack to be observed was a web crack inclined between t he load point and support. W eb crack s in specimen VU had a maximum width of 0.001 in. at a shear of 243 kip, and did not change in width as load was removed after the service load test Following service load testing specimen V U was loaded to u ltimate capacity. Stiffness decreased gradually as load increased beyond the level of the service load tests. Loss in stiffness is attributed to formation and growth of diagonal cracks. Web cracks that formed at lower loads were observed to spread into the bottom flange during the latter stages of testing. Flexural cracks were not observed P eak load in specimen HU corresponded to lateral splitting failure in the bottom flange, which resulted in an abrupt loss of load. Specimen V U supported a maximum shear of 635 kip. Strand slip data are not shown in Figure 7 8 LVDT data indicate that strand slip was negligible at lower loads. At higher loads cracks caused shifting of the frame holding the LVDTs thereby compromising the strand slip data. Data from specimens with similar strand bond patterns and b etter instrumentation suggest that strand slip was pattern. WN The primary feature s of specimen WN ( Figure 3 17 ) were the lack of an embedde d bearing plate and strand bond pattern ( Figure 3 5 ) that placed (20) fully bonded strands below the web. Four additional strands were fully bonded at the edges

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164 of the flange, resulting in a total of (24) fully bonded s trands. Other variables in WN included no horizontal bars in the end region and modified confinement reinforcement. The modified confinement scheme had fewer, but larger, bars than specified by the FDOT. Shear displacement shear slip and crack pattern results for specimen WN are shown in Figure 7 9 Cracking in WN was first observed during service load testing at a shear of 198 kip. An inclined web crack between the load point and support was the first to be observed. C rack s widths in specimen WN partially cl osed during the unloading stage of the service load test. Following s ervice load testing specimen WN was loaded to ultimate capacity. Stiffness decreased gradually as load increased beyond the level of the service loa d tests. Loss of stiffness is attributed primarily to flexural cracks which were first observed at a shear of 435 kip. Strand slip initiated at approximately the same load. Popping sounds indicative of strand slip were heard with increasing frequency as the load approached a peak shear of 507 kip. At peak shear, the strands s lipped suddenly resulting in opening of the crack in front of the bearing pad and a subsequent loss of load. Capacity of WN was limited by strand concrete bond and failure of WN i s labeled as a bond shear failure. WB The prim ary feature of specimen WB ( Figure 3 17 strand bond pattern ( Figure 3 5 ) that placed (20) fully bonded strands below the web. Four additional strands were fully bonded at the edges of the flange, resulting in a total of (24) fully bonded strands. Other variables in WN included presence of an embedded bearing plate, and modified confinement reinforcement. The modified confinement

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1 65 scheme had few er, but larger, bars than specified by the FDOT. Shear displacement, shear sli p and crack pattern results for specimen WB are shown in Figure 7 10 Cracking in W B was first observed during service load testing at a shear of 175 kip. An inclined web crack between the load point and support was the first to be observed. C racks widths in specimen WB partially cl osed during the unloading stage of the service load test. Following s ervice load testing specimen W B was loaded to ult imate capacity. Stiffness decreased gradually as load increased beyond the level of the service load tests. Loss of stiffness is attributed primarily to flex ural cracks which were first observed at a shear of 380 kip. The first flexural crack occurred b elow the load and intersected cracks in the flange that had formed prior to load testing due to prestress transfer. Additional flexural cracks were observed at a shear of 494 kip. Specimen WB had the greatest ductility and reached the largest displace ment of any test specimen. The displacement at peak load was approximately 1.05in. Peak shear for WB was 612 kip. At peak shear the strands slipped abruptly and the crack in front of the bearing pad opened suddenly. Strand slip and cracking resulted in a sudden loss of load. The bearing plate and confinement reinforcement in specimen WB maintained the structural integrity of the bottom flange above the bearing through out load testing Because the bottom flange held together above the bearing the str and concrete bond was also maintained at high load levels in WB Capacity of the WB was governed by strand concrete bond and failure of WB is labeled as a bond shear failure.

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166 FN The primary features of specimen FN ( Figure 3 18 ) were lack of an embedded strand bond ( Figure 3 5 ) pattern that placed (24) fully bonded strands in the outer portions of the bottom flange. Other variables in FN included no horizontal bars in the e nd region and modified confinement reinforcement. The modified confinement scheme had fewer, but larger, bars than specified by the FDOT. Shear displacement, shear sli p and crack pattern results for specimen FN are shown in Figure 7 11 Cracking in FN was first observed during service load testing at a shear of 174 kip. An inclined web crack between the load point and support was the first to be observed. Additional inclined cracks formed and intersect ed splitting cracks in the bottom flan ge that had formed prior to load test ing due to prestress transfer. Shear in the service load test reached 237kip, but for safety reasons the load was immediately removed and cracks were marked after the specimen was unloaded. The concern wit h specimen FN was that the strand bond pattern and lack of a bearing plate could affect a sudden failure. C racks widths in specimen FN partially cl osed during the unloading stage of the service load test. Following service load testing specimen FN was l oaded to u ltimate capacity. Stiffness decreased as load increased beyond the level of the service load tests but not to the degree observed with other specimens. Loss of stiffness is attributed to formation and growth of diagonal cracks. Web cracks tha t formed at lower loads were observed to spread into the bottom flange during the latter stages of testing. Flexural cracks were not observed

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167 Specimen FN reached a peak shear of 375 kip. This was the smallest peak of any specimen in the test program. At peak shear the strands slipped suddenly and the crack in front of the bearing opened. Slip and cracking was accompanied by a subsequent drop in load. Failure of specimen FN is labeled as a lateral splitting failure because failure occurred in large p art due to transverse splitting cracks in the bottom flange. Failure of specimen FN can be understood by considering the strut and tie model shown in Figure 7 12 During latter stages of the ultimate load test s hear load was c arried through the web into the bottom flange by concrete compression struts. Once in the bottom flange the load split into three separate load paths. The two outer paths connected to nodes at the fully bonded outer stands. The inner path was in the sam e plane as the web and connected to an inner node above the centerl ine of the bearing pad. At outer nodes equilibrium in the y direction was maintained by tie forces in the strands. Y direction equilibrium at the inner node was maintained by tension forc e in the concrete. At peak load strands at the outer nodes slipped and the crack in front of the bearing pad propagated into the center of the bottom flange thereby cutting the concrete tie ( Figure 7 13 ). The strut and tie concep t shown in Figure 7 12 is supported by strain data from the confinement reinforcement which formed the transverse tie b etween the outside nodes. Strain in the confinement reinforcement i ncreased after peak load. Once the concret e tension tie failed at peak load, force from the inner load path transferred to the outer load paths. Accordingly, a dditional force was generated in the confinement reinforcement to maintain x direction equilibrium at the outer nodes. This additional

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168 for ce is responsible for the post peak increase in strain observed in the confinement reinforcement ( Figure 7 14 ) FB The primary features of specimen FB ( Figure 3 18 ) were an embedded be aring plate and t strand bond pattern ( Figure 3 5 ) that placed (24) fully bonded strands in the outer portions of the bottom flange. Other variables in FB included no horizontal bars in the end region and modified confinement reinforce ment. The modified confinement scheme had fewer, but larger, bars than specifi ed by the FDOT. Shear displacement, shear sli p and crack pattern results for specimen FB are shown in Figure 7 15 Cracking in FB was first observed d uring service load testing at a shear of 158 kip. An inclined web crack between the load point and support was the first to be observed. C racks widths in specimen FB partially cl osed during the unloading stage of the service load test. Following service load testing specimen FB was loaded to ultimate capacity. Specimen FB reached a peak shear of 409 kip. Failure of FB i s categorized as a later splitting failure. Circumstances and f ailure behavior of specimen FB we re the same as those reported for spec imen FN. As such, a detailed description of the failure mode is not repeated here. DC S pecimen DC ( Figure 3 19 ) was detailed according to the 2010 FDOT Inte rim Design Standards (FDOT, 2010 ). Variables in specimen D C included FDO T specified confinement reinforcement and bearing plate in the bottom flange no horizontal reinforcement in the end region, and the design strand pattern ( Figure 3 5 ) which had

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169 (39) fully bonded strands. Shear displacement, sh ear slip, and crack pattern are shown in Figure 7 16 Cracks in DC were first observed during the service load tests at a shear of 174 kip. Inclined web cracks between the load point and support were the first to be observed. C r acks partially cl osed during the unloading stage of the service load test Following service load testing specimen D C was loaded to ultimate capacity. Stiffness decreased gradually as load increased beyond the level of the service load tests. Because f lexural cracks were not observed, the loss in stiffness is attributed to formation and growth of diagonal cracks. Ultimate capacity was signaled by web crushing followed immediately by movement of the portion of the specimen above the inclined cracks rel ative to that below the inclined crack. This failure i s classified as a web shear failure. Loss of capacity after the web shear failure was abrupt. Specimen HC supported a maximum shear of 7 53 kip Figure 7 16 shows that strand slip in specimen DC was negligible prior to the peak load. Strand slip reported in the figure after peak load was likely exaggerated by cracking of the bottom flange at the end of the load test. L ack of slip observed in DC and other specimens with the design strand bond pattern is attributed to the relatively large qu antity of strands. DM Detailing of specimen HC ( Figure 3 19 ) was effectively identical to the 2010 FDOT Interim Design Standards (FDOT 2010), with the exception t hat the modified confinement reinforcement scheme was u sed in the bottom flange. Modified confinement had fewer, but larger, bars than specified by the FDOT. Other variables in

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170 specimen DM included a bearing plate in the bottom flange no horizontal rein forcement in the end region, and Figure 3 5 ) which had (39) fully bonded strands. Shear displacement, shear slip and crack pat tern results for specimen DM are shown in Figure 7 17 Cracks in DM were first observed during the service load tests at a shear of 166 kip. Inclined web cracks between the load point and support were the first to be observed. C racks partially cl osed during the unloading stage of the service load tes t Following service load testing specimen DM was loaded to ultimate capacity. Stiffness decreased gradually as load increased beyond the level of t he service load test Because flexural cracks were not observed, the loss in stiffness is attributed to fo rmation and growth of diagonal cracks. Failure of specimen DM was a hybrid between lateral splitting and web shear. At peak load o ne of the inclined cracks had a sudden ly increase d in width. The load dropped approximately 5 k ip after the crack opened. Opening of the crack and loss in load occurred in part due to peeling movement of the bottom flange. Loading continued for approximately 15 sec until the web c rush ed and the load fell abruptly. After web crushing the top portion of the specimen slid alo ng the cracking plane relative to the lower portion. Concrete spalled away from the web on both sides of the specimen during the web failure. Specimen DM supported a maximum shear of 7 0 3 kip Longitudinal splitting cracks were observed on the bottom of D M after testing, indicative of lateral splitting failure. Figure 7 17 shows that strand slip in specimen DM was negligible prior to the peak load. Strand slip reported in the figure after peak load was likely exaggerated by

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171 crack ing of the bottom flange at the end of the load test. L ack of slip observe d in DM is attributed to the relatively large quantity of strands Confinement Reinforcement and Bearing Plates Strain gages were used to monitor bearing plates and select confineme nt reinforcement assemblies during load testing. Strain data were then used to calculate stresses and forces in the confinement reinforcement and bearing plates. Stresses and forces were calculated at a shear of 375 kip and at each speci acity. Analyses were conducted at a shear of 375 kip because this force corresponds to the maximum capacity of specimen FN. It is also near the factored shear force in the prototype bridge from which some the specimens were designed. Girders W and F Conf inement reinforcement strain in specimens WN, WB, FN, and FB was monitored during prestress transfer and during load testing. Bearing plate strain was also monitored in WB and FB. Strain from prestress transfer and load testing were superimposed to deter mine total strain in the confinement reinforcement and bearing plates. In was assumed that strain did not change between prestress transfer and load testing. Although it is unlikely that strain was constant it is necessary to make this assumption in ord er to estimate total strain. Specimens WN, WB, FN, and FB each had the modified confinement reinforcement scheme ( Figure 3 11 ) which placed five assemblies of confinement reinforcement above the bearing. Three of the five assembl ies in each specimen were instrumented with gages ( Figure 7 18 ) Gages were placed to measure the transverse (x x) strain.

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172 Combined s train fro m prestress transfer and load testing w as multiplied by the steel modulus of elastici ty to determine stress in the confinement reinforcement. D ata indicate that confinement stresses were typically less than yield stress. One bar in specimen FN and one bar in WN had reached yield stress as ultimate load. Average stresses for each specim en at a shear force of 375 kip are shown in Figure 7 19 Fig ure 7 20 shows average stresses at ultimate capacity. The largest stresses occurred in specimens WN and FN which did not have bearing plates At a shear of 375 kip, the average confinement stress in WN and FN was 3.5 times greater than the average stress in the specimens with bearing plates (WB and FB). At ultimate load the average stress in WN and FN was 2.5 times greater than WB and FB. T he se differences in stress are attributed to the presence of the steel bearing plate in WB and FB. The stiffness of the plate attracted transverse forces thereby reducing the forces (and stress) in the confinement reinforcement. Average confinement s tress varied according to the reinforcement layer. Average stresses in the middle and bottom layers were 6 to 8 times greater than stress in the top layer. I t is believed that tension formed in the bottom flange as shear wa s delivered from the relatively narr ow web to the wi der bearing pad. This tension wa s likely the cause of the greater stress in the bottom and middle layers of confineme nt. Analytical modeling is presented in Chapter 8 to explore this effect. Stress distribution in the confinement reinforc ement also varied in the y direction. For specimens with fully bonded strands placed below the web (WN and WB) the average stress in reinforcement at 8in. and 15in. was 1.6 to 2.1 times greater than the stress in reinforcement at 2in. The opposite trend was observed in specimens with fully

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173 bonded strands placed in the outer flange (FN and FB). Average stress in reinforcement 2in. from the end of FN and FB was typically 2 times greater than average stress in reinforcement placed at 15in. Similar trends w ere noted in confinement behavior at prestress transfer as discussed in Chapter 6. The mechanics presented in Figure 6 8 and Figure 6 9 are believed to be culpable in the stress changes observed in stres s in the y direction. Discussion of these mechanics can be found in Chapter 6 and are not repeated here. Strand bond pattern also affected the magnitude of the average stresses. At a shear of 375 kip, confinement reinforcement in specimens FN and FB had an average stress that was 2.5 times greater than the average stress in WN and WB. The additional stress in FN and FB is attributed to strand bond pattern which placed fully bonded strands in the outer portion of the flange. This pattern caus ed transvers e tension as described in Figure 7 4 Transverse forces in confinement reinforcement and bearing plates (WB and FB only) were estimated by multiplying transverse stresses by the respective cross sectional areas. Linear interpolat ion was used to estimate forces in the confinement assemblies that were not monitored with gages. Results are presented in Table 7 1 Forces from r einforcement with compressive stress were not included in the results. Only the x direction components of forces in the top layer were included. Total transverse force between specimens WN and WB was consistent, suggesting that the presence of a bearing plate did not change the transverse force demand in these specimens.

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174 Transverse force s in specimens FN and FB were not consistent T he be aring plate specimen (FB) had approximately 50% less transverse force. The difference in force between FB and FN is attributed to the bearing plate mechanics in specimen FB Experimental data ind icate that the bearing plate in FB carried an in plane bending m oment during loading This behavior resulted in tensile and compressive forces in the bearing plate ( Figure 7 21 ) The causes of the in plane moment are the force a nd eccentricity of the outside strands ( Figure 7 4 ). By carrying in plane moment, the plate reduced the magnitude of transverse forces typically as sociated with the outer strands In plane bending of the plate in Specimen WB was not observed. Girders H and V Strain gages were placed on confinement reinforcement and bearing plates in specimens HC and VC to monitor strain during loading ( Figure 7 22 ). S tresses and forces in these elements were estimated i n the same manner as was done for specimens in girders W and F. Forces at ultimate load are shown in Figure 7 23 and are due to applied load only Confinement strain data were not collected during prestress transverse in specim ens VC and HC, and the effects of transfer are not included in Figure 7 23 In calculating the forces it was assumed the total strain in the confinement and plates was less than the yield strain. This assumption appears valid fo r HC and VC because yielding was only reached in two of the 36 bars that were monitored in girders W and F, and because the yielded bars occurred in specimens without bearing plates. The estimated tensile force carried by all confinement reinforcement was 25.7 kip and 30.3 kip for specimens HC and VC, respectively. These forces equate to approximately 4% of the reaction at ultimate load. The largest confinement

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175 reinforcement forces occurred near the end of the specimens. At locations farther away from th e end, the confinement reinforcement ca rried compressive forces, thus confirming the theoretical behavior presented i n Figure 7 4 The transition from tensile to compressive action in the confinement reinforcement is estimated t o have occurred at distances approximately 40in. and 50in. from the specimen ends ( Figure 7 23 ). The flexural depth ( d ) of the non composite member was 49in. Comparing the distribution of confinement forces with the flexural dep th shows that all tension in the confinement reinforcement occurred within d of the member end. Current AASHTO LRFD requirements specify that confinement reinforcement must extend at least 1.5 d from the member end. The experimental results suggest that t his requirement is conservative, and that more effective placement of confinement reinforcement is possible. Other researchers (Tadros et al. 2010) have also suggested that the required distribution of confinement reinforcement should be reduced to less t han 1.5 d Bearing Plates Eight of the ten experimental specimens had embedded steel bearing plates. Strain in each bearing plate was monitored during load testing. Average stresses in the bearing plates were calculated by multiplying the average experi mental strain by the elastic modulus. Bearing plate stresses due applied load (effects of prestress transfer not included) are presented in Figu re 7 24 At ultimate load the average stresses ranged from 2.4 ksi (FB) to 10.6 ksi (VU). The relatively low average stress in specimen FB was due to in plane bending of the plate as discussed previously. Bearing plate forces were calculated by multiplying the average stresses by the cross section areas ( Figure 7 25 ). Net tension force in the bearing plates at ultimate

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176 load ranged from 96.2 (VU) to 16.5 kip (FB). The average tension force at ultimate load was 62.9 kip. Tension forces in the bearing plates are compared to the total transverse force in Figure 7 26 For this figure the total transverse force is defined as the combined transvers e force in the bearing plate plus confinement reinforcement. Forces in Figure 7 26 are due to applied loads only. On average the bearing plates carried 60% to 71 % of the total transverse force due to the applied load The p ortion of transverse force carried by the bearing plate s at prestress transfer was evaluated using data from specimens WB and FB. As shown in Figure 7 27 c ontribution of the bearing plate at prestress transfer was affected by the strand bond pattern. The bearing plate in specimen FB (bonded strands in outer flange) carried almost 77% or the total transvers e force at prest ress transfer, whereas the plate in specimen WB (inner strands bonded) carried 52% of the transverse force at transfer. Experimental data presented in this section indicate that bearing plates in FIB girders will typic ally carry more than 50% of transverse splitting force s Thus for purposes of designing confinement reinforcement it is conservative to assume that the bearing plate will carry no more than 50% of transverse force. Variable Comparisons M aximum superim posed shear for each specimen are reported in Figure 7 28 and Table 7 2 Values ranged from a high of 766 kip (HC) to a low of 375 kip (FN), with an average of 612 kip. The large degree of variation in the se resu lts is a testament to the effect that detailing can have on end region behavior and capacity, even for members having the same cross section and materials properties. Effects of the variables are discussed below and are summarized in Table 7 3

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177 Horizontal Reinforcement The 2008 FDOT interim standard for FIB 54 girders (FDOT 2008) called for horizontal bars to be placed in girder end regions. For reasons unrelated to the current test progr am, this detail was changed such that t he 2010 FDOT interim design standard (FDOT 2010) eliminated horizontal bars. Effects of the horizontal reinforcement can be evaluated using results from specimens HC and DC. Specimens HC and DC were effectively identical with the exception of horizontal rei nforcement placed in HC. F ailure loads of these specimens were within 2% of each other and b oth specimen s failed in a web shear mode. This result suggests that the relatively small amount of horizontal reinforcement placed in specimen HC had negligible effect on behavior or capacity. Previous research by the author (Ross et al. 2011b) has shown that horizontal reinforcement improves ductility in girders having a critical failure mode of bond shear. Specimens HC and DC failed in web shear, thus indicatin g t hat horizontal reinforcement had ne gligible impact when web shear wa s the critical failure mode. Embedded Steel Bearing Plate FDOT details call for embedded steel plates to be placed at the end of I girders above the bearing location. Inclusion of the plates in the FDOT detail was based on recommendations by Cook and Reponen (2008) and was implemented to p revent cracks at the bottom corner of girders during fabrication. Embedded steel bearing plates were included as a variable in the current test prog ram to evaluate t he effects of bearing plates on bottom flange confinement Specimens WB and WN had identical detailing with the exception of the bearing plate which was excluded from specimen WN. Specimen WB had a bearing plate and a capacity of 612 kip. This was 21% greater than the 507 kip capacity of WN. Both

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178 specimens failed in bond shear mode. The additional capacity in specimen WB is attribu ted to the confining effect of the bearing pl ate that helped maintain structural integrity of the bottom fl ange above the bearing. Because the bottom flange held together, strand concrete bond in WB was maintained at loads beyond which specimen WN (no bearing plate) lost strand concrete bond. Specimens FB and FN also had identical detailing with exception of t he bearing plate which was excluded from FN. Specimen FB had a bearing plate and a capacity of 409 kip. This was 9% larger than the 375 kip capacity of specimen FN Both specimens failed in laterally splitting mode. The additional capacity of specimen FB is attributed to the bearing plate, however the effect of the bearing plate was not as pronounced as the effect between specimens WN and WB. Confinement Reinforcement Three different confinement reinforcement schemes ( Figure 3 11 ) were used in the test specimens. The current FDOT confinement scheme was used in specimens HC, VC, and DC. A modified confinement scheme was used in specimens WN, WB, FN, FB, and DM. The modified confine ment scheme had fewer but larger bars than th e FDOT scheme. Specimens HU and VU had the final scheme, in which confinement reinforcement was totally omitted. FDOT vs. No Confinement Specimens HC, VC, HU, and VU contained comparable vari ables and can be used to evaluate FDOT confinemen t relative to specimens with no confinement. HC and VC had FDOT confinement reinforcement and failed in a web shear mode. The capacity of HC and VC was on average 13% larger than the capacity of HU and VU which had no confinement reinforcement. HU and VU failed in a later splitting mode. Thus omission of confinement reinforcement

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179 allowed lateral splitting failure of the bottom flange and decreased capacity by 13%. Or, conversely, the presence of confinement reinforcement forced failure away from the bottom flange thereby increasing capacity by an average of 13%. FDOT vs. Modified Confinement Detailing of specimens DC and DM ( Figure 3 9 ) was identical with the exception of confinement reinforcement. DC had FDOT confinement reinforcement and a capacity of 753 kip, whereas DM had modified confinement reinforcement and a capacity of 703 kip. F ailure mode was different between these specimens. In specimen DC the FDOT confinement reinforcement was sufficient to prevent lateral splitting fai lure, thereby forcing a web shear failure. Confinement reinforcement in DM was insufficient to prevent lateral splitting of the bottom flange. Thus the current FDOT detail for confinement provides more effect ive confinement at ultimate load than the modi fied scheme. O ne reason that the FDOT scheme was superior is because it placed c onfinement bars in front of the bearing where they can act ed as stirrup Confinement reinforcement as stirrups was postulated by Csagoly (1991 ) ( Figure 2 9 ). Confinement bars were not provided away from the bearing in the modified scheme This allowed propagation of cracks in front of the bearing of specimen DM ( Figure 7 29 ). Strand Quantity Strand quantity had a greater ef fect on specimen capacity than any other variable in the test program. A verage capacity of specimens with (39) fully bonded strands was 48% greater than the average capacity of specimens with only (24) fully bonded strands. The relationship between stran d quantity and experimental capacity is described in Figure 7 30 The figure shows a linear trend line that was fit to the

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180 experimental data. The trend line has an R 2 value of 0.69, indicating a reason able degree of correlation be tween experimental capacity and strand quantity. Current AASHTO LRFD requirements limit the quantity of partially shielded strands to 25% of the total strand count Providing limits on strand shielding is considered good practice in light of the experimen tal results. Based on experimental data, every strand that was shielded resulted in a roughly proportional decrease in capacity. The data also suggest, however, that the means by which AASHTO LRFD limits strand shielding can be improved. Rather th an lim iting shielding to an arbitrary percentage, it is more rational to limit shielding according to the total number of bonded strands required to provide the necessary end region capacity. If sufficient strands are available to support the required capacity, than shieldin g of the remaining strands can reasonably be permitted As will be discussed later, the minimum longitudinal reinforcement requirements of AASHTO section 5.8.3.5 can be employed to determine the necessary strand quantity for a given load dem and. Strand Placement S trand placement can be evaluat ed using results from WN, WB, FN, and FB. Fully bonded strands in WN and WB were placed primarily in the center of the bottom flange below the web. In FN and FB, fully bonded strands were placed in t he outer portions of the flange ( Figure 3 5 ) Specimens WN and WB ( strands below the web ) failed in a bond shear failure mode and at an average load that was 43% greater than specimens FB and FN ( fully bon ded strands in the outer flange). Specimens FB and FN failed in lateral splitting mode. Crack patterns associated with the different strand patterns and failure modes are shown in Figure 7 31

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181 T o maximize end region capacity and prevent lateral splitti ng failures it is desirable to place strands as close to the cross section centerline as practical. Doing so minimize s the horizontal eccentricity between prestressing forces and the equal but opposite internal force This in turn reduces the propensity for lateral splitting in the bottom flange. Code Comparisons Experimental moments and shears in this section include both the applied load and self weight of the specimens. Experimental moment is denoted as M ex p and is defined as the maximum moment occur ring during testing at the section below the point load. Experimental shear is denoted as V ex p and is defined as the maximum shear occurring during testing at the near support. Nominal capacities were calculated using the material properties listed in Table 7 4 These values are representative of the tested properties of materials in the experimental girders. The following paragraphs explain the calculation procedures used to determine nominal capacities. Nominal Moment Capaci ty None of the experimental specimens failed in flexure; however nominal moment capacities were still calculated for reference purpose s. Capacity was calculated using principals of strain compatibility and equilibrium. Typical assumptions for concrete in flexure were applied. Nominal moment capacity is denoted as M n Shear associated with nominal moment is denoted as V Mn AASHTO LRFD Nominal Shear Capacity. Concrete contribution to shear capacity was calculated using the General Procedure from sectio n 5.8.3.4.2 of AASHTO LRFD (2007). This procedure is based on the modified compression field theory

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182 (MCFT). Steel contribution wa s calculated using AASHTO LRFD E quation 5.8.3.3 4. AASHTO LRFD nominal shear capacity is denoted as V n LRFD ACI Nominal Shea r Capacity. Concrete contribution was calculated using section 11.3.3 of ACI 318 (2011). Provisions in this section are commonly referred to as the ACI detailed method. Steel contribution was calculated using the provisions of section 11.4.7. ACI nomin al shear capacity is denoted as V n ACI Nominal Tie Capacity (Minimum longitudinal reinforcement) Nominal tie capacity calculations are based on the minimum longitudinal steel requirement in AASHTO LRFD 5.8.3.5 Equation 5.8.3.5 2 requires that sufficien t longitudinal reinforcemen t be provided to carry tie forces at the bearing. Bond shear failure is likely when the tie is insufficient. Procedures from Ross et al. (2011b) were u sed to calculate the shear force that accompanies the nomina l tie capacity. These procedures encompass the AASHTO LRFD requirements, bu t were derived for application to test specimens Shear associated with nominal tie capacity is denoted as V n T In making the tie calculations, a required development length of 72 in. was assumed for the prestressing strands. The available tie force in the strands was reduced proportionally to the assumed available development of 22in. For each specimen the experimental moment was less than the calculated nominal moment capacity ( Table 7 5 ). This result is in agreement with experimental specimens in which no flexural failures were observed. Most specimens carried experimental moments that were between 60% and 75% of their nominal moment capacity.

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183 Nominal and experimen tal shear capacities are compared in Table 7 6 The AASHTO LRFD and ACI nominal shear capacities are based on web shear failure, which was only observed in four of ten specimens Bond shear failure, the assumed failure mode of th e AASHTO tie capacity, was only observed in two of the ten specimens. Because of inconsistencies between code assumed and experimentally observed failure modes the comparisons shown in Table 7 6 are useful for relative compariso ns only. Although inconsistent with failure modes, calculated nominal capacities were typically conservative relative to the experimental results ACI shear calculations were the most conservative and resulted in nominal capacities 34% less on average than the experimental results. AASHTO shear and AASHTO tie nominal capacities were 12% and 6% less on average, respectively, than the experimental results. Specimens FN and FB were the only specimens with calculated nominal capacities greater than the e xperimental shear forces. These specimens failed in lateral splitting This type of failure is not explicitly considered in ACI or AASHTO code provisions. Because ACI and AASHTO codes do not account for lateral splitting failure, code based capacities f or specimens FN and FB were unconservative (i.e. greater than experimental capacity). This result demonstrates the need for code provisions that account for lateral splitting failure. The nominal tie method was the most accurate for calculating end regi on capacity of the experimental specimens. Capacities calculated by the nominal tie method were 6% smaller on average than the ex perimental capacities It must be noted, however, that nominal capacity calculated by the tie method is highly dependent on t he values

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184 that are assumed for the required and available development lengths. The AASHTO LRFD code does not give specific requirements for selecting these values. Rather the spite of the ambiguity in code language, the agreement shown between experimental and nominal tie capacities demonstrate the utility of this method for designing I girder end regions. In particular, this method is useful in selecting strand quantities th at are unlikely to result in bond shear failures. Summary and Conclusions Ten uniquely detailed FIB 54 specimens were load tested in three point bending at a shear span to depth ( a/d ) ratio of 2.0. Variables in the test program included: Presence/absence of confinement reinforcement Quantity and configuration of confinement reinforcement Presence/absence of horizontal reinforcement Quantity of vertical reinforcement Presence/absence of embedded steel bearing plates Strand quantity Strand placement The fol lowing conclusions are made: Differences in detailing have significant effect on the end region capacity, even for members having the same cross section. All t est specimen s used the FIB 54 cross section, yet experimental capacities ranged from a maximum o f 766 kip to a minimum of 375 kip. Horizontal rei nforcement in the end region has negligible effect on the capacity of members failing in web shear. The test specimen with horizontal reinforcement had no significant increase in capacity relative a compara ble specimen without horizontal reinforcement. Embedded steel bearing plates provide confinement to the bottom fl ange, thereby improving end re gion capacity Test specimens with bearing plates had 9% to 21% greater capacity relative to comparable specimens without bearing plates. Confinement reinforcement can be used to mitigate lateral splitting failure, thereby imp roving end region capacity Test specimens with confinement reinforcement

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185 per current FDOT specifications failed in web shear mode and at an a verage load 13% higher than comparable specimens without confinement Specimens without confinement failed in lateral splitting To mitigate lateral splitting failure c onfinement reinforcement must have sufficient quantity and effect ive placement Latera l splitting failure w as observed in specimens with confinement reinforcement placed only above the bearing. A comparable specimen with confinement place d throughout the strand transfer length failed in web shear and at a 7% higher load Bearing plates car ry a significant portion of transverse splitting forces. Up to 79% of the transverse tension was carried by bearing plates in the test program. For purposes of designing confinement reinforcement it is conservative to assume that b earing plates carry 50% or less of the transverse splitting force. Girders with fully bonded strands in the outer flange have greater transverse splitting forces than due girders with fully bonded strands place d below the web. In the test program, transverse force in confinement reinforcement was up to 2.5 times larger in specimens with strands in the outer flan ge relative to those with strands below the web. Strand quantity had the greatest effect on end region capacity of any variable in the te st program. Specimens with 39 ful ly bonded strands had an average capacity that was 4 3% greater than specimens with 24 fully bonded strands. There was a reasonable degree of correlation (R 2 =0.69) between quantity of fully bonded strands and experimental end region capacity. As such, de sign of strand shielding based on longitudinal tie capacity a ppears to be a rational design approach. This approach may give better results than the arbitrary shielding limits imposed by current AASHTO LRFD specifications. There is need for code provision s that explicitly address lateral splitting failure. C urrent shear and longitudinal tie provisions resulted in nominal capacities that were unconservative (too large) for some specimens failing in lateral splitting.

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186 Figure 7 1 Web shear failure (Photo courtesy of B.E. Ross) A B Figure 7 2 Bond shear f ailure A) B ottom view B) S ide view (Photos courtesy of B.E. Ross)

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187 A B Figure 7 3 Lateral splitting f ailure A) B ottom view B) S ide end view (Photos courtesy of B.E. Ross) Figure 7 4 Lateral splitting failure m echanics

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188 A Release cracks not shown. Initial cracks shown bold in red Final cracks shown blue. B Figure 7 5 Specimen HC load test summary. A) S hear displacement, B) C rack pattern

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189 A Release cracks not shown. Ini tial crack shown bold in red Final cracks shown blue. B Figure 7 6 Specimen HU load test summary. A) S hear displacement B) C rack pattern

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190 A Release cracks not shown. Initial crack shown bold in red Final cracks shown blue. B Figure 7 7 Specimen VC load test summary. A) S hear displacement B) C rack pattern

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191 A Release cracks not shown. Initial cracks shown bold in red Final cracks shown blue. B Figure 7 8 Specimen VU load test summary. A) S hear displacement B) C rack pattern

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192 A Release cracks shown black Initial crack shown bold in red. Final cracks shown bl ue. B Figure 7 9 Specimen WN load test summary. A) S hear displacement/slip B) Crack pattern

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193 A Release cracks shown black Initial crack shown bold in red. Final cracks shown blue. B Figure 7 10 Specimen WB load test summary. A) S hear displacement/slip B) C rack pattern

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194 A Release cracks shown black Initial crack shown bold in red. Final cracks shown blue. B Figure 7 11 Specimen FN load test summary. A) S hear displacement/slip B) C rack pattern

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195 Figure 7 12 Strut and tie behavior specimen FN. (Photo courtesy of B.E. Ross ) Figure 7 13 Longitudinal splitting cracks on bottom of specimen FN. Release cracks shown black. Final cracks shown blue. (Photo courtesy of B.E. Ross)

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196 Figure 7 14 Confinement reinfo rcement strain specimen FN

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197 A Release cracks shown black Initial crack shown bold in red. Final cracks shown blue. B Figure 7 15 Specimen FB load test s ummary. A) S hear displacement/slip B) C rack pattern

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198 A Release cracks shown black Initial crack shown bold in red. Final cracks shown blue. B Figure 7 16 Specimen DC load test summary. A) S hear displacement/slip B) C rack pattern

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199 A Release cracks shown black Initial crack shown bold in red. Final cracks shown blue. B Figure 7 17 Specimen DM load test summary. A) S h ear displacement/slip B) C rack pattern

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200 Figure 7 18 Strain gage placement girders W, F, and D Figure 7 19 Confinement stress at shear = 375 kip

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201 Fig ure 7 20 Confinement stress at ultimate capacity Figure 7 21 Transverse (x x) stress profiles at bearing plate centerline

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202 Figure 7 22 Strain gage placement girders H and V

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203 Figure 7 23 Specimens HC and VC confinement reinforcement and bearing plate transverse (x x) forces due to maximum applied load

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204 Figu re 7 24 Bearing plate stress due to applied load Figure 7 25 Bearing plate force due to applied load

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205 Figure 7 26 Percent of transverse force due to applied loads carried by bearing plate Figure 7 27 Percent of transverse force carried by bearing plate in WB and FB

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206 Figure 7 28 Maximum superimposed shear A B Figure 7 29 Girder D bottom flange cracking. A) Specimen DC with l imited bottom flange cracking in front of bearing B) Specimen DM with se ver e b ottom flange cracking in front of bearing (Photos courtesy of B.E. Ross)

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207 Figure 7 30 Relationship between strand quantity and end region capacity Figure 7 31 Comparison of FB (left) and WB (right). Release cracks shown black. Final cracks shown blue. (Photos courtesy of B.E. Ross)

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208 Table 7 1 Transverse forces in W and F specimens WN (kip) WB (kip) FN (kip) FB (kip) Shear of 375 kip Confinement reinforcement 50 15 107 27 Bearing plate 0 36 0 30 Total 50 51 107 58 Ultimate load Confinement reinforcement 95 40 107 35 Bearing plate 0 70 0 30 Total 95 111 107 65 Table 7 2 Maximum superimposed shear Specimen Maximum superimposed shear (kip) Maximum shear / average shear HC 766 1.25 HU 666 1.09 VC 698 1.14 VU 635 1.04 WN 507 0.83 WB 612 1.00 FN 375 0.61 FB 409 0.67 DC 753 1.23 DM 703 1.1 5 Average 612 1.0 0

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209 Table 7 3 Variable comparisons Variable Relevant specimens Result Horizontal reinforcement HC, DC Negligible effect on end region capacity in specimens failing in web shear Bearing plate WN, WB, FN, FB 9% to 21% capacity increase from bearing plate FDOT vs. no confinement reinforcement HC, HU, VC, VU 13% capacity increase from FDOT confinement reinforcement FDOT vs. modified confinement reinforcement DC, DM 7% capacity increase from FDOT confinement reinforcement Strand quantity All Average capacity increase of 18.4 kip / bonded strand Strand placement WN, WB, FN, FB 43% capacity increase for strands placed near centerline relative to strands placed in outer flange Table 7 4 Material properties for capacity calculations Property Value Prestressing strands ultimate strength 285 ksi Vertical reinforcement yield strength 68 ksi Concrete deck compressive strength 6500 psi Concrete girder compressive strength 11000 psi

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210 Table 7 5 Experimental moments and nominal moment capacities Specimen M exp (kip ft) M n (kip ft) V exp (kip) V Mn (kip) M exp /M n HC 7384 10295 793 109 8 0.72 HU 6478 10295 697 1098 0.63 VC 6746 10295 725 1098 0.66 VU 6155 10295 662 1098 0.60 WN 4954 6570 534 700 0.75 WB 5939 6570 639 700 0.90 FN 3716 6720 402 716 0.55 FB 4035 6720 436 716 0.60 DC 7262 10295 780 1098 0.71 DM 6793 10295 730 1098 0 .66 Table 7 6 Experimental shear and nominal shear capacities AASHTO Shear ACI Shear AASHTO Tie S pecimen V exp (kip) V nLRFD (kip) V exp / V nLRFD V nACI (kip) V exp / V n ACI V n T (kip) V exp / V n T HC 793 59 0 1.34 490 1.62 678 1.17 HU 697 590 1.18 490 1.42 678 1.03 VC 725 590 1.23 490 1.48 657 1.10 VU 662 590 1.12 490 1.35 657 1.01 WN 534 528 1.01 454 1.18 507 1.05 WB 639 528 1.21 454 1.41 507 1.26 FN 402 528 0.76 454 0.89 514 0.78 FB 436 528 0.83 454 0.96 514 0.85 DC 780 590 1.32 490 1.59 657 1.19 DM 730 590 1.24 490 1.49 657 1.11 Average 1.12 1.34 1.06

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211 CHAPTER 8 ANALYTICAL EVALUATIO N OF GIRDERS UNDER A PPLIED LOADS FE modeling was conducted to 1) provide a better understanding of the elastic behavior of the end region prior to cracking and 2) to evaluate the effects of bearing pad stiffness and width on end region elastic stresses. The FEA program Adina (R&D 2009) was used to conduct all modeling and analysis All models were linear elastic. S train gage and displacement data from experimental work conducted on pretensioned concrete beams ( Ross et al. 2011a ) were used to validate the FEA model. Hereafter the beams tested by Ross et al are Model Configuration The FE model was configured to be computationally efficient, yet able to capture the overall behavior of the beam as well as the local behavior of the end region. The ability of the model to capture the distribution of transverse tensile strain in the end reg ion was of particular interest. The model was also designed such that the geometric and material properties could be adjusted to evaluate the sensitivity of the end region behavior to such parameters. The coordinate system defined in C hapter 4 was also us ed in the FE models ( Figure 8 1 ). The origin was located at the end of the beam nearest the point load, at the centerline of the cross section, and at the bottom of the beam. The X axis was oriented horizontal ly across the cross section, the Y direction was oriented horizontal ly along the length of the beam, and the Z direction was oriented vertical ly Figure 8 2 shows the model configuration. T he shear span (distance from the load to the near support) and a small distance beyond the shear span were modeled with 27 node 3D solid elements on a primarily rectangular mesh. The remainder of the beam

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212 was modeled with 1D beam elements, with the transition from beam to solid elements made using rigid 2D shell elements and 1D rigid links. R igid shell and link elements ( Figure 8 3 ) coupled the displacements of the 3D solid elements with the displacements and rotations of the 1D beam elements. Transitioning to beam elements reduced the computation demand of the model while still modeling the global beam behavior and boundary conditions. Beam elements were placed at the centroid of the cross section and were assigned cross sectional properties equivalent to the physical beam. At the far support, a rigid link was provided to connect the beam elements to the physical location of the bearing pad at the bottom of the beam. A xial and shear stiffness of the bearing pad at the far support were modeled with 1D springs in the Z and Y directions respectively. At the near support, the axial and shear stiffness of the bearing pad was modeled with multiple spring elements in each of the X, Y, and Z directions. P osition and quantity of spring elements matched the discretization of the solid elements used to model the beam ( Figure 8 4 ). S tiffness was assigned to each spring in proportion to the tributary area represented by the spring Figure 8 5 defines key geometric variables of the model end r egion. G eometric variables were set up to allow variation of features such as shear span to depth ratio, bearing pad size and location, span length, and the location of the applied load. Additional geometric variables are defined on the cross section sho wn in Figure 8 6 The cross section, boundary conditions and load were symmetrical about the Y Z plane, allowing for only half of the beam to be considered in the FE model ( Figure 8 6 ). A top view of t he model shown in Figure 8 7 gives the position of the model relative to the physical geometry of the beam.

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213 C oncrete modulus of elas ticity for each model was 5300ksi, and ratio was 0.2. The modulus of elastici ty value was chosen to match the tested ma terial properties from the physical beams used for model validation The typical model configuration described above was validated by comparison with experimental data, and was then used in more general investigati ons of the stress and strain state in the end region. Details of the validation and general investigations are contained in the proceeding sections. Small Beam Model The configuration described above was used to model the small beams tested by Ross et al (2011) Dimensions, elements sizes, and spring properties of the model are listed in Table 8 1 V ariables in this table are defined in Figure 8 5 and Figure 8 6 The experimental test set up being modeled element types, and element density are shown in Figure 8 8 Stiffness values for the springs in the Z direction were based on experimental load displ acement data from LVDTs located over the bearing pads on the small beam tests ( Figure 8 9 ). From these data, a representative axial stiffness of 1150 kip/in was chosen. At the far support, the full axial stiffnes s was assigned to the single spring at the bearing point. At the near support the axial stiffness was distributed to the springs based in proportion to tributary area. Stiffness of springs at both the near and far support s in the pad shear direction s (X & Y) were based on properties reported for similar sized bearing pads ( Yura et al. 2001 ). Model Validation and Verification Prior to comparing FE results with experimental data, convergence of the FE solution was verified by comparing the proposed model w ith a model containing a more refined mesh. Figure 8 10 shows the transverse ( x x ) strain in the bottom bulb at the

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214 near support for the proposed and refined mesh densities. Note that the sect ion geometry and str ain values we re symmetric about the Y Z plane and that only half of the bottom bulb is shown in the figure. The strain v alues and strain distributions we re similar for both models, with the maximum transverse strain occurring at the centerline of the bea m directly above the bearing pad (Z=0, X=0). The refined model reported a maximum strain that was only 0.1% greater than the maximum value from the proposed model. Based on the degree of correla tion with the refined mesh, elements si zes used in the propos ed model we re considered appropriate. Comparison with experimenta l data indicated that the FE model did an adequate job of capturing both the global and local linear elastic behavior of the physical test beams. G lobal behavior is compared in the load dis placement plot in Figure 8 12 D isplacement in the figure (both experimental and analytical) is the vertical displacement at the load point, and was corrected to remove displacement due to deformation of the bearing pads. Within the elastic range, the FE model stiffness wa s 23% less stiff than the average ex perimental beam stiffness, but was still within the scatter of the experimental data. The profile of the transverse (x x) strain at the near end of the beam is shown in Figure 8 11 Strain profiles we re compared at a load of 15kip, as this load was well within the elastic range fo r each of the test beams. E xperimental data came from strain gages mounted at the end of the beams 5in. above the beam bot tom Shape of the strain profile wa s consistent betwe en experimental data and the FE model with the peak occurring at th e centerline of the beam. M agnitudes of the strains calculated by

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215 the FE model we re larger than the average of the experimental data, but we re still within the scatter of the data. Figure 8 13 shows the load versus strain relationship for gage S5 which was located longitudinally on the bottom of the beam directly below the applied load. Experimental data from gage S5 was very consistent between tests. At the location of S5, the slope of th e load strain curve from the FE model was 20% less than the average slope of the experimental data. Figure 8 14 shows the load versus strain relat ionship for gages S11 and S12. These gages were located on the top of the beam on either side of the applied load. V alues from gages S11 and S12 were averaged to form the curves for the individual tests. V alues reported by the FE model a t the locations of S11 and S12 we re identical because the FE model employed symmetry about the Y Z plane. The slope of the l oad strain curve reported by FE model was 5% greater than the average slope of the experimental data. Finally, the maximum principal tensile strain was evaluated over the region shown in Figure 8 16 The maximum principle tensile strain occurred at the intersection of the web and the bottom bulb ( Figure 8 15 ). The strain concentration at the web b ulb interface correlates with the location of cracks observed during testing. The proposed FE model captured the general behavior of the physical beam, as well as the local behavior of the end region. In most cases the FE results were within the scatter of the experimental data. Based on the correlations presented above, the proposed FE model wa s considered adequate for conducting more general evaluation s of the concrete girder end region.

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216 Parametric Studies The FE model configuration presented previous ly was used to evaluate parameters affecting the strain state in the end region including: b earing pad stiffness, cross section geometry, steel bearing plates and bearing pad geometry. Bearing Pad Stiffness Four additional mode ls were created to evaluate s ensitivity of the end region strains to changes in bearing pad stiffness. In these models, the axial or shear stiffness of the bearing pad was either doubled or halved relative to the stiffness of the original model. By using half or double the stiffness properties of the original small beam model, the additional models cover the range of stiffness values for similar sized bearing pads reported by Yura et al. (2001). Details and results from the additional models are presented in Table 8 2 Information regarding the original model is also included in the table for reference. Strain results were evaluated over the region shown in Figure 8 16 For each model, the maximum transverse tensile strain was located at the centerline of the beam directly above the bearing pad ( Figure 8 16 ). Changes to bearing pad shear stiffness ( Kv ) had negligible effect on maximum transverse (x x) strain over the range of values tested. However, c hanges to the axial stiffness ( Ka ) of the bearing pads did affect the maximum transverse strain For the region considered, doubling the axial stiffness resulted in a 2.7% reduction in maximum transverse strain whereas halving the axial stiffness resulted in a 1.5% increase in maximum transverse strain Bearing Pad Geometry To evaluate the effect of bearing pad width on the transverse strain in the end region, FE models of the Florida I Beam (FIB) and a rectangular cross section ( Figure

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217 8 17 ) were created using the modeling configuration described previously Details of the models are given in Table 8 3 The bearing pad width, W b was varied from of 8.55 in. to 16.15 in. Because half symmetry models we re used, the bearing pad width, W b, is equal to half of the total bearing pad width. Thus the FE model with W b of 16.15 in. corresponded to a total bearing pad width of 32.3 in. This dimension is similar to the 32 in. width specified in the FDOT design st andard s (FDOT 2009c) For convenience models were assigned a label based on cross section shape and nominal W b dimension. For example, the label FIB 10 was assigned to the model with the FIB cross section and a bearing pad width of 10.45 in. The label R 15 was given to the m odel with the rectangular cross section and a bearing with of 15.20 in. S tiffness and spacing of the individual springs comprising the bearing pad at the near support were held constant even as the bearing pad width varied. Howev er, the total stiffness of the bearing pad changed as additional springs were added or removed to change the width of the bearing pad. The individual spring stiffness, as well as the total bearing pad stiffness, are listed in Table 8 4 In each model, total the stiffness of the far support matched the stiffness of the near support. Transverse (x x) strain results from the models were normalized by the maximum flexural ( y,max ) tensile strain from the FIB model. The maximum flexural strain was located at the bottom of the beam below the load point ( Figure 8 18 ). The value of y,max was slightly different for the FIB and rectangular cross sectio ns, however for a given section it did not vary as the bearing pad width changed. For a half symmetry applied load of 67 kip (experimental load of 134 kip) y,max was 91 microstrain for the FIB

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218 model, and for the same load, was 61 microstrain for the r ectangular section model. The transverse strains for each model were normalized by y,max from the FIB model. For the FIB cross section, two types of behavior were observed as the bearing pad width was adjusted. First, when the pad width was narrow, the transverse strains were distributed in a bottle shape between the bearing pad and the bottom of the web ( Figure 8 19 similar to a split cylinder te st, with transfer tensile strain forming perpendicular to compressive loads. The maximum transverse strain occurred above the bearing pad, as shown in Figure 8 20 As the pad width increased, flexural strains increased at the bo ttom edge o f the flange as the load spread to the far edge of the bearing pad ( Figure 8 21 transverse strain occurred at the bottom of the section as shown in Figure 8 22 To further investigate the relations hip between transverse strain and bearing pad width, strain at three points on the end of the beam were plotted against the bearing pad width ( Figure 8 23 ). Points were located at the end of the beam (Y=0 in.) along the plane of symmetry (X=0 in.) at Z coordinates of 0 in., 5 in., and 9 in. Looking first at the point Z = 0 in., it can be seen that the maximum transverse strain increased as the bearing pad width al so increased. This condition wa s a consequence of flange bending behavior. For the point at Z= 9 in., the transverse strain increased as the bearing pad width decreased. Thus the strain at Z = 9 in. was maximum when the beam experie nced bursting behavior, and was smaller when flange bending dominated the behavior. The strain at Z = 5 in. remained fairly constant as the pad width changed. The optimum bearing pad width, i.e. the width that minimized the transverse strain, was

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219 approxi mately 21 in. This is also the width where the behavior changed from bursting to flexural behavior. Figure 8 24 shows the normalized transverse strains in the end region for four models with different bearing pad widths. V ariati ons in the transverse strain between the different models only occurred in portions of the beam adjacent to the bearing pad. the Z Y and Z X planes. Regardless pad width, the greatest transverse strains always occurred that the end of the beam. Transverse strain distributions in the end region of the rectangular section are shown in Figure 8 25 for models with four different bearing pad w idths. As previously noted, the transverse strains were normalized by y,max from the FIB model. T he scale and c olor contours are different from earlier figures of the FIB section The figure shows that the magnitudes of the strains in the rectangular s ection were considerably less than for the FIB section. For instance, the maximum normalized transverse strain in the R 8 model was only 38% of the maximum from the FIB 8 model. For R 16, the maximum normalized transverse strain was only 14% of the maxim um from model FIB 16. The greatest strain in the rectangular section model s occurred in the model with the narrowest bearing pad. Conversely, the transverse strains were least in the model with the greatest pad width. Although the transverse strain varied as the pad width changed, the location of the maximum transverse strain always occurred at the end of the beam. A parametric study of bearing pad width was also conducted using the small beam FE model ( Figure 8 26 ). Results we r e similar to the FIB model. Regardless of bearing

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220 pad width, maximum transverse strains always occurred at the end of the beam. Under the flexural mode, maximum transverse strain occurred at the end of the beam at bottom of the section. For the bursting mode, maximum strain occurred at the end of the beam and at a distance of approximately 60% of the flange depth above the bearing pad. The transition between bursting and flexural behavior occurred when the bearing pad width was approximately twice the we b width. This pad width also corresponded to the lowest value of peak transverse strain. Effect of Steel Bearing Plate The FDOT standard detail for the FIB end region specifies (FDOT 2009c) a in. thick x 12 in. x 36 in. steel bearing plate be embedded w here the beam contacts the bearing pad. The bearing plate protects concrete in the region of high bearing stresses, and can be configured to aide in the constructability of skewed and/or sloped girders. Due to the location of the plate its e ffect on the transverse (x x) strain was of interest. To evaluate the effects of the bearing plate, the plate was added to the FIB models used in the previous section. The bearing plate was modeled with 4 node 2D shell elements positioned at the bottom of the beam ( Fi gure 8 27 ). The bearing plate discretization was double that of the adjacent 27 node solid elements, thus each node from the plate elements aligned with a node from the adjacent solid element ( Figure 8 28 ). F ull composite behavior between the bearing plate and the concrete was assumed in the model The parametric study of bearing pad width presented in the previous section was repeated for the model with the bearing plate. Figure 8 29 shows the normalized transverse strain at the end of the beam vs. the bearing pad width for models with and without the steel bearing plate. As was done previously, the strain values in the figure were normalized by the maximum flexural

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221 tensile strain ( y,max ) ( Figure 8 18 ) below the load point. Figure 8 29 shows that the presence of the steel bearing plate reduced the transverse strain at point Z=0. At a bearing pad width of 17 in., the model with th e bearing plate reported 20% less transverse strain at point Z=0 than the model without the bearing plate. The reduction in strain was more pronounced at greater pad widths. For example, the bearing plate model reported 33% less transverse strain at a b earing pad width of 32 in. Results also indicated that t he influence of the bearing plate was limited to those portions of the beam closest to the plate. At point Z =9, the presence of the bearing plate had insignificant effect on transverse strain. Figure 8 30 shows the transverse strain distribution for models with different bearing pad widths. Similar to the FIB model that did not include the bearing plate, Figure 8 30 shows that the bearing plate mo pad widths respectively. When compared to the model without the bearing plate, the reduction of transverse strain is attributed to the additional confinement provided by t he plate. This effect was most significant when the bearing pad width was widest, and when the maximum transverse strains occurred closest to the plate. The models only evaluated the effect of the plate in the range of elastic behavior, and did not consi der contributions that the bearing plate may make after cracking and at ultimate strength. Bearing Pad Width Effect on Transverse Force S mall beam, FIB, and FIB with bearing plate FE models developed in previous sections were used to evaluate the relatio nship between bearing pad width and

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222 transverse force. As with all models in this chapter, the analysis was linear elastic and considered the effects of applied loads only. Transverse force was calculated by integrating transverse stress over the area show n in Figure 8 31 Boundaries of the integration area w ere selected to capture those portions of the girder near the bearing pad subjected to steep strain/stress gradients due to the reaction force and to include portions of the bottom flange where confinement reinforcement is placed to carry transverse tension. Stress distributions beyond the integration area were not significantly affected by changes in bearing pad width. Analyzing transverse forces over th e selected area gav e a broad picture of pad width effects in the end region, whereas analysis of strain data in previous sections only looked at maximum effects and effects at discrete points. The integration area used in transverse force calculation wa s located at the cen terline of the considered cross section. Dimensions of the integration area were determined as a function of the bottom flange width ( W f ) so that similar integration calculations could be conducted on beams with different geometries. Discrete normal (x x) stress values from center nodes in the integration area were multiplied by the associated y z areas to obtain the transverse (x x) force ( Figure 8 32 ). Total transverse tensile force was taken as the sum of all element tensile f orces. Compressive forces (when they occurred) were ignored in calculations of the total transverse force. I.e. total tensile force is equal to the gross tension and was not reduced by compressive forces. This approach was taken because it wa s assumed t hat transverse compressive forces would be supported by concrete, and t hat confinement reinforcement w ould be designed to carry tensile forces. The magnitude of tension

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223 force in the reinforcement wa s assumed unaffected by compression forces carried by con crete. Figure 8 33 presents the variation in transverse force as a function of the bearing pad width in the FE models. For the considered models and geometries, the transverse force was equal to 13% to 28% of the reaction force. Transverse force was smallest relative to the reaction force when the bearing pad width was approximately 60% of the flange width. This ratio of bearing to flange width also corresponded to the change in behavior between bursting and flexural behavior as discussed in previous sections. For bearing pad to flange width ratios greater than 0.5 the FIB with bearing plate model had the lowest normalized transverse force. This is attributed to the stiffness of the bearing plate which attracted transverse for ce when the bearing pad width approached the flange width Transverse force in the bearing plate was not included in the data presented in Figure 8 33 FDOT design standards (FDOT 2009c) for FIB girders result in a bearing pad to flange width ratio of 0.84. For this ratio, the calculated transverse tens ile force in the bottom flange wa s equal to approximately 25% of the reaction force in the model without a plate, and approximately 17% of the reaction force in the model with a pla te. These relationships reflect l inear elastic behavior and would likely change after cracks form in the bottom flange. Parametric Study Conclusions Linear elastic FE models were used to evaluate the effects of applied load on I beam and rectangular shape d end regions. Variables in the models included bearing pad width, bearing pad stiffness, cross section shape, and the presence of embedded steel bearing plates The following conclusions are based on results of the evaluations :

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224 The location of maximum t ransverse strain always occurs at the end of the beam regardless of bearing conditions or cross section. le changes to the bearing conditions have little effect beyond those portions of the beam nearest to the bearing. For the range of stiffness values reported for neoprene bearing pads, variations in pad shear stiffness have negligible effect on the transverse strain in the end region. However, variations in pad axial stiffness can change the transverse strain by +/ 3%. Depe nding on the width of the bearing pad, two types of strain distributions ( behavior s) occur in the end region I girders. A behavior denoted as occurs when the bearing pad width is narrow, and the transverse strain is distributed in a bottle shap ed manner. However the pad width is large, and transverse strain is dominated by flexural strains in the flange. pad width increases. pad width decreases. pad width is approximately equal to three times the web width. This pad width also corresponds to the optimal width for minimizing transverse tensile strain The magnitude of transverse strains in rectangular sections are only 14% to 38% of the transverse strains in similar ly dimensioned I shaped flanged sections. This reduction i n transverse strain is one of the benefits of using end blocks on girders with I shaped section s When the bearing pad width is less than the web width (as in the rectangular models), the transverse strains increase as pad width decreases. Steel bearing p lates reduce the magnitude of transverse strain in the concrete nearest to the plate location. Bearing plates have greatest effect when the bottom T ransverse force in the bottom flange above the bearing pad and du e to applied load is minimized when the bearing pad width is approximately equal to 60% of the flange width. For typical FIB girders and bearing conditions, t ransverse force in the bottom flange above the bearing pad due to applied load can be estimated by multiplying the reaction force by 25%.

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225 Figure 8 1 Coordinate system relative to load and supports Figure 8 2 FE Model Configuration Figure 8 3 Rigid shell and link elements

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226 Figure 8 4 Bearing Pad Figure 8 5 End Region Dimensions

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227 Figure 8 6 FE Model Symmetry Figure 8 7 FE Model Top View

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228 Figure 8 8 Comparison of small beam test set up, FE model details, a nd FE mesh

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229 Figure 8 9 Bearing pad axial stiffness Figure 8 10 Transverse strain ( x x) at end of beam for proposed and refined mesh

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230 Figure 8 11 Small beam transverse (x x) strain profile (V=15kip) Figure 8 12 Small beam load vs. deflection at load point

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231 Figure 8 13 Small beam load vs. strain S5 (y y) Figure 8 14 Small beam load vs. average of strain S11 and S12 (y y)

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232 Figure 8 15 Maximum principal tens ile (P1) strain location Figure 8 16 Sensitivity study maximum transverse (x x) strain

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233 Figure 8 17 FIB and rectangular section FE models Figure 8 18 Location of maximum flexural strain (normalizing strain)

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234 Figure 8 19 Bursting behavior Figure 8 20 Norm alized transverse (x x) strain at end of FIB 8

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235 Figure 8 21 Flexural behavior Figure 8 22 Normalized transverse (x x) strain at end of FIB 16

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236 Figure 8 23 Normalized transverse (x x) strain vs. bearing pad width

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237 Figure 8 24 Normalized transverse (x x) strain vs. bearing pad width, FIB

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238 Figure 8 25 Normalized transverse (x x) strain vs. bearing pad width, Rectangular Section

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239 Figure 8 26 Normalized transverse (x x) strain vs. bearing pad width, small beam

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240 Fi gure 8 27 Steel bearing plate beam and model

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241 Figure 8 28 Bearing Plate Discretization Figure 8 29 Effect of bearing plate and bearing pad width on transverse (x x) strain

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242 Figure 8 30 Normalized transverse (x x) strain vs. bearing pad width, FIB Section with steel bearing plate

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243 Figure 8 31 Integration area for transverse force Figure 8 32 Element x x stress and y z area

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244 Figure 8 33 Transverse (x x) force vs bearing geometry

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245 Table 8 1 Small beam FE model g eometry Dimension/Property Value A 29 in B 11 in C 90 in D 28 in CGz 17 in Lp 10 in Wp 5 in Lb 7 in Wb 6.5 in Le 2 in Near support Ka 8 kip/in N ear support Kv 0.05 kip/in Far support Ka 1150 kip/in Far support Kv 10 kip/in 3D solid element size Approximately rectangular 1 in x 1 in x1 in 2D shell element size Approximately square 1 in x 1 in 1D beam element size 9 in Table 8 2 Bearing stiffness sensitivity study details Model ID Axial stiffness (kip/in) Shear stiffness (kip/in) Max tensile transverse strain (e x ) for V = 15 kip (microstrain) Change in max tensile transverse strain Original 11 50 10 26.64 -x1/2 Axial stiffness 575 10 27.03 +1.5% x2 Axial stiffness 2300 10 25.91 2.7% x1/2 Shear stiffness 1150 5 26.67 +0.1% x2 Shear stiffness 1150 20 26.61 0.1% Table 8 3 Model details: para metric study of bearing pad width a 120 in b 32 in c 1032 in d 80 in CGz 47.7 in Lp 16 in Wp 6 in Lb 10 in Wb Varies

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246 Table 8 4 Bearing pad properties Half Symmetry Total Wb Ka Kv Ka Kv FIB 8 R 8 8.55 in. 2710 kip/in. 5.4 kip/in. 5420 kip/in. 10.8 kip/in. FIB 9, R 9 9.50 in. 2995 kip/in. 6.0 kip/in. 5990 kip/in. 12.0 kip/in. FIB 10, R 10 10.45 in. 3280 kip/in. 6.6 kip/in. 6560 kip/in. 13.2 kip/in. FIB 11, R 11 11.40 in. 3565 kip/in. 7. 2 kip/in. 7130 kip/in. 14.4 kip/in. FIB 12, R 12 12.35 in. 3850 kip/in. 7.7 kip/in. 7700 kip/in. 15.4 kip/in. FIB 13, R 13 13.30 in. 4135 kip/in. 8.3 kip/in. 8270 kip/in. 16.6 kip/in. FIB 14, R 14 14.25 in. 4420 kip/in. 8.9 kip/in. 8840 kip/in. 17.8 kip /in. FIB 15, R 15 15.20 in. 4710 kip/in. 9.4 kip/in. 9420 kip/in. 18.8 kip/in. FIB 16, R 16 16.15 in. 4995 kip/in. 10.0 kip/in. 9990 kip/in. 20.0 kip/in. Axial stiffness of individual springs at near support = 31.7 kip/in. Shear stiffness of individual springs at near support = 0.0635 kip/in.

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247 CHAPTER 9 A NALYTICAL EVALU ATION OF GIRDERS DUR ING PRESTRESS TRANSF ER This chapter presents FE modeling that was conducted to 1) provide a better understanding of the elastic behavior of the end region during and immediate ly after prestress transfer, 2) quantify lateral forces in the bottom flange within the end region, and 3) evaluate the effects of variables such as transfer length and embedded steel bearing plates on end region behavior. The FE program ADINA (R&D 2009) was used to conduct the modeling. All models were linear elastic and were intended to model pre cracked behavior. Strain gage and displacement data from construction of girders H and V were used to validate the FE model. The Hoyer effect was not conside red in this chapter, b ut will be addressed in C hapter 11 Model Configuration The coordinate syste m defined in C hapter 4 was also used for FE models in this chapter ( Figure 9 1 a). The FE model configuration was d esigned to be computationally efficient, yet able to capture the overall beh avior of girders as well as local behavior of x) tensile strain in the bottom flange was of partic ular interest. Conditions during and immediately after prestress transfer were considered using the model. During and after prestress transfer, the test girders we re supported at each end by the stressing bed ( Figure 9 1 b). Tra nsfer of prestress created negative be nding moments in the test girders which were partially counteracted by self weight. After sufficient prestress force h ad be en transferred the self weight wa s overcome and the girders camber upward. A t this stage girders we re supported vertically (Z direction) at each end by the stressing bed. Girders also deform ed (shorten ed ) longitudinally due to

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248 prestress forces. Friction forc es we re generated between test girders and the stressing bed and act ed t o resist shortening. In this chapter, friction forces were assumed to be small and were thus neglected in development of the FE model. The restraining force from uncut strands was also assumed to be negligible. These assumptions appear valid based on co mparison with experimental data, as presented in the next section. Details of the FE model are shown in Figure 9 2 The near end of the girder was modeled with 27 node 3D solid elements on a primarily rectangular mesh. Geometry of the solid elements matched the FIB 54 test girders. The extent of the solid elements was selected to fully capture the effects of the prestress and bearing forces on the end region. The remainder of the beam was modeled with 1D beam e lements, with the transition from beam to solid elements made using rigid 2D shell elements and 1D rigid links. Rigid shell and link elements coupled the displacements of the 3D solid elements with the displacements and rotations of the 1D beam elements. Transitioning to beam elements reduced the computational demand while still modeling the global girder behavior and boundary conditions. Beam elements were placed at the centroid of the cross section and were assigned cross sectional properties equivalen t to the FIB 54 test girders. A rigid link was provided to connect the beam elements to the physical location of the bearing at the bottom of the girder at the far end. The embedded steel bearing plate at the near end was modeled using shell elements. Bou ndary and loading conditions of the FE model were consistent with the conditions of the physical test girders during and after prestress release. Vertical displacement was restrained along the bottom edge of the model at the near support and at the bottom of the rigid link at the far end. Prestressing forces were applied to

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249 both ends of the model. Application of prestressing at the near end is discussed in detail later in this section At the far end, prestressing was applied as a single point load at a height equal to the Z centroid of the prestressing force. The cross section, boundary conditions and loads were symmetrical about the Y Z plane, allowing for only half of the beam to be considered in the FE model. As such, transverse (x x) translations were restrained at all nodes on the plane of symmetry. Self This fea ture wa s employed by assigning mass density to the materials in the model, and assigning the direction and magnitu de of gravity, and then allowing ADINA to calculate the body forces associated with self weight. The FE model was developed such that nodes in the bottom flange mesh aligned with the prestress ing strand layout. Because element nodes coincided with the s trand locations, the prestressing force could b e applied as point loads to nodes within the transfer length ( Figure 9 2 ). Prestressing in the FE model was based on test girders H and V which contained (39) fully b onded 0.6 in. diameter prestressing strands ( Figure 9 3 ). Prestressing forces occurring at the centerline of the cross section (plane of symmetry) were reduced by 50% to account for the model symmetry. Forces fro m the partially debonded strands were not included in the model. This simplification appears reasonable based on the validation presented in the next section. It is further justified by considering that t he partially debonded strands in the test girders d id not transfer loads within the area of primary interest. Individual steel strands were not explicitly included in the model.

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25 0 A transfer length of 1 7.5 in. was used. This length wa s approximately half of the transfer length calculated using AASHTO LRF D provisions A shorter length was used for multiple reasons. First, strand transfer lengths are shortest during and immediately after transfer (Barnes et al, 1998) which wa s the time that strain data were taken for validation. Second, the AASHTO LRFD t ransfer lengths are conservatively long relative to experimental data (Barnes et al., 1998). The t ransfer length in the FE model wa s denoted as T L to distinguish it from the physical and code calculated transfer lengths. Based on experimental data, the el astic prestress loss after all strands were released was approximately 10%. Elastic loss was indirectly considered in the FE model by reducing the magnitude of the applied prestress forces. Elastic loss was assumed to be proportional to the number of rel eased strands. For example, a 10% elastic loss was applied to models with all strands released, and a 5% elastic loss was applied to models with half of the strands released. The concrete modulus of elasticity for each model was set at 4700ksi, and the tested material properties from test girders used for validation. The model configuration was validated by comparison with experimental data, and was then used in more general investigations of the stress and strain state in the end region. Details of the verification and validation are contained in the next section. Model Validation and Verification A verification study was conducted to determine that the mesh used in the proposed FE model had sufficient density to capture the end region behavior. Figure 9 4 shows the proposed mesh density and a refined mesh density, which was used for comparison. The refined mesh was twice a s dense as the proposed mesh.

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251 Principal tensile stress results from the proposed and refined models are compared in Figure 9 5 Differences between refined and proposed meshes occur red primarily in elements adjace nt to the applied prestress forces. Locations away from the prestress forces had similar stress magnitudes and distributions for both meshes. Based on thi s comparison the proposed mesh wa s deemed acceptable for evaluating behavior away from the prestres s forces, and the refined mesh wa s required for evaluations near the prestress forces. During prestress transfer in the physical girders (H and V) used for validation, strands farthest away from the girder centerline were cut first with subsequent strand cut s made progressively closer to the centerline ( Figure 3 24 ). Based on this release pattern, two stages were considered in the model validation. During stage 1 only the outer strands were released. During stage 2 all strands were released. Comparisons with the experimental data indicate that the FE model did an adequate job of capturing both the global and local linear elastic behavior of the physical test beams. The exaggerated displaced shape calculated by th e FE model is show in Figure 9 6 for stage 2 (all strands cut). Camber at mid span calculated by th e FE model was 0.90 in., which wa s within 2 % of the experimentally measured camber of 7/8 in. Cracking was not observed visually during or immediately after prestress transfer in girders H and V. Data from strain gages, however, indicate that cracking may have occurred in the physical girders as the prestressing strands were being cut As shown in Figure 9 7 the magnitude of tensile strain reported by the gages exceeded the expected concrete rupture strain of 132 microstrain. The expected rupture strain was

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252 derived from empirical relationships for elastic modulus and rupt ure strain in ACI 318 (2011). Based on the location and magnitude of the tensile strains calculated by the FE model, it is not surprising that strain gages reported strains greater than the expected cracking strain. This result suggests that the FE model captured the behavior of the physical girders at both stages of prestress transfer. With the exception of the locations presented in Figure 9 7 the linear elastic FE model calculated strain values at most locatio ns were below the experimental rupture strain. Experimental data from most strain gages also demonstrated linear elastic behavior. Data from these gages were used to validate the linear elastic strains calculated by the FE model. Transverse (x x) strain wa s of particular interest because transverse concrete behavior is coupled with confinement reinforcement behavior. Strain data from gages embedded in the physical girders are presented in Figure 9 8 along with s train data from the FE model. As demonstrated in the figure, the FE m odel wa s in good agreement with the experimental data throughout the end region and at both stages. Gages located at Y = 2 in. were near the cracking that occurred prior to stage 1, hen ce the variability in those data points. Longitudinal (y y) strains at the edge of the bottom flange are compared in Figure 9 9 Strains predicted by the FE model were within the scatter of the strain data at stag es 1 and 2. The good agreement between the FE model and the longitudinal experimental data suggest that the transfer length used in the model (17.5 in.) was consistent with the transfer length in the physical girders.

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253 Figure 9 10 compares the vertical (z z) strain from the FE model and the test girders. Trends and magnitudes were consistent between FE model and experimental data. The largest vertical strains occurred at the end of the girder (y = 0 in.) Vertica l strains were larger during stage 2 than stage 1. Strain and displ acement data from the FE model we re in good agreement with experimental data. The occurrence and location of cracki ng in the experimental girders we re consistent with the locations of ma ximum tensile strains c alculated by the FE model. It wa s concluded that the model accurately captured the global and local behavior of the physical girders at multiple stages of prestre ss transfer and that the model wa s adequate for more general parametri c studies. Transverse Force Quantification Transverse tension forces in the bottom flange at the near suppo rt we re of interest because they are resisted by confinement reinforcement in the event that the concrete cracks. This section describes the procedu re used to quantify the transverse (x x) force from the validated FE model. Transverse force was calculated by integrating transverse stress over the area shown in Figure 9 11 This is the same area that was use d previously for investigating the effects of bearing pad width ( Figure 8 32 ). Boundaries of the integration area were selected to capture those portions of the girder end subjected to steep stress gradients due to prestressing. Boundaries were also selected to include portions of the bottom flange where confinement reinforcement is placed to carry transverse tension. Boundaries of the integration area were defined as a function of bottom flange width ( W f ) so that similar integrations could be performed on girders with varied cross sections.

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254 Discrete x x stress values from center nodes in the integration area were multiplied by the associated y z areas to obtain transverse forces ( Figure 9 12 ). The total transverse tensile force was calculated as the sum of all element tensile forces. Lateral force in the steel bearing plate was calculated in a similar manner. Compressive forces (when they occurred) were ignored in calcul ations of transverse force. I. e., transverse tensile force equal s the gross tension and was not reduced by compressive forces. This approach was taken because transverse compressive forces are supported by concrete and do not typically lead to cracking o f concrete or tension loading of confinement reinforcement. Parametric Studies Strand Release Parametric Study Transverse (x x) stresses and forces change d throughout prestress transfer as strands we re sequentially cut. A parametric study was conducted t o investigate the relationship between transverse force and the quantity of cut strands. This study used FE models of girders with FIB 54 and AASHTO Type IV cross sections. The AASHTO girder model had the same configuration as the FIB model ( Figure 9 2 ), with the exception of having cross section dimensions of an AASHTO Type IV girder. Prestressing forces were applied as point loads over a transfer length of 17.5 in. Steel bearing plates were not included. Elast ic prestress losses were considered in the models. Losses were assumed to vary linearly from 0% when no strands were released to 10% when all strands were released. This magnitude of elastic loss was consistent with experimental data from girders H and V

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255 Strands in the experimental FIB girders were released from outside in and bottom to top ( Figure 3 24 ). To model this process, prestressing forces were added sequentially to FE models beginning at the location of outermost strands. Figure 9 13 show the locations of prestressing forces at different phases of prestress transfer in the FIB 54 model. Transverse (x x) stress distributions are also shown. When only outer stran ds were released, the tensile stresses were concentrated within 10 in. of the girder end. Tensile stresses reduced in magnitude, but occurred over a greater portion of the integration area after inner strands were released. Stresses shown in the figure w e re due to prestressing forces and self weight. The bottom flange of the AASHTO Type IV section houses fewer strands than the FIB bottom flange. To normalize this difference, the quantity of strands in both AASHTO and FIB models was designed to be approxi mately 50% of the maximum possible strand quantity for the given section. Strand locations in the FIB model also matched the experimental girders H and V The transverse tensile force at the cross section centerline was calculated at each stage of prestre ss release following the previously described integration procedure. Calculated forces are plotted as a function of the percentage of cut strands in Figure 9 14 The calculated forces presented in the figure we re normalized by the final prestress force for each girder. For both girders the largest transverse tensile force occurred when approximately 40% of the strands were released. This percentage corresponds to the stage when only the strands in the outer po rtion of the flange had been cut. Transverse force decreased as the inner strands were cut. This observation is consistent with

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256 experimental strain data that reported the largest transverse tensile strains when the outer strands were released and a comme nsurate reduction in those tensile strains as the inner strands were released. The FIB 54 model had higher ratios of transverse force to final prestress force and slend er bottom flange. Because of the greater width strands in the FIB flange had a greater moment arm about the cross section centerline than did strands in the AASHTO flange. Figure 9 14 also demonstrates the proble m of partially debonding inner strands and fully bonding outer stra nds. In this circumstance, inner strands do not transfer prestress force at the end of the girder and consequently do not reduce the transverse tensile force at the centerline. This situa tion occurred in the experimental program in specimens FN and FB. F lange splitting cracks formed at the end of these girders at the centerline of the cross section. A similar situation and similar cracks were observed in experimental AASHTO Type IV girde rs by Llanos et al (2009). Bearing Plate Contribution The validated FE model was used to evaluate transverse force carried by embedded steel bearing plates due to prestressing forces. This evaluat ion considered the same stages of prestress transfer as we re used in model validation. For stage 1 only the outer strands were released. For stage 2 all of the strands were released. The presence or absence of the steel bearing plate was also included as a variable, resulting in four unique variable combinatio ns. Figure 9 15 and Figure 9 16 present the transverse (x x) stress distributions along the plane of symmetry for each of the four variations considered. Transverse force was

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257 calculated using the previously described integration procedure. Table 9 1 lists the maximum stresses and total forces of each model variation. Calculated f orce in the bottom flange was approximately 67 kip a t stage 1. When the steel bearing plate was present, it attracted approximately 7 kip, or 10% of the transverse force. The steel bearing plate also changed the transverse stress distribution in the concrete adjacent to the plate, but did not change the t otal transverse force. Calculated transverse force during stage 2 was approximately 27 kip. When the embedded steel plate was present it attracted 3 kip, or approximately 10% of the force. This percentage is similar to stage 1. Presence of the steel pla te changed the stress distribution in the concrete near the plate but it did not significantly affect the total transverse force at the end of the girder. Transfer Length Parametric Study This section presents results of a parametric study investigating the effect of transfer length on the magnitude of the transverse tensile force. FE models were created with transfer lengths that varied from 12.5 in to 47.5 in. This range included lengths shorter than were observed in the experimental program as well as lengths longer than calculated using the AASHTO LRFD code. The FIB model without a steel bearing plate was used in this study. Models considered the stage shown in Figure 9 13 when 50% of the strands were cu t. This stage was selected because it corresponded to the largest transverse tensile forces. The previously described integration procedure was used to calculate transverse tensile forces at the cross section centerline. Transverse force at the centerl ine had an approximately linear relationship with the transfer length ( Figure 9 17 ). The largest force corresponded to the shortest transfer length. Transverse tensile force decreased as the

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258 transfer length is inc reased. Thus, physical girders with relatively short transfer lengths have greater transverse forces and stresses than girders with longer transfer lengths. According to the data in Figure 9 17 a 50% reduction in transfer length affect ed a 50% increase in transverse tensile force. For example, reducing the transfer length 50% from 40 in. to 20 in. resulted in an approximately 50% increase of transverse force from 48 kip to 70 kip. Transverse tensile stresses due to prestressing forces are shown in Figure 9 20 and Figure 9 18 for sections through the centerline (CL) and bottom flange (MID). Tensile stre sses formed near the member e nds regardless of transfer length. The y dimension of the tensile stress area was linearly related to the transfer length used in the FE models ( Figure 9 20 ). Phase 1 experimental girders had a transfer length nea r 18in. For this transfer length, the FE model calculated that transverse tensile stress at the MID section of the bottom flange had a y dimension of approximately 11in. Transverse stress at the MID section is plotted as a function of y coordinate in Figu re 9 21 for transfer lengths of 17.5 in. and 42.5in. S hapes of the stress distributions in the figure are representative of other bottom flange sections when only the outer strands had been cut. Transverse tensi le stresses were largest near the member end, and were distribution in an approximately triangular shape. End Stresses due to Prestress Forces Analytical results have shown that the largest stresses from the prestressing force occur at the girder end su rface ( Figure 9 13 ). In the experimental program, flange splitting cracks were often observed at the end surface ( Figure 9 22 ). This section presents a study of stresses a t the end surface due to prestressing forces. Results from

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259 this study will later be used in development of a model for serviceability design of bottom flanges. The FIB model without a steel bearing plate was used to study end stresses. Self weight was el iminated to isolate the effects of the prestressing force on the section. A transfer length of 17.5 in. was used in the models. This length was chosen because previous results demonstrated that short transfer lengths produced the largest transverse effe cts. The refined mesh ( Figure 9 5 ) was used in this study because stresses near the prestress forces (strands) were used in results interpretation. Strand pattern and strand cutting sequence demonstrated in Figure 9 13 was used in this study. This strand layout and cut pattern matched girders H, V, and D from the experimental program. Four lines at the end surface of the model were selected for evaluation ( Figure 9 23 ). Lines were selected based on the location of cracks observed in the test girders ( Figure 9 22 ) and to give a representative analysis of the entire bottom flange end. A height of 15in.was used for the centerline (CL) and the web line (WEB) based on the height of flange splitting cracks in test girders. Height of the mid flange (MID) and flange edge (EDGE) lines were limited by the flange height at those locations. Transverse (x x) stresses were con sidered along each line. This was done because tension stresses at the end of the bottom flange primarily act ed in the x direction. This wa s evident from the vertical orientation of cracks in the experimental girders ( Figure 9 22 ). It was also observed in comparisons of transverse (x x) and principal tension stresses at the end of the FE model ( Figure 9 24 ). Transverse and

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260 principal te nsion stresses we re effectively the same at areas away from the prestressing forces. Stresses along each line were calculated at each stage of prestress transfer using an outside to in strand cutting pattern. Stress concentrations occurred in the FE model at nodes where prestress forces were applied ( Figure 9 24 ). In lieu of the concentrated stress values, stres ses at these nodes were taken as the average stress from t he adjacent nodes. This resulted in stress dis tributions such as that shown in Figure 9 25 Figure 9 25 shows the stress distribution at the mid flange line for the stage when 50% of the strands had been cut. During this stage the two strands located on the mid flange line were cut and resulted in compressive stresses near the strand locations. The average stress along each line varied with the different stages of strand cutting as shown in Figure 9 26 The box markers on Figure 9 26 indicate the stage when strands on an individual line were cut. Average stress on a given line fell abruptly when strands along that line were cut. For example, average stress at the centerline went from 170 psi tension prior to cutting the centerline strands to 680 psi compression after the centerline strands were cut. Average stresses are summarized in Table 9 2 for each evaluation line. Tensile stress on a given line was greatest when only the strands outboard (closer to outside of flange) of the line had been cut. Maximum tensile stresses ranged from 1.12 ksi to 0.39 ksi. The largest compressive stresses o ccurred after all strands had been cut. Maximum compressive stresses ranged from 0.68 ksi to 0.41 ksi. The average compressive stress after all strands had been cut was 0.57 ksi.

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261 Transverse tensile stresses occurred at the end of each evaluation line a nd for a distance of approximately 10in. from the girder end. The typical integration procedure was used to calculate the transverse tension force at sections along the MID an d EDGE lines. These locations we re of particular interest because of their prox imity to flange splitting cracks observed in the experimental girders. The maximum transverse force occurr ed when strands outboard of each sectio n had been cut. Cutting of strands along the section reduced the transverse tension force by 45% at the MID s ection and 28% at the EDGE line. Transverse Action due to Self Weight The test g irders camber ed upward during prestress transfe r after the girder self weight wa s overcome by the prestressing moment. In this condition the girders we re supported vertically at the bottom edge at each end ( Figure 9 1 ). The FIB FE model was used to evaluate the transverse stresses and forces that occur red due to the self weight during this condition. Prestress loads in the model were removed leaving only the mass proportional load which modeled the girder self weight. Boundary conditions remained the s ame as previous models in this c hapter. Because prestress loads were removed and self weight remained, the displaced shape of the mode l was sagging rather than cambering. Figure 9 27 shows the transverse (x x) stresses at the centerline and end due to self weight Transverse tensile stresses we re largest at the bottom of the girder near the end. Magnitude of transver se stresses due to self weight we re small relative to transverse stress due to prestressing as calculated in the previous section. This is in part because the self weight model was based on test girders H and V which were only appro ximately 35% as long as typical production girders with the same cross section.

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262 Thus the self weight stresses reported in Figure 9 27 we re also only 35% of stresses in typical production girders. The typical integ ration pro cedure was used to calculate a transverse force of 6.7kip at the centerline. Self weight reaction in the half symmetry FE model was 12.0 kip. This reaction corresponded to a full reaction of 24 kip in the physical test girders. Thus the transv erse force was equal to 28% of the physical reaction. This result is similar to the relationship derived between reactio n force and transverse force shown in Figure 8 33 Transverse stresses at the girder end wer e calculated at the same four lines ( Figure 9 23 ) that were previously used to evaluate the effects of prestressing forces. Figure 9 28 shows stress that occurred at each line. Stresses below Z=2in. a re not shown because numerical errors occurred in the FE model near the boundary condition. Maximum and average stresses at each line are summarized in Table 9 4 A verage stresses i n the table conservatively ignore d compressive stresses below Z=2in. The maximum tension stress was greatest at the centerline and was 3.4 times larger than at the line through the flange edge. The centerline section also had the largest average tension stress. At lines through the outer flange (MID and EDGE) the average stress was ne gligible or compressive. A verage stresses at lines through the inner portion of the flange (CL and WEB) were tensile Average tensile stresses at the CL and WEB lines we re related to the reaction force by a factor of 1000. For example, the reaction force in the physical girders was 26 kip and the average tensile force on the inner lines was approximately 26 psi.

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263 Parametric Study Summary and Conclusions Linear elastic fin ite element modeling was used to evaluate stresses and forces in the bottom flange of Florida I girders during prestress transfer. Each stage of prestress transfer (strand cutting) was considered in the models. Stresses and forces due to girder self weig ht were also evaluated. Stresses due to the Hoyer effect were not considered in this chapter. Thus the conclusions below are based only on the effects of the prestress force and girder self weight Conclusions assume strand cutting from outside to insid e ( Figure 3 24 ). The following conclusions are made based on results of the evaluations: For the given release sequence, the largest transverse (x x) tensile stresses during prestress transfer occur at the centerl ine of a section at the girder end. Centerline tension stresses are greatest when only the strands in the outer portion of the flange have been cut. Cutting of inner strands reduces this transverse tension. Embedded steel bearing plates carry transverse tension during and after prestress transfer. In the linear elastic range plates in FIB girders ca rry 10% of the tension force due to prestressing The portion carried by the plates does not vary during different stages of strand cutting. Transverse stres s and forces are inversely proportional to strand transfer length. Thus the greatest transverse effects occur in girders with the shortest transfer lengths. A 50% reduction in transfer length affect s an approximately 50% increase in transverse tension. Du ring prestress transfer the maximum transverse tensile stress on an arbitrary vertical line through the bottom flange occurs when only the strands outboard (closer to edge) of the line have been cut. Cutting of strands along or inboard (closer t o centerli ne) of a line relieve tensile stresses on that line. Transverse stresses at the end of the bottom flange are compressive after all strands have been cut. An average compressive stress of 570 psi was calculated by the finite element models for conditions i n experimental girders H and V. Self weight reaction produces transverse tension forces in the bottom flange above the bearing. For Florida I beams, the transverse tension force due to self weight equals 28% of the reaction.

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264 Figure 9 1 Coordinate system and f ree body diagram of girder after prestress transfer

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265 Figure 9 2 FE model d etails

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266 Figure 9 3 St rand layout and element mesh Figure 9 4 Verification study mesh densities

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267 Figure 9 5 Verification study principal tensile stresses Figure 9 6 Displaced shape

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268 Figure 9 7 Comparison of experimental and FE model strains at cracks

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269 Figure 9 8 Comparison of experimental and FE model transverse (x x) strain Figure 9 9 Comparison experimental and FE model longitudinal (y y) strain

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270 Figure 9 10 C omparison experi mental and FE model vertical (z z) strain Figure 9 11 Integration area for lateral force

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271 Figure 9 12 Element x x stress and y z area

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272 4 strands c ut (20%) 10 strands cut (50%) 17 strands cut (87%) All strands cut (100%) Figure 9 13 Transverse (x x) stress at stages of prestres s transfer

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273 Figure 9 14 Transverse force vs. % strands released

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274 With bearing plate No bearing plate Figure 9 15 Transverse (x x) stress distribut ion at stage 1 (outer strands cut) with bearing plate and without bearing plate

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275 W ith bearing plate No bearing plate Figure 9 16 Transverse (x x) stress distribution at stage 2 (all strand s cut) with bearing plate and without bearing plate

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276 Figure 9 17 Transverse force vs. length of prestress transfer

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277 Figure 9 18 Transverse stress distribution 1 7.5in. transfer length

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278 Figure 9 19 Transverse stress distribution 42.5in. transfer length

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279 Figure 9 20 Length of tension area vs. transfer length Figu re 9 21 Transverse (x x) stress at MID section through bottom flange

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280 Figure 9 22 Flange splitting cracks at girder end Figure 9 23 Lines for stress calculations

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281 Figure 9 24 FE model stresses at girder end (50% strands cut) Figure 9 25 Transverse (x x) str ess at mid flange line (50% strands cut)

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282 Figure 9 26 Average transverse (x x) stress at end of girder due to strand cutting Figure 9 27 Transverse (x x ) stress due to self weight

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283 Figure 9 28 Transverse (x x) stress due to self weight

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284 Table 9 1 Bearing plate study summary of transverse (x x) stresses an d forces With bearing plate No bearing plate Max x x stress at integration point (ksi) Transverse tension force (kip) Max x x stress at integration point (ksi) Transverse tension force (kip) Outer strands cut (stage 1) 0.94 60.2 concrete 6.6 plate 66. 8 total 1.16 66.9 All strands cut (stage 2) 0.15 24.9 concrete 3.0 plate 27.9 total 0.15 26.6 Table 9 2 Summary of transverse (x x) stress at girder end due to strand cutting Line Maximum stress at any stage (ksi) Stress at stage when strands on line were cut (ksi) Stress after all strands were cut (ksi) CL 1.12 0.68 0.68 WEB 1.02 0.06 0.63 MID 0.85 1.25 0.41 EDGE 0.39 0.25 0.54 Average 0.85 0.22 0.57 Table 9 3 Summary of transverse (x x) stress at girder end due to strand cutting Section Maximum force at any stage (kip) Force at stage when strands on line were cut (kip) MID 36.1 20.3 EDGE 15.8 11.3 Table 9 4 Transverse (x x) stress due to self weight CL WEB MID END Maximum tension (psi) 44 42 27 13 Average stress (psi) 28 21 0.9 10 (comp.)

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285 CHAPTER 10 ULTIMATE STRENGTH DE SIGN MODEL The 2007 AASHTO LRFD Bridge Design Specifications contain prescriptive requirements for the quantity and placement of confinement reinforcement located in the bottom flange of pretensioned concrete I girders. This chapte r proposes a rational model that can be used to design confinement reinforcement as an alter native to the prescriptive requirements of AASHTO LRFD The model considers a wide range of conditions and variations, yet is intended to be practical enough for use by bridge design engineers. Variables in the design model include: flange and bearing g eometry, strand size and placement, effective prestress force, concrete and steel material properties, and the effects of steel bearing plates. Derivation of the model is presented, and the model is compared to experimental results from the published lite rature. The proposed design model can be used to calculate the quantity of confinement reinforcement required to p revent lateral splitting failure at ultimate load. The model is formulated to capture the multitude of variables that exist in pretensioned girders, but be practical enough for use by bridge designers. The model does not consider the function of confinement reinforcement in controlling cracks during prestress transfer. This topic, however, is covered in the C hapter 11 Experimental and ana lytical work from the previous chapters has shown that confinement reinforcement carries transverse tension forces due to prestressing and applied loads. By carrying these forces the confinement reinforcement functions to prevent lateral splitting failure and provides a normal force whereby strand tension forces can be transferred to the concrete once strut and tie behavior has initiated. The ultimate strength design model considers both of

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286 these fu nctions. Forces generated due to these functions are ref erred to as the transverse tie force ( F TT ), and the strand anchorage force ( F SA ). Strand anchorage and transverse tie functions of confinement reinforc em ent are analogous to the local zone and general zone reinforcement in post tensioned (PT) structures. Figure 10 1 shows the manner in which the anchorage zone in a post tensioned (PT) structure is partitioned into local and general zones. The local zone is a highly stressed region that resides immediately under the anchorage de vice and requires significant confinement reinforcement to prevent bursting stresses from causing localized failure. It is within the local zone that PT forces are transferred to the concrete. The general zone in a PT structure is the area where PT force s are transmitted throughout the member. Conceptually the end region of a pretensioned beam can be divided into a local and general zone ( Figure 10 1 ). General zone size is comparable to that of a PT anchorage and can be designed by the same approach as is used for PT anchorage zones. Pretensioned local zones, however, are longer because force transfer occurs gradually throughout the transfer length rather than through an anchorage device. Large, very localized lateral bursting stresses that are present immediately under the anchorage in a PT local zone are thus avoided in pretensioned end regions. In pretensioned local zones the concrete immediately surrounding a prestressing strand is subjected to radial stresses from the Hoy er effect, which is illustrated in Figure 10 2 The Hoyer effect occurs due to Poisson expansion of the strands in the lateral direction when the strands are cut at prestress transfer. The beneficial effect of this expansion is to generate sufficiently large frictional forces at the concrete strand interface to transfer the prestressing force into the

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287 concrete. As illustrated in Figure 10 1 this has been shown to occur in a relatively uniform manner ove r the transfer length. Confinement reinforcement is typically placed such that the some bars support loads from both local and general zones. Accordingly, c onfinement force due to the transverse tie is also utilized as the force required for strand anchor age. The proposed design procedure calculates the load demand on confinement reinforcement as the larger of the local and general zone loads. Or in other words, the model calculates confinement reinforcement required for the greater of the strand anchora ge or transverse tie force. Model Derivation Transverse Tie Force Calculation of the transverse tie force is based on the strut and tie models shown in Figure 10 3 This figure describes transfer of the ultimate reaction ( R u ) fro m the web, through the bottom flange and into the bearing pad. The struts and ties are symmetric about the z (vertical) axis. Compressive force BC Z equals the ultimate reaction and is carried to the support through three separate load paths. Force in each path is assumed to be proportional to the quantity of strands associated with that path; strands in the flange are assumed to connect to D nodes and strands below the web are assumed to connect to node F Thus the vertical (z direction) component of load traveling path C D E can be calculated by Equation 10 1 : 10 1 Where: CD Z = DE Z = E Z = R u = n f = z component of force in member CD z component of force in member DE Reaction at node E Factored r eaction force number of strands in the flange ( )

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288 Using the strut and tie model shown in Figure 10 4 a the slope of s trut CD can be determined as follows: 10 2 Where: t f = b f = b w = Minimum thickness of bottom flange Bottom flange width Web width z component of force in member CD Cross sections from AASHTO, FDOT, Nebraska Department of Roads, and Washington State Department of Transportation were used to determine Equation 10 2 If exceptionally slender bottom flanges such as that shown in Figure 10 4 b are used, then Equation 10 2 does not apply and t he angle must be calculated directly. Member DE slope can be calculated by E quation 10 3 When the bearing width is close to the flange width ( Figure 10 3 a), the slope calculated by Equation 10 3 is positive indicating that x component of force in member DE acts in the positive x direction. When the bearing width is smaller than the flange width ( Figure 10 3 b), the slope of member DE is negative, indi cating that the x component acts in the negative direction. 10 3 Where: W b = Width of bearing The horizontal (x direction) force component s in member s CD and DE are calculated by E quation s 10 4 and 10 5 respectively. These equations are derived from the vertical (z d irection) force component from E quation 10 1 and the slope s from E quations 10 2 and 10 3 10 4 ( ) ( ) ( )

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289 10 5 The transverse tie force is equal to the force in member DF and can be calculated from equilibrium in the x direction at node D : 10 6 Substituting for CD X and DE X and simplifying, E quation 10 6 can be rewritten as: 10 7 Strand A nchorage Force Strand anchorage force refers to the normal force required to generate strand forces through friction. This f orce must be resisted by the concrete tensile strength the confinement reinforcement or both to ensure that the frictional force transfer between strands and concrete is maintained. If the concrete tensile strength and confinement are not sufficient bond is lost and the strand slip s In addition to friction, f orce transfer between strands and concrete also occurs due to adhesion, mechanical interlock. Adhesion and mechanical interlock, however, are relatively small and are conservatively neglected. Also, it is thought unlikely that adhesion and mechanical interlock are significant at ultimate load after concrete around the stran ds has cracked. A t ultimate load it is assumed that internal forces in the end region can be described by strut and tie modeling as was done in calculating the transverse tie force. Strut and tie models conservatively neglect concrete tensile strength. Th is assumption will also be made in calculation of the strand anchorage force. Concrete around the strands will be assumed to have cracked and unavailable to provide the normal force required to generate friction at the ( ) ( ) ( )

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290 strand concrete interface. In calcu lating the strand anchorage force, it is assumed that all of the normal force is supplied by confinement reinforcement. Aknoukh ( 2010 ) presented a similar friction based approach for designing confinement reinforcement. The Aknoukh model considered stra nd anchorage through on a horizontal section using a friction coefficient of 1.4. The proposed method is distinct from Aknoukh because it considers anchorage forces on vertical sections through the bottom flange, and because it uses a more conservative (a nd realistic) friction coefficient of 0.4. The proposed model is also distinct in that transverse tie forces are considered. Equilibrium in the direction of the strand length requires that the total frictional force at the strand concrete interface be eq ual and opposite of the effective prestress in the strand. The normal force required to generate the frictional force is equal to the frictional force divided by the friction coefficient at the strand concrete interface. Based on this rationale, the norm al force required to develop the effective prestress in an individu al strand can be calculated by E quation 10 8 : 10 8 Where: F N = A ps = f pe = Normal force on an individual strand required to develop prestress Cross sectional area of prestressing strands Effective prestres s Coefficient of friction between concrete and strand, taken as 0.4 Although seven wire strand does not have a circular cross section, it is believed that this simplification does not significantly affect the results of the strand anchorage force model The same assumption was made by Oh et al (2006) in the development of a strand transfer length model. Using this assumption t he Oh model correlated well with experimental data T he round strand assumption is also considered reasonable for the current mo del derivation. ( )

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291 Figure 10 5 illustrates the idealized normal stress acting on a single strand within the transfer length. The normal stress ( f N ) can be calculated by assuming that the normal force ( F N ) required to prevent stran d slip is distributed evenly around the circumference and along the transfer length. The geometric properties of the strand can then be used to form equation 10 9 : 10 9 Where: f N = d p = Normal stress at strand concrete interface Diameter of prestressing strand Substituting E quation 10 8 into E quat ion 10 9 into gives: 10 10 The transverse (x direction) component of the normal force on an individual strand can be calculated u sing a pressure vessel analog y by multiplying the stress in E quation 10 10 by the projected area of the strand over the transfer length: 10 11 Whe re: F Nx = Transverse normal force on an individual strand Substituting E quation 10 10 into E quation 10 11 and simplifying gives: 10 12 The total x direction force along an arbitrary section can be determined from the product of the transverse component and the number of strands along the section. This force is defined as the strand anchorage f orce and is give n as: ( ) ( ) ( ) ( )

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292 10 13 Where: F SA = n c = S trand anchorage force N umber of strands along critical section Equation 10 13 can be used to calculate the strand anchorage force on any arbitrary section. The maximum strand anchorage force occur s through the section that intersects the maximum number of strands. Quantity and Placement Preceding sections have presented equations for ca lculating the transverse forces resisted by confinement reinforcement at ultimate load. The design force in the confinement reinforcement is equal to the greater of the transverse tie or strand anchorage forces: 10 14 Where: F CR u = Factored d esign force in confinement reinforcement The reason for using the greater for the transverse tie or strand anchorage for ces can be understood by considering the forces acting on a node in the bottom flange strut and tie model. For example, forcing acting on node D in Figure 10 3 come from struts in the concrete and ties in the reinforcement. In d eriving the transverse tie force it was shown that the forces at node D are based on equilibrium and geometri c properties. The same forces act ing on node D are also the forces that generate the strand forces (acting in the y direction at node D) through f riction. Additional strand anchorage f orce is not required. Thus confinement reinforcement capacity need only be the greater of the strand anchorage force or the transverse tie force. The quantity of confinement required at ultimate load is equal to the confinement reinforcement design load divided b y the specified yield stress of the reinforcement: ( ) ( )

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293 10 15 Where: A CR = f yCR = Required area of confinement reinforcement Yield stress of confinement reinforcement The proposed model is intended for use in load an d resistance factor design (LRFD). Accordingly an appropriate strength reduction ( ) factor is needed. For strut and tie modeling, such as that used to derive the transverse tie force, the ACI (2008) code uses a strength reduction factor 0.7 5. This valu e is also recommended for use in the proposed ultimate strength design model. Data from the e xperimental program demonstrate that steel bearing plate s contribute confinement to the bottom flange at ultima te load. To account for this the proposed design model allows the bearing plate to replace up to 50 % of the confinement required by E quation 10 15 The plate is not allowed to totally replace confinement reinforcement because the confining influence of the plate on its own was not enough to prevent lateral splitting failure in experiments. Bearing plates should not be considered as confinement reinforcement unless the bearing width and the spacing between plate anchorage points are both greater than 75% of the flange width. T hese requirements ensure that the bearing plate is in tension ( Figure 10 3 b), and is sufficiently anchored to provided confinement. The confining effect of end diaphragms has also been shown to prevent splitting failures in experi mental tests ( Ross et al. 2011b ). End diaphragms, however, are not present during prestress transfer and therefore do not constitute a replacement for confinement reinforcement. Results from the experimental program demonstrate that confinement reinforc ement is most effective when placed near the end of the girder. As such, confine ment reinforcement ( )

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294 required by E quation 10 15 should be placed as close to the end of the girder as reasonable but should also be placed over a dist ance of at least the transfer length Model Comparison with Experimental Results In this section the proposed design model i s evaluated against experimental data from 41 unique tests of pretensioned concrete girders reported in the literature ( Llanos et al. 2009, Ross et al. 2011 a Morcous et al. 2010 Tadros et al 2010 Deatherage et al 1994 ). Figure 10 6 compares confinement reinforcement installed in each test girder with the required confinement reinforcement calculated usin g the proposed model (Equation 10 15 ). The factored reaction force used to calculate the transverse tie force ( F TT ) was taken as the nominal shear strength. Provided confinement reinforcement, plotted on the vertical axis, was t aken as the area of confinement reinforcement placed within the transfer length. If present, the embedded steel bearing plate area was allowed to contribute up to 50% of the confinement requirement. Prestress losses were assumed to be 20 percent. Point s that fall below the solid line have less confinement than calculated by the model, and are predicted to fail due to splitting or lateral bursting. The proposed model correctly identified all but two of the specimens that failed in lateral splitting, bea ring, or similar modes. Splitting and similar failures are denoted by the markers. The model incorrectly predicted failure in eight cases, as denoted by the diamond shaped markers that fall below the solid line. In most cases where the failure mode was not accurately predicted, the provided confinement reinforcement was within 1.5 in 2 of the calculated requirement, indicating a desirable degree of conservatism in the model. on Figure 10 6 shows the greatest level of disagreement with the proposed model. This data point represents a Florida Bulb Tee section ( Tad ros et al. 2010 ), which had only 35 % of the calculated confinement reinforcement, but still did not fail due

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295 to lateral splitting. Shear reinforcement in this specimen terminated in a hook at the bottom of the beam. Hook tails were placed under the strands, were oriented transverse to the axis of the beam, and extended to the edge of the bottom flange. Additional splitting resistance demo nstrated by the specimen is attributed in part to the confinement provided by these hook tails. Confining effects from hooks are neglected in the proposed model due to inadequate hook development. The Florida Bulb Tee was supported on a steel plate durin g testing. Splitting resistance of the specimen is also attributed to frictional force between the girder and plate. Friction force at the bearing is thought to have had a greater impact on the bottom flange confinement than the hook tails from the verti cal reinforcement. Figure 10 6 represents four tests of Washington wide flange girders ( Tadros et al. 2010 ); each girder had identical calculated and provided confinement reinforcement. Numerous strands were located in the outer portion of the slender bottom flanges. During prestress transfer, it was observed that splitting cracks formed in the bottom flanges. Although not explicitly identified in the research, photographs of the failed beams suggest t hat lateral splitting action occurred during testing. The ultimate strength design model was also compared to the experimental data pool using the maximum shear force. For each data point, the maximum shear force reported in the literature was substituted into the model in lieu of the factored reaction force. As with the comparison at nominal shear capacity, the model also compares well with the maximum experimental s hear forces ( Figure 10 7 the model. As with the FL Bulb Tee section discussed in Figure 10 6 the indicated specimens in Figure 10 7 were also supported on steel plates during testing. These plates were not

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296 embedded plates and were not considered in the model calculations; however they are thought to have provided additional splitting resistance to the FL and PC Bul b Tee specimens. This result indicates that the model may be conservative for girders that are supported on rigid surfaces such as steel plates or concrete bent caps. Figure 10 8 shows the data set if the external steel be aring p lates used in the tests we re considered to provide confinement similar to embedded steel bearing plates. The external steel bearing plate s were only considered if they were wide enough to provide confinement ( Figure 10 3 b). Exte rnal steel bearing plat es were not considered in specimen s that al so had embedded plate s. A ccuracy of the model in cat egorizing failure model improved wh en the external bearing plates were considered. All but one of the incorrectly categorized results wa s within 0.5 in 2 of the solid black line that denotes the border between failure modes. Summary and Conclusions A rational design model was developed for designing confinement reinforcement at ultimate strength. The model considers s trand anchorage and transverse tie requirements which are analogous to local and general zone requirements in post tensioned concrete members. The ultimate strength model was compared to 4 1 unique tests of pretensioned concrete girders reported in the liter ature. The model was found to have good agreement with the published test results. The model is recommended for the design of confinement reinforcement and bearing plates at ultimate load.

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297 Figure 10 1 Local and general zones Figure 10 2 Illustration of transverse and frictional forces caused by the Hoyer effect

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298 Figure 10 3 Transverse tie force strut and tie models

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299 Figure 10 4 Node layout Figure 10 5 Strand anchorage force

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300 Figure 10 6 Design model compared to nomina l strength of experimental girders Figure 10 7 Design model compared to experimental girders at maximum shear

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301 Figure 10 8 Design model compared to exper imental girders at maximum shear (external bearing plates considered)

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302 CHAPTER 11 SERVICABILITY MODEL Experimental and analytical research pre sented in previous chapters demonstrates that transverse tensile stress in the bottom flange of pretensioned I girders can lead to flange splitting cracks during fabrication It is believed that the following behaviors contribute to tensile stress and flange cracking: Hoyer effect Eccentric prestres s forces Self weight reaction Flange splitting cracks can reduce the durabil ity of concrete I girders by allowing contaminates to enter the bottom flange and initiate corrosion of prestressing steel or chemical attack on the interior concrete. A serviceability design model is presented in this chapter for quantifying bottom flang e splitting stress. Stress from the model can be compared to concrete tensile capacity to determine the likelihood of bottom flange splitting cracks. The serviceability model is derived from a variety of sources including the work of other researchers, f inite element modeling, and basic mechanics. The proposed model contains empirical features specific to FIB girders. Although this formulation is not broadly applicable, the model could conceivably be re tooled for use with other cross sections. Experi mental and analytical research indicates that the largest transverse tensile stresses in the bottom flange occur at the member end. The majority of flange splitting cracks in the experimental girders were located at or close to the specimen ends. Accordi ngly, t he serviceability model provides equations for calculating the worst case transverse tensile s tress occurring at member ends. Calculated stresses at the member end can be compared to concrete tensile strength criteria to evaluate the likelihood of flange splitting cracks. Possible strength criteria are discussed later in this chapter.

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303 In the final section of this chapter, experimental cracks data are compared to stresses calculated from the proposed model. The model and data are found to have a hi gh degree of correlation. Causes of Bottom Flange Splitting at Prestress Transfer Flange splitting cracks in the bottom flange are caused by transverse splitting stresses that occur due to a combination of the Hoyer effect, eccentric prestress forces, and the self weight reaction. The following sections describe the mechanics associated with of each of these effects. Hoyer Effect The diameter of a prestressing strand decreases during pretensioning due to the Poisson effect ( Figure 11 1 a and b). When tension is released during prestress transfer the strands expand towards their original diameter. Expansion is partially restrained by the surrounding concrete resulting in normal stresses and proportional frictional forces at the strand concrete interface. This behavior was named for Ewald Hoyer, the German Engineer who first wrote of radial expansion of prestressing strands (Hoyer 1939). Expansion of prestressing strands is greatest at the edge of the concrete wher e strand tension is zero after prestress transfer ( Figure 11 1 d). At locations beyond the transfer length the strand expansion is negligible because strand tension is nearly the same before and after release. Cha nge in radial expansion is approximately linear between the concrete edge and the end of the transfer length (Oh et al. 2006). Consequently, radial and annular stresses in the concrete also vary linearly along the transfer length. Variable expansion of the strands leads to a wedge like shape after prestress transfer. This shape creates mechanical bond between strand and concrete. Additional bond improvement comes from the radial stresses at the interface, which allow the generation of

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304 frictional forces Wedge action and frictional forces are thus beneficial consequences of the Hoyer effect because th ey enable the transfer of prestress forces The Hoyer effect can also have detrimental consequences on the behavior and capacity of pretensioned girders. Concrete surrounding strands crack s when stresses due in part to the Hoyer effect exceed concrete tensile capacity. Eccentric Prestress Forces Tension forms in the bottom flange as prestressing forces from the outer strands are transferred to the concret e ( Figure 11 2 ). This tension forms in response to the eccentricity between prestressing forces from outer strands and the equal and opposite resultant force in the member. Tension is partially relieved as inner strands are released. This process has been demonstrated experimentally and analytically in previous chapters and is dependent on the strand bond pattern and strand cutting pattern. Tension stress due to ec centric prestress forces is bottom flange away from the web. Strands in the experimental program and in analytical models were cut from the outside in ( Figure 3 5 ). This detension oing pattern is assumed in the equations derived in this chapter. Self Weight Reaction Girders camber upward during prestress transfer after the prestressing moment exceeds the self weight moment ( Figure 11 3 ). After cambering, girders are supported by reactions at each end. Tensile stresses form in the bottom flange above the reaction points due to the flange bending illustrated in Figure 11 4 Previous analyses show t ha t self weight reactions produce tensile and compressi ve transverse stresses in the FIB bottom flange ( Figure 9 28 ). Analysis also demonstrate that self weight reaction stresses are small relative to peeling stre sses, and that average stress on

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305 sections through the outer flange is near zero or slightly compressive ( Table 9 4 ). Because of this, self weight reaction stresses on sections through the outer portion of the FIB bottom flange are conservatively neglected in the proposed serviceability model. This assumption may not be reasonable for other cross sections and for long span FIB girders. Transverse Splitting Stress Model Derivation Experimental results indicate that vertical splitting cracks can occur at multiple locations in the bottom flange ( F igure 11 5 ). The proposed model focuses on splitting cracks through the outer portion of the flange. Bottom flange splitting cracks below the web are not considered because they are associated with extreme strand bond patterns that are not permitted in FDOT production girders. Splitting cracks below the web were observed in the experimental program, but only in specimens with bonding patterns that placed fully bonded strands in the outer flange and shielded strands below the web. An outside in cut pattern is commonly used in FDOT production girders. As such, the serviceability model assumes an outside in cut pattern. This pattern was used in construction of the experimental girders, as well as the FE models used to develop the serviceability model. The model does not apply to girders with other cut patterns. Two critical conditions are considered in the design model: Maximum Pee ling. Previous e xperimental and analytical research show that the maximum peeling stres s along a given section occurs when only the outboard (closer to the outside edge) strands a re cut ( Figure 11 6 ). This condit ion is referred to as the Combined. This condition occurs when strands along a given section are cut and Hoyer stresses are superimposed with peeli ng stress. It is referred to as condition.

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306 T he model does not consider stress conditions when inboard (closer to the centerline) strands have been cut. Previous analytical work shows that cutting of inboard strands reduces peelin g stresses on a given section. Hoyer Stress Hoyer stress is calculated using a model dev eloped by Oh et al. (2006). The Oh model is based on equilibrium, material constitutive properties, and strain compatibility. It assumes radial expansion of a steel cylinder surrounded by concrete ( Figure 11 7 ). Equation 11 1 is for calculating radial stress at the steel concrete interface. Figure 11 8 shows the radial stress distribution calculated from Equation 11 1 for a strand in the experimental girders. As described by the Hoyer effect, radial stress is greatest at the member end and reduces to near zero at the end of the transfer length 11 1 Where: p = r o = p = f pz = E p = r j = c = f cz = E c = c = Radial stress at strand concrete interface Strand radius before pretensioning Strand Poisson ratio Axial stress in strand Strand Elastic Modulus Strand radius immediately after pretensioning Concrete Poisson ratio Concrete stress in directi on parallel to strand Concrete Elastic Modulus Concrete cover distance The equation above assumes linear elastic behavior. Recognizing the possibility of concrete cracks forming near the strand, the Oh model also includes features to calculate the avera ge stress in cracked concrete Applying these features results in stresses that are smaller than those calculated by assum ing linear elastic behavior. Cracking features in the Oh model ( )

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307 are neglected in the current model development. This approach allows superposition of Hoyer stresses with stres ses derived from linear elastic finite element modeling. Stress calculated by Equation 11 1 is not sensitive to concrete cover ( c ) distance for cover values greater than approximately 10 times the strand diameter ( Figure 11 9 ). By assuming that the cover distance is large relative to the strand diameter the term in the denominator of Equati on 11 1 approaches negative one and Equation 11 1 can be simplified to: 11 2 Assuming large concrete cover distance is conservative and results in slightly higher calculated stresses. For typical strand diameters and minimum cover d imensions, this assumption increase s the calcul ated stress by less than 2%. The serviceability model considers stresses at the girder end. At this location, strand expansion and th e associated Hoyer stresses are at their maximum Axial stress in the strand ( f pz = 0 ) and concrete ( f cz = 0 ) are equal to zero at the member end, which reduces Equation 11 2 to: 11 3 Where: p edge = Radial stress at strand concrete interface at end of member Concrete circumferential stresses are a function of the interfacial stress, strand size, concrete cover, and distance from the strand. Oh et al. provide the following equatio n for calculating circumferential stresses: ( ) ( )

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308 11 4 Where: = r = R = Radial stress at strand concrete interface at end of member Ordinate in the radial direction Radius of prestressing strand Figure 11 10 shows the concrete stress distribution calculated by Equations 11 3 and 11 4 for a single st rand in the experimental girders. Values used to calculate the stress distribution are listed in Table 11 1 The maximum concrete stress is 7.35ksi and occurs adjacent to the strand. Stress decreases rapidly wit h increasing distance from the strand. At locations 2in. from the strand concrete interface the stress is less than 0.125ksi. Large Hoyer stress adjacent to strand can cause local damage and cracking in the concrete. If tension through the flange is suf ficient, then the l ocalized cracking may propagate and form a crack through the entire flange. For this reason it is important to check the average stress due to the Hoyer effect through the flange thickness. Rather than calculating average stress from the stress distribution described by Equation 11 4 average stress in the model is calculated indirectly using the interfacial stress. This is done to simplify the design model for design purposes and to avoid int egration of concrete stress such as shown in Figure 11 10 Average stress calculated indirectly from the interfacial stress is the same as average stress calculated by integrating Equation 11 4 Applying equilibrium to an idealized strand, the interface stress must equal the internal stress in the strand ( Figure 11 11 a). Equilibrium can also be applied along a section cut through t he strand and concrete ( Figure 11 11 b) to show that the resultant force acting on the strand is equal and opposite the concrete force. This equilibrium condition is described by Equation 11 5 ( )

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309 11 5 Where: d b = d y = f hs = h f = Strand diameter Differential length in y direction Average Hoyer stress on the section from a single strand Thickness of flange at section under consideration Rearranging Equation 11 5 average stress due to the Hoyer Effect can be described as: 11 6 The average Hoyer stress on a given line is a function of the quantity of strands on that line. For sections with multiple strands the average stress can be calculated by multiplying the stress from Equa tion 11 6 by the number of strands. Both shielded and bonded strands along a section displace the area of concrete that carries Hoyer stresses. The denominator in Equation 11 7 is adjusted to account for displaced concrete due to all strand s : 11 7 Where: f h = n s = n st = Average stress on the section du e t o Hoyer Effect Quantity of fully bonded strands on section under consideration Quantity of all strands on section under consideration The serviceability model considers stress at the end of the member. At this location the interfacial stress between t he strand and the concrete can be calculated using Equation 11 3 Substituting Equation 11 3 into Equation 11 7 results in Equati on 11 8 for calculating the average Hoyer stress on a line through the bottom flange at the member end: 11 8 ( ) ( ) ( ) ( )

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310 Peeling Stress Peeling stress calculations are based on the free body diagram shown in Figure 11 12 This diagram is a simplified illust ration of forces acting on the outer portion on a bottom flange during prestress transfer. Prestressing forces from the eccentric outer strands ( F pos ) create a moment about the Z axis. Moment equilibrium is maintained by x direction tensile stresses in t he concrete acting on the Y Z cut plane. This equilibrium condition is described in equation 11 9 : 11 9 Where: F pos = x p = F tos = l y = Prestressing force from strands outboard of cut plane Distance from cut plane to centroid of prestressing force T ransverse tension force acting on cut plane due to eccentric prestressing Internal moment arm in y direction Rearranging Equation 11 9 results in the following equation for the transverse tension force due to th e eccentric strands: 11 10 Transverse tensile force in Equation 11 10 is the resultant of peeling stress in the concrete at the member end, wh ich is assumed to have a triangular tensile stress distribution. Peeling stress is assumed to be largest at the member end and zero at a distance l tos from the end ( Figure 11 12 ). Previous FE modeling shows that a triangular stress distribution and a value of 10in. for l tos are reasonable assumptions for the FIB cross section with outer strands cut ( Figu re 9 21 ). The following equation of equilibrium ensures that the resu ltant force from the assumed p eeling stress distribution is equal the transverse tensile force: 11 11 Where: f tos = Peeling stress ( ) ( ) ( )

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311 l tos = h f = Length of the assumed tensile stress distribution Thickness of the flange at the section under consideration Equation 11 11 can be rearranged to solve for the peeling stress at the member end: 11 12 Strands along a given section displace the concrete area that carries peeling stress. The denominator in Equation 11 12 must be adjusted to account for the area displaced by shielded and bonded strands. Doing so results in: 11 13 The term l y in Equation 11 13 is the length of the internal moment arm in the y direction. The value of l y varies according to the quantity of cut strands, shape of the cross section, and location with in a given cross section. Equation 11 14 and 11 15 are empirical equations for calculating l y in FIB girders. These equations were found to give values of l y and conseque ntly of F tos that are in agreement with previous FE results. 11 14 11 15 Where: l y1 = l y2 = h f = x = Internal moment arm in the y direction for maximum peeling condition Internal moment arm in the y direction for combined condition Thickness (z dimension) of the flange at the section under consideration x ordinate of the section under conside ration Transverse forces calculated using Equation 11 14 and Equation 11 15 are compared with FE results in Table 11 2 and Table 11 3 Results are compared for the MID and EDGE sections ( Figure 9 23 Figure 3 4 ). Val ues from the model ( ) ( ) ( ) ( )

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312 equations are within 1% of FE results for all but the combined condition at the MID section, for which the model is 7% conservative. Consistency between the model and FE results indicates that Equations 11 14 and 11 15 are acceptable approximations for calculating l y in FIB girders. Substituting l y1 and l y2 in into Equation 11 13 results in Equations 11 16 and 11 17 These equations are calibrated for sections through the outer portion of the bottom flange in FIB girders. They should not be used in conjunction with other girder s hapes, or at sections in the FIB bottom flange that are below the web. 11 16 11 17 Self Weight Reaction Stress Analytical modeling has shown that self weight reaction stress at the end surface of FIB girders can be neglected at locations in the outer portion of the bottom flange. As such, the self weight reaction stress ( f sw ) in the serviceability model is assumed to be zero. This assumption may not be reasonable for all cross sections. Superposition of Stresses Horizontal spitting stress is defined as the superposition of Hoyer, peeling, and self weight reaction stresses: 11 18 Where: f hsp = f h = f tos = f sw = Horizontal splitting stress Average Hoyer effect stress Peeling stress Self weight reaction stress As previ ously discussed, stress due to self weight reaction is negligible at the end face of the FIB bottom flange. Self weight reaction is included in Equation 11 18 only as a reminder ( ) ( ) ( )

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313 that self weight effects may be cr itical in some long span girders and in girders with other cross sections. For FIB girders, Equation 11 18 can be reduced to: 11 19 Two critical conditions have been discussed for horizontal splitting stresses. The maximum peeling condition occurs when only the strands outboard of a section are cut. Strands at the secti on in question are not yet cut in the maximum peeling condition and Hoyer stress on the section is assumed to be zero. The combined condition occurs when strands on a section have been cut and peeling stress is superimposed with Hoyer stress. The maximum horizontal splitting st ress on a given section is the greater of the stress from the maximum peeling or combined conditions: 11 20 11 21 Where: f hsp1 = f hsp2 = Horizontal splitting stress for maximum peeling condition Horizontal splitting stress for combined condition In FIB girders transve rse splitting stresses is checked for the five outermost columns of strands ( Figure 11 13 ). Stresses are checked at strand locations becaus e Hoyer stresses are greatest near prestressing strands, and because splitting cracks in the experimental program were observe d to intersect strands. Stress is check ed at each of the five locations for both of the cr itical stress conditions. M aximum stre ss from these locations and conditions is compared to concrete tensile strength criterion, which is discussed later. Stress Calculations for Experimental Girders In this section the serviceabili ty model is used to compute stresses at the end of specimen WN ( Figure 11 14 ). The end of specimen WN had two fully bonded strands placed at the outside of the flange. All other strands in the outer flange were shielded. ( ) ( ) ( )

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314 Hoyer stresses were calculated using Equation 11 8 and are summarized in Ta ble 11 4 The value of interfacial pressure ( p ) listed in Ta ble 11 4 was calculated using Equation 11 3 and the values from Table 11 1 The calculated Hoyer stress is zero for all but section A. This is because the model assumes that Hoyer stresses from shielded strands are negligible. Peeling stresses were calculated using Equations 11 16 and 11 17 and are summarized in Table 11 5 Peeling stresses at section B require additiona l discussion. The maximum peeling condition is intended to have the maximum peeling stress, however, it has a lower peeling stress than the combined condition at section B. This is because empirical equations for the internal moment arm resulted in a sho rter arm, and consequently at larger peeling stress, for the combined condition. This limitation of the model only affects section B and is of little concern. As shown later in the chapter, splitting stress at section B does not govern in any of the stre ss calculations for the experimental specimens. Also, this limitation makes the model is conservative at section B because it superimposes the larger peeling stress with the Hoyer stress. Horizontal splitting stresses were calculated using Equations 11 20 and 11 21 and the stresses from Ta ble 11 4 and Table 11 5 Results are presented graphically in Figure 11 15 The maximum calculated splitting stress at the end of WN occurs at section A during the combined condition. Because no peeling stress occurred at section A, the entire calculated splitting s tress is due to the Hoyer effect Splitting stresses at the other sections in WN are smaller than at section A because Hoyer stress from the shielded strands is assumed to be negligible. Calculated splitting stresses at sections B through E are solely due to peeling stresses cau sed by the bonded strands at section A.

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315 The same procedures used above for WN were also used calculate transverse splitting stresses for each specimen in the experiment al program. Additionally, stresses were calculated for four additional specimens from F IB 63 girders that were constructed at the same time as specimens W, F, and D. Strand shielding patterns for the FIB 63 specimens are shown in Figure 11 16 and Figure 11 17 Complete det ails of these specimens will be available in a forthcoming FDOT report (Ross et al. in preparation). The serviceability model was derived for calculating stresses at the end of pretensioned I girders. To test the applicability of the model to other locations, it was also used to estimate stress in specimens WN, WB, and SL (FIB 63) where shielding terminated. The maximum transverse splitting stress for each specimen and location are listed in T able 11 6 along with the governing section, governing stress condition, and flange splitting crack data. When stresses were calculated at two l ocations on the same specimen, crack data were assigned to the location where the cracks were observed in the physi cal girder. For example, no splitting cracks were observed at the end of specimen WN and the table lists zero for the crack length and area. Splitting cracks were observed 10 ft away from the end of WN, and the table lists the length and area of those cr From T able 11 6 it can be observed that the co mbined stress condition governs for each specimen and location. For the combined condition Hoyer stress accounted for 85% of th e splitting stress, on average. The remaining 15% (on average) was from peeling stress. This result indicates the significance that the Hoyer effect has on flange splitting cracks. Section C has the governing (maximum) stress in 12 of 17 specimens and lo cations. Experimental observations support this result. Flange splitting cracks were more likely to be observed at section C than at any other location in the experimental program The governing

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316 stre ss from the model never occurs at sections B or E. Th is result supports the pre vious statement that model limitations at section B do not impact overall results. Model Comparison with Experimental Crack Data Stresses calculated using the serviceability model correlate well with crack data from the experiment al girders ( T able 11 6 and Figure 11 18 ). This can be seen from the linear curve in Figure 11 18 that is fit to the stress and cr ack data from the specimen ends. The line has an R 2 value of 0.85, indicating a high degree of correlation between calculated stresses and experimental crack lengths. When stress and crack data away fro m the ends (WN, WB, and SL) are included, correlatio n drops to 0.73. This suggests that the model is more accurate for calculating stress at member ends than at sections away from the end. Additional data are required, however, to quantify the degree t o which the model can reasonably be applied to locatio ns away from the member end. A high degree of correlation i s also observed when the c alculated stresses a re compared to the area of the flange splitting cracks in the experimental girders ( Figure 11 19 ). Consideri ng the random nature of cracking in concrete this level of correlation suggests that the model does an excellent job of capturing the physical phenomenon which cause bottom flange splitting cracks. It is common in prestressed concrete design to compare co ncrete tensile stress to the square root of the compressive strength. Dashed vertical lines in Figure 11 18 and Figure 11 19 indicate 1.20ksi which is equal to (for ci in ksi). This value is approximately equal to the x intercept of the linear curves fit to the data. The x intercept corresponds to the stress belo w which flange cracking are unlikely according to the sample data. All but one of the spec imens and locations in the sample have stresses higher than this value. The lone location

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317 below this value, SL (5ft.), did not have flange splitting cracks in the experimental girder. A more conservative stress limit, and one that is already used in othe r circumstances by AASHTO LRFD, is This is approximately half of the limit indicated by the experimental data. Additional data are required to calibrate the reliability associated with different splitting stress criteria. Nevertheless, available data suggest that the proposed model is an adequate tool for calculating transverse splitting stress in the bottom flange of FIB girders. Summary and Conclusions A model was derived for calculating transverse splitting stresses in the bottom flange of FIB girders. The model considers contributions to splitting stress from the Hoyer effect and from the horizontal eccentricity of strands in the outer flange. Stresses due to these effects are referred to as Hoyer stresses and peeling stresses, respectively. Self weight also contributes to transverse splitting stress, however effects of self weight are considered negligible in the outer flange of FIB girders. The work of Oh et al (2006) was utilized to derive an equation for Hoyer stress An equation for peeling stress was derived using FE modeling and basic mechanics. The equation for peeling stress contains empirical relationships that are specific to FIB girders. The model was compared to crack data from the experimental girders and was found to have a high degree of correlation wi th said data. An R 2 value of 0.80 was obtained for linear trend line that was fit to the calculated and experimental data. Analysis indicates that flange splitting cracks are likely when the calculated splitting stress exceeds (for ci in ksi). A lower threshold stress is recommended for controlling flange splitting cracks. One possible threshold is which is currently used by AASHTO LRFD to limit concrete tensile stresses in situations similar to the FIB bottom flan ge.

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318 Figure 11 1 Hoyer Effect A) Strand before stressing, B) Strand after prestressing, C) Concrete cast around strand, D) Stresses and forces after transfer.

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319 Figure 11 2 Flange tension due to outer strands Figure 11 3 Camber due to prestress force

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320 Figure 11 4 Self weight reaction effects F igure 11 5 Flange splitting in experimental girder (Photo courtesy of B.E. Ross)

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321 Figure 11 6 Strand cutting conditions Figure 11 7 Strand p hysical analog (B ased on Oh et al. 2006 )

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322 Figure 11 8 Calculated radial stress ( p ) distribution (Based on Oh et al. 2006) Figure 11 9 Effect of cover distance on calculated radial stress ( p )

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323 Figure 11 10 Concrete stress distribution due to Hoyer Effect Figure 11 11 Stresses at plane cut through strand and concrete

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324 Figure 11 12 Bottom flange free body diagram Figure 11 13 Analysis sections for FIB bottom flange

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325 Figure 11 14 Strand bond and shielding pattern specimen WN Figure 11 15 Transverse (x x) splitting stress at end of specimen WN

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326 Figure 11 16 Strand pattern CN, PT, and LB Figure 11 17 Strand pattern SL end (left), SL 5ft from end (right)

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327 Figure 11 18 Calculated transverse splitting stress vs. experimental crack length Figure 11 19 Calculated transverse splitting stress vs. experimental crack area

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328 Table 11 1 Strand and concrete properties of experimental girders Concrete Elastic Modulus 4700 ksi Concrete Poisson Ratio 0.2 Strand Elastic Modulus 29,000 ksi Strand Poisson Ratio 0.3 Strand radius prior to jacking 0.3 in. Strand radius after jacking 0.29 94 in. Table 11 2 Model vs. FE for maximum peeling stress condition Section h f (in.) x (in.) l y 1 (in.) F tos Model (kip) F tos FE (kip) Model / FE EDGE 10.5 12 46.4 11.4 11.3 1.01 MID 12.9 8 85.5 20.6 20.3 1.01 Table 11 3 M odel vs. FE for combined stress condition Section h f (in.) x (in.) l y 2 (in.) F tos Model (kip) F tos FE (kip) Model / FE EDGE 10.5 12 33.7 15.7 15.9 0.99 MID 12.9 8 45.7 38.5 36.1 1.07 Ta ble 11 4 Hoyer stresses end of specimen WN Section n s p (ksi) d b (in.) n st h f (in.) f h (ksi) A 2 7.36 0.6 2 8.5 1.21 B 0 7.36 0.6 2 8.5 0 C (EDGE) 0 7.36 0.6 3 8.5 0 D 0 7.36 0.6 3 8.5 0 E (MID) 0 7.36 0 .6 3 8.5 0 Table 11 5 Peeling stresses at end of specimen WN Section F pos (kip) x p (in.) x (in.) h f (in.) n st d b (in.) l y1 (in.) l y2 (in.) f tos1 (ksi) f tos2 (ksi) A NA NA 16 8.5 2 0.6 NA NA 0 0 B 88 2 14 9.5 2 0.6 43.7 36.0 0.097 0.118 C (EDGE) 88 4 12 10.4 3 0.6 38.7 45.9 0.212 0.178 D 88 6 10 11.6 3 0.6 33.4 61.5 0.322 0.175 E (MID) 88 8 8 13.2 3 0.6 28.0 87.5 0.441 0.141

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329 T able 11 6 Transverse splitt ing stresses and splitting crack data Specimen Max transverse splitting stress (ksi) Section Critical Condition Length of flange splitting cracks (in.) Area of flange splitting cracks (in 2 ) HC 1.29 C Combined 0 0 HU 1.29 C Combined 40 0.112 VC 1.29 C C ombined 0 0 VU 1.29 C Combined 41 0.087 WN (10 ft.) 1.63 C Combined 32 0.05 WB (10 ft.) 1.63 C Combined 99 0.292 WN (end) 1.21 A Combined 0 0 WB (end) 1.21 A Combined 0 0 FN 1.73 D Combined 190 0.469 FB 1.73 D Combined 115 0.295 DC 1.29 C Combined 104 0.239 DM 1.29 C Combined 41.5 0.112 PT 1.81 C Combined 142 0.316 LB 1.81 C Combined 183 0.429 CN 1.81 C Combined 175 0.368 SL 1.25 C Combined 73 0.144 SL (5 ft.) 0.99 D Combined 0 0

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330 CHAPTER 12 CONCLUDING REMARKS Confinement reinforcement is placed in the bottom flange of pretensioned I girders to enclose the prestressing strands at member end s The 2007 AASHTO LRFD Bridge Design Specifications contain prescriptive requirements for the quantity and placement of confinement reinforcement The s e require ment s are based on limited experimental data and apparently do not have a theoretical underpinning. A vailable research has demonstrated the beneficial aspects of confinement reinforcement but has not established the function that confinement reinforcement serve s. Experimental and analytical work presented in this document address these limitations in the current understanding of confinement reinforcement. O utcomes of the work include: An understanding of the function s of confinement reinforcement during prestress transfer and at ultimate load An understanding of the interaction between confinement reinforcement and other design variables A serviceability design model for the bottom flange at prestress transfer An ultimate strength design model for confin ement reinforcement This chapter begins with summaries of the experimental and analytical research programs presented in this document. C onclusions of the programs are then summarized and are discussed in terms of the four outcomes presented above. The final section of this chapter offers design and detailing recommendations for the end region of FIB girders. Experimental Program Summary Ten uniquely detailed FIB 54 test specimens were built and tested. Variables in the test program included: Presence/ab sence of confinement reinforcement

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331 Quantity and configuration of confinement reinforcement Presence/absence of end region horizontal reinforcement Quantity of end region vertical reinforcement Presence/absence of embedded steel bearing plates Strand quanti ty Strand placement Strain data w ere collected from the concrete and reinforcement during and immediately after prestress transfer. Formation and propagation of crack s in the specimens were monitored during prestress transfer and in the weeks and months following prestress transfer. Effects of the test variables on behavior and cracking were compared using strain and crack data. Specimens were t aken to the FDOT Structures Resear ch Center in Tallahassee, FL, w ere cast in place slabs were poured on the spe cimens After the slabs were sufficiently cured, specimen s where load tested in three point bending. Load was applied at a shear span to depth ratio of 2.0 to determine ultimate shear capacity. Strain, load, strand slip, and displacement data were colle cted during load testing. Data were used to compare the effects of test variables on ultimate capacity and behavior. Analytical Program Summary Finite element (FE) modeling was used to analyze girders during prestress transfer and under service loading. FE models were linear elastic a nd were intended to capture pre cracking behavior of the girders. Experimental data were used to validate the FE model s Models compared well with experimental data and were found to effectively capture overall girder beh avior as well as the local behavior in the end region. Validated models were the n used to conduct parametric studies of prestress transfer and loading. Parametric studies of prestress transfer assumed an outside in strand cutting pattern. Variables in t he parametric studies included: Transfer length

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332 Quantity of cut s trand s Embedded b earing plate Self weight Bearing pad width Bearing pad stiffness Bottom flange geometry Conclusions Function of Confinement Reinforcement T ransverse tensile stresses form in the bottom flange of pretensioned I girders during prestress transfer and during loading. Cracks form in the bottom flange when tensile stress exceed s the concrete tensile strength Confinement reinforcement is placed in the bottom flange to control con crete cracking and to carry transverse tensile loads after the concrete cracks. Crack control is a serviceability function of confinement reinforcement and is of primary concern during prestress transfer. During transfer cracks are most likely at the gi rder ends where transverse splitting stresses are the highest. To best control cracks, confinement reinforcement should be placed as n ear the member end as practical, and should also be placed throughout the strand transfer length. At ultimate strength confinement reinforcement carries transverse tension forces. Transverse tension forces can lead to lateral splitting failure i f sufficient bottom flange confinement is not provided In addition to mitigating lateral splitting failure, c onfinement reinfor cement also assists in force transfer between strands and concret e, thereby reducing but not eliminating the prop ensity of a girder to fail in bond shear mode. To best perform these function s confinement reinforcement should be placed throughout the str and transfer length.

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333 Interaction of Variables with Confinement Reinforcement E mbedded steel bearing plates and variations in strand bond pattern have significant effect on the load carried by confinement reinforcement. Embedded steel bear ing plates provi de additional confinement to the bottom flange of I girders and decrease load demand on confinement reinforcement In the test program, the p resence of a steel bearing plate reduced forces in confinement reinforcement during prestress transfer by up to 50 % relative to forces in spe cimens without bearing plates. Presence of a steel bearing plate also aided in crack control of flange splitting cracks. Confinement reinforcement carries transverse tensile forces which occur to eccentric p restress forces from strands in the outer portion of the flange. Thus strand bond patterns with bonded strands in the outer flange create large r load demand on confinement reinforcement than patterns with bon d ed strands below the web In the test program, specimens w ith fully bonded strands in the outer flange had up to 2.3 times more force in the confinement reinforcement during prestress transfer than did specimens with fully bonded strands placed below the web. Flange splitting cracks were also more severe in specime ns with strands in the outer flange. Bottom Flange Serviceability Design Model A serviceability design model was derived to calculate stresses in the bottom flange of FIB girders during prestress transfer. The model considers stresses due to the Hoyer Eff ect, eccentric prestressing forces, and girder self weight. An outside to in strand cutting pattern is assumed by the model and th e model contains features that we re derived empirically for FIB girders. Stresses calculated by the model were found to have excellent correlation (R 2 =0.8) with flange splitting crack data collected from the experimental girders.

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334 Confinement Reinforcement Ultimate Strength Design Model An ultimate strength design model was derived to calculate the amount of confinement reinforc ement required to anchor prestressing strands at ultimate load and to prevent lateral spli tting failure. Strand anchorage and lateral splitting criteria are analogous to local zone and general zone requirements in post tensioned concrete structures. The ultimate strength model considers girder geometric properties, prestressing strand layout, and geometric properties of the bearing. The effect of embedded steel bearing plates is included in the model. The model is general enough for application in wide variety of circumstances, as evidenced by favorable compa rison with experimental data Data from the current study and from the experimental results in the literature were used for comparison In almost all cases the model accurately categorized experime ntal specimens which failed in lateral splitting mode. Recommendations Confinement reinforcement currently specified by the FDOT (FDOT 2009b) performed well in the research program with respect to serviceability and ultimate strength criteria. Confinement reinforcement helped to control bottom flange splitting cracks and mitigate lateral splitting failures. Continued use of the current FDOT confinement detail is recommended. The current detail places confinement over a distance approximately 1.2 d from th e member end and has tighter spacing of reinforcement over the bearing locat ion. Both of these practices a re validated by experimental and analytical work presented in this document. In special cases where additional crack control or lateral splitting ca pacity is required, #4 bars can be used for confinement reinforcement in lieu of the currently specified #3 bars. As with confinement reinforcement, embedded steel bearing plates also performed well in the research program with respect to serviceability and strength criteria. Bottom flange splitting cracks were smaller and ultimate strengths were larger in test specimens with bearing plates.

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335 As such, the continued use of steel bearing plates is recommended. Use of longer studs on bearing plates is reco mmended for future research. It is believed that longer studs engage a grea ter portion of concrete, thereby providing additional confinement to the bottom flange. Wider (in the direction of the span length) bearing plates are also recommended as a test v ariable. Wider bearing plates may prevent cracking near the member end and thereby improve bond shear capacity. Of all the variables in the research program, strand quantity and strand shielding pattern had the greatest effect on test s pecimen behavior and capacity. The following recommendations are made regarding the design of strand layouts and strand shielding patterns: Fully bonded strands should be placed as close to the cross section centerline and with as much top cover as practical. This practi ce will reduce the likelihood of bottom flange splitting cracks and lateral splitting failure. Placement of fully bonded strands at the outermost location in the third row should be avoided. This location has a high propensity for splitting cracks. Curren t AASHTO LRFD limits on termination of strand shielding at a given section are recommended for controlling flange splitting cracks within the transfer length of partially shielded strands. Confinement reinforcement is believed unnecessary at these locatio ns if shielding termination complies with the AASHTO limits. The percentage of shielded strands can reasonably exceed the 25% limit specified by AASHTO LRFD if sufficient reinforcement and strands are provided to meet minimum longitudinal steel requirement s at the girder end. As currently specified by AASHTO LRFD, any lack of full development must be considered when the evaluating the minimum longitudinal steel P artially shielded strands (when used) should be placed towards the outside of the bottom f lange. Clustering of shielded strands below the web is strongly discouraged. Prestress force in the outermost strands in the bottom two ro ws should be reduced from the currently specified level. A prestress force of 10 kip is recommended in order to su pport reinforcement during fabrication. This practice will reduce the likelihood of bottom flange splitting cracks and lateral splitting failure.

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336 Final Comments Pretensioned concrete I sinc e the 1950s. The recently introduced Florida I Beam (FIB) presents new opportunities and challenges Because of a relatively wide bottom flange, FIB girders can support more prestressing and can span longer distances than th e formerly used AASHTO girders. The wide bottom flange can also be problematic if splitting cracks and lateral splitting failure are not considered by designers Confinement reinforcement, embedded bearing plates, and strand bond patterns can be us ed to control the likelihood of bottom flange splitting crack s and lateral splitting failure The s erviceability and ultimate strength models presented in this document are tools for designing effective confinement reinforcement, bearing plates, and strand bond patterns Well designed FIB girders add t o the durability, strength, and

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337 LIST OF REFERENCES AASHTO LRFD Bridge Design Specifications 4 th Edition. American Association of State Highway and Transportati on Officials (AASHTO). Washington, DC Aknoukh, A. (2010) The Effect of Confinement on Transfer and Development Length of 0.7 Inch Prestressing Strands Concrete Bridg e Conference. Phoenix, AZ Barnes, R., Burns, N., and Kreger, M. (1998 ). "Development Length of 0.6 Inch Prestressing Strand in Standard I Shaped Pretensioned Concrete Beams." Rep. No. 1388 1, Texas Department of Transportation, Austin, TX. Breen, J., Burdet, C., Sanders, D., Wollmann, G. Anchorage Zone Reinforcement for Post Tensi oned Concrete Girders National Highway Cooperative Research Program. Transportation Researc h Board. Washington, DC. ACI 318 11 American Concrete Institute (ACI), Farmington Hills, MI. 30. Florida Department of Transportation, Tallahassee, FL. Csagoly, P. (1991). "A Shear Moment Model for Prestres sed Concrete Beams." Rep. No. 9900 1550, Florida Department of Transportation, Tallahassee, FL. Deatherage, J., Burdette, E., and Chew, C. (1994). "Development Length and Lateral Spacing Requirements of Prestressing Strand of Prestressed Concrete Bridge Gi rders." PCI J 39(1), 70 83. Englekirk, R. E., and Beres, A. (1994). "Need to develop shear ductility in prestressed members." Concr.Int 16(10), 49 56. Fallaha, S. (2009). Telephone and E mail correspondence with Brandon Ross. FDOT. (2008 ). Interim Desig Florida Department of Transportation, Tallahassee, FL. FDOT. (2009a). "Temporary Design Bulletin C09 01." Florida Department of Transportation, Tallahassee, FL. FDOT. (2009b). "Temporary Design Bulletin C09 03." Florida Departm ent of Transportation, Tallahassee, FL. FDOT. (2009c). "Structures Design Guidelines." Florida Department of Transportation, Tallahassee, FL.

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338 Transportation, Tallahassee, FL. FD OT. (2010 ). Florida Department of Transportation, Tallahassee, FL. FHWA. (2010) "Federal Highway Administration National Bridge Inventory." http://www.fh wa.dot.gov/bridge/nbi/mat09.cfm ( accessed December 1, 2010). String [In German]. Kaufman, M. K., and Ramirez, J. A. (1988). Re Evaluation of the Ultimate Strength Behvaior o f High Strength Concrete Prestressed I ACI Struct.J 85(3), 295 303. Kuchma, D., Kim, K. S., Nagle, T. J., Sun, S., and Hawkins, N. M. (2008). "Shear tests on high strength prestressed bulb tee girders: Strengths and key observations." ACI Struct.J 105(3), 358 367. Llanos, G., Ross, B., and Hamilton, H. (2009). "Shear Performance of Existing Prestressed Concrete Bridge Girders." Rep. No. BD 545 56, Florida Department of Transportation, Tallahassee, FL. Magus, R. (2010). Brandon Ross notes from pre construction meeting. Dura Stress, Leesburg, FL. Maruyama, K., and Rizkalla, S. H. (1988). Shear Design Consideration for Pretensioned Prestressed Beams. ACI Struct.J 85(5), 492 498. Morcous, G., Hanna, K., Tadros, M. (2010). Bottom Flange Reinforceme nt in NU I Girders. Nebraska Department of Roads. Lincoln, NE. 2010. Nolan, S. (2009). Telephone and E mail correspondence with Brandon Ross. Oh, B., Lim, D. ACI Struct J 94(50), 549 557. Patzlaff, Q., Morcous, G., Hanna, K., and Tadros, M. (2010). "Bottom Flange Reinforcement of Precast Prestres sed Bridge I Girders." 2010 Concrete Bridge Conference. R&D Inc. (2009). "ADINA." Finite element analysis software version 8.6 Watertown, MA.

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339 Roberts, C. (1990). Behavior and Design of Local Anchorage Zone of Post Tensioned Concrete Members M.S. Thesi s. Universi ty of Texas. Austin, TX. Ross, B., Hamilton, H., Consolazio, G. (2011 a Experimental and Analytical Evaluations of Confinement Reinforcement in Pretensioned Concrete Beams. Trans Research Record. 2251, 59 67. Ross, B., Ansley, M., Hamilton H. Load Testing of 30 year old AASHTO Type III Highway Bridge Girders. PCI J 56(4), 152 163. Ross, B. Hamilton, H., Consolazio G. End Region Detailing of Pretensioned Concrete Bridge Girders Florida Department of Transportation. Tallahas see, FL. (In preparation) Russell, B. W., and Burns, N. H. (1996). "Measured transfer lengths of 0.5 and 0.6 in. strands in pretensioned concrete." PCI J ., 41(5), 44 65. Shahawy, M., Robinson, B., and deV Batchelor, B. (1993). "An Investigation of Shear S trength of Prestressed Concrete AASHTO Type II Girders." Florida Department of Transportation, Tallahassee, FL. Tadros, M., Badie, S., Tuan, C. Evaluation and Repair Procedures for Precast/Prestressed Concrete Girders with Longitudinal Cracking in the Web National Cooperative Highway Research Program, Report 654. Transportation Research Board. Washington, DC. 2010. Yura, J., Kumar, A., Yakut A., Topkaya, C., Becker, E. and Collingwood, J. (2001) Elastomeric Bearing Pads: Recommend Test Metho ds. National Cooperative Highway Research Program report 449. Transportation Research Board. Washington, DC. 2001.

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340 BIOGRAPHICAL SKETCH Brandon E. Ross hails from the great state of Wyoming. He attended the University of Wyoming, ea rning a Bachel or of Science in architectural e ngineering (20 01) and a Master of Science in civil e ngineering (2002). Upon completion of his degrees at the University of Wyoming he worked as a structural engineer for PCS Structural Solutions of Seattle, WA, and Engineer ing Systems Solutions (ES 2 ) of Idaho Falls, ID. He obtained a Professional Engineer (Idaho #12054) license in 2005. A marquee project from his early career was the structural design of Our Lady of the Snows Catholic Church in Sun Valley, ID. The decisio n to pursue a PhD. and academic of the beach. Brandon is married to Michelle (Stone), an accomplished c horal conductor. The couple has three children. Brandon has accepted a position at Clemson University as an Assistant Professor and will begin fall semester 2012.