FINITE-ELEMENT MODELING OF A DAMAGED PRESTRESSED CONCRETE BRIDGE Except where reference is made to the work of others, the work described in this thesis is my own or was done in collaboration with my advisory committee. This thesis does not include proprietary or classified information. _____________________________________________ Kelli Ann Shapiro Certificate of Approval: ________________________ ________________________ Mary L. Hughes Robert W. Barnes, Chair Assistant Professor Associate Professor Civil Engineering Civil Engineering ________________________ ________________________ Anton K. Schindler Joe F. Pittman Assistant Professor Interim Dean Civil Engineering Graduate School FINITE-ELEMENT MODELING OF A DAMAGED PRESTRESSED CONCRETE BRIDGE Kelli Ann Shapiro A Thesis Submitted to the Graduate Faculty of Auburn University in Partial Fulfillment of the Requirements for the Degree of Master of Science Auburn, Alabama May 10, 2007 iii FINITE-ELEMENT MODELING OF A DAMAGED PRESTRESSED CONCRETE BRIDGE Kelli Ann Shapiro Permission is granted to Auburn University to make copies of this thesis at its discretion, upon the request of individuals or institutions and at their expense. The author reserves all publication rights. ________________________ Signature of Author ________________________ Date of Graduation iv VITA Kelli Ann Shapiro, daughter of Bruce and Mischell Shapiro, was born on February 3, 1981, in Salt Lake City, Utah. In June of 1999, she graduated with honors as Valedictorian from Ansbach American Middle/High School in Ansbach, Germany. She began school at Brigham Young University in September 1999 on academic scholarship and received a Bachelor of Science in April 2004. She entered graduate school at Auburn University in August 2004 and completed a Master of Science degree in Civil Engineering with an emphasis in Structural Engineering in May 2007. After completing graduate school, she began work as a stress analyst at Marshall Space Flight Center in Huntsville, Alabama. v THESIS ABSTRACT FINITE-ELEMENT MODELING OF A DAMAGED PRESTRESSED CONCRETE BRIDGE Kelli Ann Shapiro Master of Science, May 10, 2007 (B.S., Brigham Young University, 2004) 258 Typed Pages Directed by Robert W. Barnes Spans 10 and 11 of the Interstate Highway 565 bridge structure in Huntsville, Alabama were noticed to be cracked shortly after their construction. Alabama Department of Transportation (ALDOT) employees investigated and concluded that the probable cause of the cracking was stress at the continuous support due to the temperature differential between the bridge deck and the bulb-tee girders. Further investigation to determine the cause of the cracking, the results of the cracking, and the possible repair methods was conducted by ALDOT in cooperation with Auburn University personnel. It was concluded that fiber-reinforced polymer (FRP) repair was feasible, and a repair procedure was devised. In order to measure the effect of the repair, load tests were planned to occur both before and after the repair. On June 1 and 2, 2005, the pre-repair load tests were conducted. vi A finite-element model (FEM) was created to provide a basis for an analytical comparison to measured data and observed bridge behavior. The model was designed to simulate the current behavior of the bridge and to predict the change in behavior due to the repair work. Modeling results supported the hypothesis that rather than behaving as a continuous two-span beam, the bridge displayed behavior consistent with a continuous beam including a hinge located in the cracked region. An additional goal of the analytical modeling was to determine which of the strain gauges used in the pre-repair bridge tests should be reassigned to other locations of the bridge for the post-repair tests. It was determined that eight gauges should be relocated from the face of the girder near the top pf the web to the base of the FRP reinforcement. Results of the analytical modeling warranted the prediction that the FRP repair would return the bridge to near fully continuous behavior. Further analysis will be necessary after the repair is complete and the post-repair test has been conducted to determine the results of the repair on the behavior of the bridge. vii ACKNOWLEDGEMENTS I would like to thank my loving Heavenly Father for putting in my life all of the people and circumstances which have helped me accomplish this goal. Thanks go also to Dr. Barnes for his wisdom and wit. Thanks to Bill Fason for his work on the bridge, the load test results, and many of the figures and diagrams. And finally, thanks to all of my family and friends for their love, encouragement, and support. viii Style manual used Kate L. Turabian A Manual for Writers of Term Papers, Theses, and Disserations. 6 th ed. Computer software used Microsoft Word, Microsoft Excel, ABAQUS CAE 6.5-1, ABAQUS CAE 6.6-1, Microsoft Paint ix TABLE OF CONTENTS LIST OF TABLES................................................................................................ xii LIST OF FIGURES ............................................................................................. xiii CHAPTER 1: INTRODUCTION...........................................................................1 Background......................................................................................1 Objectives ........................................................................................1 Research Approach ..........................................................................2 Thesis Outline ..................................................................................2 CHAPTER 2: FINITE-ELEMENT MODELING OF MULTIGIRDER BRIDGES ........................................................................................4 Introduction......................................................................................4 AASHTO LRFD Requirements.......................................................4 Finite-Element Modeling of Bridges Without Load Testing Verification ...................................................................5 Finite-Element Modeling of Bridges With Load Testing Verification ...................................................................9 Summary of the Findings...............................................................17 CHAPTER 3: BRIDGE DESCRIPTION AND HISTORY .................................19 Introduction....................................................................................19 Historical Overview.......................................................................19 Details of the Cracked I-565 Bridge Structure ..............................23 Previous Investigations of Girder Cracking...................................35 Proposed Repair System ................................................................39 CHAPTER 4: LOAD TESTING PROCEDURE..................................................43 Introduction....................................................................................43 Applied Loads................................................................................43 Instrumentation ..............................................................................52 Data Acquisition and Processing ...................................................65 Data Used to Evaluate and Refine Finite-Element Models ...........65 CHAPTER 5: FEM DEVELOPMENT AND VERIFICATION..........................67 Introduction....................................................................................67 x Girder Cross Section......................................................................67 Reinforced Concrete Deck.............................................................70 Mesh Size.......................................................................................70 Diaphragms....................................................................................75 Barrier Rails...................................................................................77 Bearing Pads ..................................................................................78 Element Selection ..........................................................................79 Modulus of Elasticity.....................................................................82 Seams .............................................................................................83 Prestressed Reinforcement.............................................................87 Connections....................................................................................89 Support Conditions ........................................................................90 Load Application ...........................................................................90 Model Refinement .........................................................................92 Modeling of FRP............................................................................94 CHAPTER 6: RESULTS......................................................................................99 Introduction....................................................................................99 Finite-Element Modeling of the Existing Structure.......................99 Finite-Element Modeling of the FRP-Repaired Structure ...........118 CHAPTER 7: DISCUSSION..............................................................................133 Introduction..................................................................................133 Analysis........................................................................................133 Inferences Regarding Bridge Behavior........................................143 Gauge Location Analysis.............................................................144 Forecast for Repair.......................................................................148 CHAPTER 8: SUMMARY AND CONCLUSIONS..........................................152 Summary of Study .......................................................................152 Conclusions..................................................................................153 Recommendations........................................................................154 REFERENCES ....................................................................................................156 APPENDICES .................................................................................................159 APPENDIX A: EXPLANATION OF DATA PRESENTED IN APPENDICES B?H................................................................160 Introduction.............................................................................160 Girder Numbering ...................................................................160 Longitudinal Stop Positions ....................................................160 Locations for Deflection Measurements .................................165 Locations for Strain Readings.................................................165 xi Locations for Crack Opening Devices ....................................166 APPENDIX B: DEFLECTIONS......................................................................169 APPENDIX C: BOTTOM-FIBER STRAINS .................................................174 APPENDIX D: A7 LOAD POSITION STRAIN PROFILES..........................179 APPENDIX E: A9 LOAD POSITION STRAIN PROFILES..........................188 APPENDIX F: C7 LOAD POSITION STRAIN PROFILES..........................197 APPENDIX G: C9 LOAD POSITION STRAIN PROFILES..........................206 APPENDIX H: LOAD TEST DATA...............................................................215 APPENDIX I: NOTATION AND ABBREVIATIONS .................................234 xii LIST OF TABLES Table 4.1 Test Truck Wheel Group Loads ............................................................. 44 Table 4.2 Locations of the Nine Longitudinal Stop Positions ................................ 51 Table 5.1 Section Properties of Simplified BT-54 Cross Section........................... 69 Table 5.2 Summary of Seam Locations.................................................................. 85 Table 5.3 Test Truck Wheel Group Pressure Loads ............................................... 91 Table 6.1 Comparison between Pre- and Post-Repair Models of Midspan Deflection Measured on Span 11.......................................................... 126 Table 6.2 Comparison between Uncracked and Post-Repair Models of Midspan Deflection Measured on Span 11.......................................................... 127 Table 7.1 Compressive Stress Changes, due to Truck Loads, in Prestressing Steel at the Seam Locations of the Pre-Repair Model .................................. 141 Table 7.2 Strain Gauge Evaluation?Girder 7...................................................... 146 Table 7.3 Strain Gauge Evaluation?Girder 8...................................................... 147 Table 7.4 Maximum Closing Displacements for Each Seam and Load Position . 150 Table A.1 Locations of the Nine Longitudinal Stop Positions .............................. 164 Table A.2 Transverse Lane Positions .................................................................... 165 Table A.3 Crack Opening Device Locations ......................................................... 166 Table H.1 Pre-Repair Load Test Data for Transverse Position A ........................ 216 Table H.2 Pre-Repair Load Test Data for Transverse Position B ......................... 222 Table H.3 Pre-Repair Load Test Data for Transverse Position C ......................... 228 xiii LIST OF FIGURES Figure 2.1 Diaphragm-to-Girder Connection Detail Using a Rigid Link (Tedesco, Stallings, and Tow 1995) .......................................................................... 7 Figure 3.1 Typical Pattern of Cracking in End Region of Precast Girder (Barnes et al. 2006) .................................................................................................. 20 Figure 3.2 Cracked Pretensioned Bulb-Tee Girders (Barnes et al. 2006)................ 22 Figure 3.3 Epoxy-Injected Cracks............................................................................ 22 Figure 3.4 Bridge Cross Section (Swenson 2003) ................................................... 24 Figure 3.5 BT54 Cross Section Dimensions (Swenson 2003) ................................. 25 Figure 3.6 Plan View of the Two-Span Continuous Unit (ALDOT 1987) .............. 26 Figure 3.7 Detailed Plan View of the Two-Span Continuous Unit (ALDOT 1987) ............................................................................... 27 Figure 3.8 Elevation View of the Two-Span Continuous Unit (ALDOT 1987)...... 28 Figure 3.9 Girder End Strand Pattern (Swenson 2003)............................................ 28 Figure 3.10 Girder Midspan Strand Pattern (Swenson 2003) .................................... 29 Figure 3.11 Girder Numbering System (Fason and Barnes 2004)............................. 29 Figure 3.12 Bent Bar Detail at Continuity Diaphragm (Swenson 2003) ................... 30 Figure 3.13 Girder Line 1 Cracking (Fason and Barnes 2004).................................. 31 Figure 3.14 Girder Line 2 Cracking (Fason and Barnes 2004).................................. 31 Figure 3.15 Girder Line 3 Cracking (Fason and Barnes 2004).................................. 32 Figure 3.16 Girder Line 4 Cracking (Fason and Barnes 2004).................................. 32 Figure 3.17 Girder Line 5 Cracking (Fason and Barnes 2004).................................. 33 Figure 3.18 Girder Line 6 Cracking (Fason and Barnes 2004).................................. 33 xiii Figure 3.19 Girder Line 7 Cracking (Fason and Barnes 2004).................................. 34 Figure 3.20 Girder Line 8 Cracking (Fason and Barnes 2004).................................. 34 Figure 3.21 Girder Line 9 Cracking (Fason and Barnes 2004).................................. 35 Figure 3.22 Cracked Girder with Continuity Reinforcement Details (Barnes et al. 2006)..................................................................... 37 Figure 3.23 Influence of Shear on Required Bottom-Flange Tensile Resistance (Barnes et al. 2006)............................................................... 39 Figure 3.24 Longitudinal Configuration Profile for FRP (Barnes et al. 2006) .......... 41 Figure 3.25 Cross-Sectional Configuration for FRP near the Continuity Diaphragm (Swenson 2003) ................................................................... 41 Figure 3.26 Cross-Sectional Configuration for FRP away from the Continuity Diaphragm (Swenson 2003) ................................................................... 42 Figure 4.1 ST-6400 Wheel Group Configuration .................................................... 45 Figure 4.2 ST-6902 Wheel Group Configuration .................................................... 46 Figure 4.3 ST-6400 Load Truck............................................................................... 47 Figure 4.4 ST-6902 Load Truck............................................................................... 47 Figure 4.5 Transverse Truck Position A .................................................................. 48 Figure 4.6 Transverse Truck Position B................................................................... 48 Figure 4.7 Transverse Truck Position C................................................................... 48 Figure 4.8 Longitudinal Stop Positions for Test Trucks .......................................... 49 Figure 4.9 Load Truck in Stopped Position ............................................................. 50 Figure 4.10 Installed ERSG........................................................................................ 53 Figure 4.11 Installed Deflectometer........................................................................... 53 Figure 4.12 Girder 7 Span10 East Face...................................................................... 56 Figure 4.13 Girder 7 Span 10 West Face ................................................................... 56 Figure 4.14 Girder 7 Span 11 East Face..................................................................... 57 xiv Figure 4.15 Girder 7 Span 11 West Face ................................................................... 57 Figure 4.16 Girder 8 Span 10 East Face..................................................................... 58 Figure 4.17 Girder 8 Span 10 West Face ................................................................... 58 Figure 4.18 Girder 8 Span 11 East Face..................................................................... 59 Figure 4.19 Girder 8 Span 11 West Face ................................................................... 59 Figure 4.20 Approximate Locations for Cross Sections 1 through 4......................... 61 Figure 4.21 Strain Gauge Instrumentation at Cross Sections 2 and 3........................ 61 Figure 4.22 Strain Gauge Instrumentation at Cross Sections 1 and 4........................ 62 Figure 4.23 Installed Deflectometer Locations .......................................................... 63 Figure 4.24 Installed Deflectometers ......................................................................... 64 Figure 4.25 Van Setup during Testing ....................................................................... 66 Figure 5.1 Cross-Sectional Dimensions for (a) BT54 and (b) Simplified BT54 ..... 68 Figure 5.2 Bridge Cross Section............................................................................... 70 Figure 5.3 Cross Section of Coarsest Mesh ............................................................. 71 Figure 5.4 Cross Section of 9-in. Mesh.................................................................... 72 Figure 5.5 Mesh Size Stress Comparisons ............................................................... 73 Figure 5.6 Mesh Size vs. Computer Time................................................................ 73 Figure 5.7 ABAQUS Bridge Model Depicting a 9-in Mesh.................................... 74 Figure 5.8 Cross Section of Continuity Diaphragm, Thickness = 16?..................... 75 Figure 5.9 Cross Section of Midspan Diaphragm, Thickness = 8?.......................... 76 Figure 5.10 Model Simulation of Installed Midspan Diaphragms............................. 76 Figure 5.11 Barrier Rail Cross Section ...................................................................... 77 Figure 5.12 Bridge End View Showing Barrier Rail ................................................. 78 Figure 5.13 Bridge End View Showing Bearing Pad................................................. 79 xv Figure 5.14 Examples of (a) an 8-Node Brick Element, (b) a 4-Node Shell Element,and (c) a 4-Node Tetrahedral Element (adapted from ABAQUS 2006)...................................................................................... 81 Figure 5.15 Mesh of Midspan Diaphragm ................................................................. 81 Figure 5.16 Cracked Girder with Seam Open Due to Loading.................................. 84 Figure 5.17 Girder Line 7 Cracks with Seams Superimposed (Fason and Barnes 2004) .................................................................................... 86 Figure 5.18 Girder Line 8 Cracks with Seams Superimposed (Fason and Barnes 2004) .................................................................................... 86 Figure 5.19 Prestressing Reinforcement Profile......................................................... 88 Figure 5.20 Truck Loading with Load Arrows Indicating Wheel Group Loads........ 91 Figure 5.21 Comparison between Models with and without Correctly Defined Seams ........................................................................................ 94 Figure 6.1 Bottom-Fiber Strain Data for the Uncracked Bridge Model?A7 Load Position ................................................................................................. 101 Figure 6.2 Bottom-Fiber Strain Data for the Uncracked Bridge Model?A9 Load Position ................................................................................................. 101 Figure 6.3 Bottom-Fiber Strain Data for the Uncracked Bridge Model?C7 Load Position ................................................................................................. 102 Figure 6.4 Bottom-Fiber Strain Data for the Uncracked Bridge Model?C9 Load Position ................................................................................................. 102 Figure 6.5 Bottom-Fiber Strain Data for the Cracked Bridge Model?A7 Load Position ................................................................................................. 104 Figure 6.6 Bottom-Fiber Strain Data for the Cracked Bridge Model?A9 Load Position ................................................................................................. 104 Figure 6.7 Bottom-Fiber Strain Data for the Cracked Bridge Model?C7 Load Position ................................................................................................. 105 Figure 6.8 Bottom-Fiber Strain Data for the Cracked Bridge Model?C9 Load Position ................................................................................................. 105 Figure 6.9 Bottom-Fiber Strain Data for the Model Refinement?A7 Load Position ........................................................................................ 108 xvi Figure 6.10 Bottom-Fiber Strain Data for the Model Refinement?A9 Load Position ........................................................................................ 109 Figure 6.11 Bottom-Fiber Strain Data for the Model Refinement?C7 Load Position ........................................................................................ 109 Figure 6.12 Bottom-Fiber Strain Data for the Model Refinement?C9 Load Position ........................................................................................ 110 Figure 6.13 Bottom-Fiber Deflections for the Model Refinement?A7 Load Position ....................................................................................... 110 Figure 6.14 Bottom-Fiber Deflections for the Model Refinement ?A9 Load Position ....................................................................................... 111 Figure 6.15 Bottom-Fiber Deflections for the Model Refinement ?C7 Load Position ....................................................................................... 111 Figure 6.16 Bottom-Fiber Deflections for the Model Refinement?C9 Load Position ....................................................................................... 112 Figure 6.17 Comparing the Models with and without Diaphragms?A7 Load Position ................................................................................................. 113 Figure 6.18 Comparing the Models with and without Diaphragms?A9 Load Position ................................................................................................. 113 Figure 6.19 Comparing the Models with and without Diaphragms?C7 Load Position ................................................................................................. 114 Figure 6.20 Comparing the Models with and without Diaphragms?C9 Load Position ................................................................................................. 114 Figure 6.21 Bottom-Fiber Strain Data for the Pre-Repair Model?A7 Load Position ................................................................................................. 116 Figure 6.22 Bottom-Fiber Strain Data for the Pre-Repair Model?A9 Load Position ................................................................................................. 117 Figure 6.23 Bottom-Fiber Strain Data for the Pre-Repair Model?C7 Load Position ................................................................................................. 117 Figure 6.24 Bottom-Fiber Strain Data for the Pre-Repair Model?C9 Load Position ................................................................................................. 118 Figure 6.25 Bottom-Fiber Strain Data for the Isotropic v. Lamina FRP Models?A7 Load Position ........................................................................................ 119 xvii Figure 6.26 Bottom-Fiber Strain Data for the Isotropic v. Lamina FRP Models?A9 Load Position ....................................................................................... 119 Figure 6.27 Bottom-Fiber Strain Data for the Isotropic v. Lamina FRP Models?C7 Load Position ....................................................................................... 120 Figure 6.28 Bottom-Fiber Strain Data for the Isotropic v. Lamina FRP Models?C9 Load Position ....................................................................................... 120 Figure 6.29 Bottom-Fiber Strain Data for the Pre- v. Post-Repair Models?A7 Load Position ................................................................................................ 122 Figure 6.30 Bottom-Fiber Strain Data for the Pre- v. Post-Repair Models?A9 Load Position ................................................................................................ 122 Figure 6.31 Bottom-Fiber Strain Data for the Pre- v. Post-Repair Models?C7 Load Position ................................................................................................ 123 Figure 6.32 Bottom-Fiber Strain Data for the Pre- v. Post-Repair Models?C9 Load Position ................................................................................................ 123 Figure 6.33 Bottom-Fiber Deflections for the Pre- v. Post-Repair Models?A7 Load Position ................................................................................................ 124 Figure 6.34 Bottom-Fiber Deflections for the Pre- v. Post-Repair Models?A9 Load Position ................................................................................................ 124 Figure 6.35 Bottom-Fiber Deflections for the Pre- v. Post-Repair Models?C7 Load Position ................................................................................................ 125 Figure 6.36 Bottom-Fiber Deflections for the Pre- v. Post-Repair Models?C9 Load Position ................................................................................................ 125 Figure 6.37 Bottom-Fiber Strain Data for the Concrete v. FRP for the Post-Repair Model?A7 Load Position ................................................................... 129 Figure 6.38 Bottom-Fiber Strain Data for the Concrete v. FRP for the Post-Repair Model (close-up view)?A7 Load Position ......................................... 129 Figure 6.39 Bottom-Fiber Strain Data for the Concrete v. FRP for the Post-Repair Model?A9 Load Position ................................................................... 130 Figure 6.40 Bottom-Fiber Strain Data for the Concrete v. FRP for the Post-Repair Model (close-up view)?A9 Load Position ......................................... 130 Figure 6.41 Bottom-Fiber Strain Data for the Concrete v. FRP for the Post-Repair Model?C7 Load Position ................................................................... 131 xviii Figure 6.42 Bottom-Fiber Strain Data for the Concrete v. FRP for the Post-Repair Model (close-up view)?C7 Load Position ......................................... 131 Figure 6.43 Bottom-Fiber Strain Data for the Concrete v. FRP for the Post-Repair Model?C9 Load Position ................................................................... 132 Figure 6.44 Bottom-Fiber Strain Data for the Concrete v. FRP for the Post-Repair Model (close-up view)?C9 Load Position ......................................... 132 Figure 7.1 Strain Profile?A7 Load Position, Section 2, Girder 7, East Face....... 134 Figure 7.2 Strain Profile?C9 Load Position, Section 3, Girder 8, West Face...... 135 Figure 7.3 E33 Strain Contour for the Cracked-with-Reinforcement Model, A7 Load Position, Girder 7, East Face ....................................................... 136 Figure 7.4 Strain Profile?A9 Load Position, Section 3, Girder 7, East Face....... 139 Figure 7.5 Strain Contours in FRP for Load Position A9 ...................................... 139 Figure A.1 Girder Numbering When Looking North ............................................. 161 Figure A.2 Longitudinal Stop Positions for Test Trucks ........................................ 162 Figure A.3 Transverse Truck Position A ................................................................ 163 Figure A.4 Transverse Truck Position B................................................................. 163 Figure A.5 Transverse Truck Position C................................................................. 164 Figure A.6 Installed Deflectometer Locations ........................................................ 167 Figure A.7 Strain Profile Cross Section Locations ................................................. 168 Figure A.8 Strain Gauge Locations......................................................................... 168 Figure B.1 Bottom-Fiber Deflections for the Model Refinement?A7 Load Position ................................................................................................ 170 Figure B.2 Bottom-Fiber Deflections for the Model Refinement?A9 Load Position ................................................................................................ 170 Figure B.3 Bottom-Fiber Deflections for the Model Refinement ?C7 Load Position ................................................................................................ 171 Figure B.4 Bottom-Fiber Deflections for the Model Refinement?C9 Load Position ................................................................................................ 171 xix Figure B.5 Bottom-Fiber Deflections for the Pre- v. Post-Repair Models?A7 Load Position ................................................................................................ 172 Figure B.6 Bottom-Fiber Deflections for the Pre- v. Post-Repair Models?A9 Load Position ................................................................................................ 172 Figure B.7 Bottom-Fiber Deflections for the Pre- v. Post-Repair Models?C7 Load Position ................................................................................................ 173 Figure B.8 Bottom-Fiber Deflections for the Pre- v. Post-Repair Models?C9 Load Position ................................................................................................ 173 Figure C.1 Bottom-Fiber Strain Data for the Model Refinement?A7 Load Position ................................................................................................. 175 Figure C.2 Bottom-Fiber Strain Data for the Model Refinement?A9 Load Position ................................................................................................. 175 Figure C.3 Bottom-Fiber Strain Data for the Model Refinement?C7 Load Position ................................................................................................. 176 Figure C.4 Bottom-Fiber Strain Data for the Model Refinement?C9 Load Position ................................................................................................. 176 Figure C.5 Bottom-Fiber Strain Data for the Pre- v. Post-Repair Models?A7 Load Position ................................................................................................ 177 Figure C.6 Bottom-Fiber Strain Data for the Pre- v. Post-Repair Models?A9 Load Position ................................................................................................ 177 Figure C.7 Bottom-Fiber Strain Data for the Pre- v. Post-Repair Models?C7 Load Position ................................................................................................ 178 Figure C.8 Bottom-Fiber Strain Data for the Pre- v. Post-Repair Models?C9 Load Position ................................................................................................ 178 Figure D.1 Strain Profile Cross Section Locations for Load Position A7 .............. 179 Figure D.2 Strain Profile?Load Position A7, Section 1, Girder 7, West Face...... 180 Figure D.3 Strain Profile?Load Position A7, Section 1, Girder 7, East Face....... 180 Figure D.4 Strain Profile?Load Position A7, Section 1, Girder 8, West Face...... 181 Figure D.5 Strain Profile?Load Position A7, Section 1, Girder 8, East Face....... 181 Figure D.6 Strain Profile?Load Position A7, Section 2, Girder 7, West Face...... 182 xx Figure D.7 Strain Profile?Load Position A7, Section 2, Girder 7, East Face....... 182 Figure D.8 Strain Profile?Load Position A7, Section 2, Girder 8, West Face...... 183 Figure D.9 Strain Profile?Load Position A7, Section 2, Girder 8, East Face....... 183 Figure D.10 Strain Profile?Load Position A7, Section 3, Girder 7, West Face...... 184 Figure D.11 Strain Profile?Load Position A7, Section 3, Girder 7, East Face....... 184 Figure D.12 Strain Profile?Load Position A7, Section 3, Girder 8, West Face...... 185 Figure D.13 Strain Profile?Load Position A7, Section 3, Girder 8, East Face....... 185 Figure D.14 Strain Profile?Load Position A7, Section 4, Girder 7, West Face...... 186 Figure D.15 Strain Profile?Load Position A7, Section 4, Girder 7, East Face....... 186 Figure D.16 Strain Profile?Load Position A7, Section 4, Girder 8, West Face...... 187 Figure D.17 Strain Profile?Load Position A7, Section 4, Girder 8, East Face....... 187 Figure E.1 Strain Profile Cross Section Locations for Load Position A9 .............. 188 Figure E.2 Strain Profile?Load Position A9, Section 1, Girder 7, West Face...... 189 Figure E.3 Strain Profile?Load Position A9, Section 1, Girder 7, East Face....... 189 Figure E.4 Strain Profile?Load Position A9, Section 1, Girder 8, West Face...... 190 Figure E.5 Strain Profile?Load Position A9, Section 1, Girder 8, East Face....... 190 Figure E.6 Strain Profile?Load Position A9, Section 2, Girder 7, West Face...... 191 Figure E.7 Strain Profile?Load Position A9, Section 2, Girder 7, East Face....... 191 Figure E.8 Strain Profile?Load Position A9, Section 2, Girder 8, West Face...... 192 Figure E.9 Strain Profile?Load Position A9, Section 2, Girder 8, East Face....... 192 Figure E.10 Strain Profile?Load Position A9, Section 3, Girder 7, West Face...... 193 Figure E.11 Strain Profile?Load Position A9, Section 3, Girder 7, East Face....... 193 Figure E.12 Strain Profile?Load Position A9, Section 3, Girder 8, West Face...... 194 Figure E.13 Strain Profile?Load Position A9, Section 3, Girder 8, East Face....... 194 Figure E.14 Strain Profile?Load Position A9, Section 4, Girder 7, West Face...... 195 xxi Figure E.15 Strain Profile?Load Position A9, Section 4, Girder 7, East Face....... 195 Figure E.16 Strain Profile?Load Position A9, Section 4, Girder 8, West Face...... 196 Figure E.17 Strain Profile?Load Position A9, Section 4, Girder 8, East Face....... 196 Figure F.1 Strain Profile Cross Section Locations for Load Position C7............... 197 Figure F.2 Strain Profile?Load Position C7, Section 1, Girder 7, West Face...... 198 Figure F.3 Strain Profile?Load Position C7, Section 1, Girder 7, East Face ....... 198 Figure F.4 Strain Profile?Load Position C7, Section 1, Girder 8, West Face...... 199 Figure F.5 Strain Profile?Load Position C7, Section 1, Girder 8, East Face ....... 199 Figure F.6 Strain Profile?Load Position C7, Section 2, Girder 7, West Face...... 200 Figure F.7 Strain Profile?Load Position C7, Section 2, Girder 7, East Face ....... 200 Figure F.8 Strain Profile?Load Position C7, Section 2, Girder 8, West Face...... 201 Figure F.9 Strain Profile?Load Position C7, Section 2, Girder 8, East Face ....... 201 Figure F.10 Strain Profile?Load Position C7, Section 3, Girder 7, West Face...... 202 Figure F.11 Strain Profile?Load Position C7, Section 3, Girder 7, East Face ....... 202 Figure F.12 Strain Profile?Load Position C7, Section 3, Girder 8, West Face...... 203 Figure F.13 Strain Profile?Load Position C7, Section 3, Girder 8, East Face ....... 203 Figure F.14 Strain Profile?Load Position C7, Section 4, Girder 7, West Face...... 204 Figure F.15 Strain Profile?Load Position C7, Section 4, Girder 7, East Face ....... 204 Figure F.16 Strain Profile?Load Position C7, Section 4, Girder 8, West Face...... 205 Figure F.17 Strain Profile?Load Position C7, Section 4, Girder 8, East Face ....... 205 Figure G.1 Strain Profile Cross Section Locations for Load Position C9............... 206 Figure G.2 Strain Profile?Load Position C9, Section 1, Girder 7, West Face...... 207 Figure G.3 Strain Profile?Load Position C9, Section 1, Girder 7, East Face ....... 207 Figure G.4 Strain Profile?Load Position C9, Section 1, Girder 8, West Face...... 208 Figure G.5 Strain Profile?Load Position C9, Section 1, Girder 8, East Face ....... 208 xxii Figure G.6 Strain Profile?Load Position C9, Section 2, Girder 7, West Face...... 209 Figure G.7 Strain Profile?Load Position C9, Section 2, Girder 7, East Face ....... 209 Figure G.8 Strain Profile?Load Position C9, Section 2, Girder 8, West Face...... 210 Figure G.9 Strain Profile?Load Position C9, Section 2, Girder 8, East Face ....... 210 Figure G.10 Strain Profile?Load Position C9, Section 3, Girder 7, West Face...... 211 Figure G.11 Strain Profile?Load Position C9, Section 3, Girder 7, East Face ....... 211 Figure G.12 Strain Profile?Load Position C9, Section 3, Girder 8, West Face...... 212 Figure G.13 Strain Profile?Load Position C9, Section 3, Girder 8, East Face ....... 212 Figure G.14 Strain Profile?Load Position C9, Section 4, Girder 7, West Face...... 213 Figure G.15 Strain Profile?Load Position C9, Section 4, Girder 7, East Face ....... 213 Figure G.16 Strain Profile?Load Position C9, Section 4, Girder 8, West Face...... 214 Figure G.17 Strain Profile?Load Position C9, Section 4, Girder 8, East Face ....... 214 1 CHAPTER 1: INTRODUCTION 1.1 BACKGROUND In 1992, large and unexpected cracks were discovered in prestressed concrete girders of several recently-constructed bridge spans of I-565 in Huntsville, Alabama. Once restrained thermal deformations of the superstructure were determined to be the cause, several attempts were made to alleviate the problem over the course of the next few years. Since they were discovered, the progression of the cracks has been closely tracked by Alabama Department of Transportation (ALDOT) employees. Swenson (2003) proposed a repair using externally bonded, fiber-reinforced polymer (FRP) reinforcement. To fully assess the efficacy of this repair system, load tests were required before and after the repair. This thesis describes the development of a finite-element model (FEM) of a two- span portion of I-565. Simulations were conducted for conditions both before and after installation of the FRP reinforcement. Analytical results generated from these models shed light on the structural behavior of the damaged bridge. In addition, the model of the post-repair bridge has been used to predict changes in behavior that should be measured when the repaired structure is load tested. 1.2 OBJECTIVES The purpose of the investigation reported herein was threefold: 2 1. Use finite-element modeling to accurately simulate the behavior of a damaged, two-span unit of the I-565 superstructure. 2. Use data collected in a load test to verify the accuracy of the model and refine it as necessary. 3. Use the model to predict the performance of the two-span unit after installation of the fiber-reinforced polymer repair. 1.3 RESEARCH APPROACH ABAQUS/CAE was used to create a finite-element model of the two-span superstructure unit under investigation. Data collected from the pre-repair load test was used to validate the model?s response. Once a model was developed that described the current behavior of the bridge with reasonable accuracy, the simulated FRP repair was added to the model, and the results were analyzed for prediction of post-repair behavior. 1.4 THESIS OUTLINE A brief summary of previous studies conducted using finite-element modeling of multigirder bridges is presented in Chapter 2. Chapter 3 presents a historical overview of the I-565 bridge construction and condition, along with details of the bridge structure. Load testing of the damaged structure is described in Chapter 4. Results of this testing were used to refine the FEM bridge model. Details of the ABAQUS models are described in Chapter 5. Results of the load tests and the finite-element bridge models are presented in Chapter 6. Chapter 7 includes a discussion of the significance of these results and a forecast of the performance of the repaired structure based on the 3 analytical results. Finally, Chapter 8 consists of a summary of the study as well as the resulting conclusions and recommendations. 4 CHAPTER 2: FINITE-ELEMENT MODELING OF MULTIGIRDER BRIDGES 2.1 INTRODUCTION As the bulk of the investigation reported herein involves finite-element modeling (FEM) of a bridge deck supported by multiple longitudinal girders, it is important to first briefly explore the work which has already been conducted on this subject. There are myriad options from which to choose when selecting both the components and the construction approach for the model. From the very basic question of which structural elements to include to the more advanced question of mesh size, many issues need to be considered before beginning. It is best to learn from the experiences of others as much as possible. This chapter consists of a review of previous research that involved FEM of multigirder bridges, including comparisons with load-test results. 2.2 AASHTO LRFD REQUIREMENTS Section 4.6.3 of the AASHTO LRFD Bridge Design Specifications (American Association of State Highway and Transportation Officials 2004) provides minimum requirements for using refined methods of analysis. First, consideration is given to aspect ratios of elements, positioning and number of nodes, and other topological features which might affect the accuracy of the solution. Though normally neglected, a continuous railing, barrier, or median may be considered structurally active if full composite behavior is certain. 5 For the deck, flexural and torsional deformation must be considered, but vertical shear deformation need not be. The wheel loads on the deck should be modeled as patch loads distributed over an area approximating the wheel contact surface. For the material properties of the deck elements, if a bridge deck is solid with uniform or near- uniform depth and the stiffness is approximately equal in every in-plane direction, it can be considered isotropic (AASHTO 2004). The maximum acceptable aspect ratio of finite elements is 5.0. Sudden changes in either size or shape of finite elements should be avoided. The nodal loads need to be statically equivalent to the physical loads applied. At least five nodes per beam should be employed, though nine is preferable. For finite-element analyses which involve plate or beam elements, it is best to maintain the relative vertical distances between elements. If this is impractical, longitudinal and transverse elements may be placed at the midthickness of the plate-bending elements if the eccentricities are accounted for in the equivalent properties of the composite sections (AASHTO 2004). Inelastic behavior must be restricted to the flexure of beams or girders. Inelastic behavior resulting from shear and/or uncontrolled buckling is not allowed (AASHTO 2004). 2.3 FINITE-ELEMENT MODELING OF BRIDGES WITHOUT LOAD TESTING VERIFICATION Tedesco, Stallings, and Tow (1995) used dynamic FEM analysis in ADINA? to investigate a single-span, multigirder steel bridge with no skew. The three structural components that they included in their model were the reinforced-concrete bridge deck, the steel girders, and the steel diaphragms. For the deck slab, four-node shell elements 6 with five degrees-of-freedom (DOF) per node were chosen. These were determined to accurately reflect the membrane stresses caused by the primary flexure of the bridge while permitting the slab to experience out-of-plane flexure. In order to sufficiently represent the cracking which the bridge deck had already experienced, two approaches were utilized: the modulus of elasticity was altered to represent the effective stiffness of the slab, and the deck slab elements were defined as an orthotropic material. The report does not specify the manner used to determine the effective stiffness of the slab. Because the effects of the diaphragms were under investigation in this study, it was important for those effects to be readily available for analysis. Also, it was important that those effects be accurately reflected. This meant that the out-of-plane flexure that the girders experienced as a result of the presence of the diaphragms needed to be considered. For this reason, the girder web and flanges were modeled independently of one another. The stresses in the web were judged to not greatly affect the total girder bending moment, so three-node plate bending elements were used for the web. Because of the sensitivity of the bending moment to flange stresses, the flanges were modeled with the same shell elements that were used for the deck. This allowed for the in-plane stress as well as the slight torsional and flexural stiffness of the flanges to be accounted for by the model. The ratio of element length to girder length was approximately 1:60. The diaphragms were modeled with two-node beam elements. One line of elements was created at the mid-height of the diaphragm, and a rigid link, illustrated in Figure 2.1, was used to create nodes on the ends that were representative of both the top and the bottom of the actual diaphragm. This allowed for the total height of the diaphragms to be considered. These nodes were then attached to the girder by truss elements. The 7 element stiffness was determined by considering the stiffness of the connection plate in the bridge. Figure 2.1 Diaphragm-to-Girder Connection Detail Using a Rigid Link (Tedesco, Stallings, and Tow 1995) The type of rigid links that were used in the diaphragm was employed elsewhere in the model as well. These links were used to bridge the physical gap between elements to establish composite behavior in the model. This purpose was served by connecting the web to the flanges of the girders and the flanges to the deck. Dynamic analyses were conducted modeling the truck wheel loads as concentrated loads acting at the nodes of the deck slab elements. The results indicated that the removal of diaphragms would not have a significant effect on the bridge response. Increases in flexural stress and vertical deflection for the model without diaphragms over those for the model with diaphragms were found to be 8 and 9 percent, respectively, for the most highly stressed girders. Maximum positive deck slab bending moment increased by only 14 percent, and maximum negative deck slab bending moment decreased by almost one-half. Rigid Link 8 Zokaie (2000) presented a report on the development of live load distribution formulas for the AASHTO LRFD Bridge Design Specifications. Finite-element analyses of typical bridges were used to investigate the sensitivity of live load distribution to specific parameters such as girder spacing, span length, girder thickness, and slab thickness. Diaphragm effects were neglected. The deck slab was modeled using plate elements, and Zokaie states that the model also accounted for the eccentricity of the girders. New distribution formulas were generated based on the results of the sensitivity analyses. Accuracy of the generated formulas was evaluated by comparison with the results of finite-element models of representative bridges, but no experimental verification was reported by Zokaie (2000). Huo, Wasserman, and Zhu (2004) also used FEM to explore live load distribution of girder bending moment for a variety of bridge structures. Modeled using ANSYS? 5.7, all superstructures were analyzed in the linearly elastic range. Four-node shell elements that had six DOF per node were used to model the bridge deck slab. These were selected to incorporate both membrane and bending stiffnesses and in- and out-of- plane bending. The precast concrete girders were modeled using three-dimensional, two-node beam elements with six DOF per node. The girder elements and the slab elements were ?integrated? to reflect composite behavior. Hinges and rollers modeled the bridge supports. The finite-element results thus obtained were used as a baseline in determining whether a simplified method of calculating live load distribution factors in bridges was sufficiently accurate. The procedure, known as Henry?s method, compared favorably 9 with the AASHTO LRFD and the AASHTO standard methods as well as with the FEM results (Huo, Wasserman, and Zhu 2004). Green, Yazdani, and Spainhour (1994) created ANSYS? FEMs to study the effects of intermediate diaphragms, temperature variability, bearing stiffness, and girder skewness on precast, prestressed bridge girders. The element they selected to model the bridge girders, deck slab, and diaphragms was a three-dimensional reinforced concrete element. Though this element was capable of simulating concrete cracking and crushing, plastic deformation, and creep, these properties were not utilized because the girder behavior under the assumed service load fell well within the elastic region of the members. The connection between the girders and the diaphragms was assumed to be rigid as a result of monolithically placed concrete. Unlike the study conducted by Tedesco, Stallings, and Tow (1995), this study showed that for straight bridges, intermediate diaphragms helped to stiffen the girders and reduce maximum deflection by about 18 19 percent. While the diaphragms helped to stiffen girders in bridges with increased skew angles as well, the reduction in deflection decreased with increased skew angles (Green, Yazdani, and Spainhour 2004). 2.4 FINITE-ELEMENT MODELING OF BRIDGES WITH LOAD TESTING VERIFICATION Mabsout et al. (1997) published a comparison of four different FEM techniques used to calculate wheel load distribution factors. Using SAP90? and ICES-STRUDL II?, they created four models of a bridge made with steel girders and a concrete slab deck. The ratio of element length to girder length was approximately 1:16, which represents a significantly coarser mesh than that employed by Tedesco, Stallings, and Tow (1995). 10 For the first three models, the bridge deck was modeled using quadrilateral shell elements with five DOF per node (Mabsout et al. 1997). The first two models employed a space-frame member with six DOF per node to model the steel girders. In the first model, the centroid of the girder coincided with the centroid of the concrete slab, but in the second model an eccentricity between those centroids was imposed using a rigid link. The third model used a quadrilateral shell element for the girder web and a space-frame element for the girder flange, and once again a rigid link was used to model the eccentricity between the flange and bridge deck. Their fourth FEM used isotropic eight-node brick elements for the deck slab and quadrilateral shell elements for the girders. The models employed gave an error of approximately 5 percent when compared to the total bending moment expected at the critical section of the bridge. Expected bending moments were calculated using both strain and deflection readings from numerous load tests. From the four models employed, Mabsout et al. concluded that when investigating the load-carrying capacity of noncomplex, straight steel girder bridges, quadrilateral shell elements are sufficiently accurate for the concrete slab deck and concentric space frame elements for the girders. The other cases could be employed to accurately realize the actual boundary conditions. Barr, Eberhard, and Stanton (2001) reported on SAP2000? finite-element models that they created to evaluate the procedures for computing flexural live-load distribution factors found in AASHTO-LRFD, AASHTO Standard, and the Ontario Highway Bridge Design Code (OHBDC). For their initial model, they paid special attention to the mesh size. The need to simulate the loading with a variety of loading conditions 11 and bridge skew angles dictated the need for a fine element mesh in the deck. They therefore selected a node spacing of roughly 2 ft in the transverse direction and 1 ft in the longitudinal direction. These correspond to a ratio of element length to girder length of approximately 1:80 for two of the spans and 1:137 for one of the spans. This represents a finer mesh than those used by either Tedesco, Stallings, and Tow (1995) or Mabsout et al. (1997). A series of shell elements was used to represent the bridge deck, and rigid links connected the deck to the frame elements used to model the prestressed concrete girders. Rather than explicitly modeling the prestressing strands in the girders, the values of the modulus of elasticity for the various components of the finite-element model were measured from material tests. The intermediate diaphragms and the pier diaphragms were modeled using shell elements. The pier diaphragms were then connected, with rigid constraints, to the pier caps, which were modeled with 1-foot-long frame elements as were the columns. The elastomeric bearings were represented by releasing horizontal displacements. In conducting their investigation, Barr, Eberhard, and Stanton created a series of progressively more detailed models. Their original model, which was very similar to the model used to develop the AASHTO LRFD Specifications, did not include lifts (deck build-up over the girders), intermediate diaphragms, end diaphragms, or span continuity. Each ensuing model then added one of these elements. Model 2 included lifts. Model 3 built on Model 2 and added intermediate diaphragms. Model 4 then included end diaphragms. Finally, in Model 5, two adjacent spans were added, and the three spans were made continuous. 12 From the progression of the model, the authors were able to study the effects of lifts, intermediate diaphragms, end diaphragms, and span continuity. They concluded that incorporating the lift slightly increased the composite girder stiffness by increasing the effective thickness of the deck, which therefore increased the transverse bending stiffness relative to the longitudinal stiffness. The inclusion of the intermediate diaphragms had less impact than any of the other three variables, though at high skew angles, they were found to be slightly beneficial to the exterior girders. The end diaphragms were found to reduce the positive midspan moment, especially with a high skew angle and a torsionally stiff end diaphragm. Finally, the study found that continuity increased the longitudinal stiffness but did not affect the transverse stiffness (Barr, Eberhard, and Stanton 2001). The distribution factors calculated from Model 1 were found to be, on average, 6 percent lower than those calculated using the AASHTO LRFD Specification. This is not unexpected as the code was based on a single-span model similar to Model 1. Those calculated from Model 5, on the other hand, were approximately 28 percent lower than those calculated using the LRFD code. Similarly, the distribution factors calculated using the AASHTO Standard Specification were closer to those calculated from Model 1 than Model 5. This is also due to the fact that the AASHTO Standard Specifications do not account for the effect of skew (Barr, Eberhard, and Stanton 2001). The final model, Model 5, was judged to be most closely representative of the physical structure being modeled. In comparing moments calculated from Model 5 and those calculated from measured strains, for two of the bridge girders the magnitude of error between measured and computed moments was about the same as the discrepancy 13 between individual strain gauge readings. The largest difference was less than 6 percent, which provided strong evidence that the finite-element model ?reflected well the behavior of the prototype bridge? being studied (Barr, Eberhard, and Stanton 2001). Eamon and Nowak (2002) used ANSYS? to study the effects of multiple secondary elements, including diaphragms, on load distribution in both the elastic and inelastic ranges. They studied the effects of diaphragms for both composite steel girder bridges and prestressed concrete girder bridges. Two types of FEMs were created for their study: a simplified model, which was utilized to analyze maximum girder moments and deflections, and a more detailed model, which was used to analyze deck behavior. The simplified concrete models used three-dimensional line elements with six DOF per node to simulate the bridge girders and diaphragms. These were attached directly to the bottom of the deck, which like the sidewalk and barriers was modeled using solid elements. The solid elements used to model the deck were eight-node brick elements with three DOF per node. The reinforcing steel was not found to have a significant effect on the deck stiffness, so it was not explicitly included in the elastic analysis. The model allowed no slip between the deck and the girders. All elements in the detailed concrete models were brick elements with a mesh density that was finer than that of the simplified models. The FEM results matched field-measured deflections and strains within 5 percent. The study results indicate that diaphragms are more effective at wider girder spacings and longer spans, and an increased number of diaphragms has no significant effect. The diaphragms were found to reduce the maximum girder moment by up to 13 percent 4 percent on average. The diaphragms were found to ?pull down exterior girders and 14 raise interior girders,? which evens girder deflections (Eamon and Nowak 2002). The study concluded that the presence of secondary elements is significant to the bridge behavior. Fu and Lu (2003) reported on a nonlinear analysis using FORTRAN? and RESIDU?. The authors explain that although the steel girders in the bridge that they investigated remained within their elastic range, the concrete deck could not be adequately represented by a linearly elastic model, because concrete is a material that exhibits nonlinear behavior with a very small tensile strength. The flanges of the rolled steel I-girders were modeled with plate elements while the web was modeled with plane-stress elements. Both of these were eight-node, isoparametric, quadrilateral elements. The deck was also modeled using isoparametric quadrilateral elements. Effects of deck cracks that were predicted through stress analysis of Gauss points were distributed homogeneously throughout the entire element by modeling the element as weaker than the surrounding, uncracked elements. This weakness was modeled by setting the modulus of elasticity of the cracked element, and the stress at the affected Gauss points, to zero. The reinforcement of the deck was also explicitly modeled. Each set of reinforcement was represented by a smeared two-dimensional membrane layer with equivalent thickness, which was modeled using an isoparametric plane-stress element. This embedded membrane layer then acted ?as an integral part of the element.? The results of the study show that while the deflection results of the finite-element method are close to those measured experimentally, the results from the transformed 15 area method, which is the traditional AASHTO Standard design method, are not. The authors did not report any comparisons that showed that a linear elastic model was deficient, and the results of the nonlinear analysis are not compared to results from a linear analysis of the same model. Zhou, Rizos and Petrou (2003) presented the results of an investigation into the effects of various structural components: (a) composite action, (b) girder spacing to slab thickness ratio, and (c) presence of diaphragms. They also noted the limitation of previous studies regarding the nonlinearity of concrete. To correct this oversight, they constructed models in ANSYS?, which was readily available. The ANSYS? Solid 65 element used to model the concrete deck ?accommodates cracking and crushing of concrete and yielding of the reinforcement, among other non- linear characteristics.? It is limited, however, in that the reinforcement is ?smeared throughout the element? and ?full bond is assumed between reinforcement and concrete.? Shell elements and rigid links were used to model the steel girders and steel diaphragms, respectively. The results of the study of the effects of composite action and girder spacing to slab thickness ratio do not differ significantly from previous, linear studies. In contrast, the nonlinear behavior of the concrete does affect the results of the diaphragm analysis as compared to that found in the literature Zhou, Rizos and Petrou (2003) reviewed. This effect is only noted, however, at significantly large girder loads. Wan et al. (2004) used ANSYS? to investigate four parameters for service load conditions, including the effect of diaphragms. Eight-node shell elements were used to model the glass fiber-reinforced polymer (GFRP) deck flanges and webs and the steel 16 girders. A link element was used to model the steel diaphragms. The authors concluded that the diaphragms prevent girder rotation, increase stiffness of the entire structure, and assist slightly in the transverse load distribution through the deck. They noted, however as did Zhou, Rizos, and Petrou (2003) that the presence of diaphragms has minimal effect on the net deflection when the load is small. Xia and Brownjohn (2004) published a technique for model updating that ?can produce a systematically validated FE model by correcting uncertainties from modeling, geometry, physical parameters, and analysis.? One important aspect of this technique is to accurately model uncertainties in a structure. One approach that they propose is to model damaged zones with ?weak? elements which cover the area of the damage and are refined, using the measured data, to quantify the residual stiffness and load-carrying capacity. For finding the effective modulus of elasticity and other material properties for the structure in the undamaged state, a two-step approach was presented. First, prior to loading, a model for the uncracked structure was validated using experimental results. This provided a reasonable baseline from which to identify damage. Second, after loading, the dynamically measured data was used to post-validate the model. The authors cautioned that ?if the FE model validating goes straight to the damaged case, then the identified damage may reflect uncertain structural parameters not associated with damage; furthermore, the updating may not converge because of too large differences between the modal properties generated by the FE model and those measured? (Xia and Brownjohn 2004). The load-carrying capacity of the bridge can then be systematically validated using dynamics-based model updating techniques. 17 Chung, Liu, and Sotelino (2006) utilized ABAQUS? to investigate the effects of secondary elements on the lateral load distribution of steel girder bridges and, through nonlinear analysis, to explore the effects of deck cracking on load distribution. The concrete deck was modeled using eight-node shell elements. The steel girders and diaphragms were modeled using three-node beam elements. The connections between the deck and the girders as well as between the girders and the diaphragms were established through rigid links. The maximum difference between the predicted and the experimentally measured deflections was 9 percent at midspan of the exterior girder. The maximum difference between the calculated and measured strains was less than 7 percent. The study found that modeling the diaphragms resulted in a load distribution factor that was as much as 12 percent less than the load distribution factor determined according to the AASHTO LRFD specifications. Like Eamon and Nowak (2002), the authors concluded that the presence of secondary elements significantly helps the transverse load distribution of girder bridges. In addition, they observed that transverse deck cracking reduces the stiffness of the bridge but does not significantly affect transverse distribution of moments to girders (Chung, Liu, and Sotelino 2006). 2.5 SUMMARY OF THE FINDINGS When creating a finite-element model to study the live load effects on various bridge components, there are certain minimum requirements which must be met. These minimum requirements are well-summarized in the AASHTO LRFD Bridge Design Specifications. When selecting elements, the main concern is that the element configuration selected has a sufficiently fine mesh and sufficient degrees of freedom to 18 account for the movement of the girders or the bridge deck under the loading. The selection of element type, such as beam element or plate-bending element, is not as critical as the effects allowed for by the element selected. The studies conflict as to the significance of the inclusion of secondary elements such as diaphragms on the bridge response, and there is insufficient information to conclude that the nonlinearity of the concrete deck needs to be accounted for in order to achieve an accurate model. 19 CHAPTER 3: BRIDGE DESCRIPTION AND HISTORY 3.1 INTRODUCTION The prestressed concrete girder bridge that was studied is located in Huntsville, Alabama along northbound bridge Spans 10 and 11 of I-565. This chapter summarizes the history of the structure, its current conditions, and the proposed fiber-reinforced polymer repair system. 3.2 HISTORICAL OVERVIEW Construction of the elevated Interstate Highway 565 bridge structures began in January 1988 and was completed in March 1991 (ALDOT 1994). Single span and multispan continuous units were erected for both the northbound and southbound lanes. Bridges consist of either steel or prestressed concrete girders supporting a cast-in-place composite reinforced concrete (RC) deck. Most of the prestressed concrete girders are bulb-tee girders, either AASHTO-PCI BT54 or BT63, which were made continuous for live load by means of the cast-in-place deck and diaphragms. The other prestressed concrete girders are standard AASHTO girders (Swenson 2003). During a routine bridge inspection in 1992, hairline cracks were discovered in some of the bulb-tee girders. Because hairline cracks often form at early ages in prestressed concrete girders, this did not necessarily indicate a serious problem. Eighteen months later, another inspection was conducted in March and April of 1994. Inspectors discovered that many of the earlier cracks had propagated and widened (ALDOT 1994). 20 Typical crack widths ranged from 0.002 in. to 0.25 in. Figure 3.1 presents the pattern of cracking found in 1994 in one 54-in. girder of Span 5 (Barnes et al. 2006). Many of the cracks were inclined and as a result intersected transverse reinforcing bars. These inclined cracks were limited to a width of approximately 0.06 in. In the bottom flange, however, the cracks were vertical and therefore crossed only the longitudinal prestressing strands. These larger cracks (widths up to 0.25 in.), such as those found on the girders shown in Figure 3.2, were visible from the ground (Barnes et al. 2006). Figure 3.1 Typical Pattern of Cracking in End Region of Precast Girder (Barnes et al. 2006) Note: The bolder line on the bottom-flange cracks indicates a greater crack width. Monitoring to determine the cause of the cracks commenced. After several weeks of load testing, ALDOT personnel concluded that traffic and wind loads were not the most likely causes of the cracks. Traffic loading was an unlikely cause because the largest cracks formed where service live loads would be expected to induce compression (Barnes et al. 2006). The temperature gradient between the bridge deck and the Girder 5, Span 5, West Face Crack Pattern Precast BT-54 girder Cast-in-place deck Cast-in-place continuity diaphragm 21 underside of the superstructure was the suspected cause. The temperature gradient caused an upward deflection of the superstructure which was restrained at interior supports. This resulted in positive moments at the continuous girder ends which ultimately caused the cracks (Swenson 2003). To prevent a total collapse of the structure in the event that the girders failed, temporary, or false, supports were installed under all spans which contained cracked girders (Barnes et al. 2006). The supports were installed within 10 ft of the support bent (Swenson 2003). A small space was left between the top of the false supports and the bottom of the girders to allow for the deflection of the girders (Gao 2003). Two measures were also attempted to alleviate the problem. As shown in Figure 3.3, the cracks were injected with epoxy. Unfortunately, this proved to be relatively ineffective as new cracks later formed near some of the epoxy-injected cracks (Gao 2003). The new cracks had widths of 0.002 in. to 0.030 in. These new cracks discouraged ALDOT personnel from considering epoxy injection as a feasible final solution. The second measure to be attempted was to release some of the prestressed girders from the continuity diaphragm. To do this, the continuity diaphragm was sawed around the girder, thus allowing the girder to move independently of the diaphragm and effectively changing it from a continuous to a simply supported beam. This was performed at Bent 11, which supports the continuity diaphragm for the two-span unit modeled in the current study. The sawing technique proved too difficult and was abandoned after cutting portions of the diaphragm at only a few girder ends (Swenson 2003). 22 Figure 3.2 Cracked Pretensioned Bulb-Tee Girders (Barnes et al. 2006) Figure 3.3 Epoxy-Injected Cracks 23 Swenson (2003) proposed a fiber-reinforced polymer (FRP) repair technique to restore structural capacity. To determine the efficacy of the repair technique, load tests needed to be conducted before and after installation of the FRP. The pre-repair load tests occurred on June 1 and 2, 2005. The FRP repair system has been designed, but ALDOT has not yet accepted bids for the installation contract. Structural details of the I-565 bridge structure are presented in Section 3.3. Section 3.4 includes a brief summary of research that was conducted to determine the cause of the cracking and its potential ramifications with respect to the structural integrity of the bridge. 3.3 DETAILS OF THE CRACKED I-565 BRIDGE STRUCTURE 3.3.1 Bridge Geometry The bridge section investigated for this report consists of a two-span bridge portion composed of nine prestressed concrete bridge girders made continuous for live load and a cast-in-place reinforced concrete (RC) bridge deck. Figure 3.4 presents a cross-sectional view of the bridge. The bridge deck is 70.75- feet wide with a thickness of 6.5 in., not including the variable-depth build-up over each girder. The bridge deck was designed to act compositely with the girders. This composite action was accomplished by extending the girder stirrups into the deck slab and by roughening of the top surface of the girders (Swenson 2003). The nine girders are spaced 96 in. center-to-center. Figure 3.5 shows the dimensions of the BT54 girder used. A cast-in-place traffic barrier rail runs the length of the bridge on both edges of the deck (ALDOT 1987). 24 Figure 3.4 Bridge Cross Section (Swenson 2003) 24 8? ? 0? AASHTO BT54 girders Cast-in-place concrete barrier 3? - 4?? 64? ? 0? 70? ? 9? 6.5? 25 Figure 3.5 BT54 Cross Section Dimensions (Swenson 2003) Figures 3.6 and 3.7 depict the plan view of the portion under investigation. The total length of the two-span continuous unit is 200 ft. Figure 3.8 presents an elevation view of the two-span continuous unit. The bridge girders are BT54s with both straight and draped prestressing strands. See Figures 3.9 and 3.10 for bonding configurations and strand placement at the girder end and the girder midspan, respectively. As depicted in Figure 3.11, the bridge girders are numbered one through nine, proceeding from the west side to the east side of the bridge. Continuity was created along a girder line by casting a continuity diaphragm which restrained the rotation of the adjacent girder ends. A portion of the deck slab was cast simultaneously with the continuity diaphragms. The vertical reinforcement present in the continuity diaphragms consists of No. 4 and No. 6 mild steel reinforcing bars. Figure 3.12 depicts bent No. 6 reinforcing bars which were intended to provide 3.5? 2? 2? 36? 4.5? 6? 26? 42? 18? 10? 2? ?? chamfer 54? 6? 26 positive moment continuity extending from the ends of the prestressed concrete bulb- tee girders. Eight bars extend from 41 in. into each girder end to 8 in. into the continuity diaphragm. A vertical leg located in the continuity diaphragm is 12 in. long (Swenson 2003). 3.3.2 Crack Locations In April 2004, a team from Auburn University conducted a thorough study of the current conditions of the two-span continuous bridge unit. This study included determination of the locations of the cracks on both faces and both spans of all nine girders. For illustrations of the locations of the cracks, see Figures 3.13-3.21 (Fason and Barnes 2004). The figures differentiate between cracks that have been sealed with epoxy and those that have not. Figure 3.6 Plan View of the Two-Span Continuous Unit (ALDOT 1987) Span 10 Span 11 27 Figure 3.7 Detailed Plan View of the Two-Span Continuous Unit (ALDOT 1987) 27 Span 10 Span 11 28 Figure 3.8 Elevation View of the Two-Span Continuous Unit (ALDOT 1987) Figure 3.9 Girder End Strand Pattern (Swenson 2003) 3 @ 2? 2.5? 5 @ 2? 5 @ 2? 5 @ 2? 2 @ 1.125? 8? 8? 2? 5? 3? Fully bonded tendon (0.5? Special) Debonded tendon (48? debond length, 0.5? Special) Debonded tendon (168? debond length, 0.5? Special) Fully bonded tendon (7/16?) Span 10 Span 11 29 Figure 3.10 Girder Midspan Strand Pattern (Swenson 2003) Girder Line No. N Bent 11 Bent 10 1 2 3 4 5 6 7 8 9 Span 11Span 10 Bent 12 Area Being Inspected Continuity Diaphragm Girder End Figure 3.11 Girder Numbering System (Fason and Barnes 2004) Fully bonded tendon (0.5? Special) 2 @ 1.125? 6 @ 2? 5 @ 2? 5 @ 2? 2 @ 3? 8? 8? 2? 5? Fully bonded tendon (7/16?) 2.5? 30 Figure 3.12 Bent Bar Detail at Continuity Diaphragm (Swenson 2003) 49? 12? MK-651 bent bar detail 3? 8? Black ? 9? x 24.5? x ?? Elastomeric Bearing Pad Checked ? ?? Premolded Bituminous Filler ?? diameter dowel, 21? long MK-651 bent bar (8 per girder end made continuous) C L 31 Figure 3.13 Girder Line 1 Cracking (Fason and Barnes 2004) Figure 3.14 Girder Line 2 Cracking (Fason and Barnes 2004) 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 2 - Span 10 - West Face 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 2 - Span 11 - West Face No cracking No cracking = sealed = unsealed 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 2 - Span 10 - East Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 2 - Span 11 - East Face No cracking No cracking 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 1 - Span 10 - East Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 1 - Span 11 - East Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 1 - Span 10 - West Face 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 1 - Span 11 - West Face Bolt = sealed = unsealed 32 Figure 3.15 Girder Line 3 Cracking (Fason and Barnes 2004) Figure 3.16 Girder Line 4 Cracking (Fason and Barnes 2004) = sealed = unsealed = sealed = unsealed 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 3 - Span 10 - East Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 3 - Span 11 - East Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 3 - Span 10 - West Face 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 3 - Span 11 - West Face 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 4 - Span 10 - East Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 4 - Span 11 - East Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 4 - Span 10 - West Face 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 4 - Span 11 - West Face 33 Figure 3.17 Girder Line 5 Cracking (Fason and Barnes 2004) Figure 3.18 Girder Line 6 Cracking (Fason and Barnes 2004) = sealed = unsealed = sealed = unsealed 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 5 - Span 10 - East Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 5 - Span 11 - East Face 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 6 - Span 10 - East Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 6 - Span 11 - East Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 6 - Span 10 - West Face 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 6 - Span 11 - West Face Girder 5 - Span 10 - West Face Girder 5 - Span 11 - West Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? 1?2?3?4?5? 6? 7? 8? 9? 10? 34 Figure 3.19 Girder Line 7 Cracking (Fason and Barnes 2004) Figure 3.20 Girder Line 8 Cracking (Fason and Barnes 2004) = sealed = unsealed = sealed = unsealed 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 8 - Span 10 - East Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 8 - Span 11 - East Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 8 - Span 10 - West Face 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 8 - Span 11 - West Face cracked through seal 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 7 - Span 11 - East Face 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 7 - Span 10 - East Face cracked through seal 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 7 - Span 11 - West Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 7 - Span 10 - West Face cracked through seal 35 Figure 3.21 Girder Line 9 Cracking (Fason and Barnes 2004) 3.4 PREVIOUS INVESTIGATIONS OF GIRDER CRACKING 3.4.1 Cause of Cracking At first, it was hypothesized that the cracks were due to restraint of time-dependent or temperature-induced deformations. Load testing and monitoring of the cracked girders indicated that the magnitude of deformations due to daily temperature changes regularly exceeded that caused by representative truck loading. Therefore, ALDOT officials concluded that temperature-induced effects were responsible for the cracking (Barnes et al. 2006). Since then, Auburn University researchers have more thoroughly investigated the cracking and its potential causes (Gao 2003). Time-dependent and temperature- dependent influences were modeled analytically. During the course of this = sealed = unsealed 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 9 - Span 10 - East Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 9 - Span 11 - East Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 9 - Span 10 - West Face 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 9 - Span 11 - West Face 36 investigation, it was discovered that the staged casting of the bridge deck and diaphragms was performed in an order different from that originally specified in the contract documents. Because previous research (Ma et al. 1998) has shown that construction sequence can significantly affect the behavior of this type of bridge system, the potential effects of this change were also evaluated (Barnes et al. 2006). Time-dependent, structural analysis of a typical girder line through the complete construction sequence of a two-span continuous unit of the bridge was conducted. At the time the bridges were designed, the relevant design standards supplied little information on temperature gradients. More recent U.S. bridge design standards (AASHTO 2004) prescribe consideration of a temperature gradient of only 41.4?F for this region. A single day of testing measured a temperature difference of 43.7?F. Test notes indicate that it was not a very sunny day, so it is likely that actual temperature gradients might regularly be even higher than those measured. The site-specific values measured by ALDOT were used in the analysis (Barnes et al. 2006). Analysis indicated that creep and shrinkage alone would not have resulted in cracking of the bridge superstructure within the first 10 years of service life. When the specified deck and diaphragm casting sequence was compared to the actual casting sequence, only small differences on the order of 50 psi or less in the relevant stresses were observed. As expected, the analysis of temperature-induced stresses yielded more noteworthy results. Daily temperature-induced stress cycles of the magnitude predicted in the end regions of the prestressed girders between 700 and 1000 psi bottom-flange tensile stresses could easily induce cracking in regions with little or no precompression. Based on the time-dependent analysis results, this would have been 37 the case for the end regions of the I-565 bridges at a relatively young age (Barnes et al. 2006). The question which then remains is: why did the cracking occur within the girder itself rather than at the joint between the girder and the diaphragm where the largest tensile stresses occur? The answer is a twofold contribution from the reinforcement details, which are shown in Figure 3.22. First is that of the reinforcing bars used to establish continuity. There is both a relatively weak plane at the end of the continuity bars and a stress concentration at such a discrete transition point. The second contribution is from the debonding of the prestressing strands which occurs shortly past the end of the reinforcing bars for continuity. The increased tension found just behind these debonding points combined with the increased stress resulting from the reinforcement bars for continuity to produce cracked girders rather than separation of the girder from the diaphragm. Careful attention to reinforcing details can prevent such cracking from occurring (Barnes et al. 2006). Figure 3.22 Cracked Girder with Continuity Reinforcement Details (Barnes et al. 2006) 10 of 28 bottom-flange prestressing strands are debonded from end of girder to this section. No. 6 reinforcing bars for continuity (8 in each girder end) 38 3.4.2 Effects of Cracking on Bridge Capacity A further study was conducted to determine the residual strength of the damaged bridges. While it is possible that the effect on strength limit state performance is minimal, the amount of remaining prestressed force in the end regions is vital to the shear strength of the structure. Given the cracking pattern, it was assumed that (1) the prestress force is ineffective between the end of the girder and the cracked sections, and (2) the effective prestress force only begins to develop after the cracked section. Based on the large slip evidenced, it is also doubtful that the affected strands are capable of developing tensile resistance when subjected to significant flexural demand (Barnes et al. 2006). There are three possible behaviors of the bridge resulting from the cracks in the girders (Swenson 2003). Ideally, it is behaving as a two-span continuous structure as designed. Alternatively, it could have lost continuity completely and as a result could be acting as two independent simply-supported spans. A third possibility is that the girders act continuously but with an internal hinge at the crack locations. Each of these possible behaviors was investigated. It was concluded that the spans with girder cracking are only structurally adequate for the strength limit state if they behave as completely continuous under the influence of live loads (Barnes et al. 2006). When the structure is analyzed using either the second or third of the latter possibilities, two shortcomings are apparent in the capacity of the structure: positive bending resistance and shear resistance in the cracked end regions of the girders. Lack of continuity and the suspected lack of development of the tensile reinforcement support the conclusion that positive moments cannot be reliably resisted in these end regions. 39 Referring to Figure 3.23, the loss of shear resistance is less straightforward. Though the lack of effective prestress force in the end regions results in a decrease of the concrete contribution to web-shear cracking resistance, there is still sufficient transverse reinforcement in these regions to compensate. This is likely attributable to the conservative standard reinforcing details employed in the girder design. However, the bottom flange tensile reinforcement is inadequate to effectively resist the longitudinal component of the diagonal tension, T, resulting from shear-critical loading (Barnes et al. 2006). C T V f V s V u N u V c d v ss 0.5 d v cot? 0.5 d v cot? Figure 3.23 Influence of Shear on Required Bottom-Flange Tensile Resistance (Barnes et al. 2006) 3.5 PROPOSED REPAIR SYSTEM For a damaged bridge, there are a number of possible repair options. One which has proven effective is mechanical attachment of steel plates to the tension face of the deficient member (Tedesco, Stallings, and El-Mihilmy 1999). There are several reasons, however, why steel plates, though effective, are undesirable. These include 40 ?corrosion, difficulty in handling plates, deterioration of the bond at the steel-concrete interface and the requirement of massive scaffolding during installation.? As an alternative repair method, FRP plates have an advantage over steel plates due to their ease in handling, corrosion resistance, light weight, and high strength. Swenson (2003) presented possible repair scenarios with a recommendation for which would be most effective. The repair scenario he recommended was a 4-ply FRP system. The longitudinal and cross-sectional configurations of the 4-ply FRP strengthening system are shown in Figures 3.24 through 3.26. Note in Figure 3.24 that the bottom ply runs 130 in. from the face of the continuity diaphragm. Each ensuing ply is then 6 in. shorter. The system is designed to accomplish three complementary objectives: (1) provide adequate positive bending resistance regardless of continuity conditions, (2) provide adequate shear resistance regardless of continuity conditions, and (3) shift future cracking due to restrained time- and temperature-dependent deformations to a more benign location within or at the face of the diaphragm. The FRP product chosen for the repair discussed in this investigation is the Tyfo SCH-41 composite manufactured by Fyfe Co. This product is a ?wet lay-up system comprised of Tyfo SCH-41 reinforcing fabric and Tyfo S epoxy? (Swenson 2003). The reinforcing fabric is comprised of unidirectional carbon fibers backed with a glass veil to increase and support fabric stability during installation. The epoxy is a ?two-part adhesive used to both saturate the composite fabric and bond the fabric to the concrete.? Installation of the FRP repair system is expected in early 2007. Load testing to assess the behavior of the repaired spans will follow the FRP installation (Barnes et al. 2006). 41 Figure 3.24 Longitudinal Configuration Profile for FRP (Barnes et al. 2006) Figure 3.25 Cross-Sectional Configuration for FRP near the Continuity Diaphragm (Swenson 2003) 10 in. 130 in. 3 @ 6 in. Four plies of wet layup, CFRP fabric 6.5? Inside face of bearing pad Face of continuity diaphragm A A Section A Total effective width of FRP reinforcement bonded to girder = 30 in. Bearing pad 42 Figure 3.26 Cross-Sectional Configuration for FRP away from the Continuity Diaphragm (Swenson 2003) 6.5? Inside face of bearing pad Face of continuity diaphragm B B Section B Total effective width of FRP reinforcement bonded to girder = 58 in. 43 CHAPTER 4: LOAD TESTING PROCEDURE 4.1 INTRODUCTION In order to test the efficacy of FRP repair, tests before and after FRP application were deemed necessary. The pre-FRP load testing occurred on the mornings of June 1 and 2, 2005. There were nine longitudinal stop positions and three distinct patterns of transverse positions, creating a total of twenty-seven different load positions. Load testing occurred over the course of two nights; however, the first day?s loadings were dedicated to acoustic emissions (AE) testing, which is not within the scope of this particular investigation. Therefore, this summary will focus on the second day of testing, which occurred on the morning of June 2. 4.2 APPLIED LOADS 4.2.1 Load-Testing Vehicles Test loads were applied using two different test trucks (ALDOT ST-6400 and ST-6902) simultaneously. Because the trucks had different frames, they had slightly different weight distributions and arrangements of wheel groups. The weight distribution chosen corresponds to an ALDOT LC-6 standard load truck configuration. This configuration was selected in order to induce load effects slightly larger than values corresponding to the full service-level live load for which the bridge was designed. Figures 4.1 and 4.2 indicate the relative positions of the wheel groups for the two trucks. Figures 4.3 and 4.4 show the trucks with the load configurations used for the load tests. There is a 44 raised axle visible on the ST-6400 Load Truck that was not used during load testing. Table 4.1 reports the individual loads for each wheel group as measured using ALDOT?s portable scales approximately one week after the I-565 tests. Table 4.1 Test Truck Wheel Group Loads ST-6400 ST-6902 Left 10,750 7,850 Right 10,900 7,450 Left 18,900 19,350 Right 18,350 18,750 Left 17,200 18,600 Right 17,500 19,250 93,600 91,250 Loading (lbs) Total Front Rear 1 Rear 2 Wheel GroupAxle 4.2.2 Load Positions Figures 4.5 through 4.7 indicate the three transverse truck positions used for testing?A, B, and C. As Girders 7 and 8 exhibited some of the most severe damage, these positions were chosen to maximize the influence on these two girders. Figure 4.8 illustrates the nine longitudinal stop positions used in the load testing. Table 4.2 describes each of these stop positions. The stop positions are defined by the middle axle of the trucks being centered on the location. Five stop positions are located on Span 10, and four stop positions are located on Span 11. They range from midspan of Span 10 to midspan of Span 11. 45 Figure 4.1 ST-6400 Wheel Group Configuration 97.25 in. 96 in. 13.5 in. 75 in. 27 9 i n. 22.25 in. 22 2 i n . 13.5 in. 22.25 in. 46 Figure 4.2 ST-6902 Wheel Group Configuration 21.5 in. 21.5 in. 95.5 in. 12.5 in. 73.5 in. 28 0. 5 i n . 22 7 i n . 12.5 in. 94 in. 47 Figure 4.3 ST-6400 Load Truck Figure 4.4 ST-6902 Load Truck 48 Figure 4.5 Transverse Truck Position A Figure 4.6 Transverse Truck Position B Figure 4.7 Transverse Truck Position C 3? - 4 ?? 8? ? 0? AASHTO BT54 girders Cast-in-place concrete barrier 64? ? 0? 70? ? 9? 6.5? Girder 7 Girder 8 73.5? 75? 49? ST-6902 ST-6400 3? - 4 ?? 8? ? 0? AASHTO BT54 girders Cast-in-place concrete barrier 64? ? 0? 70? ? 9? 6.5? Girder 7 Girder 8 73.5? 75? 49? ST-6902 ST-6400 3? - 4 ?? 8? ? 0? AASHTO BT54 girders Cast-in-place concrete barrier 64? ? 0? 70? ? 9? 6.5? Girder 7 Girder 8 73.5? 75? 49? ST-6902 ST-6400 49 Figure 4.8 Longitudinal Stop Positions for Test Trucks 49 Centerline of Continuity Diaphragm on Bent 11 1200? Stop Line 2 291? Stop Line 3 151? Stop Line 4 70? Stop Line 5 12? Stop Line 6 70? Stop Line 7 128? Stop Line 8 300? Stop Line 9 600? Stop Line 1 600? Span 10 Span 11 50 During the testing, the two trucks were placed side-by-side driving northbound. Two north-south lines were painted on the deck to define each transverse position?one for each truck. An east-west line was painted to mark each stop position. Figure 4.9 shows a truck properly aligned and in position. The trucks traveled slowly north along the north-south lines; they stopped at each of the nine stop positions long enough for braking effects to dissipate and then for data collection over a period of at least three seconds. Figure 4.9 Load Truck in Stopped Position The identification used for each of the 27 load positions comes from the transverse lane and the longitudinal stop position?with the transverse position coming first. For example, the load positions along Transverse Position A are A1, A2, and so forth 51 through A9. The load positions along Transverse Position B are B1, B2, etc. And the load positions for Transverse Position C are C1, C2, etc. Table 4.2 Locations of the Nine Longitudinal Stop Positions Stop Position a No. Position Description Distance from Center of Continuity Diaphragm (in.) 1 Middle tire over the midspan of Span 10 -600 2 Front tire over Cross Section 1 b -291 3 Front tire over Cross Section 4 -151 4 Middle tire over Cross Section 1 -70 5 Rear tire over Cross Section 1 -12 6 Middle tire over Cross Section 4 70 7 Rear tire over Cross Section 4 128 8 Middle tire over the quarter-span of Span 11 300 9 Middle tire over the midspan of Span 11 600 a Trucks were stopped when the middle axles were located the specified distance from the center of the continuity diaphragm b The convention for the numbering of the cross sections is given in Section 4.3.4.1 4.2.3 Testing Sequence One repetition of static loading consisted of the two trucks driving along the bridge in one transverse position and stopping long enough for data to be collected at each of the nine stop positions. The following step-by-step procedure details how this maneuver was accomplished. 1. Paint all necessary lines on bridge deck (truck positions A, B, and C and stopping positions 1?9). 2. Align both trucks to Transverse Position A. 3. Balance data acquisition device with trucks not on continuous spans. 52 4. Drive trucks to Position 1 and record data for three seconds. 5. Repeat Step 4 for Positions 2?9. 6. Drive trucks off span and record data without load. 7. Drive trucks back to starting position and align for Transverse Position B. 8. Repeat Steps 3?6. 9. Drive trucks back to starting position and align for Transverse Position C. 10. Repeat Steps 3?6. 4.3 INSTRUMENTATION Several types of measurements were collected during the pre-FRP repair load testing. However, only longitudinal strain and vertical deflection measurements are relevant to the analysis reported in this thesis. 4.3.1 Concrete Strains For this load testing, concrete surface strains were measured using electrical-resistance strain gauges (ERSGs) bonded with epoxy directly to the surface of the concrete as depicted in Figure 4.10. Because concrete is not a homogeneous material, a gauge length several times as large as the coarse aggregate size was selected to prevent accidental measurement of strain values not representative of the concrete material as a whole. The ERSGs used in this test were 60-mm, quarter-bridge strain gauges with a resistance of 350 ? and temperature compensation appropriate for concrete or steel (Texas Measurements MFLA-60?350-1L). Installation of the strain gauges is explained in Section 4.3.3.1. 53 Figure 4.10 Installed ERSG 4.3.2 Girder Deflections Deflectometers were used to measure the amount of vertical movement that the bridge experienced under loads. These measurements were useful in determining the general behavior of the bridge. The deflectometers used were relatively elementary devices. An installed deflectometer is depicted in Figure 4.11. They were constructed primarily of a cantilevered aluminum beam with a longitudinal, quarter-bridge strain gauge attached to the underside of the beam. The beam was attached to a base that firmly supported it on the ground. An eye bolt was attached to the end of the beam, and a taut wire was attached to the underside of a bridge girder and connected to the eye bolt on the deflectometer. Figure 4.11 Installed Deflectometer 54 In order to keep the wire taut and acquire useful data when the girder deformed, the aluminum beam was pre-bent approximately three or four inches. This was done by tightening the turnbuckle attached to the wire. Once the beam was bent and the wire was in tension, the strain gauge was capable of measuring both upward and downward deflections of the bridge girder within the expected range. Installation of the deflectometers is further explained in Section 4.3.3.2. Deflectometer positions are described in Section 4.3.4.2. The deflectometers also needed to be calibrated. This was accomplished by taking a base reading of the strain gauge when the aluminum beam was in position and then taking a series of readings as the beam was carefully moved through a range of precisely measured distances. A linear relationship was established between the gauge output and the tip deflection of the aluminum beam through the entire range encountered during the actual bridge test. This relationship was then used to compute the measured girder deflection for the strain measured for each load position. 4.3.3 Sensor Installation 4.3.3.1 Strain Gauges Because concrete is a porous material, water may penetrate to the strain gauge if the surface is not sealed against moisture. Surface preparation was conducted according to the gauge manufacturer?s recommendations. The application of the gauges was performed according to the manufacturer?s instructions. To prepare the gauges, each gauge was removed from its package and taped to a clean glass plate. The tape was kept smooth and free of air bubbles during this transfer. When the concrete surface was ready, the tape with the attached strain 55 gauge was carefully removed and attached to the desired location on the girder. When that was finished, the tape was carefully peeled back to reveal the underside of the strain gauge. To attach the strain gauge, a standard 5-minute epoxy was then applied to both the strain gauge and the concrete, and the strain gauge was held in place until the gauge was attached sufficiently. After the epoxy hardened, the tape was removed completely and a layer of Dow Corning? 3145 RTV silicone rubber was applied over the entire strain gauge to provide protection against moisture and wear. 4.3.3.2 Deflectometers The installation of the deflectometers was relatively simple when compared to that of the strain gauges. After the installation location was identified, a bracket was glued into place on the girder using 5-minute epoxy. After the epoxy was set, a wire was attached to the bracket with a turnbuckle at the end of the wire. Once the deflectometer was placed securely in position on the ground, the turnbuckle was attached to the eyebolt, and the aluminum beam was pre-bent approximately 4 inches. The deflectometer strain gauge was then connected to the data acquisition system. 4.3.4 Sensor Positions Because of practical limitations, a choice had to be made between lightly instrumenting all of the girders or heavily instrumenting only some of them. It was decided to heavily instrument only two of them, and Girders 7 and 8 were selected as being representative of the occurrences of cracking. These are the first two interior girders on the east side of the bridge. Figures 4.12 through 4.19 depict the end regions of Spans 10 and 11 of Girders 7 and 8. 56 Figure 4.12 Girder 7 Span 10 East Face Figure 4.13 Girder 7 Span 10 West Face 57 Figure 4.14 Girder 7 Span 11 East Face Figure 4.15 Girder 7 Span 11 West Face 58 Figure 4.16 Girder 8 Span 10 East Face Figure 4.17 Girder 8 Span 10 West Face 59 Figure 4.18 Girder 8 Span 11 East Face Figure 4.19 Girder 8 Span 11 West Face 60 4.3.4.1 Strain Gauges Longitudinal strain data were collected at twenty-eight positions along each of the two bridge girders. Because the cracked area is of greatest concern, the bulk of the strain gauges were located close to the girder ends where the cracking had occurred. Because Span 11 was chosen to be the primary span, it had six cross sections that were instrumented with strain gauges while Span 10 had only two instrumented cross sections. The locations of Cross Sections 1 through 4 are indicated in Figure 4.20. On Span 10, Cross Section 1 is located 75.25 in. from the center of the continuity diaphragm, and Cross Section 2 is located 12.75 in. from the center of the continuity diaphragm. On Span 11, Cross Section 3 is located 12.75 in. from the center of the continuity diaphragm, and Cross Section 4 is located 75.25 in. from the center of the continuity diaphragm. Cross Sections 5 through 8 are located on Span 11 104 inches, 272 inches, 440 inches, and 608 inches from the center of the continuity diaphragm, respectively. In order to get more comprehensive data in the cracked region, Cross Sections 1?4 each had six strain gauges as depicted in Figures 4.21 and 4.22. Cross Sections 5?8 only had gauges located on the bottom of the girder. The primary purpose of the gauges along the bottom of the girder was to better determine the overall behavior of the girders, particularly the manner in which the damaged regions affected the distribution of bending moments within the structure. 61 Figure 4.20 Approximate Locations for Cross Sections 1 through 4 Figure 4.21 Strain Gauge Instrumentation at Cross Sections 2 and 3 75.25 in. from center of cont. diaphragm 75.25 in. from center of cont. diaphragm 12.75 in. from center of cont. diaphragm Cross Section 1 Cross Section 2 Cross Section 3 Cross Section 4 Span 10 Span 11 --- Strain Gage 3.5? 2? 2? 36? 4.5? 6? 26? 42? 18? 10? 2? ?? chamfer 54? 6? 3? 3? 3? 18? 6 Strain Gages Per Instrumented Cross-Section F E D C B A 62 Figure 4.22 Strain Gauge Instrumentation at Cross Sections 1 and 4 4.3.4.2 Deflectometers There were twelve deflectometers used in the load testing. These were placed at six different locations on each of the two girders as depicted in Figure 4.23. Because Span 11 was the primary span, it had four deflectometers per girder while Span 10 had only two. For Span 11, the deflectometers were located 150 in., 300 in., 450 in., and 600 in. from the center of the continuity diaphragm. These distances represent 1/8, 1/4, 3/8, and 1/2 of the span length, respectively. For Span 10, the deflectometers were located 300 in. and 600 in. from the center of the continuity diaphragm. Figure 4.24 shows several installed deflectometers. -- Strain Gauge 3.5? 2? 2? 36? 4.5? 6? 26? 42? 18? 10? 2? ?? chamfer 54? 6? 3? 3? 3? 18? 6 Strain Gauges Per Instrumented Cross-Section F E D C M A 63 Figure 4.23 Installed Deflectometer Locations 63 -- Deflectometer 150? Midspan Midspan Bent 11 150? 150? 150? 300? 300? Span 11 Span 10 D-1 D-2 D-3 D-5D-4 D-6 64 Figure 4.24 Installed Deflectometers 65 4.4 DATA ACQUISITION AND PROCESSING 4.4.1 Data Acquisition System An Optim MEGADAC data acquisition system was used to record the test data. For each truck position, sensor readings were recorded at a rate of 240 scans per second for at least 3 seconds. The entire positioning sequence was repeated three times. Figure 4.25 is a picture of the complete van setup during the load test. 4.4.2 Averaging Process There were at least 720 readings recorded for each repetition of each static load position. These 720 (or more) readings were averaged to eliminate variation due to electronic noise, resulting in a single measured deformation (strain or deflection) for each position repetition. If one of these three resulting values for a single position differed significantly from the other two values, the outlier was discarded and the two remaining values were averaged to determine a single deformation measurement for each load position. Usually there was no apparent outlier, and the deformation value was determined as the average of all three repetition results. 4.5 DATA USED TO EVALUATE AND REFINE FINITE-ELEMENT MODELS Results from only four of the load positions?A7, A9, C7, and C9?were used to evaluate the accuracy of the model and investigate the effectiveness of various modeling options. Transverse Positions A and C were selected because these positions primarily load Girders 7 and 8, respectively, and produce a more distinct response than Transverse Position B. Longitudinal Positions 7 and 9 were selected to give behavior representative of maximum load effects near the damaged regions. Position 7 had the truck wheels in a 66 position that could be expected to induce the largest shear forces near the cracked sections. Position 9 could be expected to induce the largest bending moments in the cracked regions. Positions 7 and 9 were chosen over the corresponding locations on Span 10 because Span 11 was more heavily instrumented than Span 10 and as a result had the most data for comparisons. Measured bottom-fiber strains were employed as the primary means of assessing the accuracy of various modeling options with respect to the overall behavior of the bridge superstructure. Complete results for all twenty-seven load positions for the pre-repair load testing conducted on June 2, 2005 are reported in Appendix H Figure 4.25 Van Setup during Testing 67 CHAPTER 5: FEM DEVELOPMENT AND VERIFICATION 5.1 INTRODUCTION In creating the finite-element model for the bridge using ABAQUS, there were many aspects of the geometry and material properties that needed to be considered. For the practical purposes of this model, it was permissible for some assumptions and simplifications to be used. For example, a slightly simplified girder cross section was used for ease in meshing, and as explained in Section 5.10, the cracks were modeled as a group rather than by discretizing each crack location. In addition, average material properties of concrete and prestressing steel were employed. This chapter presents the details of those and other components of the model definition. 5.2 GIRDER CROSS SECTION The first step in defining the model was to determine what the cross-sectional shape of the girders would be. The dimensions of a BT54, the girder section used in the I-565 bridge (ALDOT 1987), are shown in Figure 5.1a, but for the purposes of the model and for ease in meshing, it was decided to simplify these dimensions slightly. In order to verify the accuracy of the simplified section, section properties were computed for the simplified section shown in Figure 5.1b and on the same section with a ??chamfer on each outer corner of the bottom flange. 68 (a) (b) Figure 5.1 Cross-Sectional Dimensions for (a) BT54 and (b) Simplified BT54 3.5? 2? 2? 36? 4.5? 6? 26? 42? 18? 10? 2? ?? chamfer 54? 6? 4.5? 3? 36? 4.5? 6? 26? 42? 18? 10? 3? 54? 6? 69 The cross-sectional properties that were compared include area (A), moment of inertia (I), height (h), distance from neutral axis to top of the flange (y t ), section modulus of the area above the neutral axis (S t ), section modulus of the area below the neutral axis (S b ), and radius of gyration (r 2 ). A comparison of the computed values to the section properties of the actual BT54 is shown in Table 5.1. Percent errors were calculated by dividing the difference between the two values?the cross-sectional property value for the BT54 versus the modified shape?by the value for the BT54. As can be seen in the table, the errors associated with the simplified shape without chamfers range up to approximately three times as great as the corresponding errors associated with the simplified shape with the chamfers; however, all errors are less than one percent. This level of error was considered acceptable, and the simplified cross section without chamfer was employed for the FEM. This cross-sectional shape was then extruded 200 feet to produce a continuous girder. Table 5.1 Section Properties of Simplified BT54 Cross Section Cross- Sectional Property BT54 Modified Shape (without chamfer) Modified Shape (with chamfer) Modified Shape (without chamfer) Modified Shape (with chamfer) A (in 2 ) 659 660 659 0.15 0.07 I (in 4 ) 268100 269600 269200 0.57 0.42 h (in) 54 54 54 0 0 y t (in) 26.37 26.31 26.29 0.23 0.30 S t (in 3 ) 10170 10250 10240 0.80 0.72 S b (in 3 ) 9702 9737 9715 0.35 0.13 r 2 (in 2 ) 406.8 408.5 408.2 0.42 0.35 Percent Errors 70 5.3 REINFORCED CONCRETE DECK The reinforced concrete (RC) deck was modeled by an 849 in. by 6.5 in. rectangular cross section extruded 200 ft. This represents a slight simplification of the actual deck cross section which is depicted in Figure 5.2. That figure shows a slight, variable build- up present over the girders. It was reasoned that because the load tests measured change in strain, the rectangular approximation would sufficiently represent the deck- girder composite behavior. Figure 5.2 Bridge Cross Section 5.4 MESH SIZE The next issue to be addressed was the mesh size of the model. In order to select a mesh size, several analyses of the same basic model were run with different mesh sizes. This basic model had no diaphragms or barrier rails; it consisted solely of the deck, nine continuous girders, and a central bent?which was approximated by the continuity diaphragms as explained in Section 5.5. It was loaded with a pressure load of 1 psi on the entire deck. The four mesh sizes compared divided the length of the bridge into elements that were 6 in., 9 in., 12 in., and 15 in. long along the length of the bridge. In determining these four options, the AASHTO LRFD (2004) requirements regarding aspect ratio were considered: ?the aspect ratio of finite elements and grid panels should not exceed 8? ? 0? 3? - 4 ?? 64? ? 0? 70? ? 9? 6.5? 71 5.0.? Each of these mesh sizes conforms to the 5.0 aspect-ratio limit. The least number of elements per girder span that satisfies the AASHTO LRFD limit is ten elements. Ten elements per span results in an aspect ratio of 4.6 for the elements in the bottom flange. This is an acceptable minimum number of elements only if each element encompasses the full width of the cross section and the top and bottom flanges are each approximated as rectangles, as shown in Figure 5.3. In order to achieve more refined analysis results, at least two elements were used across the width of the cross section for all mesh sizes investigated. An example of this?the cross section for the 9-in. mesh?is shown in Figure 5.4. The coarsest (15-in.) mesh of the four mesh sizes investigated had at least 8 times the minimum number of elements along the span recommended by AASHTO LRFD. Figure 5.3 Cross Section of Coarsest Mesh 26? 72 Figure 5.4 Cross Section of 9-in. Mesh As can be seen in Figure 5.5, all of the longitudinal stress values approach one another as the distance from the bent cap (modeled as a pinned support at the bottom of each of the nine continuous girders) increases. Closer to the pinned connection, it can be seen that the stress pattern changes noticeably between that for the 15 in. mesh and that for the 12 in. mesh, also between that for the 12 in. mesh compared to that for the 9 in. mesh. The difference between the stress patterns shown for the 9-in. and 6-in. mesh values, however, is not so drastic. The other component considered in selecting the mesh size was the computational burden. Figure 5.6 depicts the run-times of each of the four models. It can be seen that as the mesh size decreased, the computer time required for the additional calculations increased significantly. The computer time for a 6-in. model was more than twice that of the 9-in. model, but the increase in accuracy was not significant enough to warrant the necessary commensurate increase in computational burden, particularly for the nonlinear aspects of the analysis that were anticipated. As a result, the 9-in. mesh as depicted in Figure 5.7 was selected for the ABAQUS model. This 9-in. mesh results in 73 a ratio of element length to girder length of approximately 1:133, which is close to that of 1:137 used by Barr, Eberhard, and Stanton (2001). -1400 -1300 -1200 -1100 -1000 -900 -800 -700 -600 0 20 40 60 80 100 Distance From Center of Bent Cap (in) Longitudi nal S t r e s s (ps i ) 6-in 9-in 12-in 15-in 6-in mesh 15-in mesh Figure 5.5 Mesh Size Stress Comparisons 0 1 2 3 4 5 6 7 8 4 6 8 10121416 Mesh Size (inches) C o m put e r Ti m e ( m i n ut e s ) Figure 5.6 Mesh Size vs. Computer Time 74 Figure 5.7 ABAQUS Bridge Model Depicting a 9-in. Mesh 74 75 5.5 DIAPHRAGMS The next step was to take the very basic model and add the continuity and midspan diaphragms as depicted in Figures 5.8 and 5.9, respectively. The midspan diaphragms and the diaphragms at the discontinuous far ends of each span have the same cross- sectional shape. FEM model diaphragms are shown in Figure 5.10. The girders were modeled as continuous girders rather than as two simply supported girders joined at the continuity diaphragm. To accomplish this, the girders were extruded 200 ft?the length of both spans?and connected at the bent with continuity diaphragms between adjacent girders. This connection was achieved using a tie constraint?which is explained in Section 5.12. Figure 5.8 Cross Section of Continuity Diaphragm, Thickness = 16? 90? 54? 36? 4.5? 5.0? 54? 3? 10? 35? 3? C.L. 76 Figure 5.9 Cross Section of Midspan Diaphragm, Thickness = 8? Figure 5.10 Model Simulation of Installed Midspan Diaphragms 4.5? 90? 54? 36? 3? 10? 4.5? 3? C.L. 77 5.6 BARRIER RAILS According to the AASHTO LRFD specifications, though normally neglected, a continuous barrier may be considered structurally active if full composite behavior is certain (AASHTO 2004). In placing the barrier rails on the bridge model, a simple extrusion of the cross-sectional shape shown in Figure 5.11 was made for the entire 200-ft. span of the bridge spans being modeled. In the actual bridge, there are transverse saw-cut joints through the rail at a few positions along the length of the bridge, so this approximation may add a slight measure of stiffness that is not actually present. An ABAQUS image showing a barrier rail is given in Figure 5.12. 17? 9? 3? 29? 6? 14? Figure 5.11 Barrier Rail Cross Section 78 Figure 5.12 Bridge End View Showing Barrier Rail 5.7 BEARING PADS For simplicity, one long bearing pad was used to represent the nine individual pads that support the girders at each end of each span. The geometry of the bearing pads was defined by an extrusion of a 7-in. by 0.75-in. rectangular cross section. The shape was extruded 794 in.?the distance between the exterior edges of the bottom flanges of the exterior girders. The centers of the bearing pads at the continuity diaphragm were placed 10 in. away from the centerline of the diaphragm, and the bearing pads at the far ends of the spans were placed such that the center-to-center distance between the bearing pads on each span was 1182 in. The mesh size for the bearing pads is 9 inches. The bearing pad at the far end of Span 10 is depicted in Figure 5.13. See Section 5.13 for more information about the support conditions. Barrier Rail 79 The elastomeric bearing pads were assigned a conservative modulus of elasticity of 450 psi?based on the design values for rubber. Poisson?s ratio for the elastomeric bearing pads was modeled as 0.5. Figure 5.13 Bridge End View Showing Bearing Pad 5.8 ELEMENT SELECTION There are many options for element types when constructing a finite-element model. For this model, three different types of elements were used. 5.8.1 Brick Elements The element selected for most of the components in the model was an 8-node linear brick such as that shown in Figure 5.14a. The default element in ABAQUS for such an element is C3D8R, which incorporates reduced integration and hourglass control as well as translational degrees of freedom in the three global directions at each node. Hourglass control relates to one of the problems associated with ?first-order, reduced-integration elements? in stress/displacement analyses. Since the elements have only one integration point, it is possible for them to distort in such a way that the Bearing pad 80 strains calculated at the integration point are all zero, which, in turn, leads to uncontrolled distortion of the mesh? (ABAQUS 2006). Hourglass control helps prevent this. Reduced integration ?uses a lower-order integration [than full integration does] to form the element stiffness? [It therefore] reduces running time, especially in three dimensions? (ABAQUS 2006). See Section 5.8.4 for a more complete explanation of reduced versus full integration. 5.8.2 Shell Elements Another type of element used in the model is a shell element such as that depicted in Figure 5.14b. Shell elements are used for the steel reinforcement, the load application, and the FRP?as explained in Section 5.11, Section 5.14, and Section 5.16, respectively. ?Shell elements are used to model structures in which one dimension, the thickness, is significantly smaller than the other dimensions? (ABAQUS 2006). A shell element has geometry-defined length and width, but the thickness is defined as a section property rather than a property of the geometry. The shell elements used in this model are 4-node elements with translational and rotational degrees of freedom at each node. The elements selected to model steel reinforcement and truck loadings employ reduced integration. For reasons explained in Section 5.8.4, the FRP elements utilize full integration. The name used in ABAQUS for the steel and load application elements is S4R. The FRP elements are S4 elements. 5.8.3 Tetrahedral Elements One other type of element used in the model is a tetrahedral element (C3D4). A tetrahedral element has 4 nodes and 4 sides, as shown in Figure 5.14c. According to the 81 ABAQUS Analysis User?s Manual (2006), ?C3D4 is recommended only for filling in regions of low stress gradient in meshes of C3D8 or C3D8R elements, when the geometry precludes the use of C3D8 or C3D8R elements throughout the model.? This is exactly the use to which these elements were put in this model. There is a location at the base of the midspan diaphragms?identified in Figure 5.15?where the geometry makes meshing with brick elements awkward, and this is where the tetrahedral elements were used. Figure 5.14 Examples of (a) an 8-Node Brick Element, (b) a 4-Node Shell Element, and (c) a 4-Node Tetrahedral Element (adapted from ABAQUS 2006) Figure 5.15 Mesh of Midspan Diaphragm tetrahedral elements 82 5.8.4 Element Integration Options For many of the elements in ABAQUS, the option exists to use either full or reduced integration. With reduced integration, ?the mass matrix and distributed loadings are still integrated exactly. Reduced integration usually provides more accurate results (provided the elements are not distorted or loaded in in-plane bending) and significantly reduces running time, especially in three dimensions? (ABAQUS 2006). When analyzing the strain results of the FRP, it was apparent that the shell elements with reduced integration were insufficient for the task. These elements did not have enough integration points to adequately reflect the buildup of FRP stresses in the transition regions near where the FRP crosses the concrete cracks. This was evident because rather than reporting one strain value, as at other nodes, ABAQUS reported four strain values for the nodes on either side of the cracked region. These represented the strain values in each of the four adjoining elements, and the values varied widely. To avoid this, it was determined to use full integration for the FRP shell elements. 5.9 MODULUS OF ELASTICITY In creating the model, a stiffer modulus of elasticity (E c ) was assigned to the prestressed girders than to the other concrete elements. The girder concrete was designed to be stronger in order to resist prestress forces at an early age. Based on previous research into the material properties of prestressed concrete, a value of 6,000,000 psi was selected as being representative of typical precast, prestressed concrete girders in the region (Roberts 2005). For the deck, the modulus of elasticity was selected by computing a value that would reflect the approximate stiffness of the composite reinforced-concrete section when 83 modeled as a single isotropic material. Based on an assumed compressive strength of 4,000 psi?which, from ACI 318 Section 8.5.1, results in a modulus of elasticity of 3,605,000 psi?and an average modulus of elasticity for reinforcing steel of 29,000,000 psi (Gere 2001), an effective E c value of 4,000,000 psi was used. This value was also used for the barrier rails despite their lighter reinforcement because they were assumed to have slightly stiffer concrete based on the low-slump mixture used to cast the rails. For the diaphragms, a modulus of elasticity of 3,605,000 psi was used. When steel reinforcement was explicitly modeled, a modulus of elasticity of 29,000,000 psi was used. The modulus of elasticity for the bearing pads is explained in Section 5.7. The modulus of elasticity for the fiber-reinforced polymer is discussed in Section 5.16. 5.10 SEAMS To approximate the behavior of a crack in a girder, a Seam was used in the FEM. This is a feature in ABAQUS which ?defines an edge or a face in [the] model that is originally closed but can open during an analysis? (ABAQUS 2004). Figure 5.16 depicts a Seam which has opened due to loading. ABAQUS/CAE ?places overlapping duplicate nodes along a [Seam] when the mesh is generated.? Typically this feature is used in fracture mechanics to investigate crack growth using contour integral analysis. As the purpose of this investigation was to model the effects of the cracks rather than to study their propagation, the Seam approximation was considered sufficient. The Seam feature allows the sides of the ?crack? to either separate or close without establishing contact with each other. This was acceptable because in the actual structure a space was already physically present between the two faces of the crack, and 84 as such, some movement in either direction was possible. However, no initial condition in the model established a specific pre-existing gap. The effects of this are discussed in Section 7.5. Figure 5.16 Cracked Girder with Seams Open Due to Loading The locations of the Seams along the girders were determined from the drawings of the crack locations found in Figures 3.13 through 3.21. A summary of the locations of the Seams used in the Pre-Repair and Post-Repair FEMs is presented in Table 5.2. The locations of the seams are compared in Figures 5.17 and 5.18 to the locations of the actual cracks in Girders 7 and 8?the instrumented girders. In addition to cracks in the girders, however, cracks are present in the faces of some of the continuity diaphragms near the girder connection. These were approximated with Seams in the girder located at the face of the diaphragm. Girder 2 is an example of a girder which has a seam defined only at the face of the continuity diaphragm. As shown in Figure 3.14, there are no cracks in the girder. But there is a crack in the continuity diaphragm adjacent to the girder, and this is why there is a seam at the face of the continuity diaphragm. 85 Table 5.2 Summary of Seam Locations for Pre-Repair and Post-Repair FEMs Distance From Diaphragm Face (in.) Distance up the girder (in.) Distance From Diaphragm Face (in.) Distance up the girder (in.) 24 up to top flange 18 up to top flange 0 a up to top flange 0 a up to top flange 2 0 a 45 none n/a 3 24 6 all sealed n/a 0 a 27 21 6 5 0 a 27 0 a 27 624 6 0 a up to top flange 7 36 18 36 up to top flange 8 36 6 48 up to top flange 9 18 up to top flange none n/a a As explained in Section 5.15.4, seams at the face of the continuity diaphragms were not modeled in the Uncracked , Cracked , and Cracked-with-Reinforcement models 4 Girder No. Span 10 Span 11 1 0 a 27 Each girder has a maximum of four Seams. One Seam could be located along the face of the continuity diaphragm to represent the cracking of the continuity diaphragm. This Seam could be located on either one or both spans. In addition to that, there could be one Seam located between 18 to 48 inches from the face of the continuity diaphragm on one or both spans to represent the cracking in the girder. Because each cracked girder end contains only one major crack, only one Seam was inserted at a location that was central to the location of the cracks present on each face of the girder. 86 Figure 5.17 Girder Line 7 Cracks with Seams Superimposed (Fason and Barnes 2004) Figure 5.18 Girder Line 8 Cracks with Seams Superimposed (Fason and Barnes 2004) = seam in FEM = crack in girder 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 7 - Span 10 - West Face 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 7 - Span 11 - West Face 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 7 - Span 10 - East Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 7 - Span 11 - East Face 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 8 - Span 10 - East Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 8 - Span 11 - East Face 1?2?3?4?5? 6? 7? 8? 9? 10? Girder 8 - Span 11 - West Face 1? 2? 3? 4? 5? 6? 7? 8? 9? 10? Girder 8 - Span 10 - West Face = seam in FEM = crack in girder 87 5.11 PRESTRESSED REINFORCEMENT Although it was determined to not explicitly model the prestress force in the prestressing strands, the presence of the prestressed reinforcing steel within the girders was not discounted. The stiffness of the prestressing steel should only have significant influence on the live load response of the girders near the cracked sections. Because of the proximity of these cracked regions to the ends of the girders, only the strands which were fully bonded were modeled explicitly. It was assumed that the partially debonded strands would add no stiffness to the cracked sections because they have little or no embedment beyond the cracked sections. As depicted in Figure 5.19, two groups of strands were modeled explicitly using the Rebar option for shell elements in ABAQUS. One line of shell elements, with a rebar layer representative of the sum of all of the straight strands in the bottom flange, was placed at the centroidal location of those strands. The draped strands were modeled in a similar manner, with one line of shell elements with a rebar layer oriented along the line of the centroid of the draped strands. In ABAQUS, the Rebar option ?is used to define layers of uniaxial reinforcement in membrane, shell, and surface elements (such layers are treated as a smeared layer with a constant thickness equal to the area of each reinforcing bar divided by the reinforcing bar spacing)? [These] can be used to add layers of reinforcement in a solid by embedding reinforced surface or membrane elements in the ?host? solid elements? (ABAQUS 2006). For more about embedding elements, see Section 5.12. 88 Figure 5.19 Prestressing Reinforcement Profile. Note: The height of the centroid of the horizontal straight strands is 5". The draped strands start at the face of the continuity diaphragm at a height of 45.5". 88 Midspan Midspan Bent 11 472? 120?472?120? Span 11 Span 10 89 5.12 CONNECTIONS As only the superstructure is expected to deform significantly and the substructure is not damaged, the model includes only the parts of the bridge above and including the girder bearing pads. Simplifications were made because the load tests measure the effects of live loads only and do not reflect changes due to the dead loads, which are always present. For example, the prestress force can be neglected in the linear elastic portion of the model if the actual structure does not crack in these regions under the effects of the test loads. Furthermore, it is not necessary to model the influence of the prestressing force on the damaged sections if, as suspected (Barnes et al. 2006), there is no longer an effective prestress force in these regions that could influence the opening and closing of the pre-existing cracks under loads. The connections between components were modeled as ties rather than as contact connections, where two components can resist each other in one direction but can separate in the other direction. A tie ?make[s] the translational and rotational motion as well as all other active degrees of freedom equal for a pair of surfaces? (ABAQUS 2006). The diaphragms are tied to the girders, just as the deck is tied to both the girders and the diaphragms. This simulates the composite action which should be occurring in the bridge structure. Also, the girders are connected to the bearing pads using a tie constraint because the dead load forces contact between these elements regardless of placement of truck loads. Another type of connection used in the model is an embedment. ?The embedded element technique? is used to specify an element or a group of elements that lie embedded in a group of host elements whose response will be used to constrain the 90 translational degrees of freedom of the embedded nodes (i.e., nodes of embedded elements)? (ABAQUS 2006). Shell elements employing the Rebar option were embedded into the corresponding girders. This effectively assumes a perfect bond between the reinforcing steel and the concrete. 5.13 SUPPORT CONDITIONS As explained in Section 5.12, only the superstructure of the bridge was modeled for this study. The boundary condition which accomplished this was a pinned support along the entire base of the bearing pads to approximate the bridge bent cap. Because this effectively restrained all translational movement at the base of the bearing pads, the vertical deformations of the bents were neglected in the finite-element analysis. 5.14 LOAD APPLICATION As per AASHTO LRFD (2004) which specifies that the wheel loads on the deck be modeled as patch loads distributed over an area approximating the wheel contact surface, the truck loads were approximated by means of planar shells that each represent one of the six main wheel groups on each of the two trucks, as depicted in Figure 5.20. The dimensions of the planar shell were 8 in. by 21.5 in. by 0.1 in. The modulus of elasticity for these elements was the same as that used for the deck?4,000,000 psi. The shell surface was then connected with tie constraints?which are explained in Section 5.12?to the deck in the proper location for each of the wheel group positions. The truck weight was applied as a pressure load distributed over the area of each wheel group element. These pressures are listed, with the truck weights they represent, in Table 5.3. 91 Figure 5.20 Truck Loading with Load Arrows Indicating Wheel Group Loads Table 5.3 Test Truck Wheel Group Pressure Loads ST-6400 ST-6902 ST-6400 ST-6902 Left 10,750 7,850 62.5 45.6 Right 10,900 7,450 63.4 43.3 Left 18,900 19,350 110 113 Right 18,350 18,750 107 109 Left 17,200 18,600 100 108 Right 17,500 19,250 102 112 93,600 91,250 -- -- Wheel Group Pressure (psi)Truck Weight (lbs) Total Front Rear 1 Rear 2 Wheel Group Axle 92 5.15 MODEL REFINEMENT The model was created in three broad stages. This section describes those stages briefly, while Section 6.2 presents them more comprehensively. 5.15.1 Uncracked Model Originally, the model was created using uncracked girders with no explicit steel reinforcement. This Uncracked model was used as a baseline for the ideal response of the bridge to live loads, as it was originally intended. It incorporated all of the basic structural features such as midspan diaphragms and barrier rails that were included in the later models. Because no cracking was expected under service-load conditions in the undamaged structure, this model did not include the Seams, nor was girder reinforcement explicitly modeled. 5.15.2 Cracked Model After the Uncracked model was completed, the Cracked model was created using the Seam feature described in Section 5.10. The locations of the Seams along the girders were determined from the pictures of the crack locations found in Figures 3.13 through 3.21 and are summarized in Table 5.2. Where the Uncracked model was the ideal model for the behavior of the bridge, the Cracked model was used as the worst-case scenario for the behavior of the damaged bridge. The actual bridge could be expected to exhibit response corresponding to this model if the prestressing strands that cross the cracks offer no resistance to crack opening or closing under live loads. 93 5.15.3 Cracked-with-Reinforcement Model It was hypothesized that because of the location and width of the original cracks, the prestressing strands had lost their prestressing force through excessive slip in this region and were functioning merely as nonprestressed reinforcement at best. To test whether the strands were still able to function as nonprestressed reinforcement across the cracks, the reinforcement was applied to the Cracked model as described in Section 5.11, and the resulting Cracked-with-Reinforcement model was analyzed. 5.15.4 Pre-Repair Model The final Pre-Repair model differs from the Cracked-with-Reinforcement model in only one way. After beginning to model the FRP repair on the Cracked-with-Reinforcement model, an error in modeling the Seams explained in Section 5.10 and identified in Table 5.2 was discovered. While the Seams away from the face of the diaphragm were all defined correctly, the Seams which were supposed to be present in some of the girders at the face of the continuity diaphragm had not been defined. It was judged that because the inclusion of the Seams would not affect the global behavior of the bridge? which is demonstrated through the bottom-fiber strain results depicted in Figure 5.21, where the results of the two models overlap one another?the decision to use the Cracked-with-Reinforcement model, as opposed to the Uncracked or Cracked models, would not be affected. As a result, the Seams were corrected in only two models?the Pre-Repair model and the Post-Repair model. The Pre-Repair model was then used to compare the current analytical behavior of the bridge with the expected behavior predicted by the Post-Repair model. 94 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) B o ttom-Fi be r S t r a i n due to Tr uc k Loa di ng ( x 10 -6 ) G7 Load Test G8 Load Test G7 Cracked-with-Reinforcement G8 Cracked-with-Reinforcement G7 Corrected Seams G8 Corrected Seams Figure 5.21 Comparison Between Models with and without Correctly Defined Seams 5.16 MODELING OF FRP After a model was created which accurately reflected the current, pre-repair behavior of the bridge, the proposed FRP repair was modeled and the results analyzed. The wet lay-up FRP system proposed for repair of the I-565 structures is expected to behave as a laminate, or thin plate. The FRP reinforcement was modeled using shell elements with a variable thickness representing the different number of layers at each position along each girder. Each layer of a composite material is referred to as a ?ply? for the purposes of this investigation (Swenson 2003). Multiple plies can be layered in order to achieve the desired material strength. The design thickness of one ply of the Tyfo SCH-42 composite that will be used for the repair is 0.04 in., so when 4 plies are present, the thickness of the shell element is 0.16 in.; for 3 plies it is 0.12 in., etc. See Section 5.8.2 95 for more details on the properties of the shell elements used to model the FRP reinforcement. The bond of the FRP to the concrete was modeled using a tie constraint as explained in Section 5.12. 5.16.1 Mechanical Theory of Fiber-Reinforced Polymers A composite material, such as fiber-reinforced polymer, is a material composed of either continuous or noncontinuous fibers which are surrounded by a weaker matrix material. This matrix serves to both distribute the fibers and transfer the load to them (Gay 2003). For a unidirectional ply, the mechanical characteristics of the fiber/matrix mixture can be calculated from the known characteristics of each of the constituents. The modulus of elasticity along the direction of the fiber depends almost entirely on the longitudinal stiffness of the fibers. In the transverse direction, the modulus of elasticity is defined by Equation 5.1 (Gay 2003): () ? ? ? ? ? ? ? ? ? ? ? ? +? = fft m f mt VE E V EE 1 1 Eq. 5.1 where E t = Modulus of elasticity in the transverse direction E m = Modulus of elasticity of the matrix E ft = Modulus of elasticity of the fiber in the direction that is transverse to the fiber longitudinal axis V f = Fiber volume fraction A guideline for the shear modulus of the composite (G lt ) is given by Equation 5.2 (Gay 2003): 96 () ? ? ? ? ? ? ? ? ? ? ? ? +? = fflt m f mlt VG G V GG 1 1 Eq. 5.2 where G m = Shear modulus of the matrix G flt = Shear modulus of the fiber V f = Fiber volume fraction The value for Poisson?s ratio ( lt ? ) is approximated by Equation 5.3 (Gay 2003): mmfflt VV ??? += Eq. 5.3 where f ? = Poisson?s ratio of the fiber m ? = Poisson?s ratio of the matrix V f = Fiber volume fraction V m = Matrix volume fraction 5.16.2 FRP as an Isotropic Material Isotropic materials are those ?having the same properties in all directions (whether axial, lateral, or any other direction)? (Gere 2001). While this is not the case with fiber- reinforced polymer, an attempt was made to model it as such for simplicity. The possibility existed that because the loading imposed on the FRP reinforcement was predominantly in the longitudinal direction, an isotropic material, which modeled the material properties of the fiber-reinforced polymer as being identical in all directions, would be sufficiently representative. In the event that modeling the FRP reinforcement 97 with laminar properties represented a significant increase in the computational burden, the potential for accurately modeling it as an isotropic material was explored. 5.16.3 FRP as a Laminar Material When ?the properties in a particular direction are the same throughout the material and the properties in all directions perpendicular to that direction are the same (but different from the first properties); then the material is classified as orthotropic? (Gere 2001). To define an orthotropic material, nine material properties are required. These include the elastic moduli in the three principle directions, the three Poisson?s ratios between those three principle directions, and the three shear moduli between them. ?Under plane stress conditions, such as in a shell element,? fewer material properties are necessary than the nine required to ?define [a conventional] orthotropic material? (ABAQUS 2006). In all of the plane stress elements, the stress perpendicular to the shell surface is equal to zero. Under these circumstances, only six material properties are required to describe the behavior: the elastic moduli of the two principal directions (E l and E t ), Poisson?s ratio between the two principal directions (? tl ), and the three shear moduli between the two principal directions and their orthogonal direction (G tl , G tp , G lp ). This simplified form of defining an orthotropic material is referred to as a laminate in ABAQUS. As explained in Section 6.3.1, this is the representation used for the FRP in the final Post-Repair model. The longitudinal elastic modulus was assumed equal to the published design value for the FRP system to be employed: 11,900,000 psi. The transverse elastic modulus was calculated from the known longitudinal elastic modulus and the Poisson?s ratio between the two principal directions provided by the 98 manufacturer, ? tl = 0.086, using Equation 5.4 (ABAQUS 2006), which dictates the minimum requirement for material stability. 2 1 =? ? ? ? ? ? ? ? ? tl t l E E ? Eq. 5.4 From this equation, the transverse elastic modulus was determined to be 2,200,000 psi. Published design values for the three shear moduli were unavailable from the manufacturer, so the values were estimated from the known, composite make-up of the material. Two of the shear moduli, G tl and G lp ?where t is the transverse direction, l is the longitudinal direction, and p is the direction perpendicular to the plane?are taken from a published design value for the shear modulus of an unspecified, unidirectional carbon/epoxy composite. That value is 610 x 10 3 psi (Gay 2003). The third shear modulus, G tp , was calculated using the isotropic relationship of epoxy between the elastic modulus and the shear modulus?which is given in Equation 5.5 (Gere 2001): )1(2 ?+ = E G Eq. 5.5 E was taken as the tensile modulus of the epoxy as given by the manufacturer?461 x 10 3 psi?and ? was taken as the published design value for Poisson?s ratio of an unspecified epoxy?0.4 (Gay 2003). From these, the final shear modulus was calculated to be 165 x 10 3 psi. 99 CHAPTER 6: RESULTS 6.1 INTRODUCTION This chapter presents analytical results generated from the various finite-element models developed for this study. The load test results which were used to verify the accuracy of these models are presented in summary in Appendix H. Where applicable, they are compared to the relevant FEM results in this chapter. The analytical results presented in this chapter are organized into two groups: results from modeling the existing structure and results from modeling the FRP-repaired structure. Both of these groups include both longitudinal strains and deflections which were output from the analysis of the corresponding FEMs. In addition to the bottom- fiber strains, which are presented in this chapter, longitudinal surface strains were also measured at various depths at several instrumented cross sections?as described in Section 4.3.4.1 and discussed in Section 7.2.1. These experimental values and the corresponding FEM results are presented graphically in Appendices D through G. 6.2 FINITE-ELEMENT MODELING OF THE EXISTING STRUCTURE 6.2.1 Uncracked Model The Uncracked model was intended to represent the behavior of the bridge if the damage had no effect on its performance. This model presents a picture of the ideal bridge behavior if no cracks were present?the intended behavior of the bridge design. 100 The longitudinal strain results for this model for each of the four representative load test positions can be seen in Figures 6.1 through 6.4. For these figures?as well as for the other figures in this chapter?the positive values on the abscissa represent Span 11 while the negative values represent Span 10. The locations of wheel groups for the truck loads are indicated by vertical arrows. Length of the arrows indicates the relative loads on the axles. The inset picture indicates the transverse position of the load trucks. The individual data markers represent strain measurements obtained during the actual load testing of the structure. The girders, deck, diaphragms, and barrier rails were modeled as discussed in Sections 5.2, 5.3, 5.5, and 5.6, respectively. This model consisted entirely of C3D8R brick elements, S4R shell elements, and C3D4 tetrahedral elements, as explained in Section 5.8. Aside from its indirect influence on the assumption of uncracked concrete behavior, the prestressing force was not explicitly considered in this model. Because the concrete was assumed to be uncracked, the stiffening attributable to steel reinforcement was neglected, except for the selection of the modulus of elasticity for the nonprestressed deck elements as described in Section 5.9. The Uncracked-model results generally exhibit more compression (or less tension) strain at the girder bottom fiber than was measured in the load tests. This is particularly evident at the cross sections near the cracked regions. The discrepancy is pronounced for the load positions near midspan (A9 and C9). This indicates that the girder bending moments in the actual structure are less negative than in the Uncracked model. Thus, this model overestimates the continuity of the cracked-girder system. 101 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Botto m-Fibe r S t r a in due t o Tr uc k Loa din g ( x 10 -6 ) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked Figure 6.1 Bottom-Fiber Strain Data for the Uncracked Bridge Model?A7 Load Position -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Botto m-Fibe r S t r a in due t o Tr uc k Loa din g ( x 10 -6 ) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked Figure 6.2 Bottom-Fiber Strain Data for the Uncracked Bridge Model?A9 Load Position 102 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bottom-Fibe r S t r a in due to Tr uc k Loa ding ( x 10 -6 ) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked Figure 6.3 Bottom-Fiber Strain Data for the Uncracked Bridge Model?C7 Load Position -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Botto m-Fibe r S t r a in due t o Tr uc k Loa din g ( x 10 -6 ) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked Figure 6.4 Bottom-Fiber Strain Data for the Uncracked Bridge Model?C9 Load Position 103 6.2.2 Cracked Model Comparison of the Uncracked model results to the corresponding load test results indicates that the cracks obviously have some effect on the bridge behavior; therefore, an attempt was made to accurately model the effects of the cracking. To this end, seams were created in the bridge girders that had visible cracking. The longitudinal strain results for the resulting Cracked model, when subjected to the four representative load test positions, can be seen?superimposed on the graphs of the corresponding results for the Uncracked model?in Figures 6.5 through 6.8. The seams were created as explained in Section 5.9, and the seam locations are detailed in Table 5.2. The effect of a seam is to create independent nodes along the two faces of the seam; this allows each side of the seam to move independently of the other side, somewhat like a tear in a piece of paper. This model represents the worst-case scenario?the bridge behavior if the steel that crosses these cracks does not contribute to the superstructure?s resistance to applied loads. This would be the case if all of the steel crossing each crack had fractured, or if the bond between the prestressing reinforcement and concrete had deteriorated to the extent that no stresses can be transferred from the concrete to the steel. 104 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bottom-F i be r S t r a i n du e to Tr uc k L o a d ing ( x 10 -6 ) G7 Load Test G8 Load Test G7 Cracked G8 Cracked G7 Uncracked G8 Uncracked Figure 6.5 Bottom-Fiber Strain Data for the Cracked Bridge Model?A7 Load Position -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bottom-Fibe r S t r a in due to Tr uc k Loa ding ( x 10 -6 ) G7 Load Test G8 Load Test G7 Cracked G8 Cracked G7 Uncracked G8 Uncracked Figure 6.6 Bottom-Fiber Strain Data for the Cracked Bridge Model?A9 Load Position 105 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bo ttom-Fibe r S t r a in due to Tr uc k Loa ding ( x 10 -6 ) G7 Load Test G8 Load Test G7 Cracked G8 Cracked G7 Uncracked G8 Uncracked Figure 6.7 Bottom-Fiber Strain Data for the Cracked Bridge Model?C7 Load Position -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Botto m-Fibe r S t r a in due t o Tr uc k Loa din g ( x 10 -6 ) G7 Load Test G8 Load Test G7 Cracked G8 Cracked G7 Uncracked G8 Uncracked Figure 6.8 Bottom-Fiber Strain Data for the Cracked Bridge Model?C9 Load Position 106 As expected, the FEM results from this model indicate no bending moment being developed near the cracks. This can be seen in the graphs where the bottom-fiber strains equal zero. However, this does not reflect the behavior observed in the load test results. The load test results indicate that bottom-fiber strains are developed at the gauge sections near the cracks. These measured strains indicate compression near the cracks when the loads are near midspan (A9 and C9). However, when the test trucks are near the cracked section in Span 11 (A7 and C7), the behavior is more complex. The measured strains near the cracks in the loaded span (Span 11) indicate bottom-fiber tension, while compression is evident near the crack on the far side of the continuity diaphragm (Span 10). 6.2.3 Cracked-with-Reinforcement Model Comparison of the results of the Cracked model to the load test results indicates that the actual cracked structure is somewhat stiffer (or more continuous) than the Cracked model. The Cracked and Uncracked model results seem to bracket the actual bridge behavior. This is particularly evident for the bottom-fiber strains for the A9 and C9 load positions. The compressive strains measured near the cracked regions indicate that significant negative moments are being developed at the crack sections for these load positions. Therefore, an attempt was made to gauge whether the additional stiffness in these regions is commensurate with the stiffness of the prestressing strands that cross the cracks. A Cracked-with-Reinforcement model was developed using the rebar function in ABAQUS as explained in Section 5.11. Two groups of reinforcing steel, the draped and undraped strands, were each modeled as one bundle. As the model only describes the response of the bridge to changes in truck loadings?and, as explained in 107 Section 3.4.2, it is unlikely that the prestress force is effective at the cracked section? no attempt was made to apply a prestressing force to the model. The longitudinal strain results for the Cracked-with-Reinforcement model with loads placed at each of the four representative load test positions can be seen?superimposed on the graphs of the Uncracked and Cracked models?in Figures 6.9 through 6.12. The deflection results for these three models are presented in Figures 6.13 through 6.16. For the strain results?and except for the Girder 7 gauge at midspan of Span 11, as explained in Section 6.5.1?the Uncracked and Cracked models consistently bracket the load test results and the Cracked-with-Reinforcement model results. This is seen most strikingly in the A9 and C9 Load Positions for the two strain gauges nearest the continuity diaphragm on each girder of Span 11. There is between a 30 x 10 -6 in./in. and 50 x 10 -6 in./in. difference at those points between the Uncracked and the Cracked models. And both the load test results and the Cracked-with-Reinforcement results fall directly in the middle of this range. For the deflection results, this relationship holds true between the three models, but the load test results generally indicate less deflection than the Cracked and Cracked- with-Reinforcement models predict. This is most pronounced for the Girder 8 results and is most evident in the A9 and C9 Load Positions. While Girder 7 exhibits the bracketing relationship of the model data to the load test data for the A9 Load Position, Girder 8 predicts more deflection in even the Uncracked model than is occurring. For the C9 Load Position at midspan, the Uncracked model predicts more deflection for both girders. This is also seen on the unloaded span for all four load positions on the Uncracked and Cracked-with-Reinforcement models. Most likely this is because the 108 concrete used in the FEMs is less stiff than the concrete in the bridge. In addition, it is possible that the pretensioning force in the bridge results in less deflection than the FEMs?which do not have a pretension force applied?predict. This could be due to the slight increase in stiffness which results from the partially debonded strands. Though these strands were not included in the models because they were not effective at the cracks, they could add a slight amount of stiffness in the middle regions on the span(s). Also, as explained in Section 6.3.2, the FEM does not reflect the build-up of the deck over the girders. This build-up would slightly increase the composite girder stiffness due to the increased total depth of the cross section. After comparative evaluation of both the strain and deflection results, it was determined that?of the three?the Cracked-with-Reinforcement model best represents the bridge behavior. -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bottom-F i be r S t r a i n du e to Tr uc k L o a d ing ( x 10 -6 ) G7 Load Test Data G8 Load Test Data G7 Uncracked G8 Uncracked G7 Cracked G8 Cracked G7 Cracked w/ Reinf G8 Cracked w/ Reinf Figure 6.9 Bottom-Fiber Strain Data for the Model Refinement?A7 Load Position 109 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bottom-Fibe r S t r a in du e to Tr uc k Loa ding ( x 10 -6 ) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked G7 Cracked G8 Cracked G7 Cracked w/ Reinf G8 Cracked w/ Reinf Figure 6.10 Bottom-Fiber Strain Data for the Model Refinement?A9 Load Position -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Botto m-Fibe r S t r a in due t o Tr uc k Loa din g ( x 10 -6 ) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked G7 Cracked G8 Cracked G7 Cracked w/ Reinf G8 Cracked w/ Reinf Figure 6.11 Bottom-Fiber Strain Data for the Model Refinement?C7 Load Position 110 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) St rain ( x 10 -6 ) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked G7 Cracked G8 Cracked G7 Cracked w/ Reinf G8 Cracked w/ Reinf Figure 6.12 Bottom-Fiber Strain Data for the Model Refinement?C9 Load Position -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 -800 -600 -400 -200 0 200 400 600 800 Distance From Center of Continuity Diaphragm (in) Bo ttom-Fibe r De fle c tion due to Tr uc k Loa din g (in) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked G7 Cracked G8 Cracked G7 Cracked w/ Reinf G8 Cracked w/ Reinf Figure 6.13 Bottom-Fiber Deflections for the Model Refinement?A7 Load Position 111 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 -800 -600 -400 -200 0 200 400 600 800 Distance From Center of Continuity Diaphragm (in) Bottom-Fibe r De fle c t ion due to Tr uc k Loa ding (in) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked G7 Cracked G8 Cracked G7 Cracked w/ Reinf G8 Cracked w/ Reinf Figure 6.14 Bottom-Fiber Deflections for the Model Refinement?A9 Load Position -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 -800 -600 -400 -200 0 200 400 600 800 Distance From Center of Continuity Diaphragm (in) Bottom-Fib e r De fle c t ion due to Tr u c k Loa ding (in) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked G7 Cracked G8 Cracked G7 Cracked w/ Reinf G8 Cracked w/ Reinf Figure 6.15 Bottom-Fiber Deflections for the Model Refinement?C7 Load Position 112 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 -800 -600 -400 -200 0 200 400 600 800 Distance From Center of Continuity Diaphragm (in) Bottom-Fibe r De fle c t ion due to Tr uc k Loa ding (in) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked G7 Cracked G8 Cracked G7 Cracked w/ Reinf G8 Cracked w/ Reinf Figure 6.16 Bottom-Fiber Deflections for the Model Refinement?C9 Load Position 6.2.4 Exploration of Midspan Diaphragm Effects When looking at Figures 6.9 through 6.12, there is a noticeable discrepancy between the experimental value of Girder 7 strain at midspan and the corresponding FEM results. Although the Cracked-with-Reinforcement model best represents the strain results at the other strain gauge locations, the discrepancy at this location is large regardless of which FEM is employed. In order to investigate whether this discrepancy is related to overestimating the influence of the midspan diaphragms, a comparison FEM without midspan diaphragms was created. Apart from the omission of these diaphragms, this model was identical to the Cracked-with-Reinforcement model. Comparisons between the results of these two models, along with the corresponding load test results, are depicted in Figures 6.17 through 6.20, with the divergent point labeled as ?A?. 113 -100 -50 0 50 100 150 200 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) B o ttom-Fibe r S t r a in due to Tr uc k Loa ding ( x 10 -6 ) G7 Load Test G8 Load Test G7 With Diaphragms G8 With Diaphragms G7 Without Diaphragms G8 Without Diaphragms A Figure 6.17 Comparing the Models with and without Diaphragms?A7 Load Position -100 -50 0 50 100 150 200 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bo ttom-Fibe r S t r a in due to Tr uc k Loa ding ( x 10 -6 ) G7 Load Test G8 Load Test G7 With Diaphragms G8 With Diaphragms G7 Without Diaphragms G8 Without Diaphragms A Figure 6.18 Comparing the Models with and without Diaphragms?A9 Load Position 114 -100 -50 0 50 100 150 200 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bottom-Fibe r S t r a in du e to Tr uc k Loa ding ( x 10 -6 ) G7 Load Test G8 Load Test G7 With Diaphragms G8 With Diaphragms G7 Without Diaphragms G8 Without Diaphragms A Figure 6.19 Comparing the Models with and without Diaphragms?C7 Load Position -100 -50 0 50 100 150 200 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bottom - Fi be r S t r a i n d u e to Tr u c k Loa d i ng ( x 10 -6 ) G7 Load Test G8 Load Test G7 With Diaphragms G8 With Diaphragms G7 Without Diaphragms G8 Without Diaphragms A Figure 6.20 Comparing the Models with and without Diaphragms?C9 Load Position 115 It is apparent from the figures that the FEM that includes the midspan diaphragms better reflects the behavior of the bridge than the FEM without diaphragms. This differs significantly from the results of the study conducted by Tedesco, Stallings, and Tow (1995) in which they determined that the removal of diaphragms would not have a significant effect on the bridge response. While this matter warrants further investigation, for this study it was decided to include the midspan diaphragms in the final model of the existing bridge behavior. The effects of the midspan diaphragms are discussed further in Section 7.2.3. 6.2.5 Further Discrepancies It is interesting to note that there is also a discrepancy between the FEMs and the load test results for some of the gauges nearer to the continuity diaphragm. Looking at Figures 6.9 and 6.11?the results for Load Positions A7 and C7, respectively?there is an obvious disparity in the results for the gauges located approximately 70 in. from the center of the continuity diaphragm. On Span 11 this is present in both girders, while on Span 10 it is only present in Girder 8. This discrepancy is not discernible when the truck is positioned away from these sections, but presents itself when a wheel group is very close to these sections?which are also very close to cracks. It is possible this may indicate some inaccuracy in crack placement on the FEM or some local effect of the concentrated load on the bridge that the FEM is not reflecting. The accuracy of the FEM results in these cracked regions is likely to be very sensitive to minor differences between the actual crack location(s) and the positioning of the seams in the model. 116 6.2.6 Final Pre-Repair Model Originally, the Cracked-with-Reinforcement model was selected as the final pre-FRP repair model. Section 5.14.4 details the changes that were made to it to produce the Pre-Repair model?seams along the face of the continuity diaphragm, which were not included in the Cracked-with-Reinforcement model, were added to create the final Pre- Repair model. Figures 6.21 through 6.24 show the analytical results of this model compared to the experimental results. The next step was to model the effects of the fiber-reinforced polymer repair on the damaged structure. -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) B o ttom-Fi be r S t r a i n due to Tr uc k Loa di ng ( x 10 -6 ) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair Figure 6.21 Bottom-Fiber Strain Data for the Pre-Repair Model?A7 Load Position 117 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Botto m-Fibe r S t r a in due t o Tr uc k Loa din g (x 1 0 -6 ) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair Figure 6.22 Bottom-Fiber Strain Data for the Pre-Repair Model?A9 Load Position -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bottom-F i be r S t r a i n du e to T r u ck Lo ad in g ( x10 -6 ) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair Figure 6.23 Bottom-Fiber Strain Data for the Pre-Repair Model?C7 Load Position 118 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Botto m-Fibe r S t r a in due t o Tr uc k Loa din g ( x 10 -6 ) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair Figure 6.24 Bottom-Fiber Strain Data for the Pre-Repair Model?C9 Load Position 6.3 FINITE-ELEMENT MODELING OF THE FRP-REPAIRED STRUCTURE 6.3.1 Comparison between Isotropic and Laminar Models for FRP The FEMs for the Post-Repair model were created by adding the fiber-reinforced polymer repair?created as explained in Sections 5.16.2 and 5.16.3?to the Pre-Repair model. Figures 6.25 through 6.28 present a bottom-fiber longitudinal strain comparison between models with isotropic FRP and laminar FRP. Section 5.16 presents the details of these FRP modeling options. 119 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) B o ttom-Fibe r S t r a in due to Tr uc k Loa ding ( x 10 -6 ) G7 Cracked w/ Reinf G8 Cracked w/ Reinf G7 Isotropic FRP G8 Isotropic FRP G7 Laminar FRP G8 Laminar FRP Figure 6.25 Bottom-Fiber Strain Data for the Isotropic v. Lamina FRP Models? A7 Load Position -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) B o ttom-Fibe r S t r a in due to Tr uc k Loa ding ( x 10 -6 ) G7 Cracked w/ Reinf G8 Cracked w/ Reinf G7 Isotropic FRP G8 Isotropic FRP G7 Laminar FRP G8 Laminar FRP Figure 6.26 Bottom-Fiber Strain Data for the Isotropic v. Lamina FRP Models? A9 Load Position 120 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bottom-F i be r S t r a i n du e to Tr uc k L o a d ing ( x 10 -6 ) G7 Cracked w/ Reinf G8 Cracked w/ Reinf G7 Isotropic FRP G8 Isotropic FRP G7 Laminar FRP G8 Laminar FRP Figure 6.27 Bottom-Fiber Strain Data for the Isotropic v. Lamina FRP Models? C7 Load Position -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bottom-F i be r S t r a i n du e to Tr uc k L o a d ing ( x 10 -6 ) G7 Cracked w/ Reinf G8 Cracked w/ Reinf G7 Isotropic FRP G8 Isotropic FRP G7 Laminar FRP G8 Laminar FRP Figure 6.28 Bottom-Fiber Strain Data for the Isotropic v. Lamina FRP Models? C9 Load Position 121 Referring to the figures, it is apparent that the behavior of the model with the laminar FRP is slightly closer than the model with the isotropic FRP to the behavior of the Cracked-with-Reinforcement model?and therefore slightly more conservative with respect to the overall contribution of the FRP to the stiffness of the bridge. Because the laminar representation more accurately models the orthotropic FRP material than the isotropic representation?and the increase in computational burden was not significant?it was determined to use the laminar FRP representation for the final Post- Repair model. 6.3.2 Pre-Repair Model vs. Post-Repair Model The longitudinal strain comparison between the final pre-FRP repair model and the post-FRP repair model is shown in Figures 6.29 through 6.32. The deflection comparison between the two models is shown in Figures 6.33 through 6.36. As explained in Section 5.7.4, the FRP was first modeled with reduced integration elements. As explained in Section 5.8.4, when it became apparent that reduced integration was insufficient for the task, full integration was utilized. Not surprisingly, the FRP has the greatest effect on the resulting strains near the cracked region. For all four load positions, there is between 0 and 25 x 10 -6 in./in. increase in compressive strain at the location of the Seams. It is interesting to note that for all four load positions, the repair acts to decrease the predicted deflection more at the midspan of the loaded girder?regardless of the longitudinal position of the load trucks?than at any other location. This effect is more evident at the A9 and C9 Load Positions than at the A7 and C7 Load Positions. The repair appears to be equally effective for both Girder 7 and Girder 8. 122 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bottom-F i be r S t r a i n du e to T r u ck Lo ad in g ( x10 -6 ) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair G7 Post-Repair G8 Post-Repair Figure 6.29 Bottom-Fiber Strain Data for the Pre- v. Post-Repair Models?A7 Load Position -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bottom - Fi be r S t r a i n d u e to Tr u c k Loa d i ng (x 1 0 -6 ) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair G7 Post-Repair G8 Post-Repair Figure 6.30 Bottom-Fiber Strain Data for the Pre- v. Post-Repair Models?A9 Load Position 123 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bottom-F i be r S t r a i n du e to T r u ck Lo ad in g ( x10 -6 ) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair G7 Post-Repair G8 Post-Repair Figure 6.31 Bottom-Fiber Strain Data for the Pre- v. Post-Repair Models?C7 Load Position -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) B o ttom-Fi be r S t r a in due to Tr uc k L o a d ing ( x 10 -6 ) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair G7 Post-Repair G8 Post-Repair Figure 6.32 Bottom-Fiber Strain Data for the Pre- v. Post-Repair Models?C9 Load Position 124 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 -800 -600 -400 -200 0 200 400 600 800 Distance From Center of Continuity Diaphragm (in) Bottom-Fibe r De fle c t ion due to Tr uc k Loa ding (in) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair G7 Post-Repair G8 Post-Repair Figure 6.33 Bottom-Fiber Deflections for the Pre- v. Post-Repair Models?A7 Load Position -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 -800 -600 -400 -200 0 200 400 600 800 Distance From Center of Continuity Diaphragm (in) B o ttom- Fibe r De fle c t ion due to Tr uc k Loa ding (in ) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair G7 Post-Repair G8 Post-Repair Figure 6.34 Bottom-Fiber Deflections for the Pre- v. Post-Repair Models?A9 Load Position 125 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 -800 -600 -400 -200 0 200 400 600 800 Distance From Center of Continuity Diaphragm (in) Bottom-Fibe r De fle c t ion due to Tr uc k Loa ding (in) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair G7 Post-Repair G8 Post-Repair Figure 6.35 Bottom-Fiber Deflections for the Pre- v. Post-Repair Models?C7 Load Position -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 -800 -600 -400 -200 0 200 400 600 800 Distance From Center of Continuity Diaphragm (in) Bottom-Fibe r De fle c t ion due to Tr uc k Loa ding (in) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair G7 Post-Repair G8 Post-Repair Figure 6.36 Bottom-Fiber Deflections for the Pre- v. Post-Repair Models?C9 Load Position 126 The deflections at midspan of Span 11 for the Pre-Repair and Post-Repair models are compared in Table 6.1. At the four load positions, the change in deflection due to the repair is on the order of 5?9 percent. For the A9 and C9 Load Positions, the change ranges between approximately 5.5?6.5 percent. For the A7 and C7 Load Positions, the change ranges from approximately 8?9 percent. Table 6.1 Comparison between Pre- and Post-Repair Models of Midspan Deflection Measured on Span 11 Pre-Repair Post-Repair A7 0.084 0.078 -0.007 -8.2 A9 0.290 0.274 -0.016 -5.6 C7 0.085 0.077 -0.008 -8.9 C9 0.287 0.270 -0.018 -6.1 A7 0.078 0.071 -0.006 -7.9 A9 0.264 0.247 -0.017 -6.4 C7 0.104 0.095 -0.009 -8.5 C9 0.351 0.329 -0.023 -6.4 Girder 7 Gi rd er 8 Deflection (in.) Percent Change Load Position Change (in.) The deflections at midspan of Span 11 are also compared between the Uncracked and the Post-Repair models. This comparison is presented in Table 6.2. The purpose of this comparison is to provide a reference for the efficacy of the repair and its effect on the global behavior of the bridge. Surprisingly, the Post-Repair model predicts results within 2 percent of the Uncracked model for all of the reported midspan deflections. At the precision which can be reliably and practically measured, the model results imply that the deflection behavior of the repaired bridge will closely match that of the original uncracked structure. 127 It is interesting to note that the results of the A9 and C9 Load Positions predict less deflection in the Post-Repair model than is present in the Uncracked model. This can be attributed to at least two possible causes. One is that the prestressing steel, which is present in the Post-Repair model, is not explicitly included in the Uncracked model. The Uncracked model, therefore, does not include the extra stiffness attributable to the steel within the uncracked girder cross section. In addition, the FEM does not account for the build-up of the deck over the girders. This build-up would slightly increase the composite girder stiffness because of the increased total depth of the cross section. Table 6.2 Comparison between Uncracked and Post-Repair Models of Midspan Deflection Measured on Span 11 Uncracked Post-Repair A7 0.077 0.078 0.000 0.3 A9 0.279 0.274 -0.005 -1.6 C7 0.076 0.077 0.001 1.6 C9 0.273 0.270 -0.003 -1.2 A7 0.071 0.071 0.001 0.8 A9 0.249 0.247 -0.003 -1.1 C7 0.094 0.095 0.002 1.9 C9 0.332 0.329 -0.003 -1.0 Girder 7 Gi rd er 8 Deflection (in.) Percent Difference Load Position Difference (in.) 6.3.3 Concrete Strains versus FRP Strains Due to practical limitations on instrumentation capabilities, some of the strain gauges that were employed in the pre-repair load testing must be abandoned in order to instrument critical portions of the newly installed FRP. In order to help determine which of the existing strain gauges to continue using during the post-FRP repair load tests, the longitudinal strains in the FRP were compared with the longitudinal strains in 128 the concrete that lies directly below it. In an effort to determine whether the FRP strains are expected to be the same as the adjacent concrete strains, comparisons were made for the bottom-fiber strain gauges as well as the strain gauges on the faces of the girders. The results for the bottom-fiber strain gauge comparisons are shown in Figures 6.37 through 6.44. For each of the four truck load positions, the figure of the entire instrumented length is presented first; a close-up figure with the repaired region directly follows each. From these figures, it can be observed that the strain in the FRP is relatively close to the value of the strain in the concrete toward the beginning and the end of the FRP regions?particularly at the end away from the continuity diaphragms and the cracks. At the seam locations, the strain in the FRP increases markedly while the strain in the concrete fluctuates slightly. This is reasonable because the FRP would be compensating for the lack of tension capacity in the concrete caused by the cracks. This also suggests that high bond stress demands are being placed on the FRP-concrete interface in these regions. In addition, it is likely?because the FRP is being put into compression?that some of the seams are closing. The horizontal displacements at the seams are further explored in Section 7.5. The experimental results for the entire girder-section strain profiles are shown with the corresponding analytical results of the Pre-Repair and Post-Repair models in Appendices D through G. 129 -350 -300 -250 -200 -150 -100 -50 0 50 100 150 -150 -50 50 150 250 350 450 550 650 Distance From Center of Continuity Diaphragm (in) Bottom-F i be r S t r a i n du e to Tr uc k L o a d ing ( x 10 -6 ) G7 Load Test G8 Load Test G7 Concrete G8 Concrete G7 FRP G8 FRP FRP Region FRP Region Seams Seams Figure 6.37 Bottom-Fiber Strain Data for the Concrete v. FRP for the Post-Repair Model?A7 Load Position -350 -300 -250 -200 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Distance From Center of Continuity Diaphragm (in) Bottom- Fibe r S t r a in due to Tr uc k Loa ding ( x 10 -6 ) G7 Load Test G8 Load Test G7 Concrete G8 Concrete G7 FRP G8 FRP FRP Region FRP Region Seams G7 Seam G8 Seam Figure 6.38 Bottom-Fiber Strain Data for the Concrete v. FRP for the Post-Repair Model (close-up view)?A7 Load Position 130 -350 -300 -250 -200 -150 -100 -50 0 50 100 150 -150 -50 50 150 250 350 450 550 650 Distance From Center of Continuity Diaphragm (in) Botto m-Fibe r S t r a in due t o Tr uc k Loa din g ( x 10 -6 ) G7 Load Test G8 Load Test G7 Concrete G8 Concrete G7 FRP G8 FRP FRP Region FRP Region Seams Seams Figure 6.39 Bottom-Fiber Strain Data for the Concrete v. FRP for the Post-Repair Model?A9 Load Position -350 -300 -250 -200 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Distance From Center of Continuity Diaphragm (in) Bottom-F i be r S t r a i n du e to Tr uc k L o a d ing ( x 10 -6 ) G7 Load Test G8 Load Test G7 Concrete G8 Concrete G7 FRP G8 FRP FRP Region FRP Region Seams G7 Seam G8 Seam Figure 6.40 Bottom-Fiber Strain Data for the Concrete v. FRP for the Post-Repair Model (close-up view)?A9 Load Position 131 -150 -100 -50 0 50 100 150 -150 -50 50 150 250 350 450 550 650 Distance From Center of Continuity Diaphragm (in) Bottom-F i be r S t r a i n du e to Tr uc k L o a d ing ( x 10 -6 ) G7 Load Test G8 Load Test G7 Concrete G8 Concrete G7 FRP G8 FRP FRP Region FRP Region Seams Seams Figure 6.41 Bottom-Fiber Strain Data for the Concrete v. FRP for the Post-Repair Model?C7 Load Position -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Distance From Center of Continuity Diaphragm (in) Bottom-Fi be r S t r a in du e to Tr uc k L o a d ing ( x 10 -6 ) G7 Load Test G8 Load Test G7 Concrete G8 Concrete G7 FRP G8 FRP FRP Region FRP Region Seams G7 Seam G8 Seam Figure 6.42 Bottom-Fiber Strain Data for the Concrete v. FRP for the Post-Repair Model (close-up view)?C7 Load Position 132 -500 -450 -400 -350 -300 -250 -200 -150 -100 -50 0 50 100 150 -150 -50 50 150 250 350 450 550 650 Distance From Center of Continuity Diaphragm (in) Botto m-Fibe r S t r a in due t o Tr uc k Loa din g ( x 10 -6 ) G7 Load Test G8 Load Test G7 Concrete G8 Concrete G7 FRP G8 FRP FRP Region FRP Region Seams Seams Figure 6.43 Bottom-Fiber Strain Data for the Concrete v. FRP for the Post-Repair Model?C9 Load Position -500 -450 -400 -350 -300 -250 -200 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Distance From Center of Continuity Diaphragm (in) Bottom-F i be r S t r a i n du e to Tr uc k L o a d ing ( x 10 -6 ) G7 Load Test G8 Load Test G7 Concrete G8 Concrete G7 FRP G8 FRP FRP Region FRP Region Seams G7 Seam G8 Seam Figure 6.44 Bottom-Fiber Strain Data for the Concrete v. FRP for the Post-Repair Model (close-up view)?C9 Load Position 133 CHAPTER 7: DISCUSSION 7.1 INTRODUCTION In analyzing the strains and deflections measured during the pre-repair load tests and those from the FEM models, it is useful to consider the information in terms of either pre-repair or post-repair results. In comparing the results of the Pre-Repair model to those of the pre-repair load tests, several conclusions can be drawn regarding the current behavior of the bridge as well as the effects of certain structural elements?such as midspan diaphragms. The Post-Repair model results provide a guideline for improving data gathering during the post-repair load test by indicating which of the existing gauges are singularly informative and which could be sacrificed in favor of collecting measurements at a different location. They also help predict the effects of the FRP repair on the bridge?s behavior. 7.2 ANALYSIS 7.2.1 Stress Contours Due to Seams In refining the Pre-Repair model, bottom-fiber strain measurements, bottom-fiber deflection measurements, and girder-section strain profile measurements were all available for comparison between the load test results and the FEM models. As can be seen in Figures 6.9?6.16?and addressed in Section 6.2?the bottom-fiber strain measurements and the bottom-fiber deflection measurements provided a feasible point of reference for this purpose. 134 Figures 7.1 and 7.2 provide a good example of how the girder-section strain profile measurements are not so useful. These illustrate the strain values at various depths on one face of a specific cross section of a girder. These figures are from Cross Section 2?which is 4.75 in. from the face of the continuity diaphragm on Span 10?and Cross Section 3?which is 4.75 in. from the face of the continuity diaphragm on Span 11? respectively. Figure 7.1 shows the strain along the East face of Girder 7 for the A7 (near cracked region) Load Position, and Figure 7.2 shows the strain along the West face of Girder 8 for the C9 (midspan) Load Position. From these figures, it is apparent that the FEM results predict a strain profile quite different from that which was measured during the bridge testing. Other profiles can be seen in Appendices D?G. 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om Bottom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure 7.1 Strain Profile?A7 Load Position, Section 2, Girder 7, East Face 135 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bottom of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure 7.2 Strain Profile?C9 Load Position, Section 3, Girder 8, West Face By evaluating the strain contours of the ABAQUS Cracked-with-Reinforcement model shown in Figure 7.3, the reason for the disparity becomes apparent. The stress contours that result from the modeled seam are significantly different from the stress contours that are present on the real structure as a result of the crack groups?which are illustrated in Figures 3.6?3.14. In addition to the fact that multiple cracks are modeled as one seam, the cracks on the physical structure tend to run in a more diagonal fashion along the girder than was used in the seam approximations. Because the stresses and strains within this cracked region change drastically over a relatively small distance, this deviation from the actual cracking pattern causes the FEM results within that cracked region to be significantly different from the load test results. 136 Figure 7.3 Longitudinal Strain Contours for the Cracked-with-Reinforcement Model, A7 Load Position, Girder 7, East Face This does not necessarily mean, however, that the FEM results from within these cracked regions are useless. Though the differences here make a comparison between the analytical and the experimental results somewhat impractical at times, comparison between the Pre-Repair and Post-Repair results within these zones is still informative. Among others, there are two likely possibilities: 1. The global, post-repair behavior of the bridge will remain consistent with the overall behavior of the bridge prior to repair. This would result in the strain changes predicted by the FEMs being very close to the changes in strains measured during the two load tests. In other words, any discrepancies that exist between the Pre-Repair model and the behavior of the existing bridge would remain approximately constant after the bridge is repaired. Stress contours due to Seam Continuity Diaphragm Span 10 Span 11 Seam in FEM Actual Crack Location 137 2. The repair of the bridge will reestablish continuity and the post-repair behavior of the bridge will more effectively be described by the Post-Repair model than the behavior of the existing bridge was predicted by the Pre-Repair model. In the event that the first possibility occurs, the change in longitudinal strains between the Pre-Repair and Post-Repair models will still accurately reflect the change in longitudinal strains on the bridge due to the repair. In this case, the strain gauges within the cracked regions will still be useful for comparative purposes. If continuity is reestablished, however, comparisons between the Pre-Repair and Post-Repair models will no longer effectively predict the change from the pre-repair to the post-repair behavior of the actual bridge. In contrast, the analytical results for the Post-Repair model will more closely match the experimental results of the post-repair load test than the Pre-Repair model matches the pre-repair load test results. Section 7.5 details the forecasted behavior of the repaired structure and the resultant effects on the continuity of the bridge girders. 7.2.2 Tension Due to Cracking at the Face of the Continuity Diaphragm As the strains along the faces of the girders were compared at the various instrumented cross sections, it was interesting to discover that the seam along the face of the continuity diaphragm on Girder 6 on Span 11 appears to correspond with tension in the FRP of Girder 7. For the A9 Load Position, which has strong influence on Girder 7, the strain profile on Girder 7 for the East face of Cross Section 3?the instrumented cross section nearest the seam at the face of the continuity diaphragm in Girder 6?is shown in Figure 7.4. Figure 7.5 shows the strain contours in the FRP with the tension area 138 indicated. Figure 7.4 indicates that the bottom flange of the concrete is in compression but the adjacent FRP is in tension. The strain contours in Figure 7.5 show that this area of tension is located primarily at a corner of the FRP. Most likely, this tension results from a combination of two factors: both the seam at the face of the continuity diaphragm and the mesh pattern of Girder 7. To explain the effect that the mesh pattern of Girder 7 has on the analytical results of the FRP strains, it is first important to understand how the results of the models for the various gauge locations are obtained. The strain values reported to be at distances? where gauges are located?from the face of the continuity diaphragm are an interpolation of the strain values obtained from ABAQUS at the nodes on the near side and far side of the elements at that point. The locations of those nodes result from the mesh size. For instance, the values for the strains shown in Figure 7.1 are an interpolation?for a location 4.75 in. from the face of the continuity diaphragm?of strain values 4 in. and 12 in. from the face of the continuity diaphragm. The tie constraint?as explained in Section 5.12?between the FRP and Girder 7 is the final link leading to the tension reading. It seems most likely that the tension reported in the FRP is due to the FRP being tied to a node nearer to the bearing pad than the node from which the strain readings are taken for the concrete. Most likely the corner FRP node is tied to the concrete node at the center of the continuity diaphragm rather than the concrete node located 4 in. from the face, which is where ABAQUS reports the concrete strain. 139 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bott om of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure 7.4 Strain Profile?A9 Load Position, Section 3, Girder 7, East Face Figure 7.5 Strain Contours in FRP for Load Position A9 Tension in FRP adjacent to the face of the continuity diaphragm Girder 8 Span 11 Girder 8 Span 10 Girder 7 Span 11 Girder 7 Span 10 140 Finally, the continuity diaphragm between Girders 6 and 7?as well as the tie connection between the girders and the bridge deck?transfers the effects of the truck loading from the cracked region in Girder 6 to Girder 7. The tie connection between the Girder and the FRP?which connects the FRP to the concrete at the center of the continuity diaphragm location rather than at a distance 4 in. from the face of the diaphragm where the concrete strains are measured?then transmits this load through the tied nodes. 7.2.3 Force Developed in Strands at Cracks As explained in Section 3.4.2, it is most likely that the prestressing tendons have slipped as a result of the cracks in the girder end and all of the prestressing force in the tendons between the crack and the end of the girder has been lost (Barnes et al. 2006). It is not feasible to test this hypothesis with the FEMs created for this project because these FEMs only reflect changes due to applied external loads. Figures 6.5?6.8 indicate that the results of the Cracked model imply that no moment will be transmitted across the crack through the concrete, but the load tests reveal that a significant amount of strain does transmit within that cracked region. This suggests that regardless of whether the prestressing is still effective in the end regions, the strands are at least anchored well enough to resist some moment at the cracked sections in the service-load range. Because these FEMs do not include complex mechanical relationships for the bond interaction between the steel and concrete, this does not indicate whether the steel will stay anchored up to yield. 141 It can be noted by evaluating Figures 6.9?6.12 that the Cracked-with-Reinforcement model reproduces the behavior of the bridge, as determined by the pre-repair load test, accurately to within 5% at four of the six bottom-fiber gauges on each girder line. If the prestressing strands were moving freely within the concrete, the Cracked model?rather than the Cracked-with-Reinforcement model?would more closely reflect the behavior of the bridge. The stress changes resulting from the A7, A9, C7 and C9 Load Positions in the Pre- Repair model in the prestressing steel at the crack locations are presented in Table 7.1. These stress changes represent reasonably low stress ranges and could likely be anchored by surrounding concrete despite any previous slip. However, it cannot be safely inferred from this whether the strands would remain anchored for a significantly greater load approaching ultimate strength. Table 7.1 Compressive Stress Changes, due to Truck Loads, in Prestressing Steel at the Seam Locations of the Pre-Repair Model Span 10 Span 11 Span 10 Span 11 A7 3.7 1.6 1.2 0 A9 3.6 12 1.6 5.3 C7 3.5 1.5 1.8 0.2 C9 3.5 12 2.2 7.4 Compressive Stress Change in Prestressing Steel (ksi) Girder 7 Girder 8 Loa d Pos i tion s 7.2.4 Effectiveness of Midspan Diaphragms As the model was created and the strains were compared to those of the 2005 pre-repair load tests, a question arose as to how effective the midspan diaphragms are. As can be 142 seen from Figures 6.17?6.20, there is a disparate point?labeled as point ?A??in the FEM models at the location of the midspan diaphragms. As explained in Section 6.2.4, a model was created that did not include the diaphragms, and the results were compared to those of the Cracked-with-Reinforcement model and the test results. Again looking at Figures 6.17?6.20, it is apparent that the diaphragms are at least somewhat effective because the FEM model with the midspan diaphragms more closely models the overall behavior of the bridge than does the FEM model without the midspan diaphragms. It is also interesting to note from the figures the extent to which the midspan diaphragms distribute the load between the girders. This is particularly apparent in Figure 6.18?which is the graph for the A9 Load Position. The resultant strains in Girder 7 are approximately twice as great for the model without diaphragms as for the model with diaphragms. This effect can be seen?though not quite as drastically?for each of the other load positions. It can therefore be concluded that, with all other structural elements being equal, the load-carrying capacity of a bridge without diaphragms should be significantly less than the load-carrying capacity for a bridge with diaphragms. The bridge with diaphragms does a much better job of distributing the applied deck loads among the supporting girders. This effect contradicts the findings of Tedesco, Stallings, and Tow (1995). In addition, this effect was not considered in the creation of the FEMs used to develop the AASHTO-LRFD live load distribution factors for girder bridges, which were formulated for bridges without midspan diaphragms (Zokaie 2000). Further exploration of this effect could prove useful for future bridge design applications. 143 The cause of the discrepancy was not determined. Possibly the diaphragms are effective in only one global direction?which is not accurately modeled by the tie constraint between the diaphragm, girders, and bridge deck in the model. Another possibility is that the midspan gauge on Girder 7 is measuring the strains incorrectly. Looking again at Figures 6.17 through 6.20, one can see that for each load position, the Girder 7 measurement is the only midspan reading that is significantly different between the FEM results and the load test results. It would be prudent to test?and hopefully disprove?this theory prior to the post-repair load testing. After evaluation of the figures, because the global behavior of the bridge model was consistent with the global behavior of the bridge as measured by the pre-repair load test, it was determined not to pursue the cause of the possibly erroneous gauge reading at midspan. 7.3 INFERENCES REGARDING BRIDGE BEHAVIOR As presented in Section 3.4.2, Swenson (2003) considered the possibility that the bridge was behaving such that the girders were continuous across the span but with hinged behavior at the crack locations near the bent. A hinge describes a relationship in a beam where the relative translation of points on the neutral axis on either side of a cross section are identical but the planes on either side of the cross section are free to rotate relative to one another. This is similar to the relationship that was created in the FEM model when the seams were defined within the girders. However, in the FEM, nodes on the faces of the seam are free to move relative to each other, while continuity is retained at points on the cross section beyond the extent of the seam. Nonetheless, the relatively 144 small amount of bending moment that can be resisted at the seam locations when unreinforced (Cracked model) is not enough to cause a significant difference with respect to a hinge in a beam model. As can be seen in Figures 6.5?6.8, the cracked girders exhibit more effective continuity than would be expected if the Cracked model (hinged behavior) was accurate. However, it is also apparent that the bridge is not behaving in a manner consistent with the best-case scenario of an uncracked?and therefore fully continuous across the span?bridge unit. What is apparently occurring is that the prestressing strands, regardless of whether or not they are actively carrying a prestressing force, are still acting as reinforcement across the cracks and effectively acting as a rotational spring which helps to partially resist bending in a simple beam model. 7.4 GAUGE LOCATION ANALYSIS One main purpose when analyzing the data of the Post-Repair model was to determine which of the concrete strain gauges to retain and which to abandon in favor of gathering data at other positions. Because there are a limited number of channels for data gathering, it is important that each of the seventy-two channels be used to collect singularly useful information. In order to determine which of the gauges were least useful, the Pre-Repair and Post-Repair model results were compared, and the differences between the two were computed at each of the gauge locations. This difference is useful because, as explained in Section 7.2.1, the change in behavior resulting from the FRP repair is of interest. If there is little change expected due to the repair, it would not be very informative to 145 measure that lack. These predicted change calculations are presented in Tables 7.2 and 7.3. If the difference was less than five microstrain for multiple load positions, the gauge was possibly not in a very vital location for assessing the change in performance attributable to the FRP repair. Another criterion by which to judge the importance of a gauge location was to evaluate the results from the pre-repair load test. If the strain was consistently between negative ten and ten microstrain for all four load positions, this also indicated that the location was not as informative as another position might be? unless a large change in strain was predicted using the Post-Repair model. From Tables 7.2 and 7.3, it is apparent that the top-most strain gauge positions, located 43.5 in. above the base of the girder?labeled as Gauge F in Figures 4.21 and 4.22?provide significantly less noteworthy information than the other girder-section strain profile gauges. This is unsurprising given the gauges? nearness to the neutral axis of the composite girder. For example, at Cross Section 2 on Girder 8, the topmost gauge location?Gauge F?indicated changes of only 1, 2, 2, and 3 microstrain for the A7, A9, C7, and C9 Load Positions, respectively. Gauge A, located 13.5 in. above the base of the girder, on that same cross section, is predicted to experience changes of 15, - 40, 8, and -5 microstrain. While the changes in strain for the Gauge A location for two of these load positions are not very significant, the changes in strain for the other load positions are very informative. Therefore, use of the topmost gauge locations should be discontinued for the post-repair load test. 146 Table 7.2 Strain Gauge Evaluation?Girder 7 A7 A9 C7 C9 A7 A9 C7 C9 F c 43.58567YYYY E28.59385YYNY D b 13.5 0 -4 0 -2 N N N N A 13.5 0 -6 0 -5 Y N Y N C 3.0 -3 -6 -3 -5 N N N N M 0. -5-10-4-10YNYN F b,c 43.5 0 -4 -2 -3 Y Y Y Y E c 28.5 0 -10 -3 -8 Y Y Y Y D b 13.52031YNYN A 13.5 -8 -30 -10 -30 Y N Y N C 3.0 -2 1 0 8 NNNN B 3.0 10 15 0 -7 Y N N N F c 43.5 6 10 7 12 Y Y Y Y E c 28.5 7 12 13 12 Y Y Y Y D 13.5 -12 -18 -12 -8 Y Y Y N A 13.550202015YYYY C 3.0 -30 -33 -20 -25 Y N N N B 3.0 0 -35 -12 -20 N N Y Y F b,c 43.5 -4 3 -2 3 Y Y Y Y E b,c 28.5-2-5-5-4YYYY D 13.5 -4 -15 -8 -12 Y N Y N A 13.5 -8 -14 -10 -12 Y N Y N C 3.0 -3-22-7-20NNNN M 0.0 -10 -22 -9 -23 N N N N c All load test results for this gauge are less than or equal to ten microstrain Ht. from Girder Base Cros s Se ct i on 3 C r os s Sect i o n 4 a (-) represents a negative change from the pre-repair model to the post-repair model b Absolute value of all changes for this gauge are less than or equal to five microstrain Change a due to FRP Repair Load test data within 10 ?? of zero? Cros s Sect i o n 1 Cros s Sect i on 2 Gauge ID 147 Table 7.3 Strain Gauge Evaluation?Girder 8 A7 A9 C7 C9 A7 A9 C7 C9 F b,c 43.5 1 1 2 2 Y Y Y Y E b 28.5 2 1 5 2 Y Y Y N D b 13.5 0 -2 0 -4 Y N N N A 13.5 3 -32 4 -2 Y N N N C 3.0 -5 -5 -3 -6 N N N N M 0. 0-420 -8NNNN F b,c 43.5 1 2 2 3 Y Y Y Y E b,c 28.5 1 1 4 3 Y Y Y Y D 13.5 -6 -10 -4 -12 Y Y Y N A 13.5 15 -40 8 -5 Y N Y N C 3.0 -14 -10 -8 -7 N N N N B 3.0 20-4012-8YNNN F b,c 43.5 -1 1 3 2 Y Y Y Y E b 28.5 -1 -3 0 -1 Y N Y N D 13.5 6 6 6 12 Y Y Y N A 13.5 15 -25 12 -2 Y N N N C 3.0 -8 0 -3 3 YNNN B 3.0 16 -39 10 -10 N N N N F c 43.5 -1 5 0 7 Y Y Y Y E b 28.5 0 2 0 2 Y N Y N D b 13.5 4 -4 3 -5 Y N Y N A 13.5 -7 -22 -3 -8 Y N Y N C 3.0 8 -10 7 -10 Y N N N M 0. -3-42-2-20NNNN Gauge ID Cr oss Section 2 c All load test results for this gauge are less than or equal to ten microstrain Ht. from Girder Base Cro ss Section 3 Cross Section 4 a (-) represents a negative change from the pre-repair model to the post-repair model b Absolute value of all changes for this gauge are less than or equal to five microstrain Change a due to FRP Repair Load test data within 10 ?? of zero? Cross Section 1 148 The eight newly available gauge channels should be transferred elsewhere. In Figures 6.37?6.44 it can be observed that at the beginning and the end of the repaired region, the strains in the concrete and the FRP reinforcement approximate one another very closely. They come closest to matching one another at the end of the repaired region farthest from the seams. In the middle of the repaired region, the strains for the concrete and FRP reinforcement differ greatly. The strains in the FRP are significantly larger than those of the concrete. If the FRP is compensating for the weakening in the concrete, this would be expected. To measure this effect in the bridge?as well as to verify that the strain in the concrete and the FRP are the same where they should be?strain gauges should be placed on the FRP reinforcement on Span 11 at the bottom-fiber gauge locations at 75.25 in. and 104 in. from the face of the continuity diaphragm on each girder. These gauges would therefore be virtually on top of the strain gauges already present on the concrete. The remaining four gauges should also be placed on the FRP reinforcement along the bottom- fiber line, but these should be located directly under the main crack location for each span of both girders. These would measure the FRP strains to see if they match the predictions of the model where there is zero concrete strain. 7.5 FORECAST FOR REPAIR Evaluating the analytical deflection results presented in Section 6.3.2, it can be concluded that the FRP repair will likely result in the bridge behavior tending towards that of a continuous structure. In addition to the additional stiffness of the FRP, any closing of cracks under applied loads would move the structural behavior of the bridge 149 toward the Uncracked model behavior for additional loads. This could occur if the starting crack width is less than the closing displacement of the seam. As explained in Section 5.10, the seam used to approximate the effects of the crack allowed the sides of the ?crack? to move both apart and towards (and past) one another in the FEM. This was acceptable because in the concrete in the actual structure a space was already physically present between the two faces of the crack, and as such, some movement in either direction was possible. However, no initial condition in the FEM established that pre-existing gap. It is possible that this lack results in the discrepancy between the model data and the load test data at the location 75.25 in. from the face of the continuity diaphragm on Spans 10 and 11, as seen in Figures 6.21 and 6.23 and discussed in Section 6.2.5. On the instrumented girders, the Post-Repair model predicted longitudinal closing displacements at the bottom-fiber seam locations of 0.0005 in. to 0.004 in?as presented in Table 7.4. Existing crack widths vary throughout the day and have been reported to range up to 0.03 in. (Swenson 2003). However, measurements taken at the time of the pre-repair load test did not indicate widths greater than 0.01 in. (Fason and Barnes 2004). More precise measurements of the existing crack widths are presently not available. It is possible that at least some of the cracks will close when external loads are applied? which would further serve to increase the continuous behavior of the bridge. Given the additional stiffness due to the FRP and the closing of some cracks, it seems probable that the strain results predicted for the Post-Repair model are fairly accurate. This accuracy will be higher for the bottom-fiber strains than for the girder-profile strains 150 because of the variation in stress contours near the cracks?as discussed in Section 7.2.1?which may still potentially affect the comparison between analytical and experimental results. Table 7.4 Maximum Closing Displacements for Each Seam and Load Position Span 10 Span 11 Span 10 Span 11 A7 1.5 2 1.5 0.5 A9 2 4 1.5 3 C7 1.5 1.5 1.5 0.5 C9 1.5 4 1.5 4 Girder 7 Girder 8 Lo a d Positio n Closing Displacements (x10 -3 in.) However, there is, among others, one possible situation wherein the additional continuity predicted by the Post-Repair model would not occur. When looking at the strain results presented for the girder profiles in Appendices D?G, one can see that the model predicts that in much of the length of the repair, the FRP reinforcement will be in compression. This is also readily apparent when looking at the bottom-fiber strain results of the post-repair model presented in Figures 6.29?6.32. As explained in Section 5.16, fiber-reinforced polymer is a composite material of Tyfo SCH-41 reinforcing fabric and Tyfo S epoxy. Just as with a piece of cloth, the material can resist a great deal of tension, but there is little resistance to compression. However, given the short unbraced length present at the crack and the resultant high elastic buckling capacity, it is unlikely that this lack would affect the efficacy of the repair. For a unit width of a four-ply portion of the reinforcing fabric, the stiffness? EI?is approximately 4000 lb-in 2 . From Equation 7.1 (Gere 2001) and for a crack width 151 of 0.01 in.?a width larger than any of the cracks present on the bridge at the time of the pre-repair load testing?this results in a buckling load of 400x10 3 kips and a critical elastic buckling stress of 2.5x10 6 ksi. The largest compressive strain predicted in the FRP corresponds to a stress of only 6 ksi. Because the elastic buckling stress is more than four hundred thousand times greater than the compressive stress predicted in the FRP, second-order effects should have negligible impact on the FRP strength. 2 2 L EI P cr ? = Eq. 7.1 where P cr = Critical load E = Modulus of elasticity I = Moment of inertia L = Crack width Given that buckling of the FRP is not likely if the bond to the concrete remains effective on either side of the crack, it is possible that cyclic loading and unloading action could serve to deteriorate the bond between the FRP and the concrete. If this occurred, the unbraced length would increase, and it is possible that the material would buckle before it reached the compressive loads predicted in the Post-Repair model and prior to reestablishing bridge continuity. Recommendations for monitoring the FRP Repair and the ensuing bridge behavior are presented in Section 8.3. 152 CHAPTER 8: SUMMARY AND CONCLUSIONS 8.1 SUMMARY OF STUDY Spans 10 and 11 of the Interstate Highway 565 bridge structure in Huntsville, Alabama were noticed to be cracked shortly after their completion in the early 1990?s. After investigation, it was concluded that stress due to the temperature differential between the bridge deck and the bulb tee girders was the probable cause. Further research into the cause of the cracking, the results of the cracking, and the possible repair methods was conducted by ALDOT in cooperation with Auburn University personnel. It was concluded that fiber-reinforced polymer (FRP) repair was feasible, and a repair procedure was devised. In order to measure the efficacy of the repair, load tests were conducted on June 1 and 2, 2005 prior to the repair. Post-repair load tests are slated to be conducted after the FRP application. A finite-element model (FEM) was created to provide a basis for an analytical comparison to measured data and observed bridge behavior. Several models were created to simulate the current behavior of the bridge. Three models of the pre-repaired bridge were created: Uncracked, Cracked, and Cracked-with-Reinforcement. When compared to the load test data, the Cracked-with-Reinforcement model was determined to be a sufficiently accurate representation of the overall behavior of the physical structure. The model results imply that rather than behaving as a continuous two-span beam?as it 153 was designed to behave?the bridge is behaving somewhere between a fully continuous structure and a continuous beam with a hinge in the cracked region. The FRP repair was then modeled to analyze the expected effects of the FRP application and to determine which of the strain gauges used in the pre-repair load tests should be relocated for the post-repair tests. 8.2 CONCLUSIONS 1. Of the Uncracked, Cracked, and Cracked-with-Reinforcement models, the Cracked-with-Reinforcement model best represents the current behavior of the bridge. 2. The girder strain profiles within the cracked regions are strongly influenced by the specific crack patterns near the location of the strain gauges. The Pre-Repair model insufficiently represents the strains on the bridge within the cracked zone. For a global representation of the behavior of the bridge, however, the Pre-Repair model with the single, representative seam per girder span is sufficient. 3. Even if the prestressing force in the tendons is lost between the crack and the end of the girder, the strands are anchored well enough to resist girder moments at the cracked section in the service load range. 4. The diaphragms have a large effect on the live load distribution between the girders of the bridge. 5. Modeling the FRP as a laminar material is more conservative than modeling it as an isotropic material. 6. For this particular repair scheme, the FRP has the greatest effect on the strains in the concrete near the cracks. 154 7. As expected, the Post-Repair model predicts less change in strain is expected at locations closer to the neutral axis than at locations nearer to the FRP. 8. The repair is equally effective for Girder 7 and Girder 8. 9. For all four load positions, the repair acts to decrease the predicted change in deflection more at midspan of the loaded girder than at any other location. 10. Though the FRP is expected to be in compression, it is expected that the induced force will not result in instability of the FRP. 11. The repaired bridge should exhibit deflections approximately the same as the original, uncracked structure. 8.3 RECOMMENDATIONS 1. Further exploration into the effects of the midspan diaphragms on the girder behavior should be conducted. The disparate point which is present in the analytical results suggests that the midspan diaphragms on the structure are not as effective as the midspan diaphragms in the model. Exploring other types of modeling connections between the girders and the diaphragms is one route for pursuing this question. 2. Alternatively, it is possible that rather than being a function of the efficacy of the diaphragms, the disparate point is the result of a faulty gauge. It is important to test? and rule out or rectify?this possibility prior to the post-repair load testing. 3. In addition to exploring the effects of the midspan diaphragms for this specific instance, further exploration into the effect of midspan diaphragms on live load distribution is recommended. AASHTO-LRFD live load distribution factors do not 155 currently incorporate the effects of midspan diaphragms, and accounting for their presence could greatly increase bridge efficiency. 4. Prior to the FRP installation, more precise widths of the existing cracks should be measured, and the progression of cracks since the last inspection should be monitored. 5. For the post-repair load test, eight gauges should be relocated from the face of the girder near the top of the web?43.5 in. from the girder base?to bottom-fiber gauge locations on the surface of the FRP reinforcement. A gauge should be placed 75.25 in. from the face of the continuity diaphragm on Span 11 on both Girder 7 and Girder 8. A gauge should also be placed 104 in. from the face of the continuity diaphragm on Span 11 on both Girder 7 and Girder 8. Each of the remaining four gauges should be placed on the bottom-fiber of the FRP so as to cross the main crack location of each instrumented girder span. 6. The post-repair tests should occur within one year of the repair, within 30 days of June 1?the date of the pre-repair load tests?and the results should be compared with the results of the pre-repair tests. Of primary interest is the manner in which the repair affects the behavior of the bridge. 7. The effectiveness of the repair should be monitored regularly. 156 REFERENCES AASHTO. 2004. AASHTO LRFD bridge design specifications. 3 rd ed. Washington, D.C.: American Association of State Highway and Transportation Officials (AASHTO). ABAQUS. 2004. ABAQUS analysis user?s manual: version 6.5-1. ABAQUS, Inc. ABAQUS. 2006. ABAQUS analysis user?s manual: version 6.6-1. ABAQUS, Inc. ACI Committee 318. 2005. Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05). Farmington Hills, MI, American Concrete Institute. Alabama Department of Transportation (ALDOT). 1987. ?Plan and Profile of Proposed State Highway: Project No. ID 565-5(21)358? Montgomery, Alabama. Alabama Department of Transportation (ALDOT). 1994. ?Cracks in Precast Prestressed Bulb Tee Girders on Structure No.?s I-565-45-11.5 A. & B. on I-565 in Huntsville, Alabama.? Montgomery, Alabama. American Association of State Highway and Transportation Officials (AASHTO). 1997 16 th Ed., Standard Specifications for Highway Bridges, Washington, D.C. Barker, Richard M, and Jay A. Puckett. 1997. Design of Highway Bridges. New York: John Wiley & Sons, Inc. Barnes, Robert W., Anton K. Schindler, Kyle S. Swenson, Ningyu Gao, and William E. Fason. 2006. Cracking and repair of prestressed concrete bridge girders made continuous for live loads. In Extending the Life of Bridges: Concrete and Composites Buildings, Masonry and Civil Structures held in Edinburgh, Scotland 13-15 June 2006, edited by M.C. Forde. Galashiels, Scotland. Barr, Paul J., Marc O. Eberhard, and John F. Stanton, 2001. Live-load distribution factors in prestressed concrete girder bridges. Journal of Bridge Engineering 6 (5): 298-306. Chung, Wonseok, Judy Liu, and Elisa D. Sotelino, 2006. Influence of secondary elements and deck cracking on the lateral load distribution of steel girder bridges. 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Effects of superstructure flexibility on strength of reinforced concrete bridge decks. Computers & Structures 82: 13-23. Zokaie, Toorak, 2000. AASHTO-LRFD live load distribution specifications. Journal of Bridge Engineering 5 (2): 131-138. 159 APPENDICES 160 APPENDIX A: EXPLANATION OF DATA PRESENTED IN APPENDICES B THROUGH H A.1 INTRODUCTION Appendices B through G contain graphical results for the concrete surface strains and girder deflections of the bridge models which have been discussed in this thesis. Appendix H contains a summary of the load test data from the pre-FRP repair load test which took place June 2, 2005 in Huntsville, Alabama. The girder numbering scheme, load testing positions, measurement locations, and other reference information are summarized in this Appendix. A.2 GIRDER NUMBERING When looking northward at the cross section of the bridge, the girders are numbered as depicted in Figure A.1 with Girder 1 on the far left, proceeding through Girder 9 on the far right. From this perspective, the west side of each of the girders is on the left of the girder, and the east side of each of the girders is on the right of the girder. A.3 LONGITUDINAL LOAD POSITIONS As depicted in Figure A.2, there are nine longitudinal stop positions located along the length of the bridge. Table A.1 describes each of these stop positions which are defined by the middle axles of the trucks being centered on the location. They range from midspan of Span 10 to midspan of Span 11. Five stop positions are located on Span 10, and four stop positions are located on Span 11. 161 Figure A.1 Girder Numbering When Looking North 161 8? ? 0? AASHTO BT54 girders Cast-in-place concrete barrier 3? - 4 ?? 64? ? 0? 70? ? 9? 6.5? 1 2 3 4 5 6 7 8 9 162 Figure A.2 Longitudinal Stop Positions for Test Trucks 162 Centerline of Continuity Diaphragm on Bent 11 1200? Stop Line 2 291? Stop Line 3 151? Stop Line 4 70? Stop Line 5 12? Stop Line 6 70? Stop Line 7 128? Stop Line 8 300? Stop Line 9 600? Stop Line 1 600? Span 10 Span 11 163 There are three transverse positions defined for which data exists. Figures A.3 through A.5 depict cross-sectional images of the transverse lane positioning. Transverse Position A centers the west wheel group of the east truck on Girder 7. Transverse Position B centers the east wheel group of the west truck on Girder 7. Transverse Position C centers the west wheel group of the east truck on Girder 8. Table A.2 lists the distances between the trucks and the east barrier rail for each of the three lanes. Figure A.3 Transverse Truck Position A Figure A.4 Transverse Truck Position B 3? - 4 ?? 8? ? 0? AASHTO BT54 girders Cast-in-place concrete barrier 64? ? 0? 70? ? 9? 6.5? Girder 7 Girder 8 73.5? 75? 49? ST-6902 ST-6400 3? - 4 ?? 8? ? 0? AASHTO BT54 girders Cast-in-place concrete barrier 64? ? 0? 70? ? 9? 6.5? Girder 7 Girder 8 73.5? 75? 49? ST-6902 ST-6400 164 Figure A.5 Transverse Truck Position C Table A.1 Locations of the Nine Longitudinal Stop Positions Stop Position a No. Position Description Distance from Center of Continuity Diaphragm (in.) 1 Middle tire over the midspan of Span 10 -600 2 Front tire over Cross Section 1 b -291 3 Front tire over Cross Section 4 -151 4 Middle tire over Cross Section 1 -70 5 Rear tire over Cross Section 1 -12 6 Middle tire over Cross Section 4 70 7 Rear tire over Cross Section 4 128 8 Middle tire over the quarter-span of Span 11 300 9 Middle tire over the midspan of Span 11 600 a Trucks were stopped when the middle axles were located the specified distance from the center of continuity diaphragm b The convention for the numbering of the cross sections is given in Section 4.3.4.1 3? - 4 ?? 8? ? 0? AASHTO BT54 girders Cast-in-place concrete barrier 64? ? 0? 70? ? 9? 6.5? Girder 7 Girder 8 73.5? 75? 49? ST-6902 ST-6400 165 Table A.2 Transverse Lane Positions Lane East Truck - Distance to East Barrier Rail (in.) West Truck - Distance to East Barrier Rail (in.) A 226.75 350.75 B 178.75 302.75 C 130.75 254.75 Note: Distances are measured from the outside edge of the west side of each truck A.4 LOCATIONS FOR DEFLECTION MEASUREMENTS Figure A.6 shows the six positions at which deflections were measured at the base of each of the two girders. There were two deflection measurements on each of the girders in Span 10 and four deflection measurements on each of the girders in Span 11. A.5 LOCATIONS FOR STRAIN READINGS Strain readings from the pre-repair load test are easily organized into groups according to the locations of the gauges. One group represents the bottom fiber gauges. These readings are best represented by looking at a profile view of the bridge section. Bottom fiber strains were taken at six places along each of the two girders. In Span 10, they were measured 75.25 in. from the center of the continuity diaphragm. In Span 11, they were measured 75.25 in., 104 in., 272 in., 440 in., and 608 in. from the center of the continuity diaphragm. The second group represents the strain along one of four cross-sectional profiles of each girder, the locations of which are shown in profile in Figure A.7. On each of the girders, two cross sections were instrumented with six gauges on the faces of the girders (Cross Sections 2 and 3), and two cross sections were instrumented with five gauges on 166 the faces of the girders (Cross Sections 1 and 4). Cross Sections 2 and 3 are located 4.75 in. from the face of the continuity diaphragm in each span. Cross sections 1 and 4 are located 67.25 in. from the face of the continuity diaphragm. The locations of the six gauges (labeled A-F) are shown in Figure A.8. Cross Sections 1 and 4 do not have a gauge B but do have bottom-fiber gauges. A.6 LOCATIONS FOR CRACK OPENING DEVICES There were four crack opening devices measuring the crack widths during the pre-repair load tests. Two were on girder 7, and two were on girder 8. Each of the crack opening devices was installed 13.5 in. from the girder base, and their locations are given in Table A.3. Table A.3 Crack Opening Device Locations Distance from Continuity Diaphragm (in.) Face Distance from Continuity Diaphragm (in.) Face Girder 7 49.5 East 47.75 East Girder 8 40 West 56 East Span 10 Span 11 167 Figure A.6 Installed Deflectometer Locations 167 -- Deflectometer 150? Midspan Midspan Bent 11 150? 150? 150? 300? 300? Span 11 Span 10 D-1 D-2 D-3 D-5D-4 D-6 168 Figure A.7 Strain Profile Cross Section Locations Figure A.8 Strain Gauge Locations 75.25 in. from center of cont. diaphragm 75.25 in. from center of cont. diaphragm 12.75 in. from center of cont. diaphragm Cross Section 1 Cross Section 2 Cross Section 3 Cross Section 4 Span 10 Span 11 --- Strain Gage 3.5? 2? 2? 36? 4.5? 6? 26? 42? 18? 10? 2? ?? chamfer 54? 6? 3? 3? 3? 18? F E D C B A M 169 APPENDIX B: DEFLECTIONS As explained in Appendix A, deflections were measured in six places along the bottom of each of the two girders, as depicted in Figure A.6. There were two deflection measurements on each of the girders in Span 10 and four deflection measurements on each of the girders in Span 11. Figures B.1 through B.4 show the comparison between the experimental deflections and the analytical deflections for each of the Uncracked, Cracked, and Cracked-with- Reinforcement models. The deflection results of the Pre-Repair model are compared with those of the Post-Repair model in Figures B.5 through B.8. 170 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 -800 -600 -400 -200 0 200 400 600 800 Distance From Center of Continuity Diaphragm (in) Bo ttom-Fibe r De fle c tion due to Tr uc k Loa din g (in) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked G7 Cracked G8 Cracked G7 Cracked w/ Reinf G8 Cracked w/ Reinf Figure B.1 Bottom-Fiber Deflections for the Model Refinement?A7 Load Position -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 -800 -600 -400 -200 0 200 400 600 800 Distance From Center of Continuity Diaphragm (in) Botto m-Fi be r De fl e c t i on due to Tr uc k Loa di ng (i n) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked G7 Cracked G8 Cracked G7 Cracked w/ Reinf G8 Cracked w/ Reinf Figure B.2 Bottom-Fiber Deflections for the Model Refinement?A9 Load Position 171 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 -800 -600 -400 -200 0 200 400 600 800 Distance From Center of Continuity Diaphragm (in) Botto m-Fibe r De fle c tion du e to Tr uc k Loa din g (in) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked G7 Cracked G8 Cracked G7 Cracked w/ Reinf G8 Cracked w/ Reinf Figure B.3 Bottom-Fiber Deflections for the Model Refinement ?C7 Load Position -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 -800 -600 -400 -200 0 200 400 600 800 Distance From Center of Continuity Diaphragm (in) B o tt om-F i b e r De fl e c t i on d u e to Tru c k Lo ad in g ( i n ) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked G7 Cracked G8 Cracked G7 Cracked w/ Reinf G8 Cracked w/ Reinf Figure B.4 Bottom-Fiber Deflections for the Model Refinement?C9 Load Position 172 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 -800 -600 -400 -200 0 200 400 600 800 Distance From Center of Continuity Diaphragm (in) Botto m-Fibe r De fle c tion du e to Tr uc k Loa din g (in) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair G7 Post-Repair G8 Post-Repair Figure B.5 Bottom-Fiber Deflections for the Pre- v. Post-Repair Models?A7 Load Position -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 -800 -600 -400 -200 0 200 400 600 800 Distance From Center of Continuity Diaphragm (in) Bo ttom-Fibe r De fle c tion due to Tr uc k Loa din g (in) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair G7 Post-Repair G8 Post-Repair Figure B.6 Bottom-Fiber Deflections for the Pre- v. Post-Repair Models?A9 Load Position 173 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 -800 -600 -400 -200 0 200 400 600 800 Distance From Center of Continuity Diaphragm (in) Bot t om-F ibe r D e fle c ti on due to Tr u c k Loa ding ( i n) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair G7 Post-Repair G8 Post-Repair Figure B.7 Bottom-Fiber Deflections for the Pre- v. Post-Repair Models?C7 Load Position -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 -800 -600 -400 -200 0 200 400 600 800 Distance From Center of Continuity Diaphragm (in) B o ttom-F i be r De fl e c t i o n due to Tr uc k Loa di ng (i n) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair G7 Post-Repair G8 Post-Repair Figure B.8 Bottom-Fiber Deflections for the Pre- v. Post-Repair Models?C9 Load Position 174 APPENDIX C: BOTTOM-FIBER STRAINS As explained in Appendix A, bottom-fiber concrete surface strain readings were taken at six locations along each of the two instrumented girders. On Span 10, they were measured 75.25 in. from the center of the continuity diaphragm. On Span 11, they were measured 75.25 in., 104 in., 272 in., 440 in., and 608 in. from the center of the continuity diaphragm. Figures C.1 through C.4 depict the comparison between the bottom-fiber strains of the Uncracked, Cracked, and Cracked-with-Reinforcement models, as well as the load test results, at each of four load positions. The results from the Pre-Repair and Post-Repair models are presented in Figures C.5 through C.8. 175 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Botto m-Fi be r S t r a i n d u e to Tr uc k L o a d in g ( x 10 -6 ) G7 Load Test Data G8 Load Test Data G7 Uncracked G8 Uncracked G7 Cracked G8 Cracked G7 Cracked w/ Reinf G8 Cracked w/ Reinf Figure C.1 Bottom-Fiber Strain Data for the Model Refinement?A7 Load Position -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bot t om-Fiber Strain due to Tr uc k Loa ding ( x 10 -6 ) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked G7 Cracked G8 Cracked G7 Cracked w/ Reinf G8 Cracked w/ Reinf Figure C.2 Bottom-Fiber Strain Data for the Model Refinement?A9 Load Position 176 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Botto m-Fibe r S t r a in due t o Tr uc k Loa din g ( x 10 -6 ) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked G7 Cracked G8 Cracked G7 Cracked w/ Reinf G8 Cracked w/ Reinf Figure C.3 Bottom-Fiber Strain Data for the Model Refinement?C7 Load Position -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Strain ( x 10 -6 ) G7 Load Test G8 Load Test G7 Uncracked G8 Uncracked G7 Cracked G8 Cracked G7 Cracked w/ Reinf G8 Cracked w/ Reinf Figure C.4 Bottom-Fiber Strain Data for the Model Refinement?C9 Load Position 177 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bott om-Fiber Strain due to Tr uc k Loa d i ng (x 1 0 -6 ) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair G7 Post-Repair G8 Post-Repair Figure C.5 Bottom-Fiber Strain Data for the Pre- v. Post-Repair Models?A7 Load Position -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bottom -Fi b e r S t rain due to Tr u c k Loa d i ng (x 1 0 -6 ) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair G7 Post-Repair G8 Post-Repair Figure C.6 Bottom-Fiber Strain Data for the Pre- v. Post-Repair Models?A9 Load Position 178 -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bottom-Fiber St rain due t o Tr u c k Loa d i ng (x 1 0 -6 ) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair G7 Post-Repair G8 Post-Repair Figure C.7 Bottom-Fiber Strain Data for the Pre- v. Post-Repair Models?C7 Load Position -100 -50 0 50 100 150 -100 0 100 200 300 400 500 600 700 Distance From Center of Continuity Diaphragm (in) Bottom - Fi be r S t r a i n d u e to Tr u c k Loa d i ng ( x 10 -6 ) G7 Load Test G8 Load Test G7 Pre-Repair G8 Pre-Repair G7 Post-Repair G8 Post-Repair Figure C.8 Bottom-Fiber Strain Data for the Pre- v. Post-Repair Models?C9 Load Position 179 APPENDIX D: A7 LOAD POSITION STRAIN PROFILES Strains were measured along the faces of specific, instrumented cross sections of the two girders, as explained in Appendix A. The A7 Load Position and the locations of the instrumented cross sections are illustrated in Figure D.1. Figures D.2?D.17 graphically compare the experimental strains along these cross sections to the analytical results from both the Pre-Repair and Post-Repair models. In addition, the strains at the corresponding locations on the FRP are presented. Figure D.1 Strain Profile Cross Section Locations for Load Position A7 Cross Section 4 Cross Section 3 Cross Section 2 Cross Section 1 Continuity Diaphragm Span 11 Span 10 G7 G8 180 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure D.2 Strain Profile?Load Position A7, Section 1, Girder 7, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure D.3 Strain Profile?Load Position A7, Section 1, Girder 7, East Face 181 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure D.4 Strain Profile?Load Position A7, Section 1, Girder 8, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure D.5 Strain Profile?Load Position A7, Section 1, Girder 8, East Face 182 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure D.6 Strain Profile?Load Position A7, Section 2, Girder 7, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure D.7 Strain Profile?Load Position A7, Section 2, Girder 7, East Face 183 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure D.8 Strain Profile?Load Position A7, Section 2, Girder 8, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure D.9 Strain Profile?Load Position A7, Section 2, Girder 8, East Face 184 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure D.10 Strain Profile?Load Position A7, Section 3, Girder 7, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure D.11 Strain Profile?Load Position A7, Section 3, Girder 7, East Face 185 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure D.12 Strain Profile?Load Position A7, Section 3, Girder 8, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure D.13 Strain Profile?Load Position A7, Section 3, Girder 8, East Face 186 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure D.14 Strain Profile?Load Position A7, Section 4, Girder 7, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure D.15 Strain Profile?Load Position A7, Section 4, Girder 7, East Face 187 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure D.16 Strain Profile?Load Position A7, Section 4, Girder 8, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure D.17 Strain Profile?Load Position A7, Section 4, Girder 8, East Face 188 APPENDIX E: A9 LOAD POSITION STRAIN PROFILES Strains were measured along the faces of specific, instrumented cross sections of the two girders, as explained in Appendix A. The A9 Load Position and the locations of the instrumented cross sections are illustrated in Figure E.1. Figures E.2?E.17 graphically compare the experimental strains along these cross sections to the analytical results from both the Pre-Repair and Post-Repair models. In addition, the strains at the corresponding locations on the FRP are presented. Figure E.1 Strain Profile Cross Section Locations for Load Position A9 Cross Section 4 Cross Section 3 Cross Section 2 Cross Section 1 Continuity Diaphragm Span 11 Span 10 G7 G8 189 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure E.2 Strain Profile?Load Position A9, Section 1, Girder 7, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bottom of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure E.3 Strain Profile?Load Position A9, Section 1, Girder 7, East Face 190 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bott om of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure E.4 Strain Profile?Load Position A9, Section 1, Girder 8, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bottom of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure E.5 Strain Profile?Load Position A9, Section 1, Girder 8, East Face 191 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bott om of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure E.6 Strain Profile?Load Position A9, Section 2, Girder 7, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bottom of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure E.7 Strain Profile?Load Position A9, Section 2, Girder 7, East Face 192 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bott om of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure E.8 Strain Profile?Load Position A9, Section 2, Girder 8, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bottom of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure E.9 Strain Profile?Load Position A9, Section 2, Girder 8, East Face 193 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bott om of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure E.10 Strain Profile?Load Position A9, Section 3, Girder 7, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bottom of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure E.11 Strain Profile?Load Position A9, Section 3, Girder 7, East Face 194 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bott om of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure E.12 Strain Profile?Load Position A9, Section 3, Girder 8, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bottom of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure E.13 Strain Profile?Load Position A9, Section 3, Girder 8, East Face 195 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bott om of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure E.14 Strain Profile?Load Position A9, Section 4, Girder 7, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bottom of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure E.15 Strain Profile?Load Position A9, Section 4, Girder 7, East Face 196 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bott om of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure E.16 Strain Profile?Load Position A9, Section 4, Girder 8, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) He ight Fr om Bottom of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure E.17 Strain Profile?Load Position A9, Section 4, Girder 8, East Face 197 APPENDIX F: C7 LOAD POSITION STRAIN PROFILES Strains were measured along the faces of specific, instrumented cross sections of the two girders, as explained in Appendix A. The C7 Load Position and the locations of the instrumented cross sections are illustrated in Figure F.1. Figures F.2?F.17 graphically compare the experimental strains along these cross sections to the analytical results from both the Pre-Repair and Post-Repair models. In addition, the strains at the corresponding locations on the FRP are presented. Figure F.1 Strain Profile Cross Section Locations for Load Position C7 Cross Section 4 Cross Section 3 Cross Section 2 Cross Section 1 Continuity Diaphragm Span 11 Span 10 G7 G8 198 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repaired Concrete Post-Repair FRP Figure F.2 Strain Profile?Load Position C7, Section 1, Girder 7, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure F.3 Strain Profile?Load Position C7, Section 1, Girder 7, East Face 199 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure F.4 Strain Profile?Load Position C7, Section 1, Girder 8, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure F.5 Strain Profile?Load Position C7, Section 1, Girder 8, East Face 200 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure F.6 Strain Profile?Load Position C7, Section 2, Girder 7, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure F.7 Strain Profile?Load Position C7, Section 2, Girder 7, East Face 201 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure F.8 Strain Profile?Load Position C7, Section 2, Girder 8, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure F.9 Strain Profile?Load Position C7, Section 2, Girder 8, East Face 202 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure F.10 Strain Profile?Load Position C7, Section 3, Girder 7, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure F.11 Strain Profile?Load Position C7, Section 3, Girder 7, East Face 203 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure F.12 Strain Profile?Load Position C7, Section 3, Girder 8, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure F.13 Strain Profile?Load Position C7, Section 3, Girder 8, East Face 204 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure F.14 Strain Profile?Load Position C7, Section 4, Girder 7, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure F.15 Strain Profile?Load Position C7, Section 4, Girder 7, East Face 205 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure F.16 Strain Profile?Load Position C7, Section 4, Girder 8, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain due to Truck Loading (x10 -6 ) H e i ght Fr om B o ttom of Gi r d e r (i n) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure F.17 Strain Profile?Load Position C7, Section 4, Girder 8, East Face 206 APPENDIX G: C9 LOAD POSITION STRAIN PROFILES Strains were measured along the faces of specific, instrumented cross sections of the two girders, as explained in Appendix A. The C9 Load Position and the locations of the instrumented cross sections are illustrated in Figure G.1. Figures G.2?G.17 graphically compare the experimental strains along these cross sections to the analytical results from both the Pre-Repair and Post-Repair models. In addition, the strains at the corresponding locations on the FRP are presented. Figure G.1 Strain Profile Cross Section Locations for Load Position C9 Cross Section 4 Cross Section 3 Cross Section 2 Cross Section 1 Continuity Diaphragm Span 11 Span 10 G7 G8 207 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain (x10 -6 ) Heig ht Fro m Bot t om of Girder ( i n ) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure G.2 Strain Profile?Load Position C9, Section 1, Girder 7, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain (x10 -6 ) He ight F r om Botto m of Gir d er (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure G.3 Strain Profile?Load Position C9, Section 1, Girder 7, East Face 208 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain (x10 -6 ) He ight F r om Botto m of Gir d er (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure G.4 Strain Profile?Load Position C9, Section 1, Girder 8, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain (x10 -6 ) He ight F r om Botto m of Gir d er (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure G.5 Strain Profile?Load Position C9, Section 1, Girder 8, East Face 209 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain (x10 -6 ) He ight Fr om Bott om of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure G.6 Strain Profile?Load Position C9, Section 2, Girder 7, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain (x10 -6 ) He ight Fr om Bottom of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure G.7 Strain Profile?Load Position C9, Section 2, Girder 7, East Face 210 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain (x10 -6 ) He ight Fr om Bott om of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure G.8 Strain Profile?Load Position C9, Section 2, Girder 8, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain (x10 -6 ) He ight Fr om Bottom of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure G.9 Strain Profile?Load Position C9, Section 2, Girder 8, East Face 211 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain (x10 -6 ) He ight Fr om Bott om of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure G.10 Strain Profile?Load Position C9, Section 3, Girder 7, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain (x10 -6 ) He ight Fr om Bottom of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure G.11 Strain Profile?Load Position C9, Section 3, Girder 7, East Face 212 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain (x10 -6 ) He ight Fr om Bott om of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure G.12 Strain Profile?Load Position C9, Section 3, Girder 8, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain (x10 -6 ) He ight Fr om Bottom of Gir d e r (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure G.13 Strain Profile?Load Position C9, Section 3, Girder 8, East Face 213 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain (x10 -6 ) He ight F r om Botto m of Gir d er (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure G.14 Strain Profile?Load Position C9, Section 4, Girder 7, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain (x10 -6 ) He ight F r om Botto m of Gir d er (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure G.15 Strain Profile?Load Position C9, Section 4, Girder 7, East Face 214 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain (x10 -6 ) He ight F r om Botto m of Gir d er (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Repair FRP Figure G.16 Strain Profile?Load Position C9, Section 4, Girder 8, West Face 0 10 20 30 40 50 60 70 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 Strain (x10 -6 ) He ight F r om Botto m of Gir d er (in) Pre-Repair Model Pre-Repair Test Post-Repair Concrete Post-Concrete FRP Figure G.17 Strain Profile?Load Position C9, Section 4, Girder 8, East Face 215 APPENDIX H: LOAD TEST DATA As explained in Chapter 4, tests before and after FRP application needed to be conducted in order to test the efficacy of FRP repair. The pre-FRP load testing occurred on the mornings of June 1 and 2, 2005. This summary focuses on the second day of testing, which occurred on the morning of June 2, 2005. There were nine longitudinal stop positions and three distinct patterns of transverse positions, making a total of twenty-seven different load positions. Appendix A further explains the load testing which resulted in the experimental results presented in Tables H.1?H.3. 216 Table H.1 Pre-FRP Repair Load Test Data for Transverse Position A H t . of ga u ge f r om gi r d e r b a s e ( i n . ) D i s t . a f r o m c e n t e r of c o nt . d i a . ( i n . ) U n i t s A1 A2 A3 A4 Defl ect om et ers Girder 7 n/a -8 in -0.31 -0.18 -0.10 -0.05 n/a -8 in -0.20 -0.17 -0.10 -0.05 n/a 8 in 0.03 0.02 0.00 -0.01 n/a 8 in 0.05 0.04 0.01 -0.01 n/a 8 in 0.06 0.04 0.02 -0.01 n/a 8 in 0.06 0.04 0.02 -0.01 n/a -8 in -0.24 -0.14 -0.08 -0.04 n/a -8 in -0.16 -0.12 -0.07 -0.04 n/a 8 in 0.03 0.02 0.01 -0.01 n/a 8 in 0.05 0.03 0.01 -0.01 n/a 8 in 0.05 0.04 0.02 0.00 n/a 8 in 0.05 0.04 0.02 0.00 13.5 -40.00 mm -0.009 -0.007 -0.005 -0.003 13.5 56.00 mm -0.007 -0.006 -0.003 -0.003 13.5 -49.50 mm -0.017 -0.003 0.007 0.021 13.5 47.75 mm -0.022 -0.020 -0.010 -0.008 0.0 104 ?? -27 -22 -8 -2 0.0 272 ?? -24 -19 -8 2 0.0 440 ?? -18 -14 -7 0 0.0 608 ?? -1 -8-4-1 0.0 104 ?? -25 -19 -8 -2 0.0 272 ?? -19 -15 -7 0 0.0 440 ?? -14 -11 -5 1 0.0 608 ?? -6 -5 1 11 b The first two crack gauges are on Girder 8 and the second two are on Girder 7 Defl ect om et ers Girder 7 Girder 8 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 C r ack Gauges b B o t t o m -fi ber S t rai n s Girder 7 Girder 8 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 217 Table H.1 cont'd Pre-FRP Repair Load Test Data for Transverse Position A H t . o f ga u ge f r o m gi r d e r b a s e ( i n . ) D i s t . a f r om c e n t e r o f c o nt . di a . ( i n . ) U n i t s A5 A6 A7 A8 A9 Defl ect omet ers Girde r 7 n/a -8 in -0.02 0.01 0.02 0.05 0.05 n/a -8 in -0.02 0.01 0.02 0.04 0.05 n/a 8 in -0.02 -0.04 -0.06 -0.10 -0.09 n/a 8 in -0.03 -0.06 -0.10 -0.18 -0.20 n/a 8 in -0.03 -0.06 -0.10 -0.20 -0.27 n/a 8 in -0.02 -0.06 -0.09 -0.20 -0.30 n/a -8 in -0.01 0.01 0.02 0.05 0.05 n/a -8 in -0.02 0.01 0.02 0.04 0.04 n/a 8 in -0.01 -0.03 -0.05 -0.07 -0.08 n/a 8 in -0.02 -0.04 -0.07 -0.13 -0.15 n/a 8 in -0.02 -0.05 -0.08 -0.16 -0.21 n/a 8 in -0.02 -0.05 -0.07 -0.16 -0.23 13.5 -40.00 mm -0.001 -0.003 -0.005 -0.008 -0.009 13.5 56.00 mm -0.002 0.002 0.004 -0.004 -0.007 13.5 -49.50 mm 0.014 -0.005 -0.010 -0.019 -0.020 13.5 47.75 mm -0.006 0.012 0.019 -0.010 -0.021 0.0 104 ?? 013250-18 0.0 272 ?? 11 27 36 75 25 0.0 440 ?? 6 19316771 0.0 608 ?? 4 12215310 0.0 104 ?? 0 8 16 0 -13 0.0 272 ?? 8 19244818 0.0 440 ?? 5 14234854 0.0 608 ?? 9 7 17 39 74 b The first two crack gauges are on Girder 8 and the second two are on Girder 7 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 Defl ect omet ers Girde r 7 Girde r 8 Crac k Gauges b B o t t o m-fi ber S t rai n s Girder 7 Girder 8 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 218 Table H.1 cont'd Pre-FRP Repair Load Test Data for Transverse Position A H t . of ga u ge f r om gi r d e r ba s e ( i n . ) D i s t . a f r o m c e n t e r o f c o nt . di a . ( i n. ) U n i t s A1 A2 A3 A4 B o t t o m -fi ber S t ra i n s Girder 7 Cross Section 1 13.5 -75.25 ?? -14 -1 5 11 0.0 -75.25 ?? -17 -2 4 9 3.0 -75.25 ?? -21 1 10 20 13.5 -75.25 ?? -23 -3 6 12 28.5 -75.25 ?? -12 -3 1 7 43.5 -75.25 ?? -10 -11 -15 -6 13.5 -75.25 ?? -17 -5 0 6 0.0 -75.25 ?? -18 -2 3 11 3.0 -75.25 ?? -13 -2 0 3 13.5 -75.25 ?? -14 -5 0 3 28.5 -75.25 ?? -9 -4 -1 0 43.5 -75.25 ?? -6 -6 -8 -4 13.5 -12.75 ?? 5330 3.0 -12.75 ?? -39 -30 -20 -14 3.0 -12.75 ?? -117 -101 -77 -57 13.5 -12.75 ?? -8 -4 -2 -1 28.5 -12.75 ?? 2333 43.5 -12.75 ?? -1 -4 -3 -5 13.5 -12.75 ?? -3022 3.0 -12.75 ?? -33 -25 -16 -8 3.0 -12.75 ?? -16-9-7-6 13.5 -12.75 ?? 0333 28.5 -12.75 ?? 1222 43.5 -12.75 ?? -2 -3 -3 -3 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 B o t t o m -fi ber S t ra i n s Girder 7 Cross Section 2 Gi rd er 8 Cross Section 2 Girder 7 Cross Section 1 Girder 8 Cr oss Section 1 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 219 Table H.1 cont'd Pre-FRP Repair Load Test Data for Transverse Position A H t . o f g a g e f r o m gi r d e r b a s e ( i n . ) D i s t . a f r o m c e n t e r o f c o nt . di a . ( i n. ) U n i t s A5 A6 A7 A8 A9 B o t t o m-fi ber S t rains Girder 7 Cross Sectio n 1 13.5 -75.25 ?? 6-5-8-17-17 0.0 -75.25 ?? 5-6-9-19-20 3.0 -75.25 ?? 11 -8 -14 -26 -26 13.5 -75.25 ?? 6 -9 -15 -27 -28 28.5 -75.25 ?? 5-3-5-1-12 43.5 -75.25 ?? 4 0 0 -1 -1 13.5 -75.25 ?? 4-5-9-16-18 0.0 -75.25 ?? 6 -6 -11 -20 -21 3.0 -75.25 ?? 0 -6 -10 -19 -20 13.5 -75.25 ?? 1-6-9-16-17 28.5 -75.25 ?? 0 -2-4-8-9 43.5 -75.25 ?? 00000 13.5 -12.75 ?? 1 3 1 -2 -3 3.0 -12.75 ?? -10 -13 -16 -26 -22 3.0 -12.75 ?? -35 -44 -63 -96 -93 13.5 -12.75 ?? -1 -3 -7 -15 -16 28.5 -12.75 ?? 4 0 -1 -3 -4 43.5 -12.75 ?? -1 1 -1-4-4 13.5 -12.75 ?? 4 0 -4 -10 -13 3.0 -12.75 ?? -3 -4 -8 -13 -14 3.0 -12.75 ?? -4 -9 -14 -22 -22 13.5 -12.75 ?? 3-2-6-14-16 28.5 -12.75 ?? 2 0 -1 -3 -3 43.5 -12.75 ?? -2 -1 -2 -2 -2 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 B o t t o m-fi ber S t rains Girder 7 Cross Section 2 Girde r 8 Cross Sec tion 2 Girder 7 Cross Sectio n 1 Girder 8 Cro ss Section 1 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 220 Table H.1 cont'd Pre-FRP Repair Load Test Data for Transverse Position A H t . of ga u ge f r om gi r d e r ba s e ( i n . ) D i s t . a f r o m c e n t e r o f c o nt . di a . ( i n. ) U n i t s A1 A2 A3 A4 B o t t o m-fi ber S t rains Girder 7 Cross Sectio n 3 13.5 -12.75 ?? -24 -16 -6 0 0.0 -12.75 ?? -23 -20 -14 -11 3.0 -12.75 ?? -28 -22 -14 -9 13.5 -12.75 ?? -27 -20 -8 -3 28.5 -12.75 ?? -7 -4 -2 0 43.5 -12.75 ?? -3 -3 -1 -1 13.5 -12.75 ?? -59 -46 -23 -15 0.0 -12.75 ?? -12 -10 -8 -7 3.0 -12.75 ?? -23 -18 -11 -7 13.5 -12.75 ?? -25 -16 -9 -3 28.5 -12.75 ?? -28 -22 -14 -11 43.5 -12.75 ?? -1000 13.5 -75.25 ?? -19 -16 -6 -4 3.0 -75.25 ?? -28 -23 -8 -6 3.0 -75.25 ?? -28 -23 -10 -6 13.5 -75.25 ?? -19 -15 -6 -4 28.5 -75.25 ?? -1 -9-3-3 43.5 -75.25 ?? -1 0 2 -2 13.5 -75.25 ?? -16 -14 -5 -4 3.0 -75.25 ?? -27 -22 -9 -4 3.0 -75.25 ?? -43 -34 -18 -11 13.5 -75.25 ?? -22 -17 -8 -5 28.5 -75.25 ?? -8 -7 -3 -3 43.5 -75.25 ?? -1 -1 2 -2 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 B o t t o m-fi ber S t rains Girder 7 Cross Section 4 Girde r 8 Cross Sec tion 4 Girder 7 Cross Sectio n 3 Girder 8 Cro ss Section 3 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 221 Table H.1 cont'd Pre-FRP Repair Load Test Data for Transverse Position A H t . of g a u g e f r om gi r d e r b a s e ( i n . ) D i s t . a f r o m c e n t e r o f c o nt . di a . ( i n. ) U n i t s A5 A6 A7 A8 A9 B o t t o m-fi ber S t rains Girder 7 Cross Sectio n 3 13.5 -12.75 ?? 5 7 1 -5 -7 0.0 -12.75 ?? -6 -6 -10 -22 -21 3.0 -12.75 ?? -5 -4 -9 -22 -22 13.5 -12.75 ?? 4117-4-10 28.5 -12.75 ?? 23000 43.5 -12.75 ?? 0430-2 13.5 -12.75 ?? -6 9 6 -21 -35 0.0 -12.75 ?? -5 -9 -17 -27 -26 3.0 -12.75 ?? -3 0 -1 -8 -12 13.5 -12.75 ?? 1 2 -2 -6 -8 28.5 -12.75 ?? -6 -3 -3 -10 -15 43.5 -12.75 ?? 00-100 13.5 -75.25 ?? -2 5 5 -8 -15 3.0 -75.25 ?? -3 11 17 -10 -25 3.0 -75.25 ?? -3 8 12 -11 -25 13.5 -75.25 ?? -1 5 5 -8 -15 28.5 -75.25 ?? -1 3 -1 -8 -10 43.5 -75.25 ?? -2 2 -4-8-4 13.5 -75.25 ?? -1 4 3 -7 -11 3.0 -75.25 ?? -1 11 20 -2 -14 3.0 -75.25 ?? -5 4 6 -9 -28 13.5 -75.25 ?? -3 3 3 -9 -17 28.5 -75.25 ?? -3 -2 -9 -15 -12 43.5 -75.25 ?? -2 3 -1 -10 -7 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 B o t t o m-fi ber S t rains Girder 7 Cross Section 4 Girde r 8 Cross Sec tion 4 Girder 7 Cross Sectio n 3 Girder 8 Cro ss Section 3 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 mE Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 222 Table H.2 Pre-FRP Repair Load Test Data for Transverse Position B H t . of ga u ge f r om gi r d e r b a s e ( i n . ) D i s t . a f r o m c e n t e r of c o nt . d i a . ( i n . ) U n i t s B1 B2 B3 B4 Defl ect om et ers Girder 7 n/a -8 in -0.31 -0.18 -0.10 -0.05 n/a -8 in -0.20 -0.17 -0.10 -0.05 n/a 8 in 0.03 0.02 0.00 -0.01 n/a 8 in 0.05 0.04 0.01 -0.01 n/a 8 in 0.06 0.05 0.02 -0.01 n/a 8 in 0.07 0.05 0.02 -0.01 n/a -8 in -0.29 -0.17 -0.09 -0.04 n/a -8 in -0.19 -0.15 -0.09 -0.05 n/a 8 in 0.04 0.03 0.01 -0.01 n/a 8 in 0.05 0.04 0.02 -0.01 n/a 8 in 0.06 0.05 0.02 -0.01 n/a 8 in 0.06 0.05 0.02 0.00 13.5 -40.00 mm -0.010 -0.009 -0.007 -0.003 13.5 56.00 mm -0.009 -0.008 -0.005 -0.003 13.5 -49.50 mm -0.016 -0.002 0.008 0.021 13.5 47.75 mm -0.022 -0.021 -0.012 -0.009 0.0 104 ?? -27 -23 -9 -3 0.0 272 ?? -24 -20 -8 1 0.0 440 ?? -18 -15 -7 0 0.0 608 ?? -14 -10 -5 1 0.0 104 ?? -31 -26 -10 -3 0.0 272 ?? -23 -19 -8 2 0.0 440 ?? -17 -13 -6 1 0.0 608 ?? -4 4 4 5 b The first two crack gauges are on Girder 8 and the second two are on Girder 7 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 C r ack Gauges b B o t t o m -fi ber S t rai n s Girder 7 Girder 8 Defl ect om et ers Girder 7 Girder 8 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 223 Table H.2 cont?d Pre-FRP Repair Load Test Data for Transverse Position B H t . o f g a u g e f r o m g i r d e r b a s e ( i n . ) D i s t . a f r o m c e n t e r o f c o n t . d i a . ( i n . ) U n i t s B5 B6 B7 B8 B9 Defl ect om eters Girder 7 n/a -8 in -0.02 0.01 0.03 0.05 0.05 n/a -8 in -0.02 0.01 0.02 0.04 0.05 n/a 8 in -0.02 -0.04 -0.06 -0.10 -0.09 n/a 8 in -0.03 -0.06 -0.10 -0.18 -0.20 n/a 8 in -0.03 -0.06 -0.10 -0.20 -0.26 n/a 8 in -0.02 -0.06 -0.09 -0.20 -0.30 n/a -8 in -0.01 0.02 0.03 0.05 0.06 n/a -8 in -0.02 0.01 0.02 0.04 0.05 n/a 8 in -0.02 -0.04 -0.06 -0.09 -0.09 n/a 8 in -0.02 -0.06 -0.09 -0.16 -0.18 n/a 8 in -0.02 -0.06 -0.10 -0.20 -0.26 n/a 8 in -0.02 -0.06 -0.09 -0.19 -0.29 13.5 -40.00 mm -0.001 -0.005 -0.007 -0.010 -0.010 13.5 56.00 mm -0.002 0.003 0.007 -0.003 -0.008 13.5 -49.50 mm 0.013 -0.006 -0.011 -0.019 -0.020 13.5 47.75 mm -0.006 0.013 0.021 -0.007 -0.020 0.0 104 ?? -1 14 26 1 -18 0.0 272 ?? 11 27 36 76 25 0.0 440 ?? 6 19316671 0.0 608 ?? 5 13 23 54 112 0.0 104 ?? 012230-19 0.0 272 ?? 11 25 33 68 22 0.0 440 ?? 7 18306368 0.0 608 ?? 12 18 25 53 101 b The first two crack gauges are on Girder 8 and the second two are on Girder 7 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 Defl ect om eters Girder 7 Gi rder 8 C r ack Gaug es b Bottom-fiber Strai n s Gi rder 7 Gi rder 8 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 224 Table H.2 cont?d Pre-FRP Repair Load Test Data for Transverse Position B H t . of ga u ge f r om gi r d e r ba s e ( i n . ) D i s t . a f r o m c e n t e r o f c o nt . di a . ( i n. ) U n i t s B1 B2 B3 B4 B o t t o m-fi ber S t rains Girder 7 Cross Sectio n 1 13.5 -75.25 ?? -14 -1 5 10 0.0 -75.25 ?? -15 -1 6 11 3.0 -75.25 ?? -21 1 11 21 13.5 -75.25 ?? -23 -2 8 16 28.5 -75.25 ?? -12 -3 1 7 43.5 -75.25 ?? -10 -11 -16 -6 13.5 -75.25 ?? -22 -7 0 7 0.0 -75.25 ?? -23 -3 6 16 3.0 -75.25 ?? -19 -3 3 11 13.5 -75.25 ?? -19 -4 0 7 28.5 -75.25 ?? -12 -5 -2 2 43.5 -75.25 ?? -7 -7 -10 -5 13.5 -12.75 ?? 532-1 3.0 -12.75 ?? -30 -22 -16 -11 3.0 -12.75 ?? -126 -115 -88 -63 13.5 -12.75 ?? -8 -3 -2 -2 28.5 -12.75 ?? 1333 43.5 -12.75 ?? -1 -4 -4 -6 13.5 -12.75 ?? -3234 3.0 -12.75 ?? -35 -28 -16 -8 3.0 -12.75 ?? -26 -19 -15 -11 13.5 -12.75 ?? -2223 28.5 -12.75 ?? 1222 43.5 -12.75 ?? -3 -5 -4 -5 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 B o t t o m-fi ber S t rains Girder 7 Cross Section 2 Girde r 8 Cross Sec tion 2 Girder 7 Cross Sectio n 1 Girder 8 Cro ss Section 1 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 225 Table H.2 cont?d Pre-FRP Repair Load Test Data for Transverse Position B H t . of g a u g e f r om gi r d e r b a s e ( i n . ) D i s t . a f r o m c e n t e r o f c o nt . di a . ( i n. ) U n i t s B5 B6 B7 B8 B9 B o t t o m-fi ber S t rains Girder 7 Cross Sectio n 1 13.5 -75.25 ?? 6-4-9-16-17 0.0 -75.25 ?? 6 -6 -10 -19 -20 3.0 -75.25 ?? 10 -8 -14 -26 -26 13.5 -75.25 ?? 8 -9 -15 -27 -28 28.5 -75.25 ?? 5-3-6-1-12 43.5 -75.25 ?? 3 0 0 -1 -2 13.5 -75.25 ?? 5 -7 -13 -22 -23 0.0 -75.25 ?? 9 -9 -15 -27 -28 3.0 -75.25 ?? 5 -9 -15 -25 -26 13.5 -75.25 ?? 3 -8 -13 -21 -23 28.5 -75.25 ?? 3-4-6-1-12 43.5 -75.25 ?? 10000 13.5 -12.75 ?? 1 3 1 -1 -2 3.0 -12.75 ?? -8 -12 -16 -26 -23 3.0 -12.75 ?? -35 -41 -62 -92 -90 13.5 -12.75 ?? 0-3-7-15-16 28.5 -12.75 ?? 4 0 -1 -3 -4 43.5 -12.75 ?? -1 0 -1-4-4 13.5 -12.75 ?? 5-1-6-15-17 3.0 -12.75 ?? -3 -7 -13 -22 -22 3.0 -12.75 ?? -6 -12 -19 -29 -26 13.5 -12.75 ?? 5-3-8-18-20 28.5 -12.75 ?? 2 -1-2-4-4 43.5 -12.75 ?? -2 -2 -2 -3 -3 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 B o t t o m-fi ber S t rains Girder 7 Cross Section 2 Girde r 8 Cross Sec tion 2 Girder 7 Cross Sectio n 1 Girder 8 Cro ss Section 1 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 226 Table H.2 cont?d Pre-FRP Repair Load Test Data for Transverse Position B H t . o f ga u ge f r om gi r d e r b a s e ( i n . ) D i s t . a f r o m c e n t e r of c o nt . di a . ( i n. ) U n i t s B1 B2 B3 B4 B o t t o m -fi ber S t rai n s Girder 7 Cross Section 3 13.5 -12.75 ?? -24 -17 -7 -1 0.0 -12.75 ?? -24 -22 -13 -9 3.0 -12.75 ?? -25 -21 -14 -11 13.5 -12.75 ?? -26 -21 -9 -4 28.5 -12.75 ?? -6 -3 -2 0 43.5 -12.75 ?? -1 -1 -1 0 13.5 -12.75 ?? -75 -61 -33 -21 0.0 -12.75 ?? -17 -14 -11 -8 3.0 -12.75 ?? -27 -24 -17 -12 13.5 -12.75 ?? -31 -22 -13 -6 28.5 -12.75 ?? -37 -31 -21 -15 43.5 -12.75 ?? -2 -2 -2 -1 13.5 -75.25 ?? -18 -15 -6 -4 3.0 -75.25 ?? -27 -23 -8 -6 3.0 -75.25 ?? -29 -24 -9 -6 13.5 -75.25 ?? -19 -16 -7 -4 28.5 -75.25 ?? -12 -10 -3 -3 43.5 -75.25 ?? -1 0 2 -2 13.5 -75.25 ?? -21 -17 -9 -7 3.0 -75.25 ?? -33 -27 -12 -6 3.0 -75.25 ?? -54 -46 -21 -13 13.5 -75.25 ?? -28 -24 -12 -8 28.5 -75.25 ?? -12 -10 -6 -8 43.5 -75.25 ?? -2 -1 1 -4 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 B o t t o m -fi ber S t rai n s Girder 7 Cro ss Section 4 Girder 8 Cross Section 4 Girder 7 Cross Section 3 Girder 8 Cross Section 3 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 227 Table H.2 cont?d Pre-FRP Repair Load Test Data for Transverse Position B H t . of g a u g e f r om gi r d e r b a s e ( i n . ) D i s t . a f r o m c e n t e r o f c o nt . di a . ( i n. ) U n i t s B5 B6 B7 B8 B9 B o t t o m-fi ber S t rains Girder 7 Cross Sectio n 3 13.5 -12.75 ?? 5 7 2 -4 -6 0.0 -12.75 ?? -6 -3 -6 -15 -15 3.0 -12.75 ?? -5 -6 -13 -28 -28 13.5 -12.75 ?? 3116-6-1 28.5 -12.75 ?? 3 3 -1 -1 0 43.5 -12.75 ?? -1 5 2 -1 -2 13.5 -12.75 ?? -8 13 10 -25 -45 0.0 -12.75 ?? -5 -9 -17 -30 -28 3.0 -12.75 ?? -6 -3 -9 -19 -23 13.5 -12.75 ?? 2 2 -6 -11 -12 28.5 -12.75 ?? -9 0 -3 -14 -20 43.5 -12.75 ?? 0 -1-3-1 0 13.5 -75.25 ?? -2 5 5 -8 -16 3.0 -75.25 ?? -3 12 19 -10 -25 3.0 -75.25 ?? -3 10 15 -12 -26 13.5 -75.25 ?? -1 6 6 -8 -14 28.5 -75.25 ?? -1 3 0 -7 -10 43.5 -75.25 ?? -1 3 -4-8-3 13.5 -75.25 ?? -4 3 1 -12 -17 3.0 -75.25 ?? -1 16 27 -2 -21 3.0 -75.25 ?? -7 16 28 -14 -40 13.5 -75.25 ?? -3 5 6 -13 -23 28.5 -75.25 ?? -5 -3 -11 -20 -16 43.5 -75.25 ?? -2 2 -4 -13 -9 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 B o t t o m-fi ber S t rains Girder 7 Cross Section 4 Girde r 8 Cross Sec tion 4 Girder 7 Cross Sectio n 3 Girder 8 Cro ss Section 3 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 mE Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 228 Table H.3 Pre-FRP Repair Load Test Data for Transverse Position C H t . of ga u ge f r om gi r d e r b a s e ( i n . ) D i s t . a f r o m c e n t e r of c o nt . d i a . ( i n . ) U n i t s C1 C2 C3 C4 Defl ect om et ers Girder 7 n/a -8 in -0.28 -0.17 -0.09 -0.05 n/a -8 in -0.19 -0.15 -0.09 -0.05 n/a 8 in 0.03 0.02 0.00 -0.01 n/a 8 in 0.05 0.04 0.01 -0.01 n/a 8 in 0.06 0.05 0.02 0.00 n/a 8 in 0.06 0.04 0.02 0.00 n/a -8 in -0.33 -0.19 -0.10 -0.05 n/a -8 in -0.21 -0.17 -0.10 -0.06 n/a 8 in 0.04 0.03 0.01 -0.01 n/a 8 in 0.06 0.05 0.02 -0.01 n/a 8 in 0.07 0.05 0.02 -0.01 n/a 8 in 0.07 0.05 0.02 0.00 13.5 -40.00 mm -0.011 -0.010 -0.008 -0.004 13.5 56.00 mm -0.010 -0.009 -0.006 -0.004 13.5 -49.50 mm -0.011 0.001 0.009 0.019 13.5 47.75 mm -0.020 -0.019 -0.011 -0.008 0.0 104 ?? -25 -21 -8 -3 0.0 272 ?? -22 -18 -8 1 0.0 440 ?? -17 -13 -6 0 0.0 608 ?? -12 -9 -3 0 0.0 104 ?? -36 -30 -12 -4 0.0 272 ?? -27 -22 -10 2 0.0 440 ?? -19 -15 -7 1 0.0 608 ?? -14 -10 0 7 b The first two crack gauges are on Girder 8 and the second two are on Girder 7 Defl ect om et ers Girder 7 Girder 8 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 C r ack Gauges b Bot t o m -fi ber S t rai n s Girder 7 Gir d er 8 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 229 Table H.3 cont'd Pre-FRP Repair Load Test Data for Transverse Position C H t . o f ga u ge f r o m gi r d e r b a s e ( i n . ) D i s t . a f r om c e n t e r o f c o nt . di a . ( i n . ) U n i t s C5 C6 C7 C8 C9 Defl ect om eters Girder 7 n/a -8 in -0.02 0.01 0.02 0.05 0.05 n/a -8 in -0.02 0.01 0.02 0.04 0.05 n/a 8 in -0.02 -0.04 -0.06 -0.09 -0.09 n/a 8 in -0.02 -0.06 -0.08 -0.16 -0.18 n/a 8 in -0.02 -0.06 -0.09 -0.18 -0.24 n/a 8 in -0.02 -0.05 -0.08 -0.18 -0.27 n/a -8 in -0.02 0.02 0.03 0.06 0.06 n/a -8 in -0.02 0.01 0.02 0.05 0.05 n/a 8 in -0.02 -0.04 -0.07 -0.11 -0.10 n/a 8 in -0.03 -0.06 -0.10 -0.18 -0.21 n/a 8 in -0.03 -0.07 -0.11 -0.22 -0.29 n/a 8 in -0.02 -0.06 -0.10 -0.21 -0.32 13.5 -40.00 mm -0.001 -0.005 -0.008 -0.011 -0.011 13.5 56.00 mm -0.003 0.005 0.010 -0.003 -0.008 13.5 -49.50 mm 0.012 -0.005 -0.010 -0.018 -0.019 13.5 47.75 mm -0.006 0.012 0.020 -0.004 -0.016 0.0 104 ?? -1 12 23 1 -16 0.0 272 ?? 9 22316823 0.0 440 ?? 5 17275864 0.0 608 ?? 5 12214810 0.0 104 ?? -1 14 27 -1 -23 0.0 272 ?? 12 29 38 79 25 0.0 440 ?? 7 20337277 0.0 608 ?? 11920541 b The first two crack gauges are on Girder 8 and the second two are on Girder 7 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 Defl ect om eters Girder 7 Girder 8 C r ack Gauges b B o t t om -fi ber S t rai n s Gi rd er 7 Girder 8 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 230 Table H.3 cont'd Pre-FRP Repair Load Test Data for Transverse Position C H t . of ga u ge f r om gi r d e r ba s e ( i n . ) D i s t . a f r o m c e n t e r o f c o nt . di a . ( i n. ) U n i t s C1 C2 C3 C4 B o t t o m-fi ber S t rains Girder 7 Cross Sectio n 1 13.5 -75.25 ?? -11 -2 5 9 0.0 -75.25 ?? -14 -2 5 9 3.0 -75.25 ?? -16 0 10 19 13.5 -75.25 ?? -20 -3 7 14 28.5 -75.25 ?? -10 -3 1 6 43.5 -75.25 ?? -8 -9 -14 -7 13.5 -75.25 ?? -24 -8 0 9 0.0 -75.25 ?? -25 -2 7 19 3.0 -75.25 ?? -24 -5 4 11 13.5 -75.25 ?? -23 -8 0 7 28.5 -75.25 ?? -14 -7 -3 2 43.5 -75.25 ?? -8 -8 -12 -5 13.5 -12.75 ?? 421-1 3.0 -12.75 ?? -16 -11 -9 -7 3.0 -12.75 ?? -119 -107 -79 -54 13.5 -12.75 ?? -7 -3 -2 -1 28.5 -12.75 ?? 1222 43.5 -12.75 ?? -1 -4 -4 -5 13.5 -12.75 ?? -2234 3.0 -12.75 ?? -29 -23 -15 -7 3.0 -12.75 ?? -41 -28 -19 -12 13.5 -12.75 ?? -5024 28.5 -12.75 ?? 1333 43.5 -12.75 ?? -3 -5 -5 -6 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 B o t t o m-fi ber S t rains Girder 7 Cross Section 2 Girde r 8 Cross Sec tion 2 Girder 7 Cross Sectio n 1 Girder 8 Cro ss Section 1 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 231 Table H.3 cont'd Pre-FRP Repair Load Test Data for Transverse Position C H t . o f g a u g e f r om gi r d e r b a s e ( i n . ) D i s t . a f r o m c e n t e r of c o nt . di a . ( i n . ) U n i t s C5 C6 C7 C8 C9 B o t t o m -fi be r S t rai n s Girde r 7 Cross Se ction 1 13.5 -75.25 ?? 6-5-8-14-16 0.0 -75.25 ?? 5-6-9-18-18 3.0 -75.25 ?? 9-7-12-23-23 13.5 -75.25 ?? 6-8-14-25-26 28.5 -75.25 ?? 5-2-5-10-10 43.5 -75.25 ?? 300-1-1 13.5 -75.25 ?? 6-8-15-26-26 0.0 -75.25 ?? 11 -10 -18 -31 -32 3.0 -75.25 ?? 5 -10 -17 -29 -29 13.5 -75.25 ?? 4-8-14-24-25 28.5 -75.25 ?? 2-4-8-13-14 43.5 -75.25 ?? 2 -1-1-1-1 13.5 -12.75 ?? 021-1-2 3.0 -12.75 ?? -5 -10 -13 -23 -21 3.0 -12.75 ?? -28 -31 -48 -76 -76 13.5 -12.75 ?? 0-3-7-13-14 28.5 -12.75 ?? 3 0 -1 -3 -4 43.5 -12.75 ?? -2 0 -1 -3 -4 13.5 -12.75 ?? 6-1-7-19-21 3.0 -12.75 ?? -2 -7 -16 -29 -29 3.0 -12.75 ?? -7 -12 -19 -29 -27 13.5 -12.75 ?? 5-3-9-20-2 28.5 -12.75 ?? 3 -1-2-5-5 43.5 -12.75 ?? -1 -2 -3 -4 -4 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 B o t t o m -fi be r S t rai n s Girde r 7 Cross Sec tion 2 Girder 8 Cross Sec tion 2 Girde r 7 Cross Se ction 1 Girde r 8 Cross Sec tion 1 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 232 Table H.3 cont'd Pre-FRP Repair Load Test Data for Transverse Position C H t . of ga u ge f r om gi r d e r ba s e ( i n . ) D i s t . a f r o m c e n t e r o f c o nt . di a . ( i n. ) U n i t s C1 C2 C3 C4 B o t t o m-fi ber S t rains Girder 7 Cross Sectio n 3 13.5 -12.75 ?? -21 -14 -6 -1 0.0 -12.75 ?? -22 -19 -11 -7 3.0 -12.75 ?? -18 -15 -11 -8 13.5 -12.75 ?? -24 -18 -7 -4 28.5 -12.75 ?? -6 -4 -2 0 43.5 -12.75 ?? -2 -1 -1 0 13.5 -12.75 ?? -87 -73 -40 -27 0.0 -12.75 ?? -21 -18 -13 -10 3.0 -12.75 ?? -28 -24 -17 -13 13.5 -12.75 ?? -35 -25 -15 -7 28.5 -12.75 ?? -43 -36 -24 -18 43.5 -12.75 ?? -1 -1 -1 -1 13.5 -75.25 ?? -15 -13 -6 -5 3.0 -75.25 ?? -24 -20 -9 -6 3.0 -75.25 ?? -26 -22 -11 -7 13.5 -75.25 ?? -17 -14 -7 -4 28.5 -75.25 ?? -10-8-3-3 43.5 -75.25 ?? 001-2 13.5 -75.25 ?? -23 -20 -10 -8 3.0 -75.25 ?? -38 -32 -13 -7 3.0 -75.25 ?? -61 -54 -28 -17 13.5 -75.25 ?? -31 -27 -13 -8 28.5 -75.25 ?? -14 -11 -6 -8 43.5 -75.25 ?? -2 -2 2 -4 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 B o t t o m-fi ber S t rains Girder 7 Cross Section 4 Girde r 8 Cross Sec tion 4 Girder 7 Cross Sectio n 3 Girder 8 Cro ss Section 3 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 233 Table H.3 cont'd Pre-FRP Repair Load Test Data for Transverse Position C H t . of g a u g e f r om gi r d e r b a s e ( i n . ) D i s t . a f r o m c e n t e r o f c o nt . di a . ( i n. ) U n i t s C5 C6 C7 C8 C9 B o t t o m-fi ber S t rains Girder 7 Cross Sectio n 3 13.5 -75.25 ?? 5 7 1 -2 -4 0.0 -75.25 ?? -3 0 -3-7-8 3.0 -75.25 ?? -4 -5 -12 -30 -29 13.5 -75.25 ?? 3 7 4 -7 -11 28.5 -75.25 ?? 1 2 -1 -1 0 43.5 -75.25 ?? -1 3 1 -2 -3 13.5 -75.25 ?? -10 15 12 -27 -49 0.0 -75.25 ?? -5 -8 -17 -28 -25 3.0 -75.25 ?? -6 -4 -11 -29 -34 13.5 -75.25 ?? 2 2 -7 -15 -15 28.5 -75.25 ?? -11 0 -4 -17 -25 43.5 -75.25 ?? 0 0 -3 -2 0 13.5 -12.75 ?? -2 4 4 -7 -13 3.0 -12.75 ?? -3 10 17 -8 -21 3.0 -12.75 ?? -3 8 13 -11 -24 13.5 -12.75 ?? -2 5 5 -6 -12 28.5 -12.75 ?? -1 3 0 -5 -8 43.5 -12.75 ?? -1 3 -3-6-2 13.5 -12.75 ?? -4 3 1 -15 -22 3.0 -12.75 ?? -3 18 33 -4 -27 3.0 -12.75 ?? -8 17 28 -18 -50 13.5 -12.75 ?? -4 7 8 -15 -26 28.5 -12.75 ?? -4 -2 -13 -22 -19 43.5 -12.75 ?? -3 4 -4 -15 -9 a (-) distance from center of dia. is on Span 10, (+) distance from center of dia. is on Span 11 B o t t o m-fi ber S t rains Girder 7 Cross Section 4 Girde r 8 Cross Sec tion 4 Girder 7 Cross Sectio n 3 Girder 8 Cro ss Section 3 Outlier Eliminated Widely Varying Data Strains Between 1 and -1 mE Outlier Eliminated Widely Varying Data Strains Between 1 and -1 ?? 234 APPENDIX I: NOTATION AND ABBREVIATIONS A area AASHTO American Association of State Highway and Transportation Officials ACI American Concrete Institute AE acoustic emissions ALDOT Alabama Department of Transportation BT bulb-tee C3D4 4-node tetrahedral element C3D8 8-node brick element C3D8R 8-node brick element with reduced integration DOF degree of freedom E or E c modulus of elasticity E ft modulus of elasticity of the fiber in the direction that is transverse to the fiber longitudinal axis EI stiffness ERSG electrical-resistance strain gauge f fiber property FEM finite-element modeling FRP fiber-reinforced polymer G shear modulus GFRP glass fiber-reinforced polymer h height I moment of inertia L crack width, length l longitudinal direction LRFD load and resistance factor design m matrix property 235 p direction perpendicular to the plane P cr critical load PCI Precast/Prestressed Concrete Institute r 2 radius of gyration RC reinforced concrete S section modulus S4 4-node shell element S4R 4-node shell element with reduced integration T tension t transverse direction V volume fraction y t distance from neutral axis to the top of the flange ? (nu) Poisson?s ratio