R. W. Barnes, N. H. Burns, and M. E. Kreger Research Report

Transcription

1 Tehnial Report Doumentation Page 1. Report No. 2. Government Aession No. 3. Reipient s Catalog No. FHWA/TX-02/ Title and Subtitle 5. Report Date Development Length of 0.6-Inh Prestressing Strand in Standard Deember 1999 I-Shaped Pretensioned Conrete Beams 6. Performing Organization Code 7. Author(s) 8. Performing Organization Report No. R. W. Barnes, N. H. Burns, and M. E. Kreger Researh Report Performing Organization Name and Address 10. Work Unit No. (TRAIS) Center for Transportation Researh 11. Contrat or Grant No. The University of Texas at Austin Researh Study Red River, Suite 200 Austin, TX Sponsoring Ageny Name and Address 13. Type of Report and Period Covered Texas Department of Transportation Researh and Tehnology Transfer Offie P.O. Box 5080 Austin, TX Researh Report (9/95-8/98) 14. Sponsoring Ageny Code 15. Supplementary Notes Projet onduted in ooperation with the U.S. Department of Transportation, Federal Highway Administration, and the Texas Department of Transportation. 16. Abstrat The use of 0.6 in prestressing strand at a enter-to-enter spaing of 2 in allows for the optimal implementation of High Strength Conrete (HSC) in preast, prestressed onrete bridge superstrutures. For this strand onfiguration, partial debonding of strands is a desirable alternative to the traditional method of draping to alleviate extreme onrete stresses after prestress release. Experimental evidene suggests that existing ode provisions addressing the anhorage of pretensioned strands do not adequately desribe their behavior. In addition, the anhorage behavior of partially debonded strands is not fully understood. Results are reported from a researh study onduted to determine the anhorage behavior of 0.6 in strands at 2 in spaing in fullsize, plant-ast AASHTO Type I I-beams. Conrete strengths ranged up to 15,000 psi. Strand featured either a bright mill finish or a rusted surfae ondition. A variety of strand debonding onfigurations were investigated. The use of pull-out apaities and strand draw-in measurements to predit the anhorage behavior of prestressing strands was also examined. Along with reommended design proedures for anhorage of prestressing strand, a review of the evolution and shortomings of existing ode provisions is presented. The use of this strand onfiguration is onluded to be safe, and partial debonding of prestressing strands is shown to be an effetive means of reduing stresses in the end regions of pretensioned beams. 17. Key Words prestressed onrete, anhorage, debonding, transfer length high strength onrete (HSC), development length 19. Seurity Classif. (of report) Unlassified Form DOT F (8-72) 18. Distribution Statement 20. Seurity Classif. (of this page) Unlassified No restritions. This doument is available to the publi through the National Tehnial Information Servie, Springfield, Virginia Reprodution of ompleted page authorized 21. No. of pages Prie

2 DEVELOPMENT LENGTH OF 0.6-INCH PRESTRESSING STRAND IN STANDARD I-SHAPED PRETENSIONED CONCRETE BEAMS by R. W. Barnes, N. H. Burns, and M. E. Kreger Researh Report Researh Projet DEVELOPMENT LENGTH OF 15-MM (0.6-IN.) DIAMETER PRESTRESSING STRAND AT 50-MM (2-INCH) GRID SPACING IN STANDARD I-SHAPED PRETENSIONED CONCRETE BEAMS onduted for the Texas Department of Transportation In ooperation with the U.S. Department of Transportation Federal Highway Administration by the CENTER FOR TRANSPORTATION RESEARCH BUREAU OF ENGINEERING RESEARCH THE UNIVERSITY OF TEXAS AT AUSTIN Deember 1999

3 Researh performed in ooperation with the Texas Department of Transportation and the U.S. Department of Transportation, Federal Highway Administration. ACKNOWLEDGMENTS We greatly appreiate the finanial support from the Texas Department of Transportation that made this projet possible. The support of the projet diretors, Mary Lou Ralls (BRG) and Arnold Cohen (DES), and program oordinator, Rihard Wilkison (DES), is also very muh appreiated. We thank Projet Monitoring Committee members David Hohmann (DES), Gerald Lankes (CST), and John Vogel (HOU). We would also like to thank Don Harley (FHWA) and Sue Lane (FHWA) for their assistane on this projet. The authors would also like to thank the employees of the Texas Conrete Company partiularly Brue Williams and Burson Patton for their ooperation during the speimen fabriation phase of this study. Graduate Researh Assistants Heather Jobson and John Grove ontributed diretly to the researh, as did Jon Kilgore (SAT). We gratefully aknowledge the hard work of Usnik Tuladhar, Justin Billodeau, Kevin Skyrmes, Gulu Sumen, Shane Hadeed, Sherman White, Cem Topkaya, Jenny Mejia, Niole Garia, Disney Burns, and a host of other student researhers who volunteered their time and efforts at the Phil M. Ferguson Strutural Engineering Laboratory. DISCLAIMER The ontents of this report reflet the views of the authors, who are responsible for the fats and the auray of the data presented herein. The ontents do not neessarily reflet the view of the Federal Highway Administration or the Texas Department of Transportation. This report does not onstitute a standard, speifiation, or regulation. NOT INTENDED FOR CONSTRUCTION, PERMIT, OR BIDDING PURPOSES N. H. Burns, P.E. #20801 M.E. Kreger, P.E. #65541 Researh Supervisors iv

4 TABLE OF CONTENTS CHAPTER 1: INTRODUCTION Bakground Objetives Sope Organization of Report Notation... 4 CHAPTER 2: ANCHORAGE BEHAVIOR IN PRETENSIONED MEMBERS Introdution Definitions Development Length Transfer Length Flexural Bond Length Code Provisions for Anhorage of Fully Bonded Strands Relevant ACI and AASHTO Code Clauses and Commentary Bakground Researh Evolution of Development Length Expression Inadequay of Existing Code Expression for Development Length Transfer Bond Theory Transfer Bond Stress Mehanisms Influene of Conrete Strength Time-Dependent Effets Other Considerations Influene of Craking Flexural Bond and Craking Code Provisions for Anhorage of Partially Debonded Strands Relevant ACI and AASHTO Code Clauses and Commentary Bakground Researh Comments on Bakground Researh Influene of Craking on the Anhorage of Pretensioned Strands Anhorage Failure Criteria and Design Philosophy Anhorage Design Design of Midspan Setion for Flexural Resistane Determination of Strand Debonding Lengths and Configuration Servie Limit State Anhorage Performane Cheks...41 v

5 2.9.4 Strength Limit State Anhorage Performane Cheks Calulation of Prestress Fores at Setions Where Strands Are Not Fully Developed...42 CHAPTER 3: TEST SPECIMEN DETAILS Introdution Speimen Identifiation Speimen Design Strand Patterns Dek Design Mild Steel Beam Reinforement Material Properties Preast Conrete Cast-in Plae Conrete Prestressing Steel Mild Reinforing Steel Fabriation of Preast I-Beams Fabriation of Composite Dek Slab CHAPTER 4: STRAND PULL-OUT TESTING Introdution Bakground CTC Pull-out Tests University of Oklahoma Test Program Stresson Test Program Speimen Preparation Test Proedure Results and Disussion Summary and Conlusions CHAPTER 5: TRANSFER LENGTH TEST PROGRAM Introdution Test Proedure Speimen Preparation Appliation of Prestress Fore Conrete Surfae Strain Measurements Transfer Length Determination Constrution of Surfae Compressive Strain Profile Determination of Average Maximum Strain (AMS) Determination of 95% AMS Value Determination of Apparent Transfer Length...83 vi

6 5.3.5 Determination of Atual Transfer Length Preision of Reported Results Results and Disussion Conrete Strength and Tendon Prestress Time Strand Surfae Condition Method of Prestress Release Comparison of Test Data with Reommended Expressions Reommended Expression for Transfer Length Summary and Conlusions CHAPTER 6: DRAW-IN TEST PROGRAM Introdution Bakground Test Proedure Determination of Draw-In Value Disussion of Results Summary and Conlusions Reommendations CHAPTER 7: DEVELOPMENT LENGTH TEST PROGRAM Introdution Test Approah Test Configuration Instrumentation Measurement of Applied Load Measurement of Displaements Measurement of Strand Slip Measurement of Strains at the Extreme Compression Fiber Data Aquisition Test Proedure Analysis Proedures Presentation and Disussion of Test Results Speimens with All Strands Fully Bonded Speimens with Four Strands Partially Debonded over Support Speimens with 50 Perent of Bottom Flange Strands Partially Debonded Speimens with More than 50 Perent of Strands Partially Debonded Effets of Craking on the Development Length of Debonded Strands Reommended Expression for Development Length vii

7 7.10 Summary and Conlusions CHAPTER 8: RECOMMENDATIONS Design Reommendations Transfer Length Development Length Design Proess Reommendations for Further Researh Strand Bond Quality Post-Slip Anhorage Strength Bond-Shear Interation Top Bar Effet CHAPTER 9: SUMMARY AND CONCLUSIONS Summary Conlusions General Conlusions Detailed Conlusions APPENDIX A: CONCRETE MIX DESIGNS APPENDIX B: MATERIAL PROPERTIES APPENDIX C: CONCRETE STRAIN PROFILES APPENDIX D: STRAND DRAW-IN RESULTS APPENDIX E: MOMENT VS. DEFLECTION CHARTS NOTATION REFERENCES viii

8 LIST OF TABLES Table 3.1: Tendon Loation and Debonding Shedule Table 3.2: Speified Jaking Stress, f pj, for Top Strands (M3 and M4) Table 3.3: Speified Properties of Preast Conrete Mixes Table 4.1: Pull-Out Test Results Bright Strand, Low Strength Conrete Table 4.2: Pull-Out Test Results Rusted Strand, Low Strength Conrete Table 4.3: Pull-Out Test Results Bright Strand, Medium Strength Conrete Table 4.4: Pull-Out Test Results Rusted Strand, Medium Strength Conrete Table 4.5: Pull-Out Test Results Bright Strand, High Strength Conrete Table 4.6: Pull-Out Test Results Rusted Strand, High Strength Conrete Table 5.1: Transfer Length Results for L Series, Bright Strand Speimens (1 in = 25.4 mm) Table 5.2: Transfer Length Results for M Series, Bright Strand Speimens (1 in = 25.4 mm) Table 5.3: Transfer Length Results for H Series, Bright Strand Speimens (1 in = 25.4 mm) Table 5.4: Transfer Length Results for L Series, Rusted Strand Speimens (1 in = 25.4 mm) Table 5.5: Transfer Length Results for M Series, Rusted Strand Speimens (1 in = 25.4 mm) Table 5.6: Transfer Length Results for H Series, Rusted Strand Speimens (1 in = 25.4 mm) Table 5.7: Effet of Rusted Surfae Condition on Normalized Transfer Length Relative to Bright Surfae Condition Table 5.8: Effet of Live Prestress Release on Normalized Transfer Length Relative to Dead Prestress Release Table 7.1: Test Configurations for Speimens Containing Bright Strand (1 in = 25.4 mm) Table 7.2: Test Configurations for Speimens Containing Rusted Strand (1 in = 25.4 mm) Table 7.3: Development Length Test Results for Speimens with All Strands Fully Bonded (1 in = 25.4 mm) Table 7.4: Development Length Test Results for Speimens with Four Strands Partially Debonded over the Support (1 in = 25.4 mm) Table 7.5: Development Length Test Results for Speimens with 50% of Bottom Flange Strands Partially Debonded Bright Strands (1 in = 25.4 mm) Table 7.6: Development Length Test Results for Speimens with 50% of Bottom Flange Strands Partially Debonded Rusted Strands (1 in = 25.4 mm) Table 7.7: Summary of Texas Teh Development Length Test Results for Speimens with 50% of Bottom Flange Strands Partially Debonded Rusted Strands (1 in = 25.4 mm) Table 7.8: Development Length Test Results for Speimens with More than 50% of Bottom Flange Strands Partially Debonded Bright Strands (1 in = 25.4 mm) Table 7.9: Development Length Test Results for Speimens with More than 50% of Bottom Flange Strands Partially Debonded Rusted Strands (1 in = 25.4 mm) Table A.1: Series "L" Conrete Mix Design Table A.2: Series "M" Conrete Mix Design Table A.3: Series "H" Conrete Mix Design Table A.4: Cast-in-Plae Dek Conrete Mix Design ix

9 Table B.1: Mehanial Properties of Beam Speimen Conrete at Time of Release and at Pull-Out Testing Table B.2: Mehanial Properties of Conrete upon Removal of Dek Shoring Table B.3: Mehanial Properties of Conrete at Time of Development Length Testing, Speimens with Bright Strand Table B.4: Mehanial Properties of Conrete at Time of Development Length Testing, Speimens with Rusted Strand Table B.5: Average Conrete Compressive Strengths Obtained from Member-Cured and Math-Cured Test Cylinders at Various Ages x

10 LIST OF FIGURES Figure 1.1: Highway Bridge Featuring Preast, Pretensioned I-Beam Superstruture... 1 Figure 1.2: TxDOT U-Beam... 2 Figure 2.1: Variation of Steel Stress with Distane from Free End of Strand (from ACI 318R-99, Fig. R12.9)... 8 Figure 2.2: Figure 2.3: Histogram Ratios of Long-Term l t Values Obtained by Kaar, LaFraugh, and Mass to l t,al from f ACI 318 Commentary ( pe db ) Histogram Ratios of Long-Term l t Values Obtained by Kaar, LaFraugh, and Mass to l t,al from ACI 318 Shear Provisions (50d b ) Figure 2.4: Histogram Ratios of Long-Term l t Values Obtained by Kaar, LaFraugh, and Mass to l t,al = 0.55f pt d b Figure 2.5: Reinforement Subjet to Tensile Fore and Bond Stress Figure 2.6: Figure 2.7: Figure 2.8: Figure 2.9: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam Prior to Appliation of Loading Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam Immediately Prior to Flexural Craking Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam After Flexural Craking in Maximum Moment Region Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam as Craking Progresses Toward Support Figure 2.10: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam at Nominal Flexural Strength Figure 2.11: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam Prior to Appliation of Loading Short Embedment Length Figure 2.12: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam Immediately Prior to Flexural Craking Short Embedment Length Figure 2.13: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam After Flexural Craking in Maximum Moment Region Short Embedment Length Figure 2.14: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam as Craking Progresses Toward Support Short Embedment Length Figure 2.15: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam at Nominal Flexural Strength Short Embedment Length Figure 2.16: Comparison of Beams with Fully Bonded Strands and Partially Debonded Strands Subjeted to Maximum Moment Figure 2.17: Method A Relationship Between Steel Stress Capaity and Bonded Anhorage Length (No General Bond Slip) Figure 2.18: Method B Relationship Between Steel Stress Capaity and Bonded Anhorage Length (General Bond Slip Allowed) Figure 3.1: Speimen Identifiation System Figure 3.2: Casting Configuration for Typial Beam Pair Figure 3.3: Dimensions of AASHTO Type I Cross Setion (1 in = 25.4 mm) xi

11 Figure 3.4: Strand Identifiation Key (1 in = 25.4 mm) Figure 3.5: Dimensions and Reinforement of Cast-in-Plae Composite Dek (1 in = 25.4 mm) Figure 3.6: Mild Steel Reinforement for Speimens L0x, M0x, and H0x (1 in = 25.4 mm) Figure 3.7: Mild Steel Reinforement for Speimens L4x, M4x, H4x, L6x, M9x, and H9x (1 in = 25.4 mm) Figure 3.8: Reinforement Details (1 in =25.4 mm) Figure 3.9: Stress-Strain Curve of Prestressing Strand (Compared with Relationship from PCI Design Handbook) Figure 3.10: "Bright" Strand Surfae Condition Figure 3.11: "Rusted" Strand Surfae Condition Figure 3.12: Reinforement for Pair of I-Beams Figure 3.13: Anhorage Zone Reinforement for Speimen L4B-C Figure 3.14: Distributing Form Release Agent over Soffit Form Surfae Figure 3.15: Plaement of Side Forms Figure 3.16: Casting and Vibrating Preast Beam Conrete Figure 3.17: Covering Preast Beams with Curing Blankets Figure 3.18: Transfer of Prestress by Flame-Cutting Figure 3.19: Forms for Cast-in-Plae Dek Slab Figure 3.20: Slab Reinforement Prior to Casting Figure 3.21: Bull-Floating Surfae of Slab after Casting Figure 4.1: Pull-Out Test Blok Details (1 in = 25.4 mm) Figure 4.2: Pull-out Test Blok at Onset of Casting Figure 4.3: Casting Pull-out Test Blok Figure 4.4: Finished Pull-Out Test Blok Figure 4.5: Pull-out Test in Progress Figure 4.6: Moustafa Pull-out Test Results for Speimens with Conrete Strengths within the Range Reommended by Logan (1997) (1 kip = 4.45 kn) Figure 4.7: Pull-Out Capaities of All Bright Strand Speimens (1 kip = 4.45 kn, 1000 psi = 6.89 MPa) Figure 4.8: Pull-Out Capaities of All Rusted Strand Speimens (1 kip = 4.45 kn, 1000 psi = 6.89 MPa) Figure 5.1: Pair of Beam Speimens after Side Form Removal Figure 5.2: First Four DEMEC Loating Diss in Line (End of Beam at Left)...78 Figure 5.3: Performing a Measurement with DEMEC Gauge Figure 5.4: Assignment of Surfae Compressive Strain Values Figure 5.5: Corretion of Strain Profile to Remove Strain Due to Beam Weight...80 Figure 5.6: Loation of Average Maximum Strain Values for Speimen with Three Transfer Zones (Beam End H4R-A) Figure 5.7: Determination of Apparent Transfer Lengths (Beam End H4R-A) Figure 5.8: Strain Contours at Horizontal Setion through Bottom Flange at Depth of Strands Figure 5.9: Surfae Compressive Strain Profiles Predited for an Atual Transfer Length of 12 in (305 mm) xii

12 Figure 5.10: Relationship Between Atual Strand Transfer Length and Apparent Transfer Length for H4x Speimens Figure 5.11: Transfer Length as a Funtion of Tendon Prestress and Conrete Strength at Release Bright Strand Speimens Figure 5.12: Transfer Length as a Funtion of Tendon Prestress and Conrete Strength at Release Rusted and Bright Strand Speimens Figure 5.13: Effet of Time on Transfer Length Bright Strand Speimens Figure 5.14: Effet of Time on Transfer Length Rusted Strand Speimens Figure 5.15: Comparison of Measured Transfer Lengths to l t f 0. 5 pt = ksi db f i Figure 5.16: Comparison to l t f 0. 5 pt = ksi db over Conrete Strength Range f i Figure 5.17: Comparison of Measured Transfer Lengths to ACI 318-R12.9 Values Figure 5.18: Comparison to ACI 318-R12.9 Values over Conrete Strength Range Figure 5.19: Comparison of Measured Transfer Lengths to Values from ACI 318 and AASHTO Standard Shear Provisions Figure 5.20: Comparison to Values from ACI 318 and AASHTO Standard Shear Provisions over Conrete Strength Range Figure 5.21: Comparison of Measured Transfer Lengths to Values from AASHTO LRFD Shear Provisions Figure 5.22: Comparison to Values from AASHTO LRFD Shear Provisions over Conrete Strength Range Figure 5.23: Comparison of Measured Transfer Lengths to Values from Bukner Expression Figure 5.24: Comparison to Values from Bukner Expression over Conrete Strength Range Figure 5.25: Comparison of Measured Transfer Lengths to Values from Zia and Mostafa Expression Figure 5.26: Comparison to Values from Zia and Mostafa Expression over Conrete Strength Range Figure 5.27: Comparison of Measured Transfer Lengths to Values from Lane Expression Figure 5.28: Comparison to Values from Lane Expression over Conrete Strength Range Figure 5.29: Comparison to Values from Modified Lane Expression over Conrete Strength Range Figure 5.30: Comparison of Measured Transfer Lengths to Values from MC90 Expression Figure 5.31: Comparison to Values from MC90 Expression over Conrete Strength Range Figure 5.32: Comparison of Measured Transfer Lengths to Values from Mithell et al. Expression Figure 5.33: Comparison to Values from Mithell et al. Expression over Conrete Strength Range Figure 5.34: Transfer Lengths from Various Studies Figure 5.35: Transfer Lengths of Strands from Various Manufaturers Figure 6.1: Relationship between Draw-In and Transfer Length Figure 6.2: Alignment Brakets for Measuring Strand Draw-In Figure 6.3: Strands Painted to Provide Referenes for Draw-In Measurements Figure 6.4: Flame-Cut Strands after Release of Prestress Figure 6.5: L6B-B Strand Draw-In Results Bright Strand, Simultaneous Flame Release (1 in = 25.4 mm) xiii

13 Figure 6.6: M9B-C Strand Draw-In Results Bright Strand, Live End of Flame Release (1 in = 25.4 mm) Figure 6.7: Measured Initial Transfer Length vs. Average Draw-In Value at Release Figure 6.8: Measured Initial Transfer Length vs. Maximum Draw-In Value at Release Figure 6.9: Measured Long-Term Transfer Length vs. Average Long-Term Draw-In Value Figure 6.10: Measured Long-Term Transfer Length vs. Maximum Long-Term Draw-In Value Figure 6.11: Histogram Ratio of Transfer Length Calulated from Average Initial Draw-In to Measured Initial Transfer Length Figure 6.12: Histogram Ratio of Transfer Length Calulated from Maximum Initial Draw-In to Measured Initial Transfer Length Figure 6.13: Histogram Ratio of Transfer Length Calulated from Average Long-Term Draw-In to Measured Long-Term Transfer Length Figure 6.14: Histogram Ratio of Transfer Length Calulated from Maximum Long-Term Draw-In to Measured Long-Term Transfer Length Figure 6.15: Histogram Ratio of Transfer Length Calulated from Average Initial Draw-In to Measured Long-Term Transfer Length Figure 6.16: Histogram Ratio of Transfer Length Calulated from Maximum Initial Draw-In to Measured Long-Term Transfer Length Figure 7.1: Rotation of Beam Setion at Support and Shearing of Neoprene Bearing Pad Test L0B-A-96 at Final Load Figure 7.2: Load Appliation Components Test H0R-D Figure 7.3: Loading Frame and Hydrauli Cylinder Used to Apply Test Loads Figure 7.4: Configuration of Supports and Applied Load for Development Length Tests (1 in = 25.4 mm) Figure 7.5: Test H9R-C-96H under Load Figure 7.6: Linear Potentiometers Used to Measure Beam Defletion Figure 7.7: Tension-Wire System for Measuring Beam Defletions Test H4R-C-72H at Final Load Figure 7.8: Linear Potentiometers Used to Measure a) Strand Slip and b) Horizontal Bearing Pad Deformation 138 Figure 7.9: Linear Potentiometers Used to Measure a) Strand Slip, b) Horizontal Bearing Pad Deformation, and ) Vertial Support Displaement Figure 7.10: Four Strain Gauges Bonded to Conrete Dek for Measurement of Extreme Compression Fiber Strains Figure 7.11: Test H4B-D-62 after Yield of Tension Reinforement Figure 7.12: Crak Pattern for Test L0B-A-96 at Flexural Failure Figure 7.13: Test L0B-D-54 at Final Load Figure 7.14: Crak Pattern for Test L0B-D-54 at Flexural Failure with Strand Slip Figure 7.15: Flexural Bond Performane of Fully Bonded Speimens Normalized Flexural Tendon Stress at Slip vs. Normalized Flexural Bond Length Provided Figure 7.16: Flexural Bond Performane of Fully Bonded Speimens Normalized Flexural Tendon Stress at Ultimate Strength vs. Normalized Flexural Bond Length Provided Figure 7.17: Craking in the Anhorage Region of M0R-C-46H at Final Load Figure 7.18: H0R-B-46 Anhorage Region after Final Load Figure 7.19: H0R-C-46H Anhorage Region after Final Load xiv

14 Figure 7.20: Flexural Bond Performane of Speimens with Four Strands Partially Debonded over Support Normalized Flexural Tendon Stress at Slip vs. Normalized Flexural Bond Length Provided Figure 7.21: Flexural Bond Performane of Speimens with Four Strands Partially Debonded over Support Normalized Flexural Tendon Stress at Ultimate Strength vs. Normalized Flexural Bond Length Provided Figure 7.22: Test L4B-D-60 Shear-Flexure Craks within Transfer Length of Strands Debonded for 72 in (1.83 m) Figure 7.23: Test L4B-C-48H Craking within Strand Transfer Lengths at Final Load Figure 7.24: Test M4B-A-60 Shear-Flexure Crak within Transfer Length of Strands Debonded 72 in (1.83 m) Figure 7.25: Test H4B-D-62 Shear-Flexure Craking within Transfer Length of Strands Debonded for 72 in (1.83 m) Figure 7.26: Test H4B-D-62 Extent of Craking at End of Test Figure 7.27: Flexural Bond Performane of Speimens with 50 Perent of Strands Partially Debonded Normalized Flexural Tendon Stress at Slip vs. Normalized Flexural Bond Length Provided Strands Debonded 72 in (1.83 m) Figure 7.28: Flexural Bond Performane of Speimens with 50 Perent of Strands Partially Debonded Normalized Flexural Tendon Stress at Ultimate Strength vs. Normalized Flexural Bond Length Provided Strands Debonded 72 in (1.83 m) Figure 7.29: Flexural Bond Performane of Speimens with 50 Perent of Strands Partially Debonded Normalized Flexural Tendon Stress at Slip vs. Normalized Flexural Bond Length Provided Strands Debonded 36 in (0.91 m) Figure 7.30: Flexural Bond Performane of Speimens with 50 Perent of Strands Partially Debonded Normalized Flexural Tendon Stress at Ultimate Strength vs. Normalized Flexural Bond Length Provided Strands Debonded 36 in (0.91 m) Figure 7.31: Test L6B-B-114 Crak Passing Aross Strands at End of 108 in (2.74 m) Debonded Length Figure 7.32: Test L6B-B-114 Craks at Final Load Figure 7.33: Test L6B-D-84 Shear-Flexure Craks within Transfer Lengths of Debonded Strands Figure 7.34: Test L6B-D-84 Craks at Final Load Figure 7.35: Crak Pattern for Test M9B-A-180 at Flexural Failure Figure 7.36: Crak Pattern for Test M9B-B-96 at Flexural Failure with Strand Slip Figure 7.37: Test H9B-D-114 Craks at End of Strand Debonded Lengths (at Final Load) Figure 7.38: Test H9R-C-96H Crak at End of 108 in (2.74 m) Debonded Length Figure 7.39: Test H9R-C-96H Craks at Ends of 72 (1.83 m) and 108 in (2.74 m) Debonded Lengths Figure 7.40: Test H9R-C-96H Craks at Final Load (Flexural Failure with Strand Slip) Figure 7.41: Flexural Bond Performane of Speimens with More than 50 Perent of Strands Partially Debonded Normalized Flexural Tendon Stress at Slip vs. Normalized Flexural Bond Length Provided Strands Debonded 108 in (2.74 m) Figure 7.42: Flexural Bond Performane of Speimens with More than 50 Perent of Strands Partially Debonded Normalized Flexural Tendon Stress at Ultimate Strength vs. Normalized Flexural Bond Length Provided Strands Debonded 108 in (2.74 m) Figure 7.43: Flexural Bond Performane of Speimens with More than 50 Perent of Strands Partially Debonded Normalized Flexural Tendon Stress at Slip vs. Normalized Flexural Bond Length Provided Strands Debonded 72 in (1.83 m) xv

15 Figure 7.44: Flexural Bond Performane of Speimens with More than 50 Perent of Strands Partially Debonded Normalized Flexural Tendon Stress at Ultimate Strength vs. Normalized Flexural Bond Length Provided Strands Debonded 72 in (1.83 m) Figure 7.45: Prinipal Tensile Stresses at Craking Assoiated with Strand Slip Figure 7.46: Prinipal Tensile Stresses at Craking Assoiated with Strand Slip f Limited to 100 psi Figure C.1: Speimen L0B-A Measured Initial and Long Term Strain Profiles Figure C.2: Speimen L0B-B Measured Initial and Long Term Strain Profiles Figure C.3: Speimen L0B-C Measured Initial and Long Term Strain Profiles Figure C.4: Speimen L0B-D Measured Initial and Long Term Strain Profiles Figure C.5: Speimen L4B-A Measured Initial and Long Term Strain Profiles Figure C.6: Speimen L4B-B Measured Initial and Long Term Strain Profiles Figure C.7: Speimen L4B-C Measured Initial and Long Term Strain Profiles Figure C.8: Speimen L4B-D Measured Initial Strain Profile (Long Term Strains Not Measured) Figure C.9: Speimen L6B-A Measured Initial and Long Term Strain Profiles Figure C.10: Speimen L6B-B Measured Initial and Long Term Strain Profiles Figure C.11: Speimen L6B-C Measured Initial and Long Term Strain Profiles Figure C.12: Speimen L6B-D Measured Initial and Long Term Strain Profiles Figure C.13: Speimen M0B-A Measured Initial and Long Term Strain Profiles Figure C.14: Speimen M0B-B Measured Initial and Long Term Strain Profiles Figure C.15: Speimen M0B-C Measured Initial and Long Term Strain Profiles Figure C.16: Speimen M0B-D Measured Initial and Long Term Strain Profiles Figure C.17: Speimen M4B-A Measured Initial and Long Term Strain Profiles Figure C.18: Speimen M4B-B Measured Initial and Long Term Strain Profiles Figure C.19: Speimen M4B-C Measured Initial and Long Term Strain Profiles Figure C.20: Speimen M4B-D Measured Initial and Long Term Strain Profiles Figure C.21: Speimen M9B-A Measured Initial and Long Term Strain Profiles Figure C.22: Speimen M9B-B Measured Initial and Long Term Strain Profiles Figure C.23: Speimen M9B-C Measured Initial and Long Term Strain Profiles Figure C.24: Speimen M9B-D Measured Initial and Long Term Strain Profiles Figure C.25: Speimen H0B-A Measured Initial and Long Term Strain Profiles Figure C.26: Speimen H0B-B Measured Initial and Long Term Strain Profiles Figure C.27: Speimen H0B-C Measured Initial and Long Term Strain Profiles Figure C.28: Speimen H0B-D Measured Initial and Long Term Strain Profiles Figure C.29: Speimen H4B-A Measured Initial and Long Term Strain Profiles Figure C.30: Speimen H4B-B Measured Initial and Long Term Strain Profiles Figure C.31: Speimen H4B-C Measured Initial and Long Term Strain Profiles Figure C.32: Speimen H4B-D Measured Initial and Long Term Strain Profiles xvi

16 Figure C.33: Speimen H9B-A Measured Initial and Long Term Strain Profiles Figure C.34: Speimen H9B-B Measured Initial and Long Term Strain Profiles Figure C.35: Speimen H9B-C Measured Initial and Long Term Strain Profiles Figure C.36: Speimen H9B-D Measured Initial and Long Term Strain Profiles Figure C.37: Speimen L0R-A Measured Initial and Long Term Strain Profiles Figure C.38: Speimen L0R-B Measured Initial and Long Term Strain Profiles Figure C.39: Speimen L0R-C Measured Initial and Long Term Strain Profiles Figure C.40: Speimen L0R-D Measured Initial and Long Term Strain Profiles Figure C.41: Speimen L4R-A Measured Initial and Long Term Strain Profiles Figure C.42: Speimen L4R-B Measured Initial and Long Term Strain Profiles Figure C.43: Speimen L4R-B Measured Initial and Long Term Strain Profiles Figure C.44: Speimen L4R-D Measured Initial and Long Term Strain Profiles Figure C.45: Speimen L6R-A Measured Initial and Long Term Strain Profiles Figure C.46: Speimen L6R-B Measured Initial and Long Term Strain Profiles Figure C.47: Speimen L6R-C Measured Initial and Long Term Strain Profiles Figure C.48: Speimen L6R-D Measured Initial and Long Term Strain Profiles Figure C.49: Speimen M0R-A Measured Initial and Long Term Strain Profiles Figure C.50: Speimen M0R-B Measured Initial and Long Term Strain Profiles Figure C.51: Speimen M0R-C Measured Initial and Long Term Strain Profiles Figure C.52: Speimen M0R-D Measured Initial and Long Term Strain Profiles Figure C.53: Speimen M4R-A Measured Initial and Long Term Strain Profiles Figure C.54: Speimen M4R-B Measured Initial and Long Term Strain Profiles Figure C.55: Speimen M4R-C Measured Initial and Long Term Strain Profiles Figure C.56: Speimen M4R-D Measured Initial and Long Term Strain Profiles Figure C.57: Speimen M9R-A Measured Initial and Long Term Strain Profiles Figure C.58: Speimen M9R-B Measured Initial and Long Term Strain Profiles Figure C.59: Speimen M9R-C Measured Initial and Long Term Strain Profiles Figure C.60: Speimen M9R-D Measured Initial and Long Term Strain Profiles Figure C.61: Speimen H0R-A Measured Initial and Long Term Strain Profiles Figure C.62: Speimen H0R-B Measured Initial and Long Term Strain Profiles Figure C.63: Speimen H0R-C Measured Initial and Long Term Strain Profiles Figure C.64: Speimen H0R-D Measured Initial and Long Term Strain Profiles Figure C.65: Speimen H4R-A Measured Initial and Long Term Strain Profiles Figure C.66: Speimen H4R-B Measured Initial and Long Term Strain Profiles Figure C.67: Speimen H4R-C Measured Initial and Long Term Strain Profiles Figure C.68: Speimen H4R-D Measured Initial and Long Term Strain Profiles Figure C.69: Speimen H9R-A Measured Initial and Long Term Strain Profiles xvii

17 Figure C.70: Speimen H9R-B Measured Initial and Long Term Strain Profiles Figure C.71: Speimen H9R-C Measured Initial and Long Term Strain Profiles Figure C.72: Speimen H9R-D Measured Initial and Long Term Strain Profiles Figure D.1: Strand Identifiation Sheme Figure D.2: Strand Draw-In Results for L0B Beam Speimen Pair (Bright Strand, Simultaneous Flame Release) Figure D.3: L4B-A Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.4: L4B-B Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.5: L4B-C Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.6: L4B-D Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.7: L6B-A Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.8: L6B-B Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.9: L6B-C Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.10: L6B-D Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.11: M4B-A Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.12: M4B-B Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.13: M4B-C Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.14: M4B-D Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.15: M9B-A Strand Draw-In Results (Bright Strand, Dead End of Flame Release) Figure D.16: M9B-B Strand Draw-In Results (Bright Strand, Live End of Flame Release) Figure D.17: M9B-C Strand Draw-In Results (Bright Strand, Live End of Flame Release) Figure D.18: M9B-D Strand Draw-In Results (Bright Strand, Dead End of Flame Release) Figure D.19: H0B-A Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.20: H0B-B Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.21: H0B-C Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.22: H0B-D Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.23: H4B-A Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.24: H4B-B Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.25: H4B-C Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.26: H4B-D Strand Draw-In Results (Bright Strand, Simultaneous Flame Release) Figure D.27: H9B-A Strand Draw-In Results (Bright Strand, Dead End of Flame Release) Figure D.28: H9B-B Strand Draw-In Results (Bright Strand, Live End of Flame Release) Figure D.29: H9B-C Strand Draw-In Results (Bright Strand, Live End of Flame Release) Figure D.30: H9B-D Strand Draw-In Results (Bright Strand, Dead End of Flame Release) Figure D.31: L0R-A Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.32: L0R-B Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.33: L0R-C Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) xviii

18 Figure D.34: L0R-D Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.35: L4R-A Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.36: L4R-B Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.37: L4R-C Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.38: L4R-D Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.39: L6R-A Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.40: L6R-B Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.41: L6R-C Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.42: L6R-D Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.43: M0R-A Strand Draw-In Results (Rusted Strand, Dead End of Flame Release) Figure D.44: M0R-B Strand Draw-In Results (Rusted Strand, Live End of Flame Release) Figure D.45: M0R-C Strand Draw-In Results (Rusted Strand, Live End of Flame Release) Figure D.46: M0R-D Strand Draw-In Results (Rusted Strand, Dead End of Flame Release) Figure D.47: M4R-A Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.48: M4R-B Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.49: M4R-C Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.50: M4R-D Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.51: M9R-A Strand Draw-In Results (Rusted Strand, Dead End of Flame Release) Figure D.52: M9R-B Strand Draw-In Results (Rusted Strand, Live End of Flame Release) Figure D.53: M9R-C Strand Draw-In Results (Rusted Strand, Live End of Flame Release) Figure D.54: M9R-D Strand Draw-In Results (Rusted Strand, Dead End of Flame Release) Figure D.55: H0R-A Strand Draw-In Results (Rusted Strand, Dead End of Flame Release) Figure D.56: H0R-B Strand Draw-In Results (Rusted Strand, Live End of Flame Release) Figure D.57: H0R-C Strand Draw-In Results (Rusted Strand, Live End of Flame Release) Figure D.58: H0R-D Strand Draw-In Results (Rusted Strand, Dead End of Flame Release) Figure D.59: H4R-A Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.60: H4R-B Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.61: H4R-C Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.62: H4R-D Strand Draw-In Results (Rusted Strand, Simultaneous Flame Release) Figure D.63: H9R-A Strand Draw-In Results (Rusted Strand, Dead End of Flame Release) Figure D.64: H9R-B Strand Draw-In Results (Rusted Strand, Live End of Flame Release) Figure D.65: H9R-C Strand Draw-In Results (Rusted Strand, Live End of Flame Release) Figure D.66: H9R-D Strand Draw-In Results (Rusted Strand, Dead End of Flame Release) Figure E.1: Test L0B-A-96 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.2: Test L0B-B-72 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.3: Test L0B-D-54 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.4: Test L0B-C-54H Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) xix

19 Figure E.5: Test M0B-A-96 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.6: Test M0B-B-72 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.7: Test M0B-D-54 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.8: Test M0B-C-54H Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.9: Test H0B-A-96 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.10: Test H0B-B-72 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.11: Test H0B-D-54 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.12: Test H0B-C-54H Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.13: Test M0R-A-96 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.14: Test M0R-B-54 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.15: Test M0R-D-46 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.16: Test M0R-C-46H Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.17: Test H0R-A-96 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.18: Test H0R-D-66 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.19: Test H0R-B-46 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.20: Test H0R-C-46H Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.21: Test L4B-B-96 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.22: Test L4B-D-60 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.23: Test L4B-A-48 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.24: Test L4B-C-48H Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.25: Test M4B-A-60 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.26: Test M4B-D-56 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.27: Test M4B-C-56H Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.28: Test M4B-B-48 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.29: Test H4B-D-62 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.30: Test H4B-C-62H Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.31: Test H4B-A-56 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.32: Test H4B-B-50 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.33: Test M4R-A-96 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.34: Test M4R-D-90 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.35: Test M4R-C-78H Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.36: Test M4R-B-56 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.37: Test H4R-A-82 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.38: Test H4R-D-78 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.39: Test H4R-B-72 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.40: Test H4R-C-72H Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.41: Test L6B-B-114 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) xx

20 Figure E.42: Test L6B-A-96 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.43: Test L6B-D-84 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.44: Test L6B-C-84H Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.45: Test M9B-A-180 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.46: Test M9B-D-114 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.47: Test M9B-B-96 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.48: Test M9B-C-96H Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.49: Test H9B-A-180 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.50: Test H9B-D-114 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.51: Test H9B-B-96 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.52: Test H9B-C-96H Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.53: Test M9R-A-180 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.54: Test M9R-D-114 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.55: Test M9R-B-96 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.56: Test M9R-C-96H Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.57: Test H9R-A-180 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.58: Test H9R-D-114 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.59: Test H9R-B-96 Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) Figure E.60: Test H9R-C-96H Normalized Moment at Critial Setion vs. Defletion (1 in = 25.4 mm) xxi

21 xxii

22 SUMMARY The use of 0.6 in prestressing strand at a enter-to-enter spaing of 2 in allows for the optimal implementation of High Strength Conrete (HSC) in preast, prestressed onrete bridge superstrutures. For this strand onfiguration, partial debonding of strands is a desirable alternative to the more traditional method of draping strands to alleviate extreme onrete stresses after prestress release. Reent experimental evidene suggests that existing ode provisions addressing the anhorage of pretensioned strands do not adequately desribe the behavior of these strands. In addition, the anhorage behavior of partially debonded strands is not fully understood. These unertainties have ombined to hinder the full exploitation of HSC in pretensioned onrete onstrution. A researh study was onduted to determine the anhorage behavior of 0.6 in strands at 2 in spaing in full-size bridge members. The experimental program onsisted of assessing transfer and development lengths in plant-ast AASHTO Type I I-beams. The influene of onrete ompressive strengths ranging from 5700 to 14,700 psi was examined. In order to onsider the full range of strand surfae onditions found in pratie, the prestressing strand featured either a bright mill finish or a rusted surfae ondition. The anhorage behavior of partially debonded strands was investigated by using a variety of strand debonding onfigurations inluding debonded strand perentages as high as 75 perent. A limited investigation of the effet of horizontal web reinforement on anhorage behavior was performed. Pullout tests were performed in an attempt to orrelate results with the bond quality of the strands used in the study. The orrelation between strand draw-in and the anhorage behavior of prestressing strands was also examined. A review of the evolution and shortomings of existing ode provisions for the anhorage of prestressing strands is presented. Results of the experimental program are reported, along with reommended design proedures based on these results and those from other studies. The use of 0.6 in strand at 2 in spaing is onluded to be safe, and partial debonding of prestressing strands is shown to be an effetive means of reduing stresses in the end regions of pretensioned girders. xxiii

23 CHAPTER 1: INTRODUCTION 1.1 BACKGROUND The vast majority of short- to moderate-span highway bridges onstruted in Texas feature preast, pretensioned girder superstruture systems. The ubiquity of this superstruture type, depited in Figure 1.1, results from the effiieny assoiated with the fabriation and eretion of preast, pretensioned bridge members. The relatively reent advent of High Performane Conrete (HPC), whih features inreased strength and/or durability, promises ontinued advanes in the strutural and eonomi effiienies exhibited by this type of superstruture. Figure 1.1: Highway Bridge Featuring Preast, Pretensioned I-Beam Superstruture High Strength Conrete (HSC) featuring a ompressive strength in exess of 9000 psi (62 MPa) represents a subset of HPC. The prestressing fore required to fully preompress the tensile zone in standard AASHTO I-beams onstruted of HSC annot be provided using the most prevalent tendon onfiguration 0.5 in (12.7 mm) diameter strands with a 2 in (50 mm) grid spaing (Castrodale, Kreger, and Burns 1988b). The use of 0.6 in (15.2 mm) strands, ommonly used in post-tensioning appliations, at the same grid spaing represents a potential solution to this problem. This larger strand size allows the introdution of forty perent more prestressing fore than the 0.5 in (12.7 mm) strand. Full preompression of the bottom fiber of the beam allows the largest possible servie load moment to be resisted without exeeding the allowable tension stress in the onrete. In addition, a forty-perent inrease in reinforement area an result in a omparable inrease in ultimate apaity. Thus, HSC beams reinfored with 0.6 in (15.2 mm) strand offer signifiantly improved performane when onsidering either servie or strength limit states. Exploitation of this symbioti relationship between higher onrete strength and larger amounts of prestressed reinforement promises bridges that benefit from having longer span lengths or fewer girders per span. Researhers at Lund University in Sweden reently onluded that the ombination of HSC and 0.6 in strands in prefabriated I-shaped girders results in a 15 perent redution in the diret girder osts (Persson, Johansson, and Johansson 1999). Eonomi benefits an also result from the ombination of 0.6 in strands (15.2 mm) with normal strength onrete. Thirty perent fewer strands may be used (ompared to 0.5 in strands) to ahieve the same prestress fore, reduing the labor osts assoiated with installing strands. The redution in number of strands inreases the eentriity of the resultant prestress fore. This, in turn, may allow the deletion of a few more strands. Although maximizing the prestress fore applied to the bottom flange is ideal for resisting in-servie load effets, it may pose diffiulties during the onstrution proess. The stresses that our in a preast beam immediately after transfer of prestress usually ditate the onfiguration of prestressing reinforement that may be used. Prior to the appliation of external loads, a large amount of prestressing in the bottom flange an result in exessive tensile 1

24 stresses in the top fibers in the end regions of the beam. These stresses are usually ontrolled by one of two methods: strand draping or debonding. Draped strands, also known as depressed or harped strands, have long been used to ontrol indued stresses at prestress transfer, or release. The prestress fore remains onstant in magnitude, but the resulting onrete stresses are ontrolled by varying the eentriity of this prestress fore. The draped strands lie within the bottom flange along the entral portion of the span, where the maximum moments are expeted. However, the draped strands rise as they approah the ends of the beam. In this manner, the onrete stresses remain within allowable limits in the end regions, where the moment due to gravity loads is relatively small. Although draping of strands has been used suessfully for deades, it has some disadvantages. Depressing the strands is done while the strands are stressed and an be dangerous. Flawed strands have been known to frature during this proess. Hold-down assemblages have also failed resulting in worker fatalities. Applying draping tehniques to 0.6 in (15.2 mm) strand intensifies this danger due to the signifiantly higher fore involved. For this reason, preasters are relutant to drape this larger-diameter strand. In addition, draped strands are loated higher in the prestressing bed anhorages, and therefore exert a large overturning moment on these anhorages. Beause most urrent prestressing beds were designed for draping of 0.5 in (12.7 mm) strand, draping of 0.6 in (15.2 mm) strands might fore the strengthening of existing anhorages. Partial debonding of strands, also known as blanketing or jaketing, is a simpler and safer alternative to draping. Rather than varying the eentriity of the strands, the prestress fore applied to the end regions of the beam is dereased by preventing bond between some of the tendons and the onrete. This is most ommonly ahieved by wrapping the area to be debonded in flexible plasti tubing and sealing the ends. This method may be used to tailor the indued onrete stresses to remain within allowable limits. Strand debonding offers an added benefit in that it an be easily applied to preast members with inlined webs, suh as the Texas Department of Transportation (TxDOT) U-beam shown in Figure 1.2. Figure 1.2: TxDOT U-Beam 2

25 The potential benefits of HSC an be realized fully through the use of 0.6 in (15.2 mm) strands at a spaing of 2 in (50 mm). In turn, use of partial strand debonding an result in the safer, simpler, and more flexible implementation of this strand onfiguration. These three elements HSC, large-diameter strand, and debonding represent an effiient ombination of materials and methods for use in preast, pretensioned bridge substrutures. The integrity of all reinfored and prestressed onrete strutures depends upon adequate anhorage of the reinforement. The existing ACI and AASHTO ode provisions onerning the anhorage of pretensioned strands are based on researh results obtained from speimens onstruted of outdated materials. In addition, the ode expressions do not adequately reflet the dispersion evident in the experimental results on whih they are based (Tabatabai and Dikson 1993). Experimental researh has revealed that the anhorage behavior of debonded tendons an differ signifiantly from that of fully bonded tendons. As a result of these studies, ACI and AASHTO odes inlude a modifiation to be applied to some debonded strands. However, it an be argued that this modifiation is speifi to the partiular speimens tested, and may not adequately reflet the anhorage behavior of debonded strands over the full range of possible loads, geometries, and member reinforement shemes. A more rational approah to prediting the anhorage behavior of debonded strands might result in an improvement of existing ode provisions. In 1988, after researhers at North Carolina State University reported muh larger than expeted values of transfer and development length for unoated strands of varying sizes (Cousins, Johnston, and Zia 1990), the Federal Highway Administration (FHWA) revised the riteria for strand development length (FHWA 1988). These revisions inluded a moratorium on the use of 0.6 in (15.2 mm) strand in pretensioned appliations, and a sixty perent inrease in the alulated value of development length for fully bonded strands. Minimum enter-to-enter strand spaing was set as four times the nominal strand diameter. By prohibiting the use of 0.6 in (15.2 mm) strand and foring 0.5 in (12.7 mm) strand to a grid spaing of at least 2 in (50 mm), these revisions effetively impeded the full exploitation of HSC in pretensioned appliations. Some researh in reent years has foused on fators that do not urrently play a role in ode expressions pertaining to anhorage behavior of pretensioned strands. Test programs (Mithell et al. 1993; Gross and Burns 1995) have indiated that strands embedded in HSC exhibit improved anhorage behavior when ompared to those ast in normal strength onrete. After a review of development length test results obtained from various researh studies, Bukner (1995) onluded that development length is a funtion of the tendon strain, or elongation, at ultimate. He proposed that the ode development length expression be modified to reflet the influene of this elongation. In order to further investigate the anhorage behavior of large-diameter prestressing strands, the Center for Transportation Researh of The University of Texas at Austin along with Texas Teh University initiated a joint researh study in 1995 entitled Development Length of 15-mm (0.6-inh) Diameter Prestressing Strand at 50-mm (2-inh) Grid Spaing in Standard I-shaped Pretensioned Conrete Beams. The details of this study, funded by the Texas Department of Transportation (TxDOT) as Researh Projet No and by FHWA as Program No. SPR 0511, are desribed in this report. After reviewing the results of several researh programs spawned in the wake of its 1988 revisions, FHWA modified these revisions in 1996 to allow the use of 0.6 in (15.2 mm) strand at a grid spaing of 2 in (50 mm) and the use of 0.5 in (12.7 mm) strand at a grid spaing of 1.75 in (44 mm)(fhwa 1996). Although this deision again allows the effetive use of HSC in pretensioned beams, unertainty remains regarding the anhorage performane of both fully bonded and debonded strands. 1.2 OBJECTIVES The stated objetive of the researh was to measure the transfer and development lengths for 0.6 in (15.2 mm) diameter prestressing strand at 2 in (50 mm) grid spaing in tests of several standard AASHTO Type I pretensioned beams. The more general objetive of the study was a better understanding of the anhorage behavior of pretensioned onrete flexural members. In order to ahieve this general objetive, several speifi objetives were identified: 1. Assess the effet of onrete strength on anhorage behavior, 2. Examine the anhorage behavior of strands exhibiting the range of surfae onditions found in pratie, and 3. Develop rational means of prediting the anhorage behavior of debonded strands. 3

26 In addition, researh effort was foused on assessing the usefulness of pull-out tests and strand draw-in measurements as indiators of anhorage behavior. Rather than investigate the effet of strand elongation on flexural bond behavior, speimens were designed to have ultimate strand elongation values of at least 3.5 perent. Thus, the results obtained should represent worst-ase behavior with regard to strand elongation. 1.3 SCOPE The researh study enompassed transfer and development length testing of thirty-six plant-ast, AASHTO Type I (Texas Type A), pretensioned onrete I-beams. Transfer length testing was performed at the plant; both immediate and long-term transfer lengths were measured. Corresponding values of strand draw-in were also measured. Pullout tests were performed in an effort to quantify strand bond quality. Development length tests were performed on thirty beams at the Phil M. Ferguson Strutural Engineering Laboratory at The University of Texas at Austin. Development length testing of the remaining six beams was arried out at Texas Teh University. In an effort to ahieve ultimate tendon elongation values exeeding 3.5 perent, a ast-in-plae, omposite dek was added to eah beam prior to development length testing. Three different levels of beam onrete strength were investigated. Compressive strengths at prestress release varied from 4000 to 11,000 psi (27 to 76 MPa). Strengths at time of development length testing ranged from 5700 to 14,700 psi (39 to 102 MPa). Speimens were reinfored with strands having either a bright or a rusted surfae ondition. A variety of strand debonding shemes were tested. Some speimens ontained strands that were all fully bonded, while other speimens featured perentages of debonded strands ranging up to 75 perent. The study inluded a limited investigation of the effet of horizontal web reinforement on anhorage behavior. 1.4 ORGANIZATION OF REPORT Chapter 2 inludes a disussion of the anhorage behavior of pretensioning strands, as well as a brief history of the development of urrent ode provisions regarding this topi. The details of the speimens tested in the experimental program are desribed in Chapter 3. Chapter 4 ontains a disussion of the issue of strand bond quality. Results of ompanion pull-out tests performed as a part of the experimental program are also presented and disussed in this hapter. The transfer length test program is desribed in Chapter 5. Results of transfer length testing are disussed and ompared with existing ode expressions as well as those suggested by other researhers. Based on the results of this test program and others, a onservative design expression for transfer length is proposed Chapter 6 fouses on the use of measured strand draw-in values to predit anhorage behavior. Test results are disussed and ompared to the results of orresponding transfer length tests. The results of the development length test program are reported and disussed in Chapter 7. Behavior of the test speimens is ompared with that indiated by the relevant ode provisions. A onservative design expression for development length is proposed based on the results of this and other relevant studies. The influene of raking on the neessary development length is disussed. Chapter 8 is a olletion of reommendations for anhorage design of prestressing strands and for further researh. A brief summary of the researh study and the resulting onlusions are presented in Chapter NOTATION There is no standard system of notation for the various properties desribed and referred to in this report. Notation systems vary among different odes and researh douments. The notation adopted in the AASHTO LRFD Code (1998) is used for terms and properties in this report. The author has seleted appropriate notation for any property noted in this report that is not defined in the AASHTO LRFD Code. Eah symbol is defined or desribed in the text upon its first appearane (and often at other instanes). A table of symbols used may be found under the heading Notation immediately prior to the referene list at the end of the report. Where possible, the notational equivalents found in the ACI (1999) and AASHTO Standard Codes (1996) are reported as well. 4

27 CHAPTER 2: ANCHORAGE BEHAVIOR IN PRETENSIONED MEMBERS 2.1 INTRODUCTION Adequate anhorage of reinforement is vital to the integrity of strutural onrete. Reinforement for onrete members and onnetions is usually proportioned based on the assumption that the reinforement is adequately anhored. One the reinforement amount and pattern are seleted, the adequay of the reinforement anhorage is heked. If the resulting anhorage apaity is defiient, the size, amount, or onfiguration of the reinforement is then altered in suh a way as to ensure that potential anhorage demands are met or exeeded. If less than adequate anhorage is provided, the struture will be unable to resist the flexural, shear or torsional fores for whih it was designed, and if atual loads approah those assumed in design, a premature failure is likely to our. Anhorage of reinforement is generally provided by bond between the reinforement and the onrete along a length of bar or tendon; by bearing of the reinforement or a mehanial attahment against the onrete; or a ombination of bond and bearing. In the ase of preast, pretensioned onstrution, anhorage of prestressing tendons is usually aomplished by means of bond along a straight length of eah tendon. This hapter inludes a desription of the urrent philosophy regarding anhorage of prestressing strands in pretensioned members. The historial development of existing ode provisions and relevant researh studies are summarized. In addition, the feasibility and potential ramifiations of alternate design philosophies and methods are disussed. 2.2 DEFINITIONS This setion provides definitions and desriptions of several terms key to the disussion of anhorage behavior Development Length Development length, l d, is the shortest bonded length of bar or tendon along whih the bar or tendon stress an inrease from zero to the stress required for ahievement of the full nominal strength at the setion under onsideration. For nonprestressed reinforement, l d usually represents the bonded length neessary to develop a stress of f y, the yield stress of the reinforement. Beause the stress in prestressing reinforement, f p, ontinues to inrease with inreasing strain, l d for prestressing strand represents the bonded tendon length neessary to fully develop f ps, the stress in the prestressing steel required for the nominal resistane of the member. Thus, if the length of tendon bonded on either side of the setion under onsideration is less than the development length, l d, the member will be unable to attain the alulated nominal resistane beause the tendon annot ahieve the required stress, f ps. Development length as defined here is known as anhorage length in European pratie. When used in European pratie, the term development length refers to the extent of the anhorage zone, i.e. the distane over whih the influene of the prestressing fore is distributed throughout the ross setion. This subjet is disussed further in the subsequent setion and in Setion For nonprestressed reinforement, the development length is alulated aording to the assumption of an average bond stress, u, that an be resisted prior to bond failure. On the other hand, the development length of pretensioned reinforement has historially been subdivided into two distint portions the transfer length and the flexural bond length eah haraterized by a unique average bond apaity Transfer Length Transfer length, l t, is defined as the bonded tendon length required to develop the full effetive prestress fore in a prestressing tendon. The term has no meaning for nonprestressed reinforement. Due to losses, the prestress level varies with time. Thus, the prestress fore of interest with regard to anhorage behavior is that orresponding to the prestress in the tendon after losses, f pe. 5

28 Transfer length has also been defined as the distane required to transfer the prestress from the tendon to the onrete (Bukner 1994). This definition an be misleading beause it ould oneivably be onstrued as indiating that the transfer length defines the extent of the pretensioned anhorage zone. In reality, the anhorage zone of pretensioned members extends beyond the transfer length of the tendons. At the end of the transfer length, equilibrium ensures that the full prestress fore has been applied to the onrete. However, Base (1958b) has demonstrated that this prestress fore is not yet fully distributed over the ross setion at this point. An additional distane is required to ahieve the distribution of stresses alulated based on the plane setions remain plane assumption of engineering beam theory. Thus, the transfer length plus this additional distane defines the full extent of the anhorage zone, whih orresponds to the European definition of development length mentioned in the preeding setion. The extent of the pretensioned anhorage zone is not expliitly addressed in North Amerian pratie. The portion of the anhorage zone orresponding to the North Amerian transfer length is known as the transmission length in European pratie. Aside from onstituting an integral portion of the development length, the transfer length is important beause of its assoiation with the extent of the pretensioned anhorage zone. The auray of any attempt to predit the atual material stresses at a speifi loation within the anhorage zone depends upon the auray of the estimation of the transfer length. For example, knowledge of the transfer zone boundaries is neessary for the aurate alulation of onrete stresses for omparison with Servie Limit State allowable stress limits at transfer and under servie loading. In this step of the design exerise, overestimation of the transfer length an produe a signifiant error with atual stress magnitudes being larger than alulated. Aurate transfer length estimation is also ruial to shear design, espeially beause shear demand is usually greatest in the transfer regions of pretensioned members. Setional shear resistane alulations require knowledge of the level of preompression in the onrete, whih in turn depends upon the loation of the setion under investigation relative to the anhorage zone boundaries. In this type of design exerise, underestimation of the transfer length is unonservative. Realisti estimation of the extent of the anhorage zone is also ritial to the design of anhorage zone reinforement. Strut-and-tie models are of great value to designers attempting to improve anhorage zone reinforement details. Safe and effiient use of these models depends upon aurate estimates for the range of possible transfer lengths. Shorter transfer lengths result in larger values of transverse tensile stresses in the anhorage zone. Upon release of the pretensioning fore, the derease in tendon tension along the transfer length results in a proportional inrease in tendon diameter. So long as the strength of the surrounding onrete remains intat, this radial expansion results in an inreased fritional bond apaity between the reinforement and the onrete. Thus, the transfer bond stresses, u t, are higher than those possible in regions where this expansion does not our. This enhaned bond apaity due to the expansion of the pretensioned reinforement was explained by Hoyer and Friedrih (1939), and is ommonly known as the Hoyer Effet. Further disussion of transfer bond theory is inluded in Setion Flexural Bond Length Flexural bond length, l fb, is defined as the distane, in addition to the transfer length, over whih the tendon must be bonded to the onrete in order that a stress f ps may develop in the tendon at nominal strength of the member. Aside from a hange in notation, the replaement of strand with tendon, and the replaement of ultimate with nominal, this is the definition of flexural bond length inluded in the Commentary to the ACI Code, in whih the urrent expression for development length was first inluded (Tabatabai and Dikson 1993). The buildup of tendon stress along the flexural bond length results from flexural bond stress, u fb, between the tendon and the surrounding onrete. As opposed to transfer bond stresses, whih result from the appliation of prestress to the member, flexural bond stresses result from the appliation of external loads and deformations (Janney 1954). Thus, flexural bond stress is analogous to the bond stress that ours along the straight development length of nonprestressed reinforement. Although flexural bond stresses must also our along the transfer length under the imposition of external loads, they are generally disregarded due to their small magnitude if the onrete remains unraked in this region. Theory involving flexural bond and the influene of raking is presented in Setion

29 2.3 CODE PROVISIONS FOR ANCHORAGE OF FULLY BONDED STRANDS The present expression for the development length of fully bonded strands was first inorporated in the 1963 version of ACI s Standard Building Code Requirements for Reinfored Conrete (ACI ; Tabatabai and Dikson 1993). It was subsequently inorporated into AASHTO s Standard Speifiations for Highway Bridges (in 1973) and LRFD Bridge Design Speifiations. This setion inludes a brief history of the evolution of the relevant provisions along with a disussion of some of their shortomings Relevant ACI and AASHTO Code Clauses and Commentary The relevant provisions for the development of prestressing strand are found in Setion 12.9 of the ACI Code (ACI ), Artile of the AASHTO LRFD Speifiation (AASHTO 1998), and Setion 9.28 of the AASHTO Standard Speifiation. Other than minor disrepanies in wording and notation, the AASHTO Standard Speifiation provisions for development length are idential to those in the ACI Code. As the AASHTO LRFD speifiations are largely similar, the ACI provisions will be reported herein and signifiant disrepanies with the AASHTO LRFD speifiation will be noted. The provisions of ACI , Setion 12.9 Development of prestressing strand that are relevant to fully bonded strands are worded as follows: Three- or seven-wire pretensioning strand shall be bonded beyond the ritial setion for a development length, in inhes, not less than 1 f ps 2 f 3 where d b is strand diameter in inhes, and f ps and f pe are expressed in kips/in 2. pe d b Limiting the investigation to ross setions nearest eah end of the member that are required to develop full design strength under speified fatored loads shall be permitted. Though the value alulated in is defined as development length, ACI and the AASHTO Standard Speifiation refrain from using the notation, l d, whih is reserved for the development length of nonprestressed reinforement. The AASHTO LRFD Speifiation uses l d to represent the development length of prestressed and nonprestressed reinforement. The ACI 318R-99 Commentary Setion R12.9 states that the development length requirements for prestressing strand are intended to provide bond integrity for the strength of the member. The Commentary goes on to state that the expression for l d given is equivalent to the expression: l d f = 3 pe d b + ( f ps f pe ) d b where the first term represents the transfer length (as defined in Setion above) and the seond term represents the flexural bond length (as defined in Setion above). To illustrate this onept, the Commentary inludes the figure reprodued here as Figure 2.1. In this figure, the steel stress is shown to inrease linearly along the transfer length. Along the flexural bond length, the slope of the depited steel stress urve dereases steadily. The Commentary goes on to state that the expressions for transfer length and flexural bond length are based on tests of members prestressed with lean strands featuring diameters of ¼, ⅜, and ½ in (6.4, 9.5, and 12.7 mm). The maximum value of f ps for these tests is reported as 275 ksi (1895 MPa). The Commentary ites papers by Hanson and Kaar (1959); Kaar, LaFraugh, and Mass (1963), and Kaar and Magura (1965) 2. 1 Notation has been modified to reflet the system of notation used throughout this report. Also, the parenthetial expression is used as a onstant without units. 2 The itation of Kaar and Magura (1965) in this portion of the Commentary appears to be a mistake. This referene is vital to the evolution of provisions regarding the development length of debonded strands, but has little relevane to the expression for development length of fully bonded strand. The fully bonded strands in this study featured 7

30 At nominal strength of member f ps - f pe Steel stress Prestress only f ps f pe f 3 pe d b l d ( f ps - f pe ) d b Distane from free end of strand Figure 2.1: Variation of Steel Stress with Distane from Free End of Strand (from ACI 318R-99, Fig. R12.9) The development length provisions of the AASHTO LRFD Speifiation differ from the original ACI in a few details. Artile of this speifiation states that the prestress fore may be assumed to inrease linearly along the transfer length and in a paraboli manner along the flexural bond length. These statements verbally mimi the relationship illustrated in Figure 2.1. The partiular shape of the paraboli profile along the flexural bond length is apparently left to the disretion of the pratitioner. The artile goes on to state that the transfer length may be taken 2 as 60 strand diameters, and that the development length may be alulated as f ps f pe db just as in ACI f Setion If ombined with the pe db expression for transfer length stated in the ACI 318 Commentary, the 3 assumed transfer length of 60d b would indiate an assumed value of f pe equivalent to 180 ksi (1240 MPa). The AASHTO LRFD Speifiation laks any statement resembling that of ACI Setion , whih limits the number of ross setions at whih development length is heked. In addition to these provisions regarding the development length of prestressing strand, the shear provisions of the ACI Code and AASHTO speifiations inlude statements onerning the transfer length of prestressing strand. Aording to ACI , the nominal shear apaity of pretensioned members when subjeted to web-shear raking is alulated as the sum of V w, the nominal shear strength provided by onrete when diagonal raking results from exessive prinipal tensile stress in the web, and V s, the nominal shear strength provided by shear reinforement. The value of V w at a setion under onsideration depends upon the ompressive stress in the onrete at the entroid (or web/flange juntion) at that setion. Setion of the Code states that when the ritial setion for shear lies within the transfer length of the prestressing tendons, the redued prestress shall be onsidered when omputing V w. The prestress fore shall be assumed to vary linearly from zero at end of tendon to a maximum at a distane from end of tendon equal to the transfer length, assumed to be 50 diameters for strand. Thus, in this portion of the Code the transfer length is assumed equal to 50d b, whih orresponds to the bonded lengths onsiderably longer than those predited by the Code expression and therefore provide no verifiation of the adequay of the expression. In addition, these results were published two years after the expression first appeared in ACI

31 f expression pe db given in Commentary Setion R12.9 when f pe is 150 ksi (1035 MPa). No referene is ited in the 3 Commentary for Setion Similar language is inluded in the shear provisions of the AASHTO Standard Speifiation. The shear provisions of the AASHTO LRFD Speifiation differ from those given above. Among the General Requirements for shear and torsion resistane, Artile Transfer and Development Lengths simply states that [t]he provisions of Artile shall be onsidered. Artile inludes the anhorage provisions desribed above. The ommentary aompanying Artile elaborates: The redued prestress in the transfer length redues V p, f p, and f pe. The transfer length influenes the tensile fore that an be resisted by the tendons at the inside edge of the bearing area. In short, this artile reminds the pratitioner that a proper estimate of the atual effetive prestress value at the setion under onsideration should be used when alulating the shear and torsional resistane aording to the provisions of the AASHTO LRFD speifiation. The final sentene of the artile ommentary indiates that the appropriate value of developed prestress should be used in alulating the required amount of longitudinal (bottom hord) reinforement required at the inside edge of the bearing area at simple end supports (Artile ). No omparable provision exists for prestressing reinforement in the ACI Code or the AASHTO Standard Speifiation Bakground Researh The existing ode provisions for the development length of fully bonded pretensioned strands are based on the results of two studies onduted in the Researh and Development Laboratories of the Portland Cement Assoiation (PCA) in the late 1950s and early 1960s. The results of these studies are reported in papers by Hanson and Kaar (1959) and by Kaar, LaFraugh, and Mass (1963). These researh studies are summarized in this setion. Beause Hanson and Kaar rely heavily upon the bond theory espoused by Janney (1954), his study is also presented here Janney (1954) Janney reports the results of a study investigating the transfer bond and flexural bond behavior of speimens pretensioned with wires or strands. Although only a few of the test speimens ontained seven-wire strand, some of the theoretial hypotheses are quite relevant. First, Janney uses an elasti, thik-walled ylinder analysis to predit the onrete stresses surrounding the tendon transfer length. Assuming elasti properties harateristi of materials in use at the time, Janney alulates that, if the onrete behaves elastially, maximum radial ompressive stresses and irumferential (hoop) tensile stresses on the order of 3300 psi (23 MPa) would result from a prestress of 120 ksi (825 MPa). Beause these irumferential tensile stresses far exeed the tensile apaity of the onrete, it an be assumed that the onrete behaves inelastially along almost the entire transfer length. Repeating this analysis with an initial prestress level and material properties harateristi of those found in modern pretensioned strutures, the elasti thik-walled ylinder analysis predits irumferential stress levels ranging from 6000 psi (41 MPa) for NSC ( E 4000 ksi [28 GPa]) to 10,000 psi (69 MPa) for HSC ( E 7000 ksi [48 GPa]). Hene, inelasti behavior along most of the transfer length is to be expeted. Janney also ontributes the theory that general bond slip, defined as slip along the entire bonded length of strand, ours when the wave of maximum flexural bond stress overlaps the region of prestress transfer bond, i.e. the transfer length. Beause flexural bond stresses are largest on either side of flexural raks, this wave of maximum flexural bond stress progresses ahead of flexural raking. As the load is inreased, the wave travels from the point of maximum moment toward the support regions for simply supported beams. The high levels of steel stress indued by raking ause the strand diameter to ontrat. When the wave overlaps the transfer bond region, this ontration ounterats the prestress transfer bond that results from the Hoyer Effet, resulting in general bond slip. This theory is further disussed in Setion 2.5 below. Janney s experimental results indiate that both transfer and flexural bond behavior improve with surfae roughness. In addition, transfer lengths appear to have dereased slightly with inreasing onrete strength Hanson and Kaar (1959) This study onsisted of an investigation of flexural bond in beams pretensioned with seven-wire strand of ¼, ⅜, and ½ in (6.4, 9.5, and 12.7 mm) diameter. In all, 47 simply-supported, pretensioned beam speimens were tested to 9

32 failure. The general proedure onsisted of evaluating the moments that resulted in initial strand end slip and in ultimate strength of eah speimen. The embedment length of strand (the bonded length of strand beyond the ritial setion) and the strand diameter were the prinipal variables studied. Other variables inluded strand surfae ondition, reinforement perentage, and onrete strength. The beam speimens had retangular ross setions featuring widths ranging from 4 to 8 in (102 to 203 mm) and reinforement depths of 5.5 to 11.5 in (140 to 292 mm). The span-to-depth ratios, ross setion dimensions, and prestress amounts were suh that diagonal shear raking should not have ourred. None was reported. Several types of prestressing steel were used. Although the ultimate strength of eah type of strand appeared to be in exess of 250 ksi (1725 MPa), a variety of stress-strain urves were exhibited. The Grade 270, low-relaxation steel prevalent in urrent pratie was not used. Hanson and Kaar alulated the average bond stress over the entire embedment length (inluding the transfer length) at both general bond slip and ultimate load. General bond slip was evidened by slip of the strand end relative to the beam end. Using these average bond stress values, they onluded that the average bond stress ourring just prior to general bond slip dereases with inreasing embedment length. Using the experimentally determined values of average bond stress at general bond slip, a hart was developed to predit the strand embedment length required to prevent general bond slip at a partiular steel stress for the three strand sizes tested. The hart is appliable only to strand initially tensioned to 150 ksi (1035 MPa) and embedded in onrete with a ompressive strength of approximately 5500 psi (38 MPa). For an ultimate steel stress of 250 ksi (1725 MPa), the hart predits that embedment lengths of 200d b for ¼ in strand and 250d b for ⅜ and ½ in strand are required to prevent general bond slip. Due to a lak of researh regarding the influene of repeated loads, prevention of general bond slip is the reommended riterion for adequate anhorage. Thus, using the design proedure reommended by Hanson and Kaar, these values represent the development length required for strands under the given onditions. In addition, Hanson and Kaar onlude that rusting of strand inreases the moment at general bond slip on average, although one speimen showed no signifiant improvement when ompared to a ompanion speimen with lean strand. They also onlude that, due to mehanial bond resistane, seven-wire strand develops additional beam strength even after general bond slip. Hanson and Kaar assert that the results of the 47 beam tests support Janney s (1954) flexural bond wave theory, onfirming that general bond slip ours when the peak of the flexural bond stress wave reahes the transfer zone Kaar, LaFraugh, and Mass (1963) This study foused on transfer lengths and the influene of onrete strength. Thirty-six retangular prisms were tested, resulting in a total of 72 transfer lengths. The 36 transfer lengths reported represent averages of two ompanion transfer lengths. Conrete ompressive strengths varied from 1660 to 5000 psi (11 to 34 MPa) at the time of prestress transfer. One mix design was used for all speimens; the strengths at transfer were varied from speimen to speimen by releasing the prestress at ages varying from one to thirty days. Strands of ¼, ⅜, ½, and 0.6-in (6.4, 9.5, 12.7, and 15.2 mm) diameter were employed. Prestress levels immediately after transfer, f pt, ranged from 146 to 180 ksi (1010 to 1240 MPa). Transfer lengths were evaluated by means of onrete surfae strain measurements performed with a Whittemore mehanial strain gauge. In an effort to evaluate the effet of time on transfer length, measurements were performed at ten ages ranging from immediately after transfer to one year. No systemati variation of transfer length with onrete strength was found for strand diameters up to ½ in. Transfer lengths appeared to derease with inreasing onrete strength for the 0.6 in strands. Transfer lengths inreased an average of six perent over the ourse of a year; all inreases were less than twenty perent. The transfer lengths measured at the end of the speimen where the strands were ut averaged about twenty to thirty perent higher than those at the dead end of the speimen. The transfer length was found to be roughly proportional to the strand diameter for all strands exept the 0.6 in strands. The 0.6 in strands exhibited transfer lengths shorter than would be expeted if the transfer length were proportional to the diameter. This disparity was attributed to slight surfae weathering of the 0.6 in strands in transit Evolution of Development Length Expression Although the experimental results of these PCA studies were used to reate the ode development length expression, nothing resembling this expression is inluded in the reports from either study. Tabatabai and Dikson (1995) desribe how the ACI Prestressed Conrete Committee transformed the researh results into the development length 10

33 expression given in Setion above. Preliminary relationships for the transfer length, the flexural bond length, and the development length were prepared by Alan H. Mattok. The full ommittee then modified Mattok s 2 reommended development length expression to arrive at the f ps f pe db expression first published in the ACI 318 Building Code. f Mattok s proposed expression for transfer length is exatly that still found in Commentary Setion R12.9: pe db. 3 Mattok derived this expression from the results of the PCA tests summarized above and data from tests performed on eight speimens for the Amerian Assoiation of Railroads. These data, inluded in the Tabatabai and Dikson (1995) paper, do not differ signifiantly from the Kaar, LaFraugh, and Mass (1964) data, exept that transfer lengths were only measured immediately after transfer. Hanson and Kaar (1959) did not publish transfer length measurements, but stated that the average transfer bond stress, u t, was assumed to be 400 psi (2.76 MPa) based on tests performed previously at PCA. In deriving his expression, Mattok adopted this value of average transfer bond stress. Mattok used the following equilibrium relationship to derive the transfer length expression: Equation 2.1 where u l Σ o = A t t ps f pe ut = average transfer bond stress = 400 psi (2.76 MPa) l t = transfer length 4 Σo = strand perimeter = πdb 3 2 πd A ps = strand ross-setional area = b 4 d b = nominal strand diameter f se = effetive strand prestress The left-hand side of the equation represents the total fore between the onrete and the steel along the surfae of the strand in the transfer length. The right-hand side represents the total fore in the strand at the end of the transfer length. Stati equilibrium of the free body onsisting of the transfer length of strand requires that the two sides of the expression be equal. Solving the equation for the transfer length yields the expression found in the ACI Commentary Setion R12.9: f -1 pedb Equation 2.2 lt = ksi f pedb 3 ksi Tabatabai and Dikson (1995) also report that the following statement was inluded in a draft of the proposed ode revisions regarding anhorage for ACI : For steel with a lean surfae, released gently to a stress of 150 ksi, the prestress at the entroid of the member ross setion may be assumed to vary linearly from zero at the fae of the member to a maximum at a distane from the end fae equal to 50 diameters for strand and 100 diameters for single wire. They theorize that this is likely the soure of the transfer length value of 50 strand diameters found in Setion of the Code shear provisions. However, this setion allows the use of 50d b regardless of the amount of prestress, the strand surfae ondition, or the method of prestress release. Current pratie involves prestress values onsiderably higher than 150 ksi (1035 MPa) after release. The method Mattok employed to arrive at an expression for flexural bond length was somewhat more omplex. In reporting the results of their study on flexural bond, Hanson and Kaar (1959) do not onlude that a limiting value of average flexural bond stress results in either general bond slip or maximum moment resistane. Rather, they agree 11

34 with Janney (1954) that general bond slip is aused when the peak of the high bond stress wave reahes the prestress transfer zone. The resulting derease in strand diameter redues the fritional resistane due to the Hoyer Effet, and general bond slip ours. Apparently, Mattok and/or the members of the Prestressed Conrete Committee found this onept diffiult to odify, so an average flexural bond stress approah was formulated based on a reappraisal of the Hanson and Kaar data. Using data obtained from some of Hanson and Kaar s beam tests, Mattok onstruted a straight-line relationship between the flexural bond length available in eah speimen (normalized in terms of strand diameter) and the inrease in strand stress due to flexure at the ritial setion 1) when general bond slip ourred and 2) at ultimate. The available flexural bond length was alulated by subtrating the estimated transfer length from the embedment length of strand. The inrease in strand stress due to flexure at general bond slip was alulated by subtrating the effetive prestress value from the value of strand stress ourring at the load ausing slip. The inrease in strand stress due to flexure at ultimate was alulated in a similar manner. Mattok stated that the straight-line relationship developed appears to be a reasonable mean line for the points representing general bond slip. Mattok s relationship to avoid bond slip is represented by Equation 2.3: l e lt Equation 2.3 f 0 9 ps f pe. ksi db where f ps = strand stress at ultimate strength l e = embedment length of strand beyond ritial setion Or, if the flexural bond length neessary to prevent bond slip is desired, Equation 2.3 may be solved for l fb : ( f f ) ps pe db Equation 2.4 l fb = 0.9 ksi Assuming Mattok s estimate of the transfer length is orret, these relationships are onservative with respet to general bond slip for eleven of the twenty speimens onsidered. They are unonservative for nine of the speimens. Thus, as inferred by Mattok, Equation 2.4 represents the average flexural bond length required to prevent general bond slip, rather than a onservative value. Prior to finalization of the 1963 Code, the expression for flexural bond length was altered, resulting in the expression shown as Equation 2.5: Equation 2.5 ( ) -1 l fb = f ps f pe d b ksi Thus, the resulting expression, whih underestimates the flexural bond length at general bond slip for ten of the twenty speimens onsidered, is even less onservative than that proposed by Mattok. The final expression for development length was obtained by adding the expressions for transfer length (Equation 2.2) and flexural bond length (Equation 2.5). The relationship still found in the present ode results: f pe 2 l d = lt + l fb = db + ( f ps f pe ) db = ( f ps f pe ) d 3 3 b Inadequay of Existing Code Expression for Development Length This setion onsists of a disussion of the problems inherent in the existing ode expression for the development length of prestressing strand. The disussion is subdivided into two parts. The first part addresses the disrepanies between the adopted expression and the researh results from whih it evolved. Potential defiienies arising from hanges in materials and design pratie over the past four deades are taken up in the seond part Disrepanies with Results of Bakground Researh Consider the urrent development length expression in omparison with the design reommendations made by Hanson and Kaar (1959). Both design approahes were developed with the goal of preventing general bond slip 12

35 prior to reahing the nominal flexural strength of the member. A omparison an be made between the development lengths predited by the two methods for a beam typial of the pratie at the time. For this example, a steel stress at nominal strength, f ps, of 230 ksi (1585 MPa) is assumed. The strands are initially tensioned to a stress of 150 ksi (1035 MPa). A value of effetive prestress after losses, f pe, of 132 ksi (910 MPa) is assumed. For ½ in (12.7 mm) diameter strands embedded in 5500 psi (38 MPa) onrete, Hanson and Kaar reommend a development length, l d, 2 of 104 in (2.64 m). Appliation of the ode expression results in ( f ps f pe ) db = 142d b = 71 in (1.8 m). 3 Examination of Hanson and Kaar s experimental results indiates that the atual embedment length required to prevent general bond slip in a speimen with these properties lay somewhere between 77 and 90 in (1.96 and 2.29 m). Thus, the development length resulting from the ode expression appears to be ten to twenty perent shorter than that atually required to prevent general bond slip. Hanson and Kaar s more onservative method results in a development length fifteen to thirty-five perent longer than required. Why do the two methods, ostensibly derived from the same body of experimental results, arrive at markedly different development length values with opposite impliations with regard to safety? One fault with the ode expression is that it does not reflet the signifiant dispersion evident in the data from the PCA studies. At every step in the evolution of the expression, attention was foused on the average, rather than extreme, behavior (Tabatabai and Dikson 1995). While the average initial transfer bond stress value of 400 psi (2.76 MPa) seleted by Mattok is not unreasonable when ompared with the PCA results, more detailed analysis shows that the average bond stresses obtained from these tests featured a oeffiient of variation of approximately 27 perent. Approximately thirty perent of Kaar, LaFraugh, and Mass s (1964) reported results yield initial transfer bond stresses less than 300 psi! 3 With dispersion suh as this, the ommon ourrene of transfer lengths signifiantly longer than those predited by Mattok s transfer length expression should be expeted. Dependene on average performane without due onsideration of extreme behavior results in poor design pratie with regard to safety. Contrast the philosophy used to formulate the strand development equation with that employed in the evolution of the development length provisions for deformed reinforing steel. Although the bond stress relationship used to formulate the relevant expressions for reinforing steel is based on average behavior, the final expressions inorporate the influene of a 0.8 redution fator to reflet the dispersion in the bakground data. The use of this hidden resistane fator results in provisions that safely bound the test data (Orangun, Jirsa, and Breen 1977). The average transfer bond stress value of 400 psi used by Mattok is representative of the average performane of the PCA tests when the equilibrium relationship given in Equation 2.1 above is solved using the prestress immediately after transfer (f pt ). However, when inorporated into the ode expression, the effetive prestress value after all losses (f pe ) is used. The use of f pe implies that the transfer length dereases as the steel stress dereases due to time-dependent losses. The results reported by Kaar, LaFraugh, and Mass (1964) show that the opposite is true. f Transfer length tends to inrease slightly with time. Thus, the inauray of the pe db expression for the transfer 3 length inreases as time-dependent losses aumulate. f The inability of the pe db expression to safely bound the long-term transfer lengths reported by Kaar, LaFraugh, 3 and Mass is demonstrated in Figure 2.2 and Figure 2.3. Figure 2.2 is a histogram representing the ratios obtained when dividing eah of the long-term transfer lengths obtained in the PCA study (l t,test ) by the transfer length f alulated by means of the pe db expression (l t,al ). In order to estimate the value of f pe orresponding to the test 3 results taken at 365 days, a redution of twenty perent was taken from the reported values of prestress immediately after transfer (f pt ). This estimation seems reasonable in light of the onrete strains reported at 56 days for one of the speimens. The histogram shows that the measured long-term transfer lengths were, on average, more than 50 f perent longer than those predited by the pe db expression. This expression underestimates the long-term 3 transfer length for more than 90 perent of the reported values! 3 Eah of these reported results represents the average of two transfer lengths taken from ompanion speimens. Thus, the atual oeffiient of variation of all the measured transfer lengths is likely larger than that reported here. 13

36 12 C. of V. = 27% Mean = 1.53 s = % 80% 8 60% 4 40% 20% More 0% l l t, test t, al Figure 2.2: Histogram Ratios of Long-Term l t Values Obtained by Kaar, LaFraugh, and Mass to l t,al from f ACI 318 Commentary ( pe db ) 3 Similar results are obtained from the 50d b expression for transfer length found in the shear provisions of the ACI Code and AASHTO Standard Speifiation. Figure 2.3 displays these results. For the speimens tested, the 50d b f expression gives slightly more onservative results than the pe db expression beause the f pe values were less than ksi (1035 MPa). Still, transfer lengths were underestimated for 80 perent of the reported results % C. of V. = 23% Mean = 1.33 s = % 8 60% 4 40% 20% More 0% l l t, test t, al Figure 2.3: Histogram Ratios of Long-Term l t Values Obtained by Kaar, LaFraugh, and Mass to l t,al from ACI 318 Shear Provisions (50d b ) 14

37 Figure 2.4 represents a omparison of the reported long-term transfer lengths to the expression l t,al = 0.55f pt d b. Rather than inluding the prestress value after losses, this expression depends on the prestress immediately after transfer. Thus, the magnitude of the predited transfer length does not derease with the age of the speimen. The oeffiient of 0.55 is used to obtain an expression that only underestimates the transfer length for about five perent of the reported results. The average value of l t, test f pt d b is 0.41 for the PCA data C. of V. = 27% Mean = 0.74 s = % 80% 60% 4 40% 20% % l l t, test t, al Figure 2.4: Histogram Ratios of Long-Term l t Values Obtained by Kaar, LaFraugh, and Mass to l t,al = 0.55f pt d b As disussed in Setion 2.3.3, the hosen expression for flexural bond length also represents average behavior l = f f d expression is only onservative with without onsideration of the dispersion of the test data. The fb ( ps pe ) b regard to general bond slip for ten of the twenty speimens onsidered. The expression l fb =. 7( f ps f pe ) d b 1 is onservative with regard to general bond slip for about ninety perent of the tests onsidered. On the other hand, the l = f f d is onservative with respet to general bond slip for about two-thirds of the expression fb ( ps pe ) b speimens, and is onservative with respet to development of nominal flexural strength for 95 perent of the speimens. Thus, the relationships for both transfer length and flexural bond length that are inorporated in the ode development length expression are unonservative for a large portion of the test results from whih they were derived. In addition, the tehnique of using a limiting uniform flexural bond stress to predit the flexural bond length neessary to prevent general bond slip does not ompletely agree with the findings of the PCA researhers (Janney 1954; Hanson and Kaar 1959). The researhers theorized that general bond slip was initiated by large magnitudes of bond stress (and the aompanying large gradients of steel stress) ourring near or in the prestress transfer region. Mattok s approah, on the other hand, depends upon a relatively uniform average bond stress along the entire flexural bond length. This assumption is adequate for assessing the bond apaity of deformed reinforing bars beause a small amount of slip tends to distribute bond resistane somewhat evenly among the deformations within the development length. However, when general bond slip is the speified failure riterion, as has been the ase historially with prestressing strand, the assumption of a uniform distribution of bond stress at failure may be unrealisti. 15

38 Inadequaies Due to Evolving Materials and Design Pratie In the years sine the development length equation was first odified, hanging material properties and design pratie have brought other potential shortomings to light. The tendons originally investigated onsisted of stressrelieved strand with a guaranteed ultimate strength of 250 ksi (1725 MPa). Present pratie ditates the almost exlusive use of low relaxation strand featuring ultimate strengths of at least 270 ksi (1860 MPa). In addition to the higher levels of effetive prestress and ultimate stress that result, the newer strands feature a ratio of ross-setional area to perimeter about six to seven perent larger than that of the strand used in the PCA researh. Thus, the bond stress neessary to develop a given strand stress is aordingly larger. As disussed in Chapter 1, the use of 0.6 in (15.2 mm) strand is inreasingly desired, and strands of this size were not inluded in the study reported by Hanson and Kaar (1959). Likewise, the onrete ompressive strengths employed in the PCA tests do not approah the strengths now possible. In 1949, Freyssinet wrote: [Transfer] bond stress an only attain a ertain maximum value whih depends on the frition and on the maximum pressure whih the onrete an exert on the wire; this maximum pressure depends on the tensile strength and on the hardness of the onrete surrounding the wire. The performane of a bond anhorage therefore depends upon the quality of the onrete (Guyon 1953). In tests on onrete speimens with onrete ompressive strengths ranging from 2800 to 7000 psi (20 to 50 MPa) at release, Ratz, Holmjanski, and Kolner (1958) found that transfer bond depends to a high degree upon the strength of the onrete. Rüsh and Rehm (1963) observed that transfer lengths dereased with inreasing onrete strength, but with onsiderable satter in the data. Tests performed at the Ferguson Strutural Engineering Laboratory indiated that transfer lengths in HSC speimens tend to be smaller than in NSC speimens (Castrodale, Kreger, and Burns 1988a). Based on experimental results, Mithell et al. (1993) proposed expressions for transfer length and development length that inlude the influene of onrete strength. Russell and Burns (1993) found that the shear raking in or near the prestress transfer zone an lead to bond failure. Just as the wave of high bond stresses assoiated with flexural raks an lead to the initiation of general bond slip, so an the bond stresses ating on either side of shear raks. If general bond slip ours in a transfer bond region that is subjet to high shear fores, the shear resistane mehanism an be ompromised, resulting in a premature shear failure. This mode of failure is independent of the flexural bond stress approah inorporated in the ode expression of development length. Thus, the expression is inadequate with respet to this type of failure. 2.4 TRANSFER BOND THEORY Upon detensioning of the pretensioned tendons at the ends of members, the tendons shorten and slip relative to the surrounding onrete along a finite length at either end. Bond stresses develop between the tendon and the onrete along this transfer length, resulting in a buildup of onrete ompressive stress parallel to the axis of the tendon. After release, there is no axial stress in the tendon at the free end. At the other end of the transfer length, sometimes referred to as the attak or front end, the stress in the tendon reahes a value of prestress that is onstant (aside from the influene of weight-indued stresses) over the entire length between transfer lengths. The integrity of the prestressed member depends upon the anhorage of the tendon(s) within the transfer length. This setion onsists of a disussion of the various mehanisms and influenes at work along the transfer length Transfer Bond Stress Consider the infinitesimally small length, dx, of reinforement embedded in onrete shown in Figure 2.5. Equilibrium along the axis of the tendon requires: where T = tendon fore = A ps f t u = bond stress Σo = tendon perimeter T + dt = T + udxσo 16

39 Solving for the bond stress results in the following: T u T+dT dx Equation 2.6 Figure 2.5: Reinforement Subjet to Tensile Fore and Bond Stress u = 1 Σo dt dx Aps = Σo df p dx whih indiates that the bond stress is proportional to the rate of hange of the tendon tension fore and the tendon stress. In other words, the bond stress is proportional to the tendon stress gradient. If the relationship between bond stress and tendon stress is extended over a finite length, l, an expression for average bond stress, u, results: Aps f p Equation 2.7 u = Σo l Over the transfer length, l t, the total hange in prestress immediately following transfer is f pt. The average transfer bond stress, u t, is given by: Aps f pt Equation 2.8 u t = Σo lt Aordingly, the transfer length an be written in terms of the average transfer bond stress: Equation 2.9 Aps f pt l t = Σo u t Mehanisms The various mehanisms that potentially ontribute to prestress transfer bond have been ategorized and desribed in a variety of ways. Three general groups of mehanisms an be identified: adhesion, frition, and mehanial resistane (Janney 1954; Hanson and Kaar 1959). Adhesion plays a minimal role in the development of transfer bond stresses beause the relative slip of the tendon with respet to the surrounding onrete destroys the adhesion between the two materials. Beause of the sliding ation of the tendon along the transfer length, frition plays a signifiant role in the development of transfer bond stresses. In order to develop fritional bond stresses, radial ompressive stresses are required. The development of these radial ompressive stresses has been attributed to a number of mehanisms. The most well known is the Hoyer Effet, desribed in Setion above, where the longitudinal ontration results in a radial expansion of the tendon. This Poisson expansion indues ompression perpendiular to the steelonrete interfae. Stoker and Sozen (1970) have also attributed radial ompressive stresses to a lak of fit mehanism. This theory holds that small hanges in the tendon ross-setion ause a wedging ation upon movement of the tendon relative to the onrete. Evans (1951) ites the fritional influene of small partiles that break free from the onrete upon slip and wedge between the tendon and the onrete. Shrinkage of the surrounding onrete an also ontribute to the radial ompressive stresses that indue fritional resistane. Mehanial resistane, or interlok, stems from the axial omponent of bearing stress existing between the tendon and the surrounding onrete that results from the helial shape of the seven-wire strand. Beause the free end of 17

40 the strand is unrestrained against twist, the resistane of the strand to unwinding is small (Stoker and Sozen 1970). However, Russell and Burns (1993a) theorize that one the strand near the free end is restrained by bond resulting from the other mehanisms, partiularly the Hoyer Effet, mehanial interlok an add signifiantly to the bond stress along the transfer length. The radial omponent of the bearing stress between the onrete and steel also ontributes to the development of fritional bond stresses. As disussed in Setion above, the irumferential onrete tensile stresses resulting from the Hoyer Effet are suh that inelasti onrete response, haraterized by limited radial raking of the onrete adjaent to the strand, should be prevalent throughout almost the entire transfer length. Only in a small region adjaent to the attak end of the transfer length are the stresses small enough that elasti behavior is expeted. For this reason, Hoyer s model of bond stresses that inrease exponentially from the attak end to the free end of the transfer length is invalid. In the portions of the transfer length where the strand expansion is greatest (near the free end), the inelasti deformations of the surrounding onrete will result in onrete response that is less stiff than in the regions where the strand expansion and resulting onrete deformation are more limited. The relationship between the strand expansion and the resulting radial ompressive stresses an be thought of as a spring system in whih the spring represents the response of the surrounding onrete. When pushed beyond its elasti limit, the spring exhibits a stiffness that dereases with inreasing deformation. Thus, in the inelasti region, the spring fore (radial ompressive stress) produed by large deformations (tendon expansion) is moderated by an assoiated derease in spring stiffness (raking of onrete). The magnitude of radial ompressive stress may remain relatively uniform along the transfer length, despite the differene in radial deformations. Sine frition stresses are typially proportional to the orresponding normal stresses on the interfae, fritional bond stresses might be expeted to remain relatively uniform along most of the transfer length. The predominately linear nature of prestress inrease within the transfer zone seen in most experimental transfer length studies supports the ontention that the transfer bond stress is relatively uniform Influene of Conrete Strength Studies indiating the influene of onrete strength on transfer bond behavior are ited in Setion above. This setion inludes a disussion of the reasons one might expet onrete strength to affet the transfer length. As disussed above, the onrete surrounding the tendon transfer length may be separated into two behavioral zones: the zone of elasti response, whih lies adjaent to the attak end of the transfer length where the stresses generated from the Hoyer Effet are relatively small; and the zone of inelasti response, whih exists along the vast majority of the transfer length where the stresses exeed the elasti apaity of the onrete. An elasti, thik-walled ylinder analysis indiates that the zone of inelasti response oupies approximately 90 to 95 perent of the transfer length for ommon prestressing materials and pratie. 4 In the zone of elasti behavior, the radial ompressive stress and resulting fritional bond stress are almost diretly proportional to the hange in steel stress and the elasti modulus, E, of the surrounding onrete. In the inelasti zone, the radial ompressive stress depends diretly upon the response of the onrete to the radial expansion of the tendon. Sine the onrete response is softened by the radial raking in this region, the stiffness of the system depends both the tensile apaity of the onrete and E. Hene, along the entire transfer length, the radial ompressive stresses and the resulting fritional stresses depend upon either the tensile apaity of the onrete, the elasti modulus of the onrete, or both. Standard North Amerian design pratie holds that both the stiffness and tensile apaity of normal-weight onrete are proportional to the square root of the onrete ompressive strength. In aordane with this line of reasoning, the average bond stress along the transfer length an be haraterized as proportional to the square root of the onrete ompressive strength. Combination of this relationship with Equation 2.9 results in the following hypothetial relationship between transfer length and onrete strength: lt 1 f 4 n = E p = 4 to 7; fpt = 180 to 200 ksi (1240 to 1380 MPa); E p f E ; f t 6. 7 f 18

41 If the tensile strength of the onrete is too small in relation to the indued stresses, splitting failure may our in the onrete between adjaent strands or in the over between strands and the surfae of the member. This mode of anhorage failure beomes more likely with the redution of strand spaing or over (thereby reduing the size of the onrete ylinder that resists the irumferential tensile stresses) and the inrease of prestress fore. Aordingly, it is important to experimentally verify that the over and lear spaing between strands are adequate to prevent anhorage failure for the range of pratial onrete strengths Time-Dependent Effets Various researh studies have indiated that prestress transfer length inreases with time. Evans (1951) reports that the transfer length of 0.08 in (2 mm) diameter wire nearly doubled in 2.5 years. Wire-reinfored speimens tested by Base (1957) exhibited transfer length inreases of up to ten perent in four months, with almost all hange ourring in the first ten to twenty days. Base also reports transfer length inreases for 0.2 in (5 mm) wire that ranged from 0 to 3 in (0 to 76 mm) within the first ten days, with no hange ourring thereafter. As disussed in Setion , Kaar, LaFraugh, and Mass (1964) found inreases of up to twenty perent for speimens prestressed with seven-wire strand. The average inrease over one year was six perent. Brue, Russell, Roller, and Martin (1994) report inreases of approximately ten perent over the first 28 days for full-size members onstruted with HSC. Lane (1992; 1998) reports no pattern to the values for perentage hange in transfer length up to an age of 365 days for retangular, onentrially prestressed speimens. However, beam speimens in the same study experiened inreases of thirty perent in the first 28 days and seven perent thereafter. Logan (1997) reports growth of measured draw-in values for poor bond quality strands of up to 66 perent in 21 days. High bond quality strands also displayed signifiant growth of measured draw-in. 5 The inrease of transfer length with time is most likely attributable to the inelasti behavior of the onrete surrounding the transfer length. Although the tendon stress tends to derease over time with the aumulation of time-dependent losses due to reep, shrinkage, and relaxation, the inelasti response of the onrete largely prevents the reovery of these stresses. Beause the onrete is stressed beyond the elasti limit in tension, some ontinued softening of the onrete grip on the tendon is possible due to stable radial rak growth and stress redistribution over time. This is a likely soure of the bond reep phenomenon that auses transfer length growth. Shrinkage of the onrete surrounding the strand might provide some additional radial ompressive stress and bond resistane over time, but this benefiial effet may be hampered due to the raked nature of the onrete along muh of the transfer length Other Considerations Numerous other fators have been ited as affeting transfer bond behavior. Several are disussed in this setion Conrete Quality and Plaement Most researhers and pratitioners would agree that proper onrete plaement and onsolidation is vital to the effetiveness of prestress transfer bond. Evans (1951) reports that a delay in onrete plaement at one end of a test speimen resulted in an exessive value of transfer length. Anderson and Anderson (1976) state that the primary ause of exessive free end slip and premature flexural bond failure in prestressed members is poor onsolidation of onrete around the strands. Unfortunately, the quality of onrete plaement and onsolidation is diffiult to quantify. Partiular attention should be paid to the workability of onrete used for pretensioned appliations. Diligene with regard to this topi is ritial when fabriating members with HSC. The signifiant in-study dispersion of transfer length results evident from studies like that of Kaar, LaFraugh, and Mass (1964) is at least partially attributable to the role that the onrete plays in the development of prestress transfer bond. Aside from the inonsistenies that may result from minor differenes in onrete onsolidation, the dependene upon inelasti onrete behavior results in signifiant variability. One phenomenon assoiated with onrete plaement that has reeived little researh effort with respet to pretensioned members is the well-known top bar effet exhibited by mild reinforing steel. Bars loated near the top of a member (in the asting position) tend to exhibit dereased bond stress apaity relative to those loated near 5 The issue of strand bond quality is addressed in Chapter 4 of this report. A disussion of the relationship between measured draw-in and transfer length is inluded in Chapter 6. 19

42 the bottom of the member. This has been attributed to the settlement of onrete beneath the top bars during onsolidation. The resulting settlement results in a slightly looser fit between the steel and onrete than ours in the bottom bars. Base (1958a) reports that transfer lengths of wires at the top of members during asting had signifiantly longer transfer lengths than wires at the bottom. Stoker and Sozen (1970) propose that anhorage length be inreased as muh as 40 perent for strands with 12 in (305 mm) or more onrete ast beneath them. Aordingly, the CEB-FIP Model Code 1990 speifies an inrease in transfer length of approximately 40 perent for top strands. The ACI and AASHTO provisions inlude an inrease of 30 perent for the development length of deformed reinforing bars ast more than 12 in (305 mm) above the bottom of the member, but no similar onsideration is inluded for prestressing strand Tendon Charateristis It is generally aepted that the onfiguration of the tendon affets the bond behavior. Seven-wire strand exhibits signifiantly larger bond apaity than straight wire. The helial pattern of the strand is thought to offer mehanial resistane that is unavailable to the straight wire. Similarly, deformations of the tendon surfae are also known to improve bond. The surfae ondition of the reinforement also effets the bond behavior. Improved bond performane has been attributed to surfae weathering of prestressing strand (ACI 318R-99, R12.9) due to the enhaned fritional resistane offered. Researh results have varied. Base (1958a) reports no disernible effet due to pre-rusting of wires. Ban, Muguruma, and Morita (1960) note transfer lengths of rusted strand approximately one-half to twothirds of those of unrusted strands. Janney (1963) found that rusted strand speimens exhibited transfer lengths about two-thirds of those found in bright strand speimens. Hanson (1969) reports a 30 perent improvement with rusted strands. Holmberg and Lindgren (1970) note that rough strand resulted in a 40 perent redution in transfer length. Logan (1997) found no evidene of benefit from the use of weathered strand. Martin and Sott (1976) argue that although rusted strand has produed shorter transfer lengths, it is an impratial prodution solution beause the optimum degree of rust is diffiult to evaluate. In addition, they state that plants generally use up strand at suh a rapid rate that assumption of a ertain degree of weathering is unreasonable. Another issue related to strand surfae ondition is that of surfae ontamination. When tensioned prior to asting, strands are espeially prone to the aidental appliation of form oil. The ontamination of strands with form oil an signifiantly degrade the frition that normally develops between the tendon and the onrete, resulting in exessive transfer lengths (Russell and Burns 1993). Logan (1997) has shown that a signifiant differene in bond performane exists among the strands produed by various manufaturers. This researh involving strand bond quality is disussed more fully in Chapter 4. Rose and Russell (1997) ite the theory that the different drawing lubriants used by various manufaturers lead to different fritional properties of the strand-onrete interfae. Wire drawn with water-soluble sodium stearates is thought to have better bond harateristis than wire drawn with non-water-soluble alium stearates. Another theory holds that the indution heating used for stress relief may burn off less of the residual lubriant than was burned off by the older tehnique of onvetion heating. The onvetion heating may also oxidize impurities on the strand surfae, whih results in a rougher surfae Method of Prestress Release Studies investigating the effet of prestress release method on transfer length have shown that sudden prestress release often results in longer transfer lengths than gradual prestress release (Base 1958a; Kaar, LaFraugh, and Mass 1963; Rüsh and Rehm 1963; Holmberg and Lindgren 1970; Rose and Russell 1997). This phenomenon is generally attributed to the dynami effets assoiated with the transfer of energy from the strand to the onrete member. Russell and Burns (1993) indiate that this effet may be more prevalent in small transfer length test speimens than in full-sale members. The CEB-FIP Model Code 1990 speifies an inrease in transfer length of 25 perent for member subjet to sudden release of prestress. 20

43 Confining Reinforement The influene of onfining reinforement was investigated by Russell and Burns (1993a). The transverse reinforement onsisted of mild steel hoops that enlosed the entire group of strands in eah speimen. No signifiant influene on transfer length was observed. The minimal effetiveness of reinforement that onfines the entire group of strands is probably due to its inability to resist the irumferential tensile strains and resulting radial raks that develop in the onrete between strands. To inrease transfer bond stresses effetively, transverse reinforement would have to be positioned to interset potential splitting planes between adjaent strands. Maximum effiieny would result from positioning reinforement immediately adjaent to the strand, where tensile stresses are largest. The large number of strands and relatively small strand spaing harateristi of most pretensioned members preludes the ost-effetive use of transverse reinforement to derease transfer length Influene of Craking The role of the radial ompressive stresses generated at the onrete-steel interfae is ruial to development of bond in the transfer length. Fritional bond stresses depend diretly on the radial ompressive stresses that are present. Craking that ours transverse to the tendon axis is extremely detrimental to transfer bond. Suh raking, resulting from the influene of flexure, shear, or torsion, results in a sharp inrease in the steel tensile stress that must be developed at the raked setion. This inrease in tensile stress reverses the benefiial Hoyer Effet along a length of strand on either side of the rak. The resulting radial ontration of the strand dereases the radial ompressive stresses present on the onrete-steel interfae. The inelasti state of the onrete surrounding the strand ontributes to this derease in radial ompressive stress. Aordingly, the transfer bond stress on the interfae dereases, reduing the amount of prestress developed in the strand and transferred to the onrete. Due to this loss of tendon and bond stress, the strand will slip until its resulting radial expansion again produes the bond stresses to equilibrate its axial tension (whih has dereased slightly during the proess). This slip indues a lengthening of the transfer length. If the applied load is sustained and the aompanying drop in onrete stresses parallel to the strand is suh that additional raking ours at proximate setions within the transfer length, the entire proess an repeat indefinitely until the bond stresses are inadequate to develop the amount of tendon stress required to resist the applied load. This type of rapidly progressing failure an also result if the applied load inreases beyond that whih initiates the raking in the transfer length. The ausative rak need not our within the transfer length to initiate this proess. As long as a rak ours lose enough that its influene in the form of radial strand ontration extends into the transfer length, the proess may begin. This phenomenon is disussed further in the subsequent setion. Limited transverse raking due to shrinkage or thermal effets has been known to our prior to the transfer of prestress. These raks generally lose upon appliation of the prestress fore to the onrete. So long as applied loads are suh that these raks do not reopen, the failure progression will not initiate. 2.5 FLEXURAL BOND AND CRACKING The diret relationship between bond stress and the steel stress gradient was derived in the preeding setion. Flexural bond stresses are those stresses generated between the onrete and reinforement that allow the variation in the steel stress along the tendon length. Prior to raking, the hange in steel stress resulting from external loads is relatively small (usually less than 20 ksi [140 MPa]). Aordingly, the flexural bond stresses present in unraked onrete are very small (typially less than 20 psi [140 kpa]). Figure 2.6 depits a portion of a simply supported beam prior to the appliation of external loads. For simpliity of disussion, the weight of the beam is negleted. Diagrams of the moment due to applied load, the steel stress, and the bond stress are shown beneath the beam. The magnitudes of the raking moment, M r, and nominal moment strength, M n, are indiated on the moment diagram. The stress in the prestressed reinforement inreases linearly along the transfer length, l t, of the tendon until the effetive prestress value, f pe, is reahed. Beause, there is no applied load, the only bond stresses present are the transfer bond stresses, u t, along the transfer length. 21

44 M M n M r f p f pe u u t l t Figure 2.6: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam Prior to Appliation of Loading Figure 2.7 depits the beam and the assoiated effets immediately prior to initiation of raking in the maximum moment region. The beam is loaded symmetrially by two onentrated loads of equal magnitude. Thus, a region of onstant moment exists between the loads, and a linear moment gradient oupies the shear span between the support and the nearest applied load. The ross setion is unraked along the entire span. Beause the full ross setion resists the applied moment, the steel stress diagram is only slightly altered from its original state. Aordingly, the flexural bond stresses are also quite small. There is no flexural bond stress in the onstant moment region beause the resulting steel stress is onstant. One the moment exeeds the raking moment, raking ours in the maximum moment region between the onentrated loads as shown in Figure 2.8. Beause the reinforement must now resist the tension fore at the raks, a pronouned inrease in steel stress ours at these loations. These steel stresses are theoretially equivalent to those alulated by raked setion analysis. Away from the region where the raking moment is exeeded, the full onrete setion is effetive in resisting tension, and the stresses in the steel remain small. 22

45 Although the average flexural bond stress between raks in the maximum moment region remains zero, loal flexural bond stresses, often referred to as in and out bond stresses, are developed between the raks. The tendon slips relative to the onrete adjaent to the raks, and these loal bond stresses transfer a portion of the tension from the steel into the onrete. Thus, ross setions that lie between raks are somewhat stiffer than indiated by a raked setion analysis beause the onrete shares some of the tensile stress. This effet is ommonly known as tension stiffening. The amount of stress transferred from the steel to the onrete and the resulting magnitude of the tension stiffening effet depend upon the loal flexural bond stresses that an be developed. M M n M r f p f pe u l t Figure 2.7: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam Immediately Prior to Flexural Craking Similarly, flexural bond stresses are required to develop the signifiant steel stress inrease that ours at the boundary between raked and unraked behavior. The length of strand labeled Crak Influene Length in Figure 2.8 lies within the region where the raking moment is not exeeded. However, signifiant flexural bond 23

46 stresses are required along this length of tendon so that the required steel stress may our at the raked setion. Thus, this region behaves similarly to the regions between the raks. On one side, the rak influene length is bounded by the outermost rak. On the other, influene of raking on the steel stress eases at the setion where relative slip between the tendon and onrete ends and bond stress is equivalent to that required for unraked setion behavior. The total hange in tendon stress that ours over the rak influene length is ditated by the differene between the tendon stress required for the unraked setion to resist the moment at one end and that required for the raked setion to resist the moment at the other. Thus, the length over whih the rak influenes the steel stress is determined by this differene in tendon stress and the flexural bond stresses that an be developed. Larger flexural bond stress apaities result in smaller rak influene lengths. In the figures that follow, the flexural bond stress apaity is indiated by the peaks of the loal bond stress profile. The flexural bond stresses that our along the rak influene length represent the flexural bond stress wave that Janney (1954) and Hanson and Kaar (1959) desribe. M M n M r f p Crak Influene Length f pe u l t Figure 2.8: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam After Flexural Craking in Maximum Moment Region 24

47 As an be seen in Figure 2.9 and Figure 2.10, flexural raking progresses toward the support as the applied load inreases. The rak influene length and aompanying flexural bond wave advane ahead of the raking. Note that as the raking spreads into the shear span, the steel stress is different at suessive rak loations. Therefore, the average flexural bond stress between raks is nonzero in the region of moment gradient. The loal bond stresses are still limited by approximately the same bond stress apaity as in the onstant moment region. M M n M r f p Crak Influene Length f pe u l t Figure 2.9: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam as Craking Progresses Toward Support 25

48 M M n M r f p Crak Influene Length f ps f pe u l t Figure 2.10: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam at Nominal Flexural Strength When the moment due to external loads equals the nominal moment apaity of the setion, the rak influene length (and flexural bond wave) are still quite removed from the transfer length of the tendon. Only a very small inrease in steel stress has ourred within the transfer length. So long as the member is more than a few weeks old, the magnitude of this inrease is suh that the prestress ourring in the transfer length at nominal strength is less than that experiened immediately after transfer, f pt. Therefore, the transfer bond apaity of the strand is not exeeded, and general bond slip (slip along the entire length of strand) annot our. Thus, the length of bonded strand between the end of the member and the ritial setion onstitutes more than enough embedment length to develop f ps without general bond slip. The next set of figures (Figure 2.11 through Figure 2.15) illustrates the same proess exept that the ritial setion for maximum moment lies substantially loser to the end of the member. Therefore, less embedded length of strand 26

49 is available to develop f ps. The sequene is nearly idential to that for the speimen with a longer embedment length until raking starts to progress toward the transfer length. The average bond stresses are slightly higher beause the same hange in steel stress must our over a shorter length of strand. Regardless, in the regions of the beam that are free of the influene of raking, the bond stresses and steel stresses are still quite small. Note that this embedment length is short enough so that when the nominal flexural strength of the beam is reahed, the rak influene length and flexural bond wave have just extended to the end of transfer length. At this point, the slightest inrease in moment would result in the rak influene length (or flexural bond wave) impinging on the transfer length. The resulting steel stress inrease in the transfer length and the aompanying derease in radial ompressive stresses would lead to general bond slip as outlined by Janney (1954) and desribed in Setion above. Thus, prevention of general bond slip depends upon effetive separation of the rak influene length and the transfer length. The embedment length featured in this seond set of figures represents the neessary flexural development length for the beam when loaded in this fashion. M M n M r f p f pe u u t l t Figure 2.11: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam Prior to Appliation of Loading Short Embedment Length 27

50 M M n M r f p f pe u l t Figure 2.12: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam Immediately Prior to Flexural Craking Short Embedment Length 28

51 M M n M r f p Crak Influene Length f pe u l t Figure 2.13: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam After Flexural Craking in Maximum Moment Region Short Embedment Length 29

52 M M n M r f p Crak Influene Length f pe u l t Figure 2.14: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam as Craking Progresses Toward Support Short Embedment Length 30

53 M M n M r Crak Influene Length f p f ps f pe u l t Figure 2.15: Applied Moment, Steel Stress, and Bond Stress Diagrams for Portion of Simply Supported Beam at Nominal Flexural Strength Short Embedment Length Avoidane of general bond slip requires that the transfer length be free from the influene of raking. Based on the behavior disussed above, the neessary development length to prevent general bond slip due to flexural raking enompasses 1) the transfer length, 2) the length of the shear span subjeted to a moment that exeeds the raking moment, and 3) the rak influene length. This is ompatible with the predition model for anhorage failure suggested by Russell and Burns (1993): If raks propagate through the anhorage zone of a strand, or immediately next to the transfer zone, then failure of the strand anhorage is imminent. If immediately next to the transfer length is defined as within the rak influene length, and failure is defined as general bond slip, this predition model agrees with that desribed above. Later in the same report, Russell and Burns (1994) state that if raks do not our within its transfer zone, a pretensioned strand will develop its prestressing fore plus any additional tensioned [si] required by external 31

54 loads. In this instane, the potential for general bond slip resulting from a rak opening just outside the transfer length, i.e. suh that the rak influene length extends into the transfer length, is overlooked. Russell and Burns go on to suggest design reommendations for the anhorage of pretensioned strands. These reommendations are based on the ondition that raking within the transfer length be avoided. This pratie is logial as long as raking is avoided not only within the transfer length, but also at any loation where the rak influene length might extend into the transfer length. In order to effetively apply this theory, a onservative assessment of the potential rak influene length must be performed. The hange in steel stress, f p, that must be developed by the bond stresses along the influene length is approximately equal to the inrease in steel stress that ours upon raking of the onrete. In other words, f p may be estimated as f p,r f p,un, where f p,r and f p,un are the values of steel stress that resist the raking moment aording to raked setion analysis and unraked setion analysis, respetively. Typial values of f p at raking for pretensioned members range up to 40 ksi (280 MPa). Generally, smaller reinforement ratios result in larger values of f p at raking. Given f p and some knowledge of the bond stresses ating along the strand, the rak influene length may be estimated using the relationship in Equation 2.7 above. Based on pull-out and push-in type tests with short embedment lengths, den Uijl (1997) proposed the following lower-bound relationship for bond stress as a funtion of slip and hange in prestress: 6 Equation 2.10 u = δ f f p p where u = bond stress (psi) δ = slip (in) f p = hange in steel stress (ksi, positive in tension) The first two terms on the right-hand side represent the bond stress resulting from sliding frition and the lak-of-fit effet. The third term represents the Hoyer effet, and the fourth term represents the mehanial interlok that results from the pith of the strand. Over the range of parameters that might be expeted along the rak influene length, the expression yields values of bond stress ranging from approximately 300 to 330 psi (2.1 to 2.3 MPa). Results of pull-out tests on strands with short embedment lengths reported by Stoker and Sozen (1970) indiate that these values represent a onservative lower bound for strand diameters up to ½ in (12.7 mm). Larger diameters were not tested. Rearranging Equation 2.7 yields: f p Aps Equation 2.11 l = u Σo Assuming a onservative value of 300 psi (2.1 MPa) for the average bond stress and a maximum value of 40 ksi (280 MPa) for f p, Equation 2.11 yields a rak influene length of slightly less than 20d b for seven-wire strand. Aordingly, the Russell and Burns riterion for prevention of general bond slip may be refined to state: If raking propagates through the transfer length of strand or through the bonded length of strand within twenty strand diameters of the transfer length, general bond slip is imminent. The effet of the reinforement ratio, ρ, on the magnitude of f p at raking is important. Beause smaller values of ρ result in larger steel stress magnitudes immediately after raking, the rak influene length should inrease with dereasing values of ρ. This suggests an alternate, or omplementary, reasoning for the inreased development length requirement proposed by Bukner (1995) for lightly reinfored members. 6 The equation presented here represents den Uijl s relationship when onverted to English units and formulated in 4 terms of the bond stress ating on the atual strand perimeter πd b rather than π db. 3 32

55 Based on test results from studies onduted at Purdue (Abdalla, Ramirez, and Lee 1993) and Florida DOT (Shahawy and Bathelor 1991), Bukner onluded that members haraterized by large values of strand elongation at nominal strength exhibited a smaller average flexural bond stress at general bond slip. Beause of the large strains that our after the strand yields, the aompanying Poisson ontration of the strand results in a signifiant derease in average bond apaity. This derease depends on the hange in strand strain, ε p, rather than strand stress, f p. Following this line of reasoning, Bukner proposes that the flexural bond length portion l fb = ( f ps f pe ) d b of the ode development length expression be magnified for values of steel strain at nominal strength, ε ps, beyond The magnifiation fator varies linearly from 1.0 to 2.0 as the ε ps varies from to Den Uijl (1997) modified Equation 2.10 above to reflet the effet of post-yield strains: u = δ ε f If this relationship is valid for large strain magnitudes, it indiates that the bond stress apaity dereases rapidly after strand yield. In flexural members with reinforement ratios small enough to allow steel strain values approahing at nominal strength, more than half of the flexural bond length may experiene strains in exess of The potentially severe degradation of bond over this length justifies the magnifiation of flexural bond length proposed by Bukner. Aording to the anhorage failure riterion suggested by Russell and Burns (1993), only raking within (or possibly near) the transfer zone of a pretensioned strand will result in bond failure. They maintain that if raking does not our in the transfer zone of a pretensioned strand, then that strand an be expeted to develop its full tension. This riterion is therefore independent of any onsideration of the available bond stress apaity along the flexural bond length. Historially, however, bond failure (in the form of general bond slip) has been assumed as dependent upon the bond stress apaity of the strand. This philosophy was evident throughout the evolution of the ode provisions disussed above. Is it possible for general bond slip to our prior to raking in or near the transfer length? In the disussion that foused on the preeding series of figures, it was taitly assumed that adequate strand bond apaity exists to develop the neessary steel stress at the ritial setion until raking in or near the transfer length aused general bond slip. This is not neessarily the ase. Consider a member in whih the loal bond stress apaity dereases signifiantly after yielding as disussed above. One flexural yielding has ourred along a portion of the flexural bond length, bond stress apaity in this region may derease rapidly aompanied by inreased loal strand slip. A signifiant share of the bond stress demand is then redistributed over a length of strand adequate to develop the steel stress neessary to resist the applied moment. As the bond stresses derease in the maximum moment region and redistribute by means of slip to the outer regions of the beam, the beam behavior starts to transition towards that harateristi of a beam reinfored with unbonded tendons anhored at the ends of the member. Aordingly, the urvature at the raked setions in the maximum moment region inreases beyond that predited by raked setion analysis. Subjeted to small inreases in applied moment, the region of strand yield extends signifiantly. The region of the beam subjeted to moments exeeding the raking moment extends only slightly. Thus, the majority of the bond stress demand progresses rapidly to the end of the raked region and beyond the outermost rak. The rak influene length inreases as more of the bond demand is redistributed to this region. Eventually, the rak influene length and assoiated flexural bond stress wave an extend to the transfer length and ause general bond slip. In summary, there are two possible modes of bond failure that result in general bond slip, both of whih are haraterized by the imposition of high flexural bond stresses on the transfer length: 1. Loal bond stress apaity is reahed and/or redued over portions of the strand subjeted to high flexural demands. The bond stresses neessary for equilibrium are then redistributed towards the transfer length of the strand. One the resulting wave of high flexural bond stress reahes the transfer length, the resulting steel stress gradient auses radial ontration of the strand thereby degrading the transfer bond stresses. With no remaining length over to whih to redistribute the required bond demand, general bond slip ours. This mode of failure orresponds to that desribed by Janney (1954). The required development length depends upon the bond apaity along the bonded length of strand when subjeted to the ritial loading. This bond apaity varies along the length of strand in aordane with the loal slip and loal hange in steel strain. p p 33

56 2. Adequate bond stress apaity exists to develop the required steel stress at nominal strength, but ahievement of this strength at the ritial setion neessitates raking A) within the transfer length of strand or B) suh that the rak influene length extends into the transfer length. Suh a rak results in radial strand ontration within the transfer length that overomes the transfer bond apaity. The resulting general bond slip redues the prestress along the entire length of strand. As the effetive prestress redues, more raking ensues and a rapidly progressing bond failure results. So long as the loal bond stress apaity is suffiient to prelude the first mode of failure, this seond failure mode apaity depends on the raking resistane of the ross setion relative to the applied loads. General bond slip an also result from a ombination of the two modes. The seond mode reflets the loation of the raking and the resulting rak influene length. The first mode reflets an extension of the rak influene length due to exessive bond demand. The progression of exessive flexural bond stresses from the peak moment region to the transfer length represents the reasoning espoused by Janney (1954) and Hanson and Kaar (1959). Neither mode of failure is uniquely addressed by the urrent ode provisions. Rather, these provisions are based on the experimental results whih may have refleted either failure mode. The average bond stress approah used to formulate the development length expression for fully bonded strands appears to be more in line with the first mode of failure, whih depends upon the loal bond apaity along the flexural bond length. Regardless of whih of the two failure modes prevailed in the PCA tests, the results reflet predominantly flexural behavior. Due to the speimen and loading geometries, all raks were of the flexural type. Russell and Burns (1993) maintain that the seond mode of failure an also be aused by shear raking. Diagonal raks that ross the transfer length (or near enough that they influene the transfer length) will also generate general bond slip and the resulting loss of effetive prestress. This loss of prestress fore an result in a premature shear failure of the member due to either or both of two auses. First, the apaity of bottom hord of the truss model for shear resistane may beome defiient as the available strand stress dereases. Seond, the shear resistane attributed to the onrete, V, may derease signifiantly in tandem with the drop in effetive prestress. Either of these effets may result in an undesirable, non-dutile mode of failure. 2.6 CODE PROVISIONS FOR ANCHORAGE OF PARTIALLY DEBONDED STRANDS The ode provisions for anhorage of fully bonded strands disussed in Setion 2.3 above are augmented for appliation to partially debonded (jaketed) strands. The additional provisions for jaketed strands are disussed in this setion Relevant ACI and AASHTO Code Clauses and Commentary ACI , Setion 12.9 inludes the following provision pertaining to partially debonded strands: Where bonding of a strand does not extend to the end of member, and design inludes tension at servie load in preompressed tensile zone as permitted by , development length speified in shall be doubled. The orresponding setion of the Commentary ites researh by Kaar and Magura (1965) and Rabbat et al. (1979) and states: Exploratory tests that study the effet of debonded strand on performane of pretensioned girders, indiated that the performane of these girders with embedment lengths twie those required by losely mathed the flexural performane of similar pretensioned girders with strand fully bonded to ends of girders. Subsequent tests indiated that in pretensioned members designed for zero tension in the onrete under servie load onditions, the development length for debonded strands need not be doubled. 34

57 The orresponding provisions for the AASHTO Standard and LRFD speifiations are substantively equivalent. In addition, Artile of the AASHTO LRFD speifiation ontains provisions that are not found in the ACI or AASHTO Standard speifiations (the statements are numbered here for onvenient referene): 1. The number of partially debonded strands should not exeed 25 perent of the total number of strands. 2. The number of debonded strands in any horizontal row shall not exeed 40 perent of the strands in that row. 3. The length of debonding of any strand shall be suh that all limit states are satisfied with onsideration of the total developed resistane at any setion being investigated. 4. Debonded strands shall be symmetrially distributed about the enterline of the member. Debonded lengths of pairs of strands that are symmetrially positioned about the enterline of the member shall be equal. 5. Exterior strands in eah horizontal row shall be fully bonded. The importane of the third statement lies with its apparent ontradition of the ACI (and AASHTO Standard) provision given above (Setion 2.3.1) and repeated here: Limiting the investigation to ross setions nearest eah end of the member that are required to develop full design strength under speified fatored loads shall be permitted. Thus, while the ACI and AASHTO Standard speifiations allow adequate anhorage to be verified by heking the development length relative to a single setion for eah end of the member, the AASHTO LRFD provision appears to indiate the importane of verifying the development of adequate setional resistane throughout members ontaining debonded strands. The AASHTO LRFD Commentary indiates that higher debonding perentages might be implemented based on suessful past pratie as long as shear resistane in the anhorage region is thoroughly investigated. The dependene of shear resistane mehanisms on the anhorage strength of reinforement is stressed. No speifi reasoning is provided for the limitations ontained in the seond, fourth, and fifth statements Bakground Researh The provision inluded in Setion of ACI is the result of the two PCA experimental studies disussed in this setion Kaar and Magura (1965) Kaar and Magura onduted experimental tests on five girder speimens to ompare the anhorage behavior of partially debonded strands to draped strands. The speimens represented half-sale models of AASHTO Type III I-girders, and were reinfored with twelve ⅜ in (9.5 mm) strand. A 3 in x 39 in (76 mm x 991 mm) ast-in-plae omposite slab was added to eah girder. The ultimate strand strength, f pu, was assumed to be 150 ksi (1035 MPa). Three of the girders were designed to ompare the anhorage behavior under the flexural effets of both stati and dynami loadings. One of these three girders featured draped strands. The other two flexural speimens featured debonded strands one with the ode-speified development length, one with twie the ode-speified development length. Eah of these speimens was subjeted to 5 million yles of design servie load and then tested statially to failure. Debonding did not affet behavior during the appliation of the servie load yles. During stati loading to destrution, general bond slip ourred in debonded strands in both of the debonded speimens. Despite the general bond slip, the speimen with twie the ode-speified development length showed only a slight defiieny in ultimate load (approximately 2 perent) when ompared with the draped strand speimen. However, the speimen 35

58 with the ode-speified development length displayed a signifiant drop in prestress level after general bond slip and resisted approximately 84 perent of the expeted failure load. Two other girders were used to ompare the shear performane of debonded and draped strands. These two girders one ontaining draped strands and one ontaining debonded strands were tested statially to destrution. The debonded strands were bonded twie the ode-speified development length beyond the ritial setion. Stirrups were spaed at 1.5 times the spaing required by the 1963 ACI Code to enourage a shear-type failure. Despite general bond slip of all debonded strands, the apaity and load-defletion behavior of the debonded speimen losely mathed that of the draped speimen. Beause of these experimental results, the 1971 version of the ACI 318 Code inluded a provision that development length for debonded strands be twie that required for fully bonded strands Rabbat et al. (1979) Rabbat et al. tested six AASHTO Type II I-girders with 5 in x 58 in (127 mm x 1473 mm) omposite onrete slabs to assess the effets of fatigue on the anhorage of debonded strands. The girders were reinfored with 0.44 in (11.1 mm), Grade 250, stress-relieved strands. The speimens were divided into two groups aording to the maximum bottom fiber stress during the yli load phase: three speimens were yled to a maximum bottom fiber stress of zero and three were yled to a maximum bottom fiber tensile stress of 6 f ' (alulated assuming an unraked setion). One speimen in eah of these groups ontained draped strands; the rest had partially debonded strands. One of the debonded speimens in eah group featured the development length speified by the ode for fully bonded strands. The remaining speimen in the zero tension group also featured this development length, but additional onfining reinforement was plaed around the strands. The remaining speimen in the 6 f ' group was haraterized by the development length reommended by the ode for debonded strands (twie that for fully bonded strands). Crak formers (sheet metal) were plaed in the bottom flange in the midspan region. All six speimens were loaded statially to the load orresponding to 6 f ' bottom fiber tensile stress in order to assure raking at the rak formers prior to initiating the yli loading program. The intention was to apply 5 million yles of servie load and then test statially to failure. All three speimens subjeted to a servie load stress of 6 f ' (one draped, one with a single development length, and one with double development length) failed prematurely due to strand frature after approximately 3 to 4 million yles. There were indiations that the strand fatigue was aggravated by fretting between the strands and the rak formers. No useful information was obtained from these tests regarding the stati ultimate load. The maximum strand end slip measured for the speimen with double the development length was in (0.15 mm) after 1 million yles and remained virtually unhanged up to the final reading at 2.5 million yles. The maximum strand end slip measured for the speimen with a single development length was in (0.6 mm) after 2.5 million yles. Twenty perent of this slip ourred after the first 1 million yles. Although this ontinued growth was extremely small, the behavior of this partiular speimen was labeled as bond fatigue. All of the speimens subjeted to zero tension during the yli load phase survived all 5 million yles. The largest strand slip was in (0.4 mm). All three speimens exhibited loads at least as large as expeted for flexural failure under stati loading to destrution. No signifiant behavioral enhanement due to the additional onfining reinforement was observed. Based on these results, it was reommended that the development length of debonded strands does not need to be doubled if no tension is allowed in the preompressed tensile zone under servie loads. Beause of the bond fatigue noted for the speimen with a single development length that was subjeted to 6 f ' servie level tensile stress, doubling the development length for debonded strands was still reommended for members in whih the preompressed tensile zone is subjet to tension under servie loads. Aordingly, the wording of ACI Setion quoted above was first inluded in the 1983 Code. Shear behavior was not investigated in this study Comments on Bakground Researh The formulation of the ode expression for the development of fully bonded strands is primarily a refletion of the first mode of failure disussed in Setion 2.5 above. This mode of failure depends on the loal bond stress that an 36

59 be developed between the steel and the onrete in the anhorage zone. The loal bond interation between the steel and the onrete does not depend on whether the strand is debonded along some remote portion of its length. Rather, the more likely soure of the differing behavior between fully bonded and partially debonded strands is the seond mode of anhorage failure that preipitated by raking in or near the transfer length. The behavior of a simply supported beam prestressed with only fully bonded strands is ompared to that of a beam prestressed with partially debonded strands in Figure In fully bonded speimens (Figure 2.16a), the anhorage zones are loated at the ends of the members. Thus, anhorage failures of fully bonded strands in these beams should only our when the span is less than approximately twie the development length. For members onstruted with 0.5 in (12.7 mm) strands, anhorage problems would only be expeted for spans of approximately 13 ft (4 m) or less. Even if the neessary development length is perent longer than that given by the urrent expression, anhorage failures would not be expeted for bridge spans longer than 20 ft (6 m). l t F p Fp M n l d M n M u M r M u M r A) Fully Bonded Strands B) Partially Debonded Strands Figure 2.16: Comparison of Beams with Fully Bonded Strands and Partially Debonded Strands Subjeted to Maximum Moment In beams that ontain partially debonded strands (Figure 2.16b), anhorage zones exist within the interior regions of the member, where they are more likely to be subjeted to signifiant flexural demand. Not only is the redued moment apaity in these regions more likely to be ritial for design, but flexural raking also ours at lower load levels than would be expeted in omparable beams with all strands fully bonded. In addition, debonding of strands results in a derease in effetive prestress fore towards the support regions, where shear demand is most pronouned. These onditions promote the likelihood that anhorage failure will initiate as a result of raking in or near the transfer length rather than beause of a progressive breakdown in the loal bond stress apaity along the flexural bond length. The moment diagram for the beam with partially debonded strands in Figure 2.16b also indiates the similarity between this type of beam and that of a beam that has some tensile reinforement terminated within the span. It is logial that the design rules appliable to terminating nonprestressed tensile reinforement also be applied when determining the bonded tendon length required to provide adequate strength under ultimate loads. Considering both of the studies ited above regarding debonded strands, all of the debonded speimens whih featured an anhorage length equal to the ode-speified development length for fully bonded strands displayed extensive raking within strand transfer lengths at ultimate. In the Kaar and Magura study, regardless of development length provided, general bond slip was first reported for eah pair of debonded strands at approximately the load that would have produed flexural raking within the transfer length. The girder that failed prematurely had suffered general bond slip due to transfer length raking in all of the debonded strands prior to 37

60 failure. Thus, 50 perent of the total number of strands had been subjeted to some loss of anhorage. At the setion where failure atually ourred, 40 perent of the bonded strands had been subjeted to anhorage deterioration, and the setional moment was 76 perent of that alulated based on the assumption of perfet bond. In the girder with twie the ode-speified development length, transfer length raking and the assoiated general bond slip had only affeted one-sixth of the total number of strands. This girder ahieved 96 perent of the alulated ultimate load. Apparently, onsiderable residual stress remained in the strands after general bond slip in both these girders. The bond fatigue ourring in one speimen from the Rabbat et al. study an be explained by the influene of raking on the transfer length. The aforementioned rak formers were loated within the transfer length of two of the strands in this speimen. The speimen was raked prior to yli loading. The magnitude of the yli load was seleted to ahieve a stress of 6 f ' in the extreme onrete fiber based on the unraked setional analysis that would typially be used for design. This ensured that with every load yle, the rak opened, and within their transfer length two strands were subjeted to stresses well in exess of the effetive prestress level. With the resulting radial strand ontration and loss of the Hoyer Effet, it is hard to imagine slip not ourring under these irumstanes. Even under this ylial demand, the slip growth appeared to stabilize prior to fatigue failure of the strands, and the maximum value of slip after 2.5 million yles was quite small. Rather than double the entire development length to prevent bond fatigue due to servie level tension in the preompressed tensile zone, it seems that a more diret and universally appliable approah would limit the allowable servie level onrete tensile stress within the transfer length to zero. Two speimens with debonded strands from the Rabbat et al. study survived the yli loading program. When these speimens were tested statially to failure, the transfer lengths of the four debonded strands were subjeted to loads well in exess of the raking load. Craking ourred within these transfer lengths, but no information on strand end slips is provided in the literature. Although these four strands likely lost some anhorage integrity, the predited ultimate moment of the member was ahieved. There were a total of 24 strands, of whih two were not prestressed. A partial loss of anhorage of suh a relatively small proportion of the total number of strands is likely to have had little effet on the ultimate apaity of the girder, partiularly if the member had enough deformation apaity to ativate steel stresses larger than expeted in the fully bonded strands. The reported final defletions, whih were equal to approximately 5 perent of the span length, that ourred without loss of moment resistane indiate that signifiant deformation apaity was observed. 2.7 INFLUENCE OF CRACKING ON THE ANCHORAGE OF PRETENSIONED STRANDS Published researh results indiate the influene of raking on the anhorage of pretensioned strands. Obdalla, Ramirez, and Lee (1993) report the results of tests onduted on five pairs of simply supported, pretensioned I-beams and box beams at Purdue University. One beam in eah pair featured debonded strands, while the other had an idential strand pattern with all strands fully bonded. Premature failures of the debonded speimens were always preipitated by web shear or flexure-shear raking within or very near the transfer length of the debonded strands. After the resulting strand slip, the girders eventually failed beause the strands ould not provide the horizontal fore required to resist the ombined flexural and shear demand. The web shear raking loads were adequately predited by the ACI/AASHTO Standard expression for V w, but flexure-shear raks generally opened at loads less than those indiated by the ACI/AASHTO Standard expression for V i. A more onservative predition for the flexure-shear raking load resulted from disregarding the prestress of any strands that were not ompletely developed at the setion under onsideration when alulating V i. While flexure-shear raks were ritial in ausing the anhorage failure of the partially debonded strands, web shear raks that extended through the transfer length resulted in the failure of fully bonded strands near the support. Based on results obtained from an extensive experimental study, Russell and Burns (1993) proposed that anhorage failures did not our if raking was prevented in the prestress transfer zone. The orresponding design proedure entails preventing flexural raks by limiting the moment in the transfer zone to the alulated raking moment, and preventing web shear raks in the transfer length by limiting the shear demand to V w in this region. Several instanes of bond/shear failures ourred in the test program. In these failures, raking led to bond deterioration along the strand transfer length. In addition to reduing the onrete ontribution to shear resistane, the aompanying loss of prestress fore rendered the strands unable to sustain the horizontal fore neessary to resist the applied shear and moment. 38

61 Previous researh has revealed two important observations onerning the interation of raking and the strand anhorage: 1. Craks that open within the transfer length, or near enough to influene the strand stress within the transfer length, result in strand slip and a partial loss of strand anhorage. Partially debonded strands are partiularly suseptible to this type of bond deterioration beause they are anhored away from the ends of members. 2. Aurate predition of setional raking resistane requires areful onsideration of the variable nature of the effetive prestress fore within the anhorage zone, espeially in members with partially debonded strands. In partiular, the ACI/AASHTO Standard expression for V i does not onsistently indiate the load that auses flexure-shear raking. This is likely beause the V i expression is based on the assumption that flexure-shear raks open first as flexure raks at the bottom fiber and then progress under the ombined influene of flexure and shear. Beause the shear raking resistane an be signifiantly redued in debonded regions, raks may also initiate at the juntion of the web and bottom flange due to the simultaneous influene of flexure and shear. This type of rak initiation is not addressed in the odes, but may be predited by means of alulating the prinipal tensile stress at the web-flange juntion. This type of raking may be visually indistinguishable from lassi flexure-shear raking beause the rak rapidly extends to the bottom fiber after initiation. The ability to predit this type of raking is vital to prevention of strand slip in some debonded strand anhorage zones. 2.8 ANCHORAGE FAILURE CRITERIA AND DESIGN PHILOSOPHY Throughout the evolution of ode provisions onerning the anhorage of fully bonded and partially debonded pretensioned strands, no lear definition of anhorage failure has been agreed upon nor adopted. Hanson and Kaar (1959) reommended that avoidane of general bond slip be the riterion for anhorage design. They maintained that although most speimens exhibited additional resistane after initiation of general bond slip, the influene of repeated loads was yet undetermined. Therefore, post-slip resistane should not be relied upon. Mattok ehoed this philosophy when proposing the flexural bond length expression to be inorporated in the 1963 ACI 318 Code. The ACI 318R-63 Commentary states that the ode provisions are intended to ensure that failure of a pretensioned prestressed member shall not our by the strand pulling through the onrete as a result of failure in flexural bond (Tabatabai and Dikson 1993). It seems lear that general bond slip was the aepted riterion for determining anhorage failure in pretensioned members at that time. By the time that the modifiations for debonded strands appeared in the Code provisions (1971 and 1983) this philosophy appears to have hanged. General bond slip of debonded strands was reported for all of Kaar and Magura s (1965) test speimens, yet some of these strands were judged to be adequately anhored, while others were not. Rather, the evaluation of adequate anhorage was based on the load-defletion behavior and ultimate strength of eah speimen. Rabbat et al. (1979) report that strand slip ourred under yli servie loads for speimens regardless of whether or not the anhorage length was determined to be adequate. The adequay of anhorage under yli loading was determined aording to whether or not the slip ontinued to inrease with repeated loading. The ode modifiations resulting from these two studies seem to reflet a shift in emphasis from preventing strand slip to ensuring adequate resistane of the member. On what riteria should anhorage design be based? Theoretially, suffiient anhorage apaity should be provided so that the performane of the member (and overall struture) is adequate with regard to the limit state under onsideration. Under the repetitive loading that haraterizes the Servie Limit State, general bond slip is unaeptable. Prevention of strand slip under repetitive loads preludes progressive bond failure due to bond fatigue, and ensures that load-defletion behavior will not suffer from inadequate bond. For the Strength (or Ultimate) Limit State, adequate anhorage performane is that whih allows the member to ahieve the required ultimate strength and fail aording to the intended (usually flexural) mehanism. Thus, the member resistane should exeed all demands that might result from potential load onfigurations. Extensive damage is not a onern when designing for the Strength Limit State as long as the ritial loads are adequately resisted. Repeated loads are not onsidered. Prevention of general bond slip is not a strit neessity under these onditions, but it allows simple alulation of member apaities aording to the standard assumption of perfet bond. Unfortunately, previous researh has shown that preventing general bond slip, partiularly in members with debonded strands, is not as simple as providing a standard strand development length. In addition to providing an 39

62 anhorage length adequate to prevent progressive failure of loal bond apaity, strand transfer lengths must be proteted from the influene of all types of raking. Current ode provisions do not adequately address this issue. On the other hand, general bond slip might be allowed when designing for the Strength Limit State if adequate strength at all setions an be ensured. This is the general approah used for determining utoff lengths of straight mild steel reinforement. A development length is alulated based on a onservative assessment of the anhorage apaity of the bar after slip. So long as this development length is provided (and a bevy of aompanying rules are satisfied), alulation of member strength aording to resistane models (flexural, shear, torsion, et.) is relatively simple. Adapting this approah to pretensioned strands ould simplify one portion of the design proess while ompliating another. For example, rather than dediating extensive analytial effort to determining the suseptibility of multiple setions to a variety of raking mehanisms, the presene of raking along the development ould be presupposed. A more onservative expression for development length would be required beause raking would hinder the rapid buildup of prestress along the transfer length that is refleted in the urrent expression. In return, the alulation of the required anhorage length would be muh simpler. Aurate alulation of resistane to moment, shear, and torsion at setions within the strand development length would depend upon due onsideration of the redued apaity of the strand. Depending upon the experimentally determined relationship between bond apaity and strand slip along the development length, employment of strain ompatibility analysis might be neessary for determination of the strand stress available from adjaent strands that are fully developed at these setions, if present. Calulation of shear resistane must be arefully onsidered when strand slip is allowed under Strength Limit State design. One slip of the strand ours within the transfer length, the development of the effetive prestress fore over the original transfer length an no longer be safely assumed. Likewise, the effetive prestress applied to the onrete is redued as well. This an signifiantly affet the onrete ontribution to shear strength, V, regardless of whih resistane model is employed for shear design. An inrease in shear reinforement an ompensate for this partial loss of onrete shear resistane. The redution of apaity in the longitudinal reinforement itself along the development length must also be onsidered. The ACI/AASHTO Standard provisions do not require evaluation of the adequay of longitudinal reinforement to resist the demands of both flexure and shear. 7 This must be heked onsidering the limited strand apaity along the development length. The AASHTO LRFD speifiation inludes this equilibrium hek (Artile ). In summary, the prevention of general bond slip under ultimate load onditions requires onsiderable omputational effort, partiularly for debonded strands. However, if slip is preluded, alulation of setional resistane is relatively simple beause perfet bond an safely be assumed. Prevention of slip requires adequate anhorage length and prevention of raking within strand transfer lengths. This might prove diffiult for some members, partiularly those with partially debonded strands. This obstale may be overome if raking is allowed within the transfer length, whih also eliminates the omputational effort required to ensure that raking does not our. This approah is analogous to that urrently used for development of nonprestressed reinforement. A more onservative development length must then be assumed, and alulation of setional resistane must be performed judiiously. Unfortunately, the reliability of this approah annot be assessed until adequate experimental evidene is obtained to determine a onservative estimate of strand development length in the presene of transfer length raking. The usefulness of this tehnique for onservatively estimating the strand apaity for use in moment and shear resistane omputation must also be experimentally assessed. The anhorage behavior of partially debonded strands has been likened to that of utoff mild steel reinforement. Although they perform similarly under the influene of external loads, eonomi onsiderations ditate different philosophies for the two reinforement types. In the ase of utoff bars, material savings are maximized when the bars are ut as short as possible without ompromising safety. For prestressing strand, on the other hand, material and labor savings are maximized when debonding lengths are minimized. The minimum amount of strand debonding is ditated by the allowable onrete (tensile and ompressive) stresses immediately after prestress transfer. One the minimum amount of debonding has been determined aordingly, the designer must verify that the resulting bonded length of strand provides adequate anhorage under the demands of the Servie and Strength Limit States. If the anhorage is judged to be defiient, the bonded length of strand annot be inreased as would be the ase with mild steel reinforement. Suh an inrease would result in exessive 7 This inadequay is addressed for the ase of mild steel reinforement by requiring that bars be extended one effetive depth, d, beyond the setion where they are no longer required to resist flexural loads (MaGregor 1996, ). There is no orresponding provision for prestressing reinforement. 40

63 onrete stresses at transfer, unless the onrete strength were inreased aordingly. A simple but highly effetive solution to this potential problem is the installation of a few prestressing strands near the top of the member. This pratie an redue the onrete stress magnitudes at transfer while signifiantly enhaning the web shear raking resistane (Russell and Burns 1993). 2.9 ANCHORAGE DESIGN The anhorage design of pretensioned members an be subdivided into a series of general proedures disussed in the subsetions below. The disussion addresses the design of simply supported members, but the general proedures an be extended to other support onfigurations as well Design of Midspan Setion for Flexural Resistane The member size, onrete strength and onfiguration of prestressing strands are determined aording to the flexural demands on the midspan setion. The amount of prestressing reinforement required is typially ontrolled by 1) the allowable onrete tensile stress at the bottom fiber under Servie Limit State loading and 2) ultimate moment resistane under Strength Limit State loading Determination of Strand Debonding Lengths and Configuration One the number, size and pattern of prestressing strands has been determined, the allowable onrete stresses immediately after transfer ditate the possible strand debonding onfigurations. Conservative assessment of the ritial onrete stresses requires a lower-bound estimate of the transfer length. ACI and AASHTO odes provide no guidane for seleting a lower-bound value for transfer length. Considering the large variability of transfer lengths, assumption of a transfer length of zero is safe and simple without being unduly onservative. Strands should not be debonded over lengths longer than neessary to satisfy allowable stress limits. If multiple strands require long debonded lengths, staggered debonding should be employed if possible (Russell and Burns 1993) Servie Limit State Anhorage Performane Cheks General bond slip should be preluded under repetitive Servie Limit State loads. Beause development of large longitudinal steel stresses is not required under servie loads, general bond slip due to exessive flexural bond demand (first bond failure mode) need not be heked for the Servie Limit State. However, the seond mode of failure general bond slip resulting from raking in or near the transfer length should be heked. This type of slip an be preluded by heking that no net onrete tensile stress ours along the bonded length of strand within 20 strand diameters of the transfer length. In ontrast with the approah for heking onrete stresses immediately after transfer, onservative design with respet to anhorage apaity requires that a onservative upper bound estimate be made of the transfer length. Theoretially, prevention of raking requires that the modulus of rupture not be exeeded in tension. However, raking of the bottom flange may have ourred previously due to a variety of auses, e.g. periodi overloads, drying shrinkage prior to prestress release, et. The limitation of zero tension prevents opening of existing raks under repetitive, servie load onditions. This hek will probably only be ritial if strand debonding extends into the midspan region of the girder Strength Limit State Anhorage Performane Cheks As disussed in Setion 2.8 above, two distint methods might be used to verify adequate anhorage performane for the Strength Limit State. The first, Method A, implements an expression for development length that results from an assumption that no strand slip ours within the transfer length. The urrent development length expression for fully bonded strands is taitly based on this assumption. The development length expression inorporates regions of transfer bond and flexural bond, and is formulated to prelude the first mode of general bond slip failure. In order for this development length to be adequate, the seond mode of general bond slip failure aused by raking that influenes the strand transfer length must also be prevented. One raking has influened the transfer length, the transfer bond apaity degrades rapidly, and the neessary development length grows longer. Thus, appliation of Method A requires that the resistane to raking be heked at the beginning (initiation of bond) and end (transfer length plus rak influene length) of eah suseptible transfer zone. At eah suh setion, several types of raking must be obviated. Prevention of flexural raking requires that the onrete stress at the extreme tensile fiber be limited under full Strength Limit State loading. This type of raking is most likely in 41

64 transfer zones that lie losest to midspan. Web shear raks may be prevented by verifying that the priniple tensile stress at the entroid (or at the juntion of web and top flange if the entroid lies within the flange) is less than a limiting value. This type of raking is most prevalent in transfer zones near supports. Craks resulting from shearflexure interation at intermediate transfer zones must also be prevented. This an be ahieved by limiting the prinipal stress at the juntion of the web and bottom flange to a ritial value. One all possible types of transfer zone raking have been preluded, the development length alulated with the assumption of enhaned transfer bond is valid. The benefit of adopting Method A is the shorter development length that results from taking advantage of enhaned bond apaity along the transfer length portion. The obvious disadvantage of this method is the amount of omputational effort that must be expended to verify that the transfer zones are not suseptible to the influene of raking under full Strength Limit State loading. The seond method, Method B, does not require this effort beause the effets of raking in the transfer zone are fatored in to the alulated development length. Aordingly, the development length expression used in Method B will result in a development lengths signifiantly larger than those alulated from the Method A expression. Beause transfer zone raking is allowed by Method B, the enhaned bond apaity offered by transfer bond is forfeited. A greater fator of safety should also be inorporated into the Method B expression beause of the potential lak of dutility that may result from strand slip. Although this method of alulating anhorage apaity is analogous to that used for nonprestressed reinforement, no signifiant researh effort has been expended to evaluate its appropriateness for design. The validity of suh an approah has yet to be verified experimentally, nor has a lower-bound value for average bond stress been suggested for appliation over a long embedment length subjeted to signifiant raking. This method s potential benefits in terms of design simpliity and broad appliability appear to justify further investigation Calulation of Prestress Fores at Setions Where Strands Are Not Fully Developed When nominal resistanes (suh as M n, V n, or T n ) are alulated at setions that lie within the tendon development length, areful onsideration must be given to the amount of prestress fore that may be relied upon. If Method A is hosen and no raking is antiipated within the strand transfer length, the available steel stress at a setion may be estimated using the bilinear relationship depited in Figure Conservative lower bound estimates of the average transfer bond stress apaity, u t, and the average flexural bond apaity, u fb, are used to predit the steel stress apaity orresponding to the bonded length provided. Calulation of the steel stress within the transfer length should not be ritial for nominal resistane alulations beause the onrete is not allowed to rak in this region. Otherwise, Method A would not be appliable. If Method B is employed, the extent of raking need not be heked, and the available steel stress at any setion may be estimated from the simple linear relationship shown in Figure For a speifi bonded length, a onservative lower bound estimate of the average bond apaity, u, an be used to alulate the steel stress available for load resistane. One the available steel stress is obtained, setional apaities may be omputed. Rather than alulate resistane apaities at a multitude of setions, the apaities at the beginning and end of the development length an be alulated, and intermediate values may be interpolated. Regardless of the method hosen, speial are must be taken to estimate the prestress fore available from a group of strands that have different bonded lengths at a setion. One the available stress and orresponding strain have been alulated for the strand with the shortest bonded length, stresses in the aompanying strands must be alulated assuming ompatibility of strains. One the available prestress fore has been alulated for a setion where strands are not fully developed, the average onrete stress resulting from this prestress fore an be alulated for use in shear and torsional resistane omputations. It is important that the redued level of prestress be onsidered at these setions so that the onrete ontribution to the nominal resistane not be overestimated. Failure to onsider the redued onrete prestress and redued steel stress available after raking and slip may result in premature failures like the post-slip shear failures reported by Russell and Burns (1993). 42

65 f ps u fb Steel Stress u t A ps Σ o A ps Σ o l t Bonded Length of Strand l d Figure 2.17: Method A Relationship Between Steel Stress Capaity and Bonded Anhorage Length (No General Bond Slip) f ps Steel Stress Method A Method B A ps Σ o u u = A ps Σ o f p x Bonded Length of Strand l d Figure 2.18: Method B Relationship Between Steel Stress Capaity and Bonded Anhorage Length (General Bond Slip Allowed) 43

66 44

67 CHAPTER 3: TEST SPECIMEN DETAILS 3.1 INTRODUCTION The speimens tested in this study onsisted of a total of thirty-six AASHTO Type I (TxDOT Type A) I-beams. Development length testing of six of the I-beams (beam pairs L0R, L4R, and L6R) was performed by researhers at Texas Teh University, and the results are reported by Burkett and Kose (1999). This hapter inludes a desription of the test speimens and details regarding their design and onstrution. 3.2 SPECIMEN IDENTIFICATION The speimen identifiation system used throughout this report is summarized in Figure 3.1 below. L Series (f i = 4000 psi) M Series (f i = 7000 psi) H Series (f i = 9000 psi) Conrete Strength M9R-C-96H Embedment Length for Development Length Test (in) Horizontal Web Reinforement (H-Bar) Indiator Number of Debonded Strands Beam End Identifier (A, B, C or D) 0 - Fully Bonded Series 4-50% Debonded Series 6 or 9-60/75% Debonded Series Strand Surfae Condition B - Bright R - Rusted First three digits (M9R) identify a pair of beams ast together. First four digits (M9R-C) identify a unique beam end. Final term (96H) offers additional information onerning development length test (embedment length at ritial setion, presene of H-bar) Figure 3.1: Speimen Identifiation System The thirty-six beams were ast in pairs. Eah pair represented a unique ombination of onrete strength, debonding onfiguration, and strand surfae ondition. These three variables are indiated by the first three digits of the speimen identifiation. Thus, M9R represents the beam pair ast with the M-Series onrete mix and rusted strands; nine (75 perent) of these strands were partially debonded. The fourth digit of the identifier speifies a partiular beam end. The beam ends were identified aording to asting position as depited in Figure 3.2. All four beam ends were essentially idential exept that horizontal web reinforement was present in End C. In some ases, the prestress release method varied among beam ends. This is explained further in Setion The use of the first four digits, suh as M9R-C, is adequate to speify eah of the seventy-two beam ends tested for transfer and development length. 45

68 End A End B End C H-Bar(s) End D WEST L L L = 40 ft (12.19 m) for Fully Bonded Series (x0x Speimens) L = 54 ft (16.46 m) for both Debonded Series (x4x, x6x and x9x Speimens) EAST Figure 3.2: Casting Configuration for Typial Beam Pair The final term ( 96H in Figure 3.1) is used to offer additional information onerning the development length test on a partiular beam end. Thus, beam end M9R-C-96H was subjeted to development length testing with an embedment length of 96 in (2438 mm) and ontained horizontal web reinforement (H). As a further example of the strand identifiation system, onsider beam end L0B-B-72. This identifies end B of the beam pair ast with L Series onrete and bright strands. The strands were fully bonded, and the development length test was performed with an embedment length of 72 in (1829 mm) relative to the ritial setion. No horizontal web reinforement was present. 3.3 SPECIMEN DESIGN Full-size AASHTO Type I (TxDOT Type A) beams were used in the study. The dimensions of this ross setion type are shown in Figure 3.3. Prior to development length testing, a ast-in-plae reinfored onrete slab (or dek ) was added to the beam. The 60 in by 6.5 in (1524 mm x 165 mm) dek was ast to model the omposite behavior typial of bridge girders and to ensure that the elongation of bottom row of strands reahed the presribed limit prior to failure. 12 in in 3 in 28 in 6 in 11 in in 5 in 3 / 4 in Chamfer 16 in Figure 3.3: Dimensions of AASHTO Type I Cross Setion (1 in = 25.4 mm) 46

69 3.3.1 Strand Patterns Figure 3.4 depits the sheme used to label speifi strands in eah speimen. The strands are depited as viewed from the end of the beam. 2 in (typ.) M L K J I H G F E D C B A 2 in (typ.) Strand ID = E Figure 3.4: Strand Identifiation Key (1 in = 25.4 mm) Table 3.1 and Table 3.2 provide the details of the various strand layouts and debonding patterns for the test speimens. Seletion of strand layouts was subjet to a variety of onstraints. To satisfy the minimum elongation requirement of 3.5 perent in the bottom row of strands at ultimate flexural strength, the beams had to be onsiderably underreinfored. In addition, beause of the relatively small dimensions of the ross-setion ompared with more typial bridge girders, plaing more than six to eight strands in the bottom flange of the normal-strength beams (L Series) would have resulted in exessive ompressive stresses in the bottom flange at release. In diret opposition to these onstraints, having a large number of strands was desirable in order to provide a variety of perentages of debonded strand. At various times during speimen design, the sponsor requested that the following perentages of strands be debonded: 0, 25, 37.5, 50, and 75 perent. If limited to a symmetrial strand pattern, at least sixteen total strands would have been required to generate all of these debonding perentages. However, given the elongation requirement and allowable stress limits, this was impossible. Generally, the beams were designed with the maximum number of strands that ould be used while satisfying ACI and AASHTO allowable stress requirements and the 3.5 perent elongation onstraint. Table 3.1: Tendon Loation and Debonding Shedule Speimen Strand ID (see Figure 3.4) ID A1 A2 A3 A4 A5 A6 B3 B4 E3 E4 G3 G4 M3 M4 L0x FB FB FB FB FB FB FB FB M0B and H0B FB FB FB FB FB FB FB FB FB FB M0R and H0R FB FB FB FB FB FB L4x and M4x FB FB FB FB FB FB H4x FB FB FB FB L6x FB FB FB FB M9x and H9x FB FB FB x = wildard plaeholder (e.g. L4x inludes L4B and L4R) FB = fully bonded strand # = debonded length of strand in inhes (1 in = 25.4 mm) = strand not present in speimen 47

70 Table 3.2: Speified Jaking Stress, f pj, for Top Strands (M3 and M4) Speimen ID f pj ksi (MPa) x0x 92 (635) L4x (1395) M4x 46 (315) x = wildard plaeholder Aording to standard pratie, strands were tensioned to 75 perent of the speified tensile strength, f pu. Thus, the jaking stress, f pj, was ksi (1395 MPa). However, the strands in the top (Strands M3 and M4) of some of the speimens were not fully prestressed. In some of the speimens with lower perentages of debonded strands or lower onrete strengths, these top strands were neessary to ontrol the top fiber tensile stresses at release. To adequately ontrol these stresses, less than full prestress was often required from these top strands. The values of f pj speified for strands M3 and M4 are given in Table 3.2 for the speimens in whih they are present. In order to satisfy allowable stress limits with regard to ompression in the bottom fiber, a pair of strands was omitted from the bottom flange in beam pairs L0x and L6x. Thus, these beams had two fewer strands in the bottom flange than their higher strength ompanions. With respet to debonding perentages/patterns, the beams are divided into three general groups. The first group, denoted with a 0 as the seond digit of the identifier, represent strands with little or no debonding. Beam pairs L0B, M0B, H0B, and L0R ontain no debonded strands. The strands in beam pairs M0R and H0R are not fully bonded beause four of the strands in the bottom flange in eah end were partially debonded for a length of 12 in (305 mm). This small amount of debonding was speified in an attempt to minimize the influene of the support reation on the development length of these strands. This is disussed more fully in Chapter 7. Beause the debonding of these strands ours only over the support, they are inluded with the fully bonded speimen group. As disussed above, beause debonding was not used to ontrol top and bottom fiber stresses at release in these fully bonded speimens, top strands were required for all speimens in the group. In addition, two of the bottom flange strands were omitted from the lower strength speimens in the group. This first group of speimens had a length 40 ft (12.19 m). Beause of the extra length provided for debonding of strands, the speimens in the seond and third group had a length of 54 ft (16.46 m). The seond group of speimens, represented by a 4 as the seond digit of the identifier, featured partial debonding of 50 perent of the bottom flange strands. A staggered debonding pattern was employed. Two of the strands (A2 and A5) were debonded for a length of 36 in (914 mm); two others (A3 and A4) were debonded for a length of 72 in (1829 mm). Beause of the use of debonding to lower the stresses in the end regions of the girders, top strands were only required for beam pairs L4x and M4x. The prestress required in these top strands dereased with inreasing onrete ompressive strength. The third group of speimens, represented by either a 6 or a 9 as the seond digit of the identifier, featured partial debonding of more than 50 perent of the bottom flange strands. Here again, a staggered debonding pattern was employed. Partially debonded strands were debonded over 36, 72, or 108 in (914, 1829, or 2743 mm) lengths. Beause of allowable ompressive stress limitations, only ten strands ould be plaed in the L6x speimens. Six of these ten strands were then partially debonded, resulting in a debonded perentage of 60 perent. The higher onrete strengths of the M9x and H9x speimens allowed the use of twelve strands, eight of whih were to be partially debonded. However, after the L6x speimens were ast, the sponsor requested that the remainder of the speimens have 75 perent of the strands partially debonded. Beause no more than twelve strands ould be plaed in these speimens (M9x and H9x), this perentage was impossible to obtain symmetrially. Aordingly, one of the strands loated in the web of the speimens (Strand G3) was debonded for a length of 36 in (914 mm). Thus, nine of the twelve strands were partially debonded in an unsymmetrial pattern. In the speimens with more than 50 perent of strands debonded, a pair of strands was plaed within the beam web (Strands G3 and G4), and another pair was plaed at the juntion of the web and the bottom flange (Strands E3 and E4). This was done in an attempt to investigate whether these strands would behave differently than their ounterparts within the bottom flange. 48

71 The debonding patterns used in these speimens violated the requirements of the AASHTO LRFD Code (1998) Setion in several ways. First, in the speimens with partially debonded strands, the number of partially debonded strands signifiantly exeeded 25 perent of the total number of strands as limited by the LRFD Code. Seond, in all rows in whih strands were debonded, more than the LRFD Code maximum 40 perent of the strands in the row were debonded. Third, in the M9x and H9x speimens, debonded strands were not symmetrially distributed about the enterline of the member as required. Finally, the exterior strands in several of the horizontal rows (Rows B, E, and G) were partially debonded. The LRFD Code requires that exterior strands in eah horizontal row be fully bonded Dek Design Design details of the ast-in-plae dek are shown in Figure 3.5. The primary purpose of the dek slab is to provide a large ompression flange for the beam. The width of the dek allows the neutral axis to be high in the member at flexural failure, resulting in a large urvature and high strains in the tension reinforement. Using strain ompatibility analysis, the dek size was seleted to result in a total elongation of at least 3.5 perent in the bottom row of strands at flexural failure. A 28-day onrete ompressive strength of 6000 psi (41 MPa) was speified for the dek. Use of a lesser strength would have required a larger dek to ahieve the same degree of strand elongation. In addition, speifying a higher 28-day onrete strength allowed for development length testing at an earlier age, thus aelerating the testing shedule. As depited in Figure 3.5, dek reinforement onsisted of two mats (top and bottom) of orthogonal #4 reinforing bars. The bars were spaed to provide a reinforement ratio that roughly approximated that of a typial bridge dek. 60 in 6.5 in #4 10 in o.. Top and Bottom (Longitudinal) 28 in #4 12 in o.. Top and Bottom (Transverse) 3 / 4 in Cover (typ.) Figure 3.5: Dimensions and Reinforement of Cast-in-Plae Composite Dek (1 in = 25.4 mm) Mild Steel Beam Reinforement Mild steel reinforement for the preast beams orresponded to that used in standard TxDOT pratie. Reinforement for the 40 ft (12.19 m) beams is shown in Figure 3.6. Reinforement for the 54 ft (16.46 m) speimens, whih ontain debonded strands, is shown in Figure 3.7. Figure 3.8 illustrates the details of eah of the bar types shown in Figure 3.6 and Figure 3.7. The bar types (R, S, X, et.) are labeled aording to TxDOT pratie. In the 40 ft beams, the V bars, whih aid in onfining the bottom flange, were plaed as shown on TxDOT standard I-beam designs. For the beams with partially debonded strands, the loation of the V bars was extended to onfine the bottom flange throughout the expeted transfer lengths of the debonded strands. The horizontal web reinforement, or H-bar(s), whih were plaed in End C of eah beam pair, also served as a deviation from standard TxDOT pratie. 49

72 50 Figure 3.6: Mild Steel Reinforement for Speimens L0x, M0x, and H0x (1 in = 25.4 mm) Bars Y Bars S (in pairs) 2" Y W 4" Y-1.5" 1" 11" 2.75" 1.5" 2" 6" TOP FLANGE BOTTOM FLANGE 7 4" = 2'-4" Bars W U H1 R (x2) X V R R V 22 4" = 7'-4" Bars R (x2) 2" Bars S Bars R Bars V (14 pairs) Bars H1 (End "C" ONLY) L/2 = 20' ELEVATION V U X 4" Max Sp Bars R (x1) Bars X R S H1 Sym about C.L. (exept for Bars H1) Y V W AASHTO TYPE I CROSS SECTION Bars U

73 51 Figure 3.7: Mild Steel Reinforement for Speimens L4x, M4x, H4x, L6x, M9x, and H9x (1 in = 25.4 mm) Bars Y Bars S (in pairs) 11" 2.75" Y W 4" Y-1.5" 1" 1.5" 2" 6" TOP FLANGE BOTTOM FLANGE 7 4" = 2'-4" Bars R S Bars W 11 4" = 3'-8" 2 2" = 4" 2" Bars S U H2 R V R R V X Bars R 6 12" = 6' 10" Bar H2 (End "C" ONLY) ELEVATION V U X Bars R Bars V (in pairs) L/2 = 27' Bars X R S H2 Y V W AASHTO TYPE I CROSS SECTION Bars U Sym about C.L. (exept for Bar H2)

74 BARS R (#4) 3.25" 2'-7" 4" 3.125" 2.25" BARS H1 (#4) 6'-6" 2.25" BARS Y (#6) BARS S (#5) 1'-0.5" BARS X (#3) 9" 2' 1'-10" 3.625" 6.25" BARS W (#5) 10" BARS V (#4) " 3' BARS U (#5) >30" Beam Length minus 3" 12'-6" for x4x Beams; 13'-4" for L6x, M9x, H9x BAR H2 (#4) Figure 3.8: Reinforement Details (1 in =25.4 mm) The most signifiant deviation in terms of mild steel reinforement was that of the shear reinforement, or R bars. Beause the development length testing proess involved the appliation of large onentrated loads relatively lose to the supports, a signifiant inrease in shear reinforement was required ompared to the TxDOT standard design for this size I-beam. The maximum applied load, and hene the shear to be resisted, depended on the geometry of eah development length test. The shear span and the expeted shear fore of eah test was diretly linked to the embedment length to be tested. Unfortunately, it was impossible to preisely determine during the design phase what embedment lengths would be tested. 52

75 In general, the shortest probable shear span was estimated for eah test series, and a maximum expeted shear fore was alulated based on the expeted flexural apaity of the speimen. Stirrups were then proportioned aording to the shear provisions of the ACI 318 and AASHTO Standard Codes to provide this shear apaity (assuming that the onrete would be able to adequately resist the resulting diagonal ompression in the beam web). These stirrup layouts have sine been heked aording to the Setional Design Model of the AASHTO LRFD Code (Setion 5.8.3) and were found to satisfy these requirements also. Beause the stirrups ( R bars) were proportioned based on onservative estimates of the expeted shear, the shear apaity provided was often well in exess of the atual applied shear during the development length tests, espeially for tests with longer embedment lengths. Horizontal web reinforement ( H bars) was plaed in one end (End C) of eah beam pair. These H bars were #4 reinforing bars bent into a hairpin and plaed inside the vertial shear reinforement in the bottom of the web. The number of bars was determined based on reommendations by Russell and Burns (1993, ), who suggested that this type of reinforement might enhane the post-slip apaity of the member. Here again, proper design of the reinforement depended on knowledge of the ultimate shear fore during development length testing. However, the embedment length and the resulting shear for End C would neessarily depend on the experimental behavior of other beam ends (A and B) in the same beam pair. An embedment length was assumed based on the existing ACI/AASHTO Code relationship for development length, and the alulations were arried out using the value of shear fore that resulted. Unfortunately, the ritial embedment length always proved to be shorter than the value assumed, and the shear applied during the test therefore exeeded that assumed during H-bar design. Consequently, the apaity provided by the H bars relative to the test shear fore proved to be smaller than that reommended by Russell and Burns. 3.4 MATERIAL PROPERTIES This setion inludes a desription of the various materials used in the onstrution of the test speimens. These materials inlude the onrete for the preast, pretensioned I-beams, the ast-in-plae onrete for the dek slab, the prestressed reinforement, and the non-prestressed, mild steel reinforement. Material properties are disussed Preast Conrete Three distint onrete mixes were used to ast the preast, pretensioned onrete I-beams at the Texas Conrete Company plant in Vitoria, Texas. A omparison of the speified properties of the three mixes is shown in Table 3.3. The mix proportions for these three onrete mixes are tabulated in Appendix A. The onrete for all three mixes displayed a slump of approximately 8 in (200 mm) at the onset of asting. The release strength, f i, was obtained in less than twenty-four hours. Table 3.3: Speified Properties of Preast Conrete Mixes Speimen Series f i psi (MPa) f psi (MPa) L 4000 (28) (34 48) M 7000 (48) (66 79) H 9000 (62) (90 103) The L-Series onrete represented onrete normally used in the pretensioned prestressed onrete industry for bridge girders. The range of f shown in Table 3.3 reflets the desired ompressive strength of the onrete at an age of 28 days. The oarse aggregate for this mix onsisted of ¾-in (19-mm) river gravel. A 28 perent fly ash replaement was used; the resulting water-to-ementitious-materials ratio was approximately The M-Series onrete was a high strength onrete also ontaining ¾-in (19-mm) river gravel. Here again, the range of f shown in Table 3.3 reflets the desired ompressive strength of the onrete at an age of 28 days. This mix featured a 25 perent fly ash replaement and a water-to-ementitious-materials ratio of Atual onrete ompressive strengths for this mix tended toward the high side of the speified strength range. 53

76 The H-Series onrete was a high strength onrete ontaining ½-in (10-mm) rushed limestone oarse aggregate. This mix featured a fly ash replaement of 35 perent and a water-to-ementitious-materials ratio of The range of f shown in Table 3.3 for this mix reflets the desired ompressive strength of the onrete at an age of 56 days. Atual ompressive strengths for this mix tended toward the low side of this speified range. A few speimens in this series never reahed the speified onrete strength range. Conrete ompressive strength and modulus of elastiity were monitored at various ages by means of the test methods desribed in ASTM C39-93 and ASTM C469-94, respetively. Cylinders dimensions were 4 in x 8 in (102 mm x 203 mm). Neoprene pads with steel end aps were used for testing. The measured mehanial properties of the onrete test speimens are tabulated in Appendix B. Two methods of uring were used for the preast onrete test ylinders. Cylinders ured by the first method, denoted as member-ured, were used for all preast beam speimens. These ylinders were plaed adjaent to (against the forms and beneath the uring blankets) the ompanion beam speimens immediately after asting. One the forms were removed from the I-beams, the test ylinders were stored in the same environment as the beams until testing. The seond method of uring, known as math uring, was also used for test ylinders ast with most of the beam speimens. This method involved using speial ylinder molds to math the temperature of the onrete in the ompanion beam. The beam onrete temperature was evaluated by means of a thermoouple plaed in the bottom flange of one beam in eah pair. This temperature, along with that of the ylinder molds, was monitored periodially, and a heating element in eah ylinder mold was turned on or off aordingly. In this manner, the uring temperature of the ylinders losely followed that of the beam. This uring system, the details of whih are more thoroughly desribed by Myers and Carrasquillo (1998), has the potential to beome widely used by preast produers in the future. Thus, these values of ylinder strength were reorded for potential use in alibrating future behavioral relationships based on the experimental data obtained from this study. The average strengths obtained from ylinders ured by both methods at various ages are tabulated in Table B.5 of Appendix B Cast-in Plae Conrete The onrete for the ast-in-plae, omposite dek slab was delivered to the Ferguson Laboratory from ready-mix supplier Capitol Aggregates of Austin, Texas. The speified 28-day strength of this onrete was 6000 psi (41 MPa). The mix proportions for this onrete are also tabulated in Appendix A. The water-to-ement ratio for this mix was approximately The slump of the onrete during asting operations was typially in the range of 2 4 in ( mm). The ylinder ompressive strength of the onrete was assessed at ages of 7, 14, and 28 days. In addition, strengths were reorded and the modulus of elastiity, E, was evaluated when shores were removed after asting as well as at the time of development length testing. Conrete ompressive strength was evaluated aording to ASTM C39-93 proedures, exept that neoprene pads in ombination with steel aps were used at the ylinder ends. Modulus of elastiity was determined aording to ASTM C Standard 6 in x 12 in (152 mm x 305 mm) ylinders were used for the ast-in-plae onrete. The measured mehanial properties of the onrete at various ages are tabulated in Appendix B Prestressing Steel The prestressing steel used in this study was 0.6 in (15.2 mm) diameter, ASTM A416, Grade 270, low relaxation, seven-wire prestressing strand. The strand was manufatured at the Houston plant of Shinko Wire Ameria (now Amerian Spring Wire) and shipped to the Texas Conrete Company in Vitoria. The ross-setional area of the strand was in 2 (140 mm 2 ) Stress-Strain Relationship Tension tests performed on samples of the strand revealed a modulus of elastiity, E p, of 28,000 ksi (193 GPa). Although the guaranteed ultimate stress, f pu, was 270 ksi (1860 MPa), the strand exhibited strengths in exess of 280 ksi (1930 MPa) prior to frature in tension tests. Beause large strains were expeted in the strands prior to flexural failure, a stress-strain relationship based on a Menegotto and Pinto power formula (Devalapura and Tadros 1992) was developed from these results. This stress-strain relationship, whih is ompared with the relationship given by the PCI Design Handbook (1999, 11-22) in Figure 3.9, was used in the analysis of development length test results. The PCI relationship was inadequate beause it did not reflet stresses higher than 270 ksi. 54

77 f ps (ksi) PCI ps = ε ps A + A = 334 ksi, B = ksi, C = 106.9, D = ksi = MPa B f 1 D [ ( ) ] D 1 + Cε ps Figure 3.9: Stress-Strain Curve of Prestressing Strand (Compared with Relationship from PCI Design Handbook) ε Strand Surfae Condition In an effort to bound the typial strand surfae onditions that might be found in pratie, half of the speimens were prestressed with strand featuring a bright surfae ondition, while the other half were prestressed with rusted strand. For this study, bright strand was defined as strand in the as-reeived ondition. This strand was stored indoors between uses. Typial bright strands are shown in Figure The strand had a smooth surfae texture that was free from rust aside from an oasional light spotting resulting from atmospheri exposure during fabriation of the beam reinforement ages. This exposure was generally limited to three days prior to asting. Beause a small amount of weathering may have ourred during this period, this strand surfae ondition may be more akin to strand identified as slightly weathered in some laboratory-researh projets. No attempt was made to lean the strand. Figure 3.10: "Bright" Strand Surfae Condition Rusted strand had been exposed to weather in the preasting yard for several months resulting in a signifiant oating of rust. Typial rusted strands are shown in Figure This orrosion had not advaned to the point of signifiantly affeting the ross-setional area of the strand, nor were orrosion produts easily removed from the surfae of the strand. No attempt was made to lean the rusted strand. 55

78 Figure 3.11: "Rusted" Strand Surfae Condition Mild Reinforing Steel The mild steel used to reinfore the beam and slab onsisted of ASTM A615 Grade 60 reinforing bars. The modulus of elastiity of this reinforement was assumed to be 29,000 ksi (200 GPa) for analysis purposes. All mild steel reinforement that ontributed to the flexural strength of the member onsisted of #4 and #5 bars. Tension tests on samples of these bars revealed a yield stress, f y, of 61 ksi (420 MPa). This value was used in the analysis of development length test results. Reinforement details are given in Figures 3.5 through 3.8. Atual reinforement is depited in Figures 3.12 through FABRICATION OF PRECAST I-BEAMS Strand for the preast beams was generally positioned and tensioned one day prior to asting. The speified jaking stress, f pj, was verified by heking both the hydrauli pressure in the jaking system and the elongation of the strands. One the strands were adequately tensioned, jaketing of any partially debonded strands ommened. Flexible polyethylene tubing was plaed around the length of strand to be debonded. A seond layer of tubing was plaed to over the slit in the first layer. The entire length of tubing was then taped to lose any gaps and to seure the tubing. After strand jaketing was ompleted, the mild steel reinforing age was fabriated. The beam reinforement is shown in Figure 3.12 and Figure

79 Figure 3.12: Reinforement for Pair of I-Beams H-bar Figure 3.13: Anhorage Zone Reinforement for Speimen L4B-C On the day that the beams were ast, operations began with leaning the prestressing bed. Form release agent was then applied to the soffit form in the manner shown in Figure The release agent was arefully squirted in a thin stream on the form so that the reinforement was not ontated. The flexible brush shown in Figure 3.14 was then used to distribute the release agent over the form area so that the bond quality of the strands was not ompromised due to ontamination. 57

80 The side forms were then plaed and seured as shown in Figure After bathing, the onrete was plaed and onsolidated by means of internal vibration as shown in Figure Test ylinders were ast from the onrete bath simultaneous with the beam asting. As disussed in Chapter 4, the blok ontaining strands for pull-out testing was ast immediately after the I-beams. One the exposed top surfae of eah I-beam was given a wirebrush finish, uring blankets were plaed as shown in Figure Finally, the entire bed was overed with tarpaulins. For most of the speimens, no steam uring was applied. However, for the few speimens ast when air temperatures were expeted to drop below approximately 50 degrees F (10 degrees C), a limited amount of steam uring was utilized. Enough steam was used to bring ambient uring temperatures up to a level generally experiened during warmer weather. Figure 3.14: Distributing Form Release Agent over Soffit Form Surfae Figure 3.15: Plaement of Side Forms 58

81 Figure 3.16: Casting and Vibrating Preast Beam Conrete Figure 3.17: Covering Preast Beams with Curing Blankets On the morning after asting, the side forms were removed. Instrumentation of the beams for transfer length testing then ommened as desribed in Chapter 5. Cylinders were tested to monitor the strength of the beam speimens prior to release. One the speified release strength was reahed, the prestress fore was transferred to the onrete by flame-utting the tensioned strands as shown in Figure After the ompletion of initial transfer length testing, the beams were transported by lift truks into storage until long-term transfer length testing was performed. 59

82 Figure 3.18: Transfer of Prestress by Flame-Cutting 3.6 FABRICATION OF COMPOSITE DECK SLAB Eah beam pair was transported by truk to the Ferguson Laboratory. One the two beams were moved into the laboratory, preparation for dek slab asting began. Reusable plywood forms were used for slab fabriation. One dek slab was ast at a time. Figure 3.19 shows the form system during assembly. One the forms were installed, leveled and sealed, form release agent was sprayed on the form surfaes. Slab reinforing bars were then plaed and seured as an be seen in Figure Figure 3.19: Forms for Cast-in-Plae Dek Slab 60

83 Figure 3.20: Slab Reinforement Prior to Casting Both the slab forms and the preast I-beam were shored during asting of the dek onrete. The ready-mix onrete was plaed within the forms by means of a rane-suspended buket. The dek slab and test ylinders were ast onurrently. Consolidation of the dek onrete was ahieved with the aid of internal vibrators. One the onrete was sreeded with a straightedge, the surfae was bull-floated as shown in Figure The surfae was then hand-floated, and a trowel-finish was applied. The onrete ured under polyethylene sheeting for one week. Figure 3.21: Bull-Floating Surfae of Slab after Casting After a few days, shores and forms were removed. After this operation the weight of the slab, whih had been transferred diretly to the floor via shoring, was transferred to the beam supports through the flexural resistane of the omposite beam. The age, onrete strength, modulus of elastiity of both the beam and slab onrete upon removal of shores and forms is reported in Table B.2 of Appendix B. One the forms and shores were removed, dek slab fabriation steps were repeated for the seond beam of the pair. 61

84 62

85 CHAPTER 4: STRAND PULL-OUT TESTING 4.1 INTRODUCTION A program of strand pull-out testing was performed to assess the bond quality of the prestressing strand used in this study. This hapter provides historial bakground on the use of this type of test, a desription of the test proedure and the results of the test program. 4.2 BACKGROUND For many years, researhers paid sant attention to the idea that strand bond quality might vary signifiantly depending on the manufaturer or, more speifially, the strand manufaturing proess. Test results obtained in 1986 at North Carolina State University (NCSU) fored pratitioners to seriously onsider this possibility. Transfer lengths of 0.5 in (12.7 mm), unoated strand measured in the NCSU study were approximately two to three times the ACI and AASHTO design value of 50d b (Cousins, Johnston and Zia 1990). The results of this study eventually led to the 1988 FHWA restritions and modifiations disussed in Setion 1.1. The modifiations inluded the inrease of alulated development length by 60% (FHWA 1988). While evaluating the NCSU results on behalf of the Preast/Prestressed Conrete Institute (PCI), Logan (1997) notied that the measured strand draw-in values for the NCSU speimens were signifiantly larger than draw-in values measured for hollow-ore slabs at his preast onrete plant. Sine the strands used in the hollow-ore slabs were produed by a different manufaturer than those in the NCSU study, Logan reommended that a test program be onduted to ompare the bond quality of strand from various manufaturers CTC Pull-out Tests Beause, there was no aepted standard test method for bond quality the PCI Prestressing Steel Committee deided in 1992 to use a simple pull-out test proedure developed by Moustafa in 1974 for testing lifting loops at the Conrete Tehnology Corporation (CTC) in Taoma, Washington. The test method onsisted of measuring the maximum pull-out fore resisted by an untensioned, 0.5 in strand embedded 18 in (457 mm) within a onrete test blok (Moustafa 1974). The 1992 test program inluded strand from seven different manufaturers. These tests were again performed at CTC under the supervision of Moustafa. Strand from three of the manufaturers exeeded the average maximum apaity of 38.2 kips (170 kn) established in the 1974 tests. The average apaity of these strands ranged from 41.2 to 42.8 kips (183 kn to 190 kn). However, strand from the remaining four manufaturers exhibited average apaities signifiantly less than this benhmark value, ranging from 19.6 to 23.5 kips (87 to 104 kn). Based on their pull-out apaities, the various strands ould be lassified in two distint behavioral groups. Logan (1997) notes that the pull-out apaity for strand used at his plant exeeded the 1974 benhmark. He also reports that the 1992 results suggest a reason for the poor performane of the NCSU strand, but abstains from stating whether or not the manufaturer of this strand was among the seven inluded in the test program University of Oklahoma Test Program Some members of the PCI Prestressing Steel Committee objeted to the use of the simple pull-out test beause it may not aurately represent the bond performane of pretensioned strand. This objetion led to a researh study undertaken at the University of Oklahoma to evaluate the effetiveness of various test methods for strand bond quality. As-reeived strand from three manufaturers was inluded in the test program (Rose and Russell 1997). Strand from one of the manufaturers was also tested with three other surfae onditions: leaned (with muriati aid), silane-treated (emulating a slightly lubriated surfae) and weathered. Transfer lengths in pretensioned beams ontaining the various strand types were measured with a detahable, mehanial (DEMEC) strain gauge. These transfer lengths were ompared with results obtained from simple (Moustafa) pull-out tests, pull-out tests of pretensioned strand, and measurements of the strand draw-in at release in the beam speimens. The Oklahoma researhers found the pull-out tests of pretensioned strand diffiult to perform. The results of these tests were inonsistent with the other methods. Thus, they reommended that these tests not be used in evaluating strand bond quality. On the other hand, the simple pull-out tests on untensioned strand yielded results that 63

86 orrelated well with the measured transfer lengths (exluding the silane-treated speimens). In spite of this orrelation, the pull-out test results were overly sensitive to hanges in transfer length; i.e. small differenes in measured transfer lengths between speimens resulted in relatively large differenes in maximum pull-out apaity in the ompanion tests. As a result, the relationship established between pull-out apaity and transfer length is impratial. For pull-out apaities as low as zero, the relationship predits transfer lengths shorter than given by ACI and AASHTO ode expressions. Thus, the data was judged to be inonlusive regarding the validity and usefulness of the simple pull-out test. The researhers reommended the use of strand draw-in measurements as the best means of assessing bond quality. Draw-in measurements are disussed in detail in Chapter 6 of this report. The loading rate used in the Oklahoma simple pull-out tests differed signifiantly from that of the Moustafa proedure. The Oklahoma researhers arefully measured strand displaements under load, and as a result, eah of their tests took approximately twenty minutes to omplete. The earlier CTC tests using the Moustafa proedure were ompleted in less than two minutes eah. Faster loading rates typially result in higher pull-out apaities. Rose and Russell hypothesize that the different loading rate aused the Oklahoma pull-out speimens to exhibit a larger apparent sensitivity to bond quality than the Moustafa test speimens. They reommend that future testing utilize the loading rate of the Moustafa Test Stresson Test Program Unsatisfied with the results of the Oklahoma study, Logan initiated a test program at Stresson Corporation in Colorado to orrelate the results of Moustafa pull-out tests with the results of development length tests of both simply-supported and antilever beam speimens (Logan 1997). The study inluded as-reeived strand supplied by five onrete produers. A sixth set onsisted of weathered strand from one of the five produers. The weathered strand was desribed has having a light oating of rust. For eah of the six groups of strands, results of Moustafa pull-out tests on the strand were ompared with measured draw-in lengths and development length test results for ten beam speimens. Four of the strand groups had average pull-out apaities above 36 kips (160 kn). Maximum pull-out resistane of these strands typially ourred immediately prior to abrupt failure at a loaded-end displaement ranging from 0.5 to 2 in (13 to 50 mm). Logan lassifies these groups as having high bond quality. The remaining two strand groups had average pull-out apaities of approximately 11 kips (49 kn). These strands pulled out gradually, and the peak resistane ourred after 6 to 8 in (150 to 200 mm) of loaded-end displaement. Little paste bond appeared between the strand and the onrete for these two groups. This indiates a lak of adhesion between the steel and onrete, whih may result from residual lubriant on the surfae of the strands. Logan lassifies these strands as having poor bond quality. Based on the results of the development length tests, Logan onludes that there is a signifiant differene in bond quality among different manufaturers. The strands lassified as having high bond quality based on their Moustafa pull-out apaities (>36 kips) all exhibited development lengths less than indiated by the ACI development length equation. The poor bond quality strands all experiened a substantial inrease in draw-in during the first 21 days (measurements were not made after 21 days) and exhibited development lengths greater than indiated by the ACI equation. Thus, Logan ontends that an average Moustafa test apaity of at least 36 kips (160 kn) with a standard deviation of ten perent or less for a six sample group should be required for 0.5-in pretensioning strand. This standard might be lowered based on future test results from strand with pull-out apaities between 12 and 36 kips. Logan reommends that the Moustafa test also be performed with a range of onrete mixes and with 0.6 in (15.2 mm) strand so as to potentially broaden its appliability. In order to assess the bond quality of the strand used in this study relative to strand used in previous researh, ompanion pull-out tests were performed for eah set of beam speimens ast. As reommended by Logan, the test program onsists of pull-out tests of 0.6 in strand embedded in onrete of various strengths. 4.3 SPECIMEN PREPARATION A single pull-out test blok ontaining six strand speimens was ast as a ompanion to eah pair of beam speimens. Pull-out test blok details are shown in Figure 4.1. The representative strand speimens were ut from the atual strand used in the ompanion beam speimens. These six strand speimens and the supporting light reinforement age were assembled at approximately the same time as the beam reinforement. The reinforement age should have had minimal effet on results beause the reinforement was loated at the extreme ends of the embedded length of strand, and no load-indued raking was observed in the test speimens. The strands were positioned to have an embedment length of 18 in (460 mm). An additional 2 in (50 mm) length of eah strand was 64

87 jaketed immediately inside the finished surfae of the onrete. Strands had a side over of 6 in (150 mm) and a enter-to-enter spaing of 12 in (300 mm). The end of eah strand was supported 4 in (100 mm) above the bottom of the blok. Eah blok was ast immediately after the plaement of the same onrete in the beam pair. The onrete was onsolidated with the same internal vibration tehnique used for the ompanion beams. Figure 4.2 and Figure 4.3 show the pull-out blok being ast, and Figure 4.4 shows the formed and finished blok. The pull-out blok forms were stripped on the same day as those for the ompanion beams. The onrete omposition of the test blok differed from that proposed by Logan. For a standard bond quality aeptane test, Logan proposes the use of a onrete mix that ontains no high-range, water-reduing admixtures. In addition, he limits the onrete strength at the time of testing to between 3500 and 5900 psi (24.7 and 40.7 MPa). In this program, the atual beam speimen onrete was used for the pull-out blok. These mixes ontained a highrange, water-reduing admixture and ahieved strengths at the time of pull-out testing that ranged from 4400 to psi (30.3 to 80.7 MPa). Conrete mix design quantities are detailed in Appendix A. 3 in # 3 Ties (typ.) TOP 0.6-in Strand 3 in 3 in 2-in Plasti Sleeve 24 in 18 in 4 in 6 in 12 in 12 in 6 in FRONT 6 in 12 in 6 in SIDE Figure 4.1: Pull-Out Test Blok Details (1 in = 25.4 mm) 65

88 Figure 4.2: Pull-out Test Blok at Onset of Casting Figure 4.3: Casting Pull-out Test Blok 66

89 Figure 4.4: Finished Pull-Out Test Blok 4.4 TEST PROCEDURE Pull-out testing was generally performed at the preast plant two to three days after asting (one to two days after release of prestress in the ompanion beam speimens). The pull-out test setup is shown in Figure 4.5. First, the bridging devie was slipped over the strand to be tested. This was followed by a 100-kip (44 kn), shear-type load ell with a enter hole. Next a 50 ton, single-ating, hydrauli ylinder was mounted on the load ell suh that the strand extended through the ylinder s enter hole. A plate and self-seating huk were then used to anhor the strand against the piston of the hydrauli ylinder. By means of a manually-ontrolled, variable-speed, air-powered pump, load was applied at an approximate rate of 20 kips (90 kn) per minute until the maximum load was reahed. The approximate displaement of the strand relative to the surfae of the blok at maximum load was reorded. The testing proedure losely mathed that proposed by Logan (1997, 87 90) with a few modifiations. First, the bridging devie did not exatly math that proposed by Logan. Nonetheless, the distane from the strand to eah load-bearing leg of the devie was approximately the same as with Logan s devie. Logan speifies the use of a pull-jak with a travel of at least 12 in (305 mm). In these tests, a enter-hole jak was used to push against a huk whih, in turn, pulled on the strand. The stroke of this jak was approximately 3 in (75 mm). However, this shorter length of travel proved adequate. The maximum pull-out apaity was always reahed at a loaded-end displaement less than 3 in. 67

90 Figure 4.5: Pull-out Test in Progress 4.5 RESULTS AND DISCUSSION Results of the 0.6 in (15.2 mm) strand pull-out tests are reported in the six tables that follow (Table 4.1 through Table 4.6). A few of the strand speimens were embedded for lengths longer than 18 in (460 mm) in the earliest bloks tested (Series L0B, L4B, L0R, M0B, M4B and H0B). These longer embedment lengths provided little signifiant information, and the results of these tests are not reported here. Thus, there are fewer than six results for the orresponding test bloks. There are four failure types listed. Frature indiates a loss of resistane due to frature of one or more of the wires omposing the strand. Abrupt Slip represents an irreoverable loss of resistane resulting from an abrupt slip. This abrupt portion of the total slip generally measured approximately 3 / 8 in (8 to 11 mm) and followed some gradual slip. Gradual indiates that the resistane first inreased and then began to diminish as the slip gradually inreased. Test Halted represents a test that was stopped deliberately after reahing a load higher than the nominal breaking strength of the strand (58.6 kips [261 kn]). 68

91 Table 4.1: Pull-Out Test Results Bright Strand, Low Strength Conrete Test ID f at Maximum Pull-out Length Failure Test Age Load at Max. Load Type psi (MPa) kips (kn) in (mm) L4B-A 46.1 (205) 1.15 (29) Abrupt Slip L4B-B 4970 (34.3) 51.0 (227) 1.15 (29) Abrupt Slip L4B-C 54.1 (241) 1.25 (32) Abrupt Slip L6B-A 58.4 (260) 1.50 (38) Frature L6B-B 58.4 (260) 0.75 (19) Frature L6B-C 57.9 (258) 2.00 (51) Frature 5500 (37.9) L6B-D 59.4 (264) 2.00 (51) Frature L6B-E 58.6 (261) 2.25 (57) Frature L6B-F 58.1 (258) 2.00 (51) Frature Table 4.2: Pull-Out Test Results Rusted Strand, Low Strength Conrete Test ID f at Maximum Pull-out Length Failure Test Age Load at Max. Load Type psi (MPa) kips (kn) in (mm) L0R-A 48.1 (214) 1.00 (25) Gradual L0R-B 5100 (35.2) 47.3 (210) 0.40 (10) Gradual L0R-C 50.2 (223) 0.20 (5) Gradual L4R-A 42.5 (189) 0.25 (6) Gradual L4R-B 47.3 (210) 2.00 (51) Gradual L4R-C 39.9 (258) 0.25 (6) Gradual 4400 (30.3) L4R-D 43.0 (177) 0.25 (6) Gradual L4R-E 45.2 (201) 1.00 (25) Gradual L4R-F 44.7 (199) 0.25 (6) Gradual L6R-A 47.8 (213) 0.25 (6) Gradual L6R-B 47.3 (210) 0.15 (4) Gradual L6R-C 48.0 (214) 0.15 (4) Gradual 5450 (37.6) L6R-D 46.8 (208) 0.15 (4) Gradual L6R-E 46.3 (206) 0.15 (4) Gradual L6R-F 48.3 (215) 0.15 (4) Gradual 69

92 Table 4.3: Pull-Out Test Results Bright Strand, Medium Strength Conrete Test ID f at Maximum Pull-out Length Failure Test Age Load at Max. Load Type psi (MPa) kips (kn) in (mm) M0B-A 58.9 (262) 0.50 (13) Test Halted 7800 (53.8) M0B-B 59.2 (263) 0.25 (6) Test Halted M4B-A 61.8 (275) 0.50 (13) Frature M4B-B 9440 (65.1) 62.1 (276) 0.55 (14) Frature M4B-C 62.1 (276) 0.45 (11) Frature M9B-A 58.0 (258) 0.75 (19) Frature M9B-B 59.3 (264) 0.70 (18) Frature M9B-C 58.5 (260) 0.80 (20) Frature 8170 (56.3) M9B-D 59.5 (265) 1.05 (27) Frature M9B-E 59.0 (262) 1.50 (38) Abrupt Slip M9B-F 58.0 (258) 1.10 (28) Frature Table 4.4: Pull-Out Test Results Rusted Strand, Medium Strength Conrete Test ID f at Maximum Pull-out Length Failure Test Age Load at Max. Load Type psi (MPa) kips (kn) in (mm) M0R-A 55.5 (247) 0.25 (6) Gradual M0R-B 53.8 (239) 0.15 (4) Gradual M0R-C 42.2 (188) 0.40 (10) Gradual 8290 (57.2) M0R-D 45.6 (203) 0.80 (20) Gradual M0R-E 41.7 (185) 0.65 (17) Gradual M0R-F 52.8 (235) 0.90 (23) Gradual M4R-A 61.3 (273) 0.50 (13) Frature M4R-B 60.6 (270) 1.00 (25) Test Halted M4R-C 59.1 (263) 1.15 (29) Test Halted 8970 (61.8) M4R-D 57.5 (256) 1.50 (38) Abrupt Slip M4R-E 61.1 (272) 0.75 (19) Test Halted M4R-F 60.6 (270) 0.50 (13) Test Halted M9R-A 53.5 (238) 1.15 (29) Gradual M9R-B 46.1 (205) 0.50 (13) Gradual M9R-C 55.2 (246) 1.80 (46) Gradual 9420 (65.0) M9R-D 33.0 (147) 1.80 (46) Gradual M9R-E 48.8 (217) 1.30 (33) Gradual M9R-F 55.0 (245) 1.10 (28) Gradual 70

93 Table 4.5: Pull-Out Test Results Bright Strand, High Strength Conrete Test ID f at Maximum Pull-out Length Failure Test Age Load at Max. Load Type psi (MPa) kips (kn) in (mm) H0B-A 54.6 (243) Abrupt Slip H0B-B (76.3) 54.1 (241) 0.75 (19) Abrupt Slip H0B-C 57.7 (257) 0.75 (19) Abrupt Slip H4B-A 43.0 (191) 2.15 (55) Gradual H4B-B 38.2 (170) 1.75 (44) Gradual H4B-C 30.0 (133) 1.50 (38) Gradual (69.3) H4B-D 33.6 (149) 1.75 (44) Gradual H4B-E 39.9 (177) 2.00 (51) Gradual H4B-F 49.3 (219) 1.90 (48) Gradual H9B-A 51.3 (228) 1.30 (33) Gradual H9B-B 59.0 (262) 1.70 (43) Abrupt Slip H9B-C 57.5 (256) 1.10 (28) Gradual (71.8) H9B-D 55.3 (246) 0.60 (15) Gradual H9B-E 57.3 (255) 0.90 (23) Gradual H9B-F 56.8 (253) 1.15 (29) Gradual 71

94 Table 4.6: Pull-Out Test Results Rusted Strand, High Strength Conrete Test ID f at Maximum Pull-out Length Failure Test Age Load at Max. Load Type psi (MPa) kips (kn) in (mm) H0R-A 47.6 (212) 0.15 (4) Gradual H0R-B 48.8 (217) 0.10 (3) Gradual H0R-C 54.8 (244) 0.20 (5) Gradual (72.3) H0R-D 55.7 (248) 0.20 (5) Gradual H0R-E 42.7 (190) 0.10 (3) Gradual H0R-F 50.1 (223) 0.15 (4) Gradual H4R-A 47.3 (210) 1.75 (44) Gradual H4R-B 50.0 (222) 1.25 (32) Gradual H4R-C 55.7 (248) 1.65 (42) Gradual (80.7) H4R-D 57.9 (258) 2.00 (51) Gradual H4R-E 59.9 (266) 0.75 (19) Frature H4R-F 58.6 (261) 0.75 (19) Frature H9R-A 52.0 (231) 1.45 (37) Gradual H9R-B 46.4 (206) 2.25 (57) Gradual H9R-C 54.3 (242) 0.15 (4) Gradual (73.7) H9R-D 44.9 (200) 0.10 (3) Gradual H9R-E 45.6 (203) 0.85 (22) Gradual H9R-F 50.6 (225) 0.20 (5) Gradual Nominal Strand Strength Logan Benhmark L4B L6B All L0R L4R L6R All Bright Strands Rusted Strands Speimen Group 58.6 kip 43.2 kip Low Mean High S.D. Figure 4.6: Moustafa Pull-out Test Results for Speimens with Conrete Strengths within the Range Reommended by Logan (1997) (1 kip = 4.45 kn) 72

95 Figure 4.6 summarizes the results of the tests performed on strands embedded within bloks with onrete ompressive strengths within the range speified by Logan for strand bond quality assessment (3500 to 5900 psi [24.7 to 40.7 MPa]). The dashed horizontal lines on the figure represent the nominal strand strength and the pull-out load orresponding to Logan s reommendation for high bond quality. As disussed in Setion 4.2.3, Logan reommends a required average pull-out apaity of 36 kips (160 kn) for 0.5 in (12.5 mm) strand. This orresponds to an average bond stress of 955 psi (6.58 MPa) over the 18 in (460 mm) embedment of the strand. To ahieve an equivalent average bond stress on a 0.6 in (15.2 mm) strand with an 18 in embedment length, a pull-out fore of 43.2 kips (192 kn) is required. 1 Thus, 43.2 kips is indiated as the Logan Benhmark in Figure 4.6. The figure illustrates that the average pull-out apaity for eah test group exeeds the benhmark value, and that all oeffiients of variation are less than 10 perent. Thus, both the bright and rusted strands used in this study appear to be apable of high bond quality. Logan s researh indiates that the transfer and development length of these strands should be less than or equal to the values given by the relevant ACI expressions. On average, the pullout apaities for the rusted strand are slightly lower than those of the bright strand. This differene may indiate slightly poorer bond quality for the rusted strands or it may reflet that the onrete strength for the L4R test blok was approximately 12 perent less than the lowest onrete strength for the bright strand speimens (L4B). Figure 4.7 illustrates the pull-out apaities of all bright strand speimens with respet to the onrete strength at the time of testing. Figure 4.8 displays the rusted strand results in a like manner. In general, the average apaities of the bright strand groups approahed or equaled the breaking strength of the strand for onrete strengths above approximately 5500 psi (40 MPa). The strands from group H4B are an exeption (f = psi). The results from this group are onspiuously lower than those of the other bright strand groups. This may be due to the rapid loss of workability experiened with the H-Series onrete mix. This mix usually started to stiffen onsiderably about fifteen to thirty minutes after mixing. Pull-out test bloks were ast from the onrete remaining upon ompletion of the beam speimens. In the partiular ase of the H4B speimens, the workers had partiular diffiulty plaing and onsolidating the onrete for the test blok. Less than ideal onsolidation of the onrete around the strands likely resulted in redued pull-out apaity of these speimens. Transfer and development length tests onduted on the beam speimens (H4B) onstruted of this partiular bath of onrete indiated no poorer bond quality than other tests involving bright strand speimens. A omparison of Figure 4.8 with Figure 4.7 shows that the pull-out apaities of the rusted strand speimens were generally less than those of the bright strand speimens over the entire onrete strength range. This is noteworthy beause it seems to ontradit the widely aepted opinion that surfae weathering inreases bond apaity (see Setion ). The average apaity of eah rusted speimen group exeeds the Logan benhmark, but two of the groups (M0R and M9R) feature oeffiients of variation that exeed the 10 perent limit reommended. The M0R strands (f = 8290 psi) and M9R strands (f = 9420 psi) have oeffiients of variation of 13 and 17 perent, respetively. The rusted strand data seem to indiate a slight inrease in pull-out apaity with inreasing onrete strength. However, any inrease is relatively small onsidering the extensive range of onrete strengths tested. 1 Beause the embedment length remains 18 in, the bonded surfae area of the strand is proportional to the diameter 0. 6 in of the strand. Thus, the orresponding pull-out fore for the 0.6-in strand is 36 kip = kip in 73

96 Nominal Strand Strength Logan Benhmark "L" Series 10 "M" Series 0 "H" Series Bright Strand Speimens Conrete Compressive Strength (psi) Figure 4.7: Pull-Out Capaities of All Bright Strand Speimens (1 kip = 4.45 kn, 1000 psi = 6.89 MPa) Nominal Strand Strength Logan Benhmark 20 "L" Series 10 "M" Series 0 "H" Series Rusted Strand Speimens Conrete Compressive Strength (psi) Figure 4.8: Pull-Out Capaities of All Rusted Strand Speimens (1 kip = 4.45 kn, 1000 psi = 6.89 MPa) 4.6 SUMMARY AND CONCLUSIONS Reent studies suggest that strand bond behavior may vary signifiantly depending upon the strand manufaturer. The Moustafa Pull-Out Test has been proposed as a means of identifying strands that are likely to exhibit substandard bond quality. Eighteen sets of Moustafa Pull-Out Tests were performed in this study. Both the bright and rusted strand types satisfied the onditions proposed for lassifiation as strands with high bond quality. Therefore, if Logan s theory holds true, the transfer and development lengths of these strands should not exeed design values suggested by the ACI and AASHTO ode expressions. 74

97 Average pull-out apaities of rusted strand speimens tended to be slightly lower than those of bright strand speimens. This trend appears to disount the ability of surfae weathering to inrease the bond apaity of sevenwire strands. Pull-out apaity may inrease slightly with inreasing onrete ompressive strength, but this trend is indefinite. Any lear trend with respet to onrete strength is obsured by the relative dispersion of test results for onrete strengths (at time of testing) greater than 8000 psi (55 MPa). Suessful implementation of HSC requires vigilant attention to onrete quality. The poor pull-out performane of one test series utilizing HSC reflets the rapid degradation of workability that may be assoiated with onrete mixes that are designed to ahieve 1-day ompressive strengths in exess of 7000 psi (48 MPa). Casting operations involving HSC should be arefully planned and monitored to insure that all onrete is plaed and onsolidated prior to initial set. 75

98 76

99 CHAPTER 5: TRANSFER LENGTH TEST PROGRAM 5.1 INTRODUCTION Transfer length testing was performed on all thirty-six beams in the researh study. One-third of the beam speimens (x0x Series) had only one transfer zone at eah end. Due to the staggered debonding of strands, a seond one-third of the beam speimens (x4x Series) featured three transfer zones at eah end, and the remaining one-third of the speimens ontained four transfer zones at eah end. This resulted in a total of 192 transfer zones for testing. Transfer lengths were determined for 184 of these zones. To the author s knowledge, this represents a larger number of results than the umulative number of transfer length results for 0.6 in (15.2 mm) strand reported previously. For almost all the speimens, testing was performed to determine transfer lengths immediately after transfer of prestress fore as well as at a later date. The later testing (hereafter referred to as long-term testing) ourred at onrete ages ranging from 19 to 148 days. This hapter desribes the proedure used to determine the transfer length for eah transfer zone tested, the results obtained from the test program, and the inferenes drawn from these results. The results are ompared to transfer length relationships developed by other researhers. 5.2 TEST PROCEDURE Transfer lengths were determined by applying the 95% Average Maximum Strain (AMS) Method to measured onrete ompressive strains resulting from the transfer of prestress fore to the onrete. Although other methods have been used in other researh studies, the 95% AMS Method is well established and has been reommended in reent FHWA studies for determining transfer lengths and for omparing results from various studies (Bukner 1994; Lane 1998). Russell and Burns (1993) explain and justify the appliation of this method. Conrete surfae ompressive strains were measured by means of a detahable mehanial (DEMEC) strain gauge with a 7.87 in (200 mm) gauge length. Figure 5.1: Pair of Beam Speimens after Side Form Removal 77

100 5.2.1 Speimen Preparation Speimen preparation ommened with the stripping of side forms early on the morning after eah pair of beam speimens was ast. Figure 5.1 shows a pair of beam speimens on the prestressing bed after removal of side forms. At eah end of eah beam, a line of DEMEC loating diss were epoxied to the bottom flange on eah side fae. Eah stainless steel DEMEC loating dis had a diameter of 0.25 in (6.3 mm) with a entral 0.04 in (1 mm) drilled hole for positioning one of the onial measuring points on the DEMEC gauge. A fast-setting, two-part epoxy was used to bond the points to the onrete surfae. A typial line of DEMEC diss was plaed at the same level as the entroid of the strands loated within 4 in (102 mm) of the beam soffit. The first dis was plaed 0.98 in (25 mm) from the end of the beam; subsequent diss were plaed at intervals of 1.97 in (50 mm). Plaement of the first four loating diss is illustrated in Figure 5.2. Eah line of diss extended well beyond the expeted transfer length(s) for the beam. Figure 5.2: First Four DEMEC Loating Diss in Line (End of Beam at Left) One all eight lines of loating diss had been plaed, preliminary readings were performed with the DEMEC gauge and reorded. Overlapping readings were taken for every 7.87 in (200 mm) interval between loating diss. Eah reading was taken twie and reorded. Readings were retaken if the reorded pair differed by more than in ( mm). Figure 5.3 shows the performane of a DEMEC gauge reading. Figure 5.3: Performing a Measurement with DEMEC Gauge 78

101 5.2.2 Appliation of Prestress Fore One all preliminary DEMEC readings were reorded, the prestress fore was applied to the beams by detensioning the prestressed strands. All strands were detensioned by means of a flame-utting proess. Gradual release methods have been used in a few previous UT researh studies, and outside researhers have ited this as a potential ause for the shorter than expeted transfer lengths that resulted. For this study, researhers wanted to ensure that a more sudden release method was used. Two distint flame-utting proedures were used, resulting in three possible release onditions for speimen ends. For approximately two-thirds of the speimen pairs, prestressing strands were detensioned by what will hereafter be termed the simultaneous release method. This method entailed the flame-utting of eah strand at loations on both ends of both beams before utting any other strands. This was aomplished by three welders who together attempted to ut eah strand simultaneously at three loations (one at eah end of the bed, and one between the two beams). In this manner, all the prestress fore from eah strand was introdued into all four of the beam ends prior to the utting of subsequent strands. The seond method of prestress release used in this study entailed flame-utting all the strands at one loation between the two beams. Thus, the prestress fore in eah strand was introdued suddenly into the interior ends of the beam pair. At the exterior ends of the pair, on the other hand, the prestress fore transferred to the onrete was gradually stepped up. An inremental onrete stress inrease resulted beause the derease in strand tension fore due to eah single strand ut on the interior ends of the beam was approximately evenly distributed among all the strands at the exterior ends of the beams. This pratie was used in an attempt to simulate a more gradual release of prestress at the exterior ends of speimens. The interior beam end transfer zones subjeted to this release method are referred to as live release transfer zones, while the orresponding exterior zones are referred to as dead release zones. This release method was used for the following beam speimen pairs: M0R, H0R, M9B, H9B, M9R, and H9R Conrete Surfae Strain Measurements Immediately after the transfer of prestress fore to the onrete, the DEMEC gauge readings were repeated on eah overlapping 7.87 in (200 mm) interval omposing eah line of loating diss. The reading and reording proedure was idential to that desribed above for the preliminary readings. The readings taken immediately after prestress release were later used to alulate onrete ompressive strain profiles and determine initial transfer lengths through the proess desribed in Setion 5.3. For eah pair of beam speimens, DEMEC readings were taken one again at an advaned age. This age ranged from 19 days (18 days after release) to 148 days (147 days after release). These readings were used to onstrut long-term ompressive strain profiles and determine the orresponding long-term transfer lengths. 5.3 TRANSFER LENGTH DETERMINATION This setion desribes the proess used to determine the initial and long-term transfer lengths based on the data obtained from DEMEC gauge readings Constrution of Surfae Compressive Strain Profile The first step in the proess involves the onstrution of the surfae ompressive strain profile for eah beam end. The ompressive strain for eah measured 7.87 in (200 mm) interval was alulated by multiplying the DEMEC gauge fator by the differene between 1) the reading reorded at the time under investigation and 2) the preliminary reading reorded for that interval. Beause overlapping readings were taken, eah loation on the line was inluded within the gauge length of three separate reading intervals. Thus, the strain value assigned to eah dis loation was alulated by averaging the strain values for the three 7.87 in (200 mm) intervals that inluded the loation. The proedure for assigning strain values to partiular points is illustrated in Figure

102 Calulated Strain for Interval Average Strain at Point Figure 5.4: Assignment of Surfae Compressive Strain Values One strain values were assigned to eah dis loation, orresponding values from either side of the beam were averaged to generate one surfae strain profile for eah end of eah beam speimen. Next, the resulting profiles of measured strain were orreted to aount for the effets of speimen weight. In most early researh, transfer length speimens were relatively small and/or prestressed onentrially. If prestressed onentrially, the speimens usually remained supported along their entire length and deformations due to weight were minimal. Even if prestressed eentrially, the speimens were relatively short and light. Aordingly, any strain resulting from member weight was very small ompared to the strains due to prestress alone. For this study, full-sale speimens were eentrially prestressed. One the prestress was applied, the beams ambered off the bed, and the member weight was transmitted to the supported ends of the beam through flexural resistane. The tensile omponent of strain that resulted from weight-indued urvature at eah point was large enough to alter the shape of the strain profile. Figure 5.5 shows both measured and orreted strain profiles for beam end H0B-C. The moment due to weight inreases with inreasing distane from the end of the beam toward midspan, as does the tensile strain omponent resulting from this moment. Therefore, the plateau value of the measured ompressive strain urve tends to derease with inreasing distane from the end of the beam in = 25.4 mm Strain Due to Prestressing Measured Strain Distane from End of Beam (in) Figure 5.5: Corretion of Strain Profile to Remove Strain Due to Beam Weight 80

103 If the strain profile is not orreted to reflet the strain due to prestress only, an erroneous value of the strain plateau is alulated. This, in turn, may result in an error on the order of 5 perent when determining the apparent transfer length. Therefore, the effet of member weight was disounted by adding the alulated magnitude of the tensile omponent to the measured ompressive strain value at eah loation. The resulting profile more aurately reflets the influene of the prestress fore alone. The magnitude of the tensile strain due to member weight at eah loation was alulated on the basis of engineering beam theory using the formulation in Equation 5.1. Where: Equation 5.1 ε w, DEMEC ε w,demec = magnitude of strain omponent due to member weight My = E I M = moment due to member weight y DEMEC = vertial distane from entroid of transformed setion to line of loating diss E = modulus of elastiity of onrete I tr = moment of inertia of transformed setion Creep strains were onsidered when performing this orretion for the long-term strain profiles. For the long-term profiles, both the immediate strain omponent and the reep strain omponent due to member weight were alulated, and a similar adjustment was made. Creep strains were alulated by the proedure desribed by Collins and Mithell (1991, 67 72). DEMEC tr Determination of Average Maximum Strain (AMS) One the strain profile was onstruted for one end of a beam speimen, the next step involved the identifiation of the average maximum strain (AMS) value for eah transfer zone. First, the strain values that lay in the likely plateau domain were identified by visual inspetion. The value of the average maximum strain was then alulated as the arithmeti mean of these strain values. Figure 5.6 illustrates both the initial and long-term average maximum strain values for eah of the three transfer zones of beam end H4R-A in = 25.4 mm Seond Debonded Length (72 in) First Debonded Length (36 in) Initial 111 days 100% AMS Distane from End of Beam (in) Figure 5.6: Loation of Average Maximum Strain Values for Speimen with Three Transfer Zones (Beam End H4R-A) 81

104 5.3.3 Determination of 95% AMS Value Aording to the 95% AMS Method, the apparent transfer length is bounded by the point where the ompressive strain profile intersets the horizontal line representing 95 perent of the average maximum strain for the transfer zone. This setion details the determination of the 95% AMS value for the initial and long-term strain profiles Initial Transfer Length The most straightforward ase is that of the initial transfer length for strands that are fully bonded. This ase is represented by the Initial profile in the first (leftmost) transfer zone in Figure 5.6. For this ase, the 95% AMS value was simply determined by multiplying the average maximum strain by For the transfer zones of partially debonded strands, only the ompressive strain indued by the strands in question was onsidered. Thus, the 95% AMS value for this ase represents a strain value that lies 95 perent of the way between the average maximum strain value for the previous transfer zone and the average maximum strain value for the transfer zone in question. Equation 5.2 depits this relationship in mathematial form. Equation % AMS i = AMSi ( AMSi AMSi 1) In this ase, simply multiplying the average maximum strain value by 0.95 would have resulted in an artifiially small 95% AMS value. The magnitude of suh an error would inrease with subsequent transfer zones. Russell and Burns (1996) reported that the average transfer lengths of partially debonded strands were somewhat shorter than those of fully bonded strands. This disrepany is likely due to the fat that these transfer lengths were obtained by applying the 0.95 fator to the total strain for the partially debonded strands, rather than the strain portion that resulted from the prestress fore in these strands Long-Term Transfer Length Appliation of the 95% AMS Method to long-term strain profiles must be rationally onsidered. Due to timedependent deformations of the speimen, long-term ompressive strains are typially on the order of two to three times the initial strains. Beause of this large inrease in strain, areless appliation of the 95% AMS Method to long-term strain profiles ould result in unreasonably short transfer lengths. Consider how the different types of time-dependent onrete deformation affet the strain profile. Creep strain is assumed to be proportional to the applied load. Thus, reep strains should result in an amplifiation of the strain profile. For this type of deformation, one expets the slope of the non-plateau portion of the strain profile to inrease at the same rate as the value of the average maximum strain. Therefore, using a fator of 0.95 to loate the intersetion value of strain remains rational. Strain due to shrinkage, on the other hand, is usually onsidered to be independent of applied load. Thus, shrinkage strains should result in a translation of the strain profile. For this type of deformation, the slope of the non-plateau portion of the strain profile remains onstant as the average maximum strain inreases. In this ase, applying a five perent redution to the long-term average maximum strain may result in a signifiantly larger redution along the distane axis than ourred for the initial transfer length estimation. Thus, if the atual transfer length remains the same as shrinkage strains inrease, using a fixed perentage AMS value to determine the transfer length will result in the erroneous onlusion that the transfer length is dereasing with time. Seleting an AMS redution fator that preisely reflets the relative amounts of reep and shrinkage strains would be diffiult. Suh a fator would differ from speimen to speimen and from age to age. The alulation proess would involve the unertainties inherent in reep and shrinkage estimations. The omputational effort would be entirely out of proportion to the minimal inrease in auray obtained. In order to keep the proess as simple as possible while erring on the side of onservatism, the following method was adopted in this study. Instead of applying the idential proedure to the long-term results as was used in the initial transfer length alulations, the long-term average maximum strains were redued by the same value of strain as were the initial average maximum strains. For example, if the initial AMS value for fully bonded strands was 100 mirostrain and the long-term AMS value was 500 mirostrain, then the 95% AMS values were alulated as 95 and 495 mirostrain, respetively. In effet, this method assumes that all time-dependent strains are of the shrinkagetype. Assuming that all time-dependent strains were aused by reep would result in a long-term 95% AMS value of 0.95(500) = 475 mirostrain. The most aurate value should lie somewhere between 475 and 495 mirostrain, 82

105 but it is safer to aept the latter value. Long-term 95% AMS values for partially debonded strands were determined in a like manner Determination of Apparent Transfer Length One eah 95% AMS value was established, the transfer length apparent from the measured onrete surfae strain profile was determined by measuring the distane between the start of bond to the point of intersetion between the strain profile and the 95% AMS value. The start of bond loation was assumed as the end of the member for fully bonded strands and the end of jaketing for partially debonded strands. Figure 5.7 illustrates the apparent transfer lengths determined from the strain profiles shown in Figure 5.6. Surfae strain profiles and the orresponding apparent transfer lengths for all speimens are reorded in Appendix C in 1 in = 25.4 mm in in 15.9 in 11.7 in 11.9 in Initial 111 days 95% AMS Distane from End of Beam (in) Figure 5.7: Determination of Apparent Transfer Lengths (Beam End H4R-A) In most previous researh studies, the value of transfer length apparent from the surfae strain profile has been assumed to be equivalent to the atual transfer length of the strand(s) in question. This pratie implies that one of the assumptions vital to engineering beam theory that plane setions remain plane holds true along the transfer length. If this assumption is true and the ross setion is in equilibrium, then the onrete stress indiated by the onrete surfae strain is proportional to the reinforing steel stress at the same depth. Although this assumption is a valuable tool in the analysis and design of regions, often termed B-regions, that lie some distane away from disontinuities and applied loads, it does not apply to anhorage zones either pre- or post-tensioned. The nonlinear distribution of stress and strain in suh disontinuous regions, or D-regions, is ommonly desribed as shear lag. Although onsiderable researh effort has been devoted to the behavior of post-tensioned anhorage zones (Breen et al. 1994), sant attention has been paid to the distribution of onrete stresses in pretensioned anhorage zones. This an be attributed to the fat that anhorage zone researh has been foused on the ontrol of high ompressive stresses immediately ahead of the anhorage devie and the tensile (or bursting stresses) that are normal to the tendon axis. Due to the gradual build-up of onrete stresses in pretensioned anhorage zones these ompressive and bursting stresses are less ritial than in post-tensioned anhorage zones. However, the extent of both types of anhorage zones (i.e. the region for whih plane setions do not remain plane) an be signifiantly larger than the length over whih the tendon prestress fore is fully developed. By measuring ompressive strains at a variety of depths within the same anhorage zone, Base (1958a) has shown this to be true for full-sale pretensioned members. The differene between the transfer length and the extent of the pretensioned anhorage zone is aknowledged by the CEB-FIP Model Code The extent of the pretensioned anhorage zone is termed the development length 83

106 (the property referred to as development length in Amerian odes is defined as anhorage length in Model Code 1990). Clause Development Length defines the distane from the end fae of the member to the onrete ross-setion beyond whih the distribution of the longitudinal stresses is onsidered linear as the development length. For retangular ross-setions with straight tendons the development length, l p, is alulated as: 2 [ bpt ] 1 2 lbpt 2 Equation 5.3 = h + ( 0.6l ) l > p Where: h = the total depth of the ross setion l bpt = transmission length of the tendon (equivalent to transfer length in Amerian odes). This expression learly reflets the influene of the member size on the disparity between the transfer length and the extent of the anhorage zone. For members with total depths less than 80 perent of the transfer length, the transfer length and the length of the anhorage zone are assumed to be equal. As the total depth of the member inreases relative to the transfer length, the extent of the anhorage zone beomes more dependent on the member size than on the transfer length. For members with I-shaped ross setions, little speifi guidane is given. Assuming that plane setions remain plane in the anhorage zone has not led to signifiant errors in many past studies beause of the type of speimens used. The majority of historial transfer length speimens were small. Speifially, the member dimensions were small relative to the transfer lengths under investigation. Thus, the stresses and strains due to prestressing were distributed fairly evenly at the end of the atual strand transfer length. Usually, these speimens featured fully bonded strands that were evenly distributed throughout the ross setion. Therefore, prestress fores had to distribute over distanes that were small, espeially in relation to the transfer length. Bukner (1994) implemented a finite element analysis that indiated that the effet of shear lag on apparent transfer length in these smaller speimens is relatively minor (less than 10 perent inrease from atual). The effet did inrease with inreasing speimen size relative to transfer length. His reported results are for speimens with rosssetional dimensions up to one-third the atual transfer length. Thus, aording to the CEB-FIP expression (Equation 5.3 above), the stress distribution should be quite linear at the end of the transfer length. Bukner also postulates that the 5-perent plateau redution inherent in the 95% AMS Method ompensates for muh of the error due to shear lag. This is unlikely, however, beause the 5-perent redution was originally intended to ounter the profile-rounding effets that result from the use of long, overlapping gauge lengths like those used in this study (Russell and Burns 1993; Base 1958a). In studies that featured larger and/or eentrially prestressed members, researhers usually attempted to minimize the potential error due to shear lag by measuring the surfae strains at the depth of the reinforement entroid. The effetiveness of this tehnique is dependent upon the ross-setional size and shape and the distribution of the prestressing reinforement. In order to illustrate the onept of shear lag and how it affets the relationship between surfae strains and tendon strains, typial strain ontours of a horizontal setion through the anhorage region are shown in Figure

107 f 0.5 E pt p f pt E p Atual Transfer Length Apparent Transfer Length (from Surfae Strains) Strands Figure 5.8: Strain Contours at Horizontal Setion through Bottom Flange at Depth of Strands The speimens in this study were quite suseptible to the effets of shear lag. First, the speimens were 28 in (710 mm) deep and as wide as 16 in (406 mm). Therefore, the prestress had to distribute over ross-setional distanes that were quite large relative to the expeted transfer length. Many of the speimens featured staggered debonding patterns. Thus, the prestress fore was often developed in only two to four strands within eah transfer length. Beause a single line of DEMEC diss was used to evaluate the surfae strain profile, distanes between developing strands and the DEMEC line differed substantially between different transfer zones within the same speimen. For example, some of the fully bonded strands lay less than 3 in (75 mm) from the DEMEC line, yet some of the groups of debonded strands were as far away as 7 in (180 mm) horizontally and 11 in (280 mm) vertially. Thus, it was neessary to adopt a proedure that would at least allow for the effetive omparison of the behavior of the various strand groups, and ideally result in an aurate estimation of the atual strand transfer length Determination of Atual Transfer Length A three-dimensional finite element model was developed to assess the relationship between the apparent and atual transfer lengths for the speimens in this study. This setion relates details regarding the finite element model and the proedure used to alulate atual transfer lengths based on the apparent transfer lengths obtained from surfae strain profiles Finite Element Model Assumptions The stress in the prestressing tendon after release was assumed to vary linearly from zero at the start of bond to f si, the level of prestress in the strand immediately after release, at the end of the atual transfer length. The onrete was assumed to be homogeneous and exhibit isotropi and linearly elasti stress-strain behavior. A value of 0.2 was assumed for Poisson s Ratio, and the Elasti Modulus was assumed equal to 4800, 6400 and 7200 ksi (33, 44 and 50 GPa) for the L-, M-, and H-Series speimens, respetively Desription A finite element mesh was onstruted to reflet eah unique ombination of onrete strength level and debonding pattern used in the test program. Symmetry was utilized to redue the mesh to a volume defined by one-half of the 85

108 I-beam ross setion by one-half of the beam length. The mesh onsisted of both 20-node (brik) and 15-node (wedge) ontinuum elements. The 20-node elements used redued integration. Element dimensions were typially 2 in x 2 in x 2 in (51 mm x 51 mm x 51 mm) or less. For elements that lay adjaent to the transfer length of the strand, the dimension parallel to the axis of the strand was redued to 1 in (25 mm) Proedure The proedure onsisted of first assuming a transfer length, and then applying the prestress fore linearly over the transfer length at eah strand loation. A linear stati perturbation analysis was then performed to determine the resulting stresses and strains in the onrete. The resulting surfae strains were evaluated along a line orresponding to the DEMEC loating dis line for the speimen being modeled. These strains were onverted to equivalent average strains over a 7.87 in (200 mm) gauge length and then subjeted to the same proedure as desribed in Setion 5.3 above to determine the apparent transfer length that would be indiated applying the 95% AMS Method to the surfae strain profile. Figure 5.9 shows the surfae ompressive strain profile that results from the finite element analysis of beam of the H4x Series with an assumed atual transfer length of 12 in (305 mm). The dashed line represents the surfae strain profile predited from standard beam theory assuming that plane setions remain plain throughout the length of the speimen. Note how this profile differs signifiantly from the surfae strain profile that results from the finite element model, whih inludes the effets of shear lag. The strands that lay losest to the DEMEC line were fully bonded. Thus, the finite element solution most losely mathes beam theory in the transfer zone for these strands. The disparity is larger in the transfer zones of the debonded strands Seond Debonded Length (72 in) First Debonded Length (36 in) 12 in 12 in 1 in = 25.4 mm in Finite Element Solution Beam Theory Distane from End of Beam (in) Figure 5.9: Surfae Compressive Strain Profiles Predited for an Atual Transfer Length of 12 in (305 mm) One the 95% AMS method was applied to the surfae strains resulting from the finite element analysis, the proess was repeated several times on the same speimen model. Eah repetition was haraterized by a different assumed value for the atual transfer length. One the proess had been repeated for several transfer lengths, a relationship between atual transfer length (over whih the tendons develop the effetive prestress) and apparent transfer length (whih is measured along the line of DEMEC loating diss on the surfae of the member) ould be plotted for eah transfer zone. The relationships obtained for the three anhorage zones of the H4x Series speimens are plotted in Figure Here again it is evident that the behavior of the fully bonded strands most losely mathes that of beam theory. The disparity between the atual and apparent transfer lengths dereases with inreasing transfer length. 86

109 24 1 in = 25.4 mm Fully Bonded Strands Strands Debonded 36 in Strands Debonded 72 in Beam Theory Apparent Transfer Length (in) Figure 5.10: Relationship Between Atual Strand Transfer Length and Apparent Transfer Length for H4x Speimens One this relationship was established for eah transfer zone, the apparent transfer length obtained from the experimental test program ould be translated into an estimate of the atual tendon transfer length. As an example, onsider the long-term transfer length of the fully bonded strands in Beam End H4R-A. The measured ompressive strain profile for this end is depited in Figure 5.7. Applying the 95% AMS Method yields the apparent transfer length of 15.4 in (390 mm) as indiated in the figure. Aording to the results of the finite element analysis as plotted in Figure 5.10, an apparent (surfae) transfer length of 15.4 in (390 mm) orresponds to an atual (tendon) transfer length of 13 in (330 mm) for fully bonded strands in the H4x speimens. The value of 13 in is therefore reported as the long-term transfer length in Table 5.6 below Preision of Reported Results Several fators must be onsidered when assessing the auray of the transfer length results gleaned from this study. First, the distane between adjaent surfae strain measurements was 1.97 in (50 mm), thus any attempt to assign a preision smaller than this value to the apparent transfer length relies on interpolated values. Seond, strain readings were not taken in the most ideal of onditions. DEMEC readings were performed by researhers who were subjeted to awkward positions and sometimes exposed to temperatures lower than 40ºF (4ºC), or as was more often the ase, in exess of 100ºF (38ºC), for hours at a time. In light of these irumstanes, it would be misleading to report final transfer length values with a preision better than 1 in (25 mm). 5.4 RESULTS AND DISCUSSION Surfae strain profiles and the orresponding apparent transfer lengths for all speimens are reorded in Appendix C. Using the proedure desribed in Setion 5.3.5, these apparent transfer lengths were onverted to atual transfer lengths. The resulting atual transfer lengths for bright strand speimens are reported in Table 5.1, Table 5.2, and Table 5.3. The results for rusted strand speimens are reported in Table 5.4, Table 5.5, and Table

110 Table 5.1: Transfer Length Results for L Series, Bright Strand Speimens (1 in = 25.4 mm) Debonded Method of Initial Long-Term Speimen Length Prestress Transfer Length ID Age Transfer Length in Release in days in A 0 Simultaneous B 0 Simultaneous L0B C 0 Simultaneous D 0 Simultaneous L4B L6B A B C D A B C D Simultaneous Simultaneous Simultaneous Simultaneous Simultaneous Simultaneous Simultaneous Simultaneous

111 Table 5.2: Transfer Length Results for M Series, Bright Strand Speimens (1 in = 25.4 mm) Debonded Method of Initial Long-Term Speimen Length Prestress Transfer Length ID Age Transfer Length in Release in days in A 0 Simultaneous B 0 Simultaneous M0B C 0 Simultaneous D 0 Simultaneous M4B M9B A B C D A B C D Simultaneous Simultaneous Simultaneous Simultaneous Dead Live Live Dead

112 Table 5.3: Transfer Length Results for H Series, Bright Strand Speimens (1 in = 25.4 mm) Debonded Method of Initial Long-Term Speimen Length Prestress Transfer Length ID Age Transfer Length in Release in days in A 0 Simultaneous B 0 Simultaneous H0B C 0 Simultaneous D 0 Simultaneous H4B H9B A B C D A B C D Simultaneous Simultaneous Simultaneous Simultaneous Dead Live Live Dead

113 Table 5.4: Transfer Length Results for L Series, Rusted Strand Speimens (1 in = 25.4 mm) Debonded Method of Initial Long-Term Speimen Length Prestress Transfer Length ID Age Transfer Length in Release in days in A 0 Simultaneous B 0 Simultaneous L0R C 0 Simultaneous D 0 Simultaneous L4R L6R A B C D A B C D Simultaneous Simultaneous Simultaneous Simultaneous Simultaneous Simultaneous Simultaneous Simultaneous

114 Table 5.5: Transfer Length Results for M Series, Rusted Strand Speimens (1 in = 25.4 mm) Debonded Method of Initial Long-Term Speimen Length Prestress Transfer Length ID Age Transfer Length in Release in days in A 12 Dead B 12 Live M0R C 12 Live D 12 Dead M4R M9R A B C D A B C D Simultaneous Simultaneous Simultaneous Simultaneous Dead Live Live Dead

115 Table 5.6: Transfer Length Results for H Series, Rusted Strand Speimens (1 in = 25.4 mm) Debonded Method of Initial Long-Term Speimen Length Prestress Transfer Length ID Age Transfer Length in Release in days in A 12 Dead B 12 Live H0R C 12 Live D 12 Dead H4R H9R A B C D A B C D Simultaneous Simultaneous Simultaneous Simultaneous Dead Live Live Dead

116 The following setions desribe the trends observed from the results of this study. The effets of onrete strength and tendon prestress, time, strand surfae ondition, and method of prestress release are disussed Conrete Strength and Tendon Prestress As disussed in Setion 2.4.1, equilibrium of fores along the strand transfer length indiates that the initial transfer length, l t,init, should be proportional to both the diameter of the strand, d b, and the equilibrium stress in the tendon immediately following release, f pt. The initial transfer length should be inversely proportional to the average transfer bond stress apaity, u tb, between the tendon and the surrounding onrete. Thus: Equation 5.4 pt t, init db. utb l f Beause muh of the onrete immediately surrounding the tendon is subjeted to tensile stress levels well beyond the elasti range (Janney 1954), the assumption that the transfer length dereases with the tendon stress over time is unreasonable. To the ontrary, these high stress levels should ause some ontinued softening of the onrete-tosteel bond with time. This softening may be attributed to growth of miroraking due to irumferential (hoop) tension and possibly reep under radial ompression. These time-dependent, inelasti effets suggest that the simplest approah to estimating the long-term transfer length, l t, would be to assume that it too is proportional to f pt and d b, while remaining inversely proportional to the initial value of u tb. As disussed in Setion 2.4.3, the average transfer bond apaity should depend most heavily on the tensile strength and stiffness of the surrounding onrete. In North Amerian pratie for normal-weight onrete, both the stiffness and tensile strength of onrete are assumed proportional to the square root of the onrete ompressive strength (ACI , 8.5.1, ). Beause the initial transfer length is determined at the time of release, it is logial to use the onrete ompressive strength at release, f i, for formulating u tb. Therefore, relationships for the initial and long-term transfer lengths may be formulated as in Equation 5.5 and Equation 5.6, respetively, where α long term represent onstants of proportionality. α init and Equation 5.5 l t, init = α init f pt f i d b Equation 5.6 l t = α long term f pt f i d b For the bright strand speimens in the test program, Figure 5.11 illustrates the relationship between the measured f pt long-term transfer lengths and db. As might be expeted for a transfer length study (Rose and Russell 1997), f i espeially one where instrumentation and measurements were performed in the field, the dispersion of the data is quite large. This dispersion alone should serve as a aution against the use of an average value in transfer length expressions for design. Based on a linear regression analysis, a entral value of α long term = ksi -0.5 (10.8 psi 0.5 /ksi, MPa -0.5 ) was determined. The orrelation oeffiient, R, for this regression has a value of The orrelation of long-term and initial transfer lengths with other likely ombinations of variables was also evaluated. In general, the value of the original tendon prestress (at time of tendon tensioning), f pj, ould be substituted for f pt with an insignifiant differene in orrelation. Likewise, the square root of the 28-day (or 56-day for the H Series speimens) onrete ompressive strength, f, ould be substituted for f i without a signifiant loss of orrelation. For the speimens in this test program, the relationship between f pj and f pt was fairly uniform, as was the relationship between f and f i. Thus, while interhange of these parameters should result in different values of the proportionality onstant, α, it should not signifiantly affet the oeffiient of orrelation. 94

117 40 30 l t = ksi 0. 5 f pt f i d b l t 1 in = 25.4 mm; 1 ksi = MPa = 0.57 ksi 0. 5 f pt f i d b 20 R = f pt db f (ksi 0.5 -in) i Figure 5.11: Transfer Length as a Funtion of Tendon Prestress and Conrete Strength at Release Bright Strand Speimens Very little orrelation was evident for relationships that did not inlude the onrete strength in some form. The maximum oeffiient of orrelation found for this type of relationship was R = 0.08 for the relationship lt f ptdb. Likewise, no signifiant orrelation was found between measured transfer lengths and expressions that inluded onrete ompressive strength (without the square root), either f i or f. This finding is logial beause the onrete surrounding the tendon should rak due to irumferential tensile stresses before radial ompressive stresses an approah the ompressive strength of the onrete. The dashed lines in Figure 5.11 represent upper and lower bounds for α long term that bound at least 95 perent of the data. The upper-bound line represents α long term = 0.57 ksi -0.5 (18 psi 0.5 /ksi, 0.22 MPa -0.5 ). Based on the data from this test program alone, this would appear to be a logial value of α long term for use in an expression to predit the transfer length of bright strand for anhorage purposes. Figure 5.12 illustrates the relationship between the measured long-term transfer lengths for the rusted strand f pt speimens and db. The bright strand data, best-fit line, and upper and lower bounds (from Figure 5.11) are f i shown in gray for omparison. Little signifiant orrelation was found for the rusted strand transfer lengths with respet to any of the parameters evaluated. On average, the rusted strand transfer lengths were shorter than those of bright strands, but the dispersion was larger. Despite the shorter average transfer lengths, the dispersion is of suh magnitude that the upper and lower bound expressions determined from the bright strand data serve as effetive estimates of the upper and lower bounds of the rusted transfer lengths. It appears that the relative disparity between the transfer lengths for bright and rusted strands is onentrated in the area of the hart where larger transfer lengths are expeted. This may indiate that the relative improvement in bond apaity resulting from surfae weathering may be effetively limited to lower onrete strength levels. These lower strength levels are typial of many of the past studies that have shown a signifiant shortening of transfer length due to surfae weathering/roughness (Ban, Muguruma and Morita 1960, Janney 1963; Hanson 1969; Holmberg and Lindgren 1970; Rose and Russell 1997). Speifi omparisons between the behavior of bright and rusted strand speimens are addressed in Setion

118 40 1 in = 25.4 mm; 1 ksi = MPa 30 Bright Strand Rusted Strand f pt db f (ksi 0.5 -in) i Figure 5.12: Transfer Length as a Funtion of Tendon Prestress and Conrete Strength at Release Rusted and Bright Strand Speimens Based on the theoretial onsiderations and orrelation results disussed above, it seems logial to base expressions f pt for estimating transfer length on the relationship lt = α db. While the test results indiate that similar f i reliability might be obtained by substituting f pj or f for the orresponding parameters, a few pratial reasons f pt also favor the use of lt = α db. Developing an expression based on f pt allows the pratitioner to freely f i substitute f pj for the sake of simpliity and speed without sarifiing onservatism. In the pretensioning industry, f i is often of more pratial design and onstrution importane than f. Through allowable stress onsiderations, the release strength determines how muh prestressing reinforement may be used in a member. Most importantly, the speified release strength usually more reliably indiates the atual release strength than the speified 28-day strength indiates the atual long-term strength. The prestress fore is not transferred to the onrete until the speified release strength has been ahieved. Thus, onfidene in the ahievement of the speified strength at release is greater than that for strength at 28 or 56 days Time While some studies have revealed signifiant inreases in transfer length with time (Evans 1951; Base 1957, 1958b; Kaar, LaFraugh and Mass 1963; Logan 1997; Lane 1998), others have exhibited less than signifiant inreases (Rüsh and Rehm 1963; Lane 1992). Figure 5.13 illustrates the effet of time on transfer length for the bright strand speimens in this study. The ratio of long-term transfer length to initial transfer length is plotted versus the time elapsed after prestress release for eah set of readings taken. Eah vertial bar represents the average ratio for a set of speimens plus or minus one standard deviation. 96

119 l t,long term l t, initial Average +/- Stand. Dev Time after Release (days) Figure 5.13: Effet of Time on Transfer Length Bright Strand Speimens The extent of the bars indiates that there was onsiderable dispersion among the various amounts of inrease within a speimen group. For the bright strand speimens, the average ratio of long-term transfer length to initial transfer length was 1.13 with a oeffiient of variation of 28 perent. Inspetion of Figure 5.13 indiates no definite trend of ontinued growth beyond an age of twenty days. Thus, it may be inferred that the preponderane of the transfer length inrease ours in the first few weeks after asting. This roughly orresponds with the findings of Base (1957, 1958b), who states that almost all hange ourred within the first twenty days, and Lane (1998), who reports an average inrease of thirty perent in the first twenty-eight days, and only seven perent thereafter. For bright strands on the ends of members subjeted to the dead release method, the average inrease with time was approximately 10 perent. On the opposite, live release, ends, there was no average inrease beyond the initial transfer length. The bright strand results indiate the possibility that higher onrete strengths might slightly inhibit the growth of transfer length with time. However, this trend is far from onlusive, espeially onsidering that no suh trend was indiated in the rusted strand speimens. The inrease of transfer length of rusted strand speimens over time is illustrated similarly in Figure Here again, the signifiant portion of the transfer length growth appears to have taken plae in the first few weeks after prestress transfer. For these speimens, the average ratio of long-term transfer length to initial transfer length is 1.17 with a oeffiient of variation of 24 perent. There was no signifiant variation in the time-dependent behavior of the rusted strand with regard to either onrete strength or release method. 97

120 l t,long term l t, initial Average +/- Stand. Dev Time after Release (days) Figure 5.14: Effet of Time on Transfer Length Rusted Strand Speimens Strand Surfae Condition A wide variety of test results have been reported with regard to the effet of strand weathering on transfer length (see Setion ). Some researhers have found transfer lengths for rusted strand as small as one-half of those for bright strand (Ban, Muguruma, and Morita 1960). Others have found no disernible improvement in the transfer length of wire (Base 1958a) or strand (Logan 1997) due to rust. Table 5.7 indiates the relative performane of rusted strands versus bright strands in this study. In an effort to equitably ompare the performane of strands with the two surfae onditions, the transfer lengths have been f pt normalized with respet to d b. For eah experimentally determined value of transfer length, a value of α was f i f pt determined based on the relationship lt = α d b. The boldfae values in Table 5.7 represent the average ratio f i of α rusted to α bright among the ompanion speimens in a set. These values therefore indiate the average ratio of the normalized transfer length for rusted strand speimens to the normalized transfer length of bright strand speimens. The row and olumn labels desribe the onrete strength series and method of prestress release that define eah ompanion set. The number of omparisons and oeffiient of variation harateristi of eah set are also inluded. 98

121 Table 5.7: Effet of Rusted Surfae Condition on Normalized Transfer Length Relative to Bright Surfae Condition L Series M Series H Series All Strength Series Simultaneous Release Initial Long Term Dead Release Initial Long Term Live Release Initial Long Term All Release Methods Initial Long Term n X C.V n X C.V n X C.V n X C.V α rusted n = Number of diret omparison ratios ( ) in set; α X = Arithmeti mean of ratios C.V. = Coeffiient of variation of ratios bright l t = α f pt f i d b On average, it appears that the rusted strand speimens had slightly shorter transfer lengths than the bright strand speimens. This was partiularly evident for the lower-strength L-Series speimens. For these speimens, the rusted strand transfer lengths averaged about 13 perent shorter than bright strand transfer lengths at release. The long-term disparity was even more pronouned, inreasing to approximately 22 perent. These alulations reinfore the observation made in Setion that the disparity between rusted and bright strand transfer lengths appeared to be onentrated among the speimens with lower onrete strengths. These strength levels are harateristi of those used in past studies for whih signifiant disparities have been found between the behavior of bright and rusted strand (Ban, Muguruma and Morita 1960, Janney 1963; Hanson 1969; Holmberg and Lindgren 1970; Rose and Russell 1997). The unpreditability of rusted strand behavior beomes apparent upon inspetion of the results for the M-Series speimens. On average, use of rusted strand in these speimens resulted in longer transfer lengths than obtained with bright strand. The behavior is most pronouned in the speimen ends that were subjeted to the live release ondition. In these speimens, the average rusted strand transfer lengths were initially approximately 30 perent longer than those for bright strand. Over time, the relative disparity inreased to almost 60 perent. The behavior of these speimens indiates that the ombination of sudden release and rusted strand may have detrimental effets on transfer bond behavior. The shok resulting from the dynami release of prestress may ause portions of the rust produt to break free of the strand surfae. Beause the onrete hardened against this rust produt rather than the underlying surfae of the strand, the separation of the rust produt from the strand may result in less frition between the strand and the onrete than would be ase for onrete ast against bright strand. This detrimental interation of rust and sudden release was less evident in the H-Series speimens, but the relative behavior of the rusted strands in the speimen ends subjeted to live release was the worst in this series as well. Unfortunately, none of the L-Series speimens were subjeted to the live release method. 99

122 5.4.4 Method of Prestress Release Studies that have investigated the effet of prestress release method on transfer length have shown that sudden prestress release usually results in longer transfer lengths than gradual prestress release (Base 1958a; Kaar, LaFraugh, and Mass 1963; Rüsh and Rehm 1963; Holmberg and Lindgren 1970; Rose and Russell 1997). In a manner similar to that used for omparing the relative performane of bright and rusted strands in Table 5.7 above, Table 5.8 ompares the performane of transfer lengths subjeted to the live method of prestress release to those subjeted to the dead release method. The L-Series speimens were only subjeted to the simultaneous release method. These three methods of prestress release are desribed in Setion above. Table 5.8: Effet of Live Prestress Release on Normalized Transfer Length Relative to Dead Prestress Release L Series M Series H Series All Strength Series Bright Strands Initial Long Term Rusted Strands Initial Long Term All Surfae Conditions Initial Long Term n X C.V. n X C.V n X C.V n X C.V α live n = Number of diret omparison ratios ( ) in set; α X = Arithmeti mean of ratios C.V. = Coeffiient of variation of ratios dead l t = α f pt f i d b Among bright strand speimens, the average performane of the live release speimens was neither onsistently better nor onsistently worse than that of the dead release speimens. Although these results might seem to ontradit those of earlier studies regarding prestress release, this may not be the ase. Although Rüsh and Rehm (1963) report transfer length inreases of up to 20 perent due to sudden prestress release, the disparity between release methods dereased with inreasing onrete ompressive strength at release, f i, in speimens ontaining seven-wire bright strand. The largest value of f i for these speimens orresponds roughly with that of the L-Series speimens in the present study. Based on their results, the lak of disparity between the results of the live and dead release methods for the M- and H-Series speimens appears rational. Sine the method of prestress release was not varied for the L-strength speimens, it is impossible to determine whether a larger disparity would have resulted at lower onrete strength levels. For the rusted strand speimens, on the other hand, onsiderable disparity exists between the live release results and the dead release results. On average, the live release method results in transfer lengths 30 to 50 perent longer than the dead release method. The apparently detrimental ombination of rusted surfae ondition and sudden prestress release was disussed in the previous setion. 100

123 It is more diffiult to assess the effets of the simultaneous release method to either the live or dead method beause there are no true ompanion speimens. Although diret omparisons are impossible to onstrut, broad inferenes may be drawn from the average α values for all speimens subjeted to eah release method. Appliation of this type of omparison indiates that the simultaneous release method yielded normalized transfer lengths omparable to those of the dead release method for both bright and rusted strand. This indiates that the detrimental effets of flame utting may be at least partially mitigated by utting eah strand at every member end on a pretensioning bed prior to utting subsequent strands. 5.5 COMPARISON OF TEST DATA WITH RECOMMENDED EXPRESSIONS The purpose of this setion is to ompare the transfer length data obtained in this study with other published expressions for transfer length alulation. The expressions are divided into two ategories depending on whether or not they reflet the influene of onrete strength. As an introdution, Figure 5.15 and Figure 5.16 ompare the data f 0. 5 pt to the upper-bound expression lt = ksi db developed in Setion and serve as examples of the f i figures to follow. In Figure 5.15, the atual transfer lengths determined from this test program are plotted versus the f 0. 5 pt transfer length alulated from the expression lt = ksi db using the measured onrete strength at f release f i and the value of prestress immediately following release, i f pt, obtained from elasti analysis. A line through the origin with a slope of unity represents the ase where the measured transfer length equals that predited by the expression. In order for the expression to serve as an adequate formula for design, this line should approximate the general trend of the data yet serve as an upper bound to at least 95 perent of the points. In the ase of Figure 5.15, beause the expression in question was developed from the test data, it satisfies these riteria with respet to the bright strand data. On the other hand, the expression does not model the trend of the rusted data well, but it still serves as an adequate upper bound in = 25.4 mm L t,meas = L t,pred Bright Strand Rusted Strand Predited Transfer Length (in) Figure 5.15: Comparison of Measured Transfer Lengths to l t = ksi 0. 5 f pt f i d b Figure 5.16 plots the ratio of alulated transfer length (based on the expression in question) to the measured transfer length versus the 28-day (or 56-day) onrete ompressive strength, f. In this type of hart, a horizontal line representing an ordinate of unity indiates perfet agreement between predited and measured values of transfer 101

124 length. If the expression in question serves as an adequate design formula, the horizontal line will serve as an upper bound to at least 95 perent of the data, and the overall trend of the data should exhibit minimal slope. Here again, f 0. 5 pt the expression lt = ksi db appears to satisfy these onditions with respet to the bright strand data. For f i the bright strand data, the expression seems slightly overonservative at lower onrete strength levels, but it remains an adequate upper bound over the full range of onrete strengths. l t, meas l t, pred in = 25.4 mm; 1000 psi = MPa Bright Strand Rusted Strand Conrete Strength, f ' (psi) Figure 5.16: Comparison to l t f 0. 5 pt = ksi db over Conrete Strength Range f i Expressions That Exlude Conrete Strength Figure 5.17 and Figure 5.18 ompare the data from the test program to the expression for transfer length inluded in f pe ACI Building Code Commentary, lt = db (ACI , R12.9). The history of this expression is presented in 3 ksi Setion 2.3. It was originally formulated as an expression for average transfer length, and its usefulness as an expression for safe design is dubious. Nonetheless, Figure 5.17 indiates that it serves as an adequate upper bound for the data from this test program. Close inspetion of Figure 5.18 reveals that it does not follow the general trend of the data with respet to onrete strength. It grows inreasingly onservative as onrete strength inreases. 102

125 40 1 in = 25.4 mm L t,meas = L t,pred Bright Strand Rusted Strand Predited Transfer Length (in) Figure 5.17: Comparison of Measured Transfer Lengths to ACI 318-R12.9 Values l t, meas l t, pred in = 25.4 mm; 1000 psi = MPa Bright Strand Rusted Strand Conrete Strength, f ' (psi) Figure 5.18: Comparison to ACI 318-R12.9 Values over Conrete Strength Range Figure 5.19 and Figure 5.20 illustrate the relationship between the data and the transfer length relationship desribed in the shear provisions of the ACI Building Code (ACI , , ) and the AASHTO Standard Speifiations (AASHTO 1996, ) in whih the transfer length is assumed equal to 50d b. This expression has muh the same relationship with the data as the one from the ACI 318 Commentary exept that it is slightly less onservative beause values of effetive prestress, f pe, are now larger than was generally assumed (150 ksi) at the time the 50d b assumption was odified. The more reently developed AASHTO LRFD Speifiations (AASHTO 1998, ) inorporate an assumed transfer length of 60d b in the shear provisions, more aurately refleting the levels of prestress ommon in ontemporary pratie. This expression (60d b ) is ompared with the test data in Figure 5.21 and Figure These figures exhibit about the same level of onservatism that is evident in Figure 5.17 and Figure

126 40 1 in = 25.4 mm L t,meas = L t,pred Bright Strand Rusted Strand Predited Transfer Length (in) Figure 5.19: Comparison of Measured Transfer Lengths to Values from ACI 318 and AASHTO Standard Shear Provisions l t, meas l t, pred in = 25.4 mm; 1000 psi = MPa Bright Strand Rusted Strand Conrete Strength, f ' (psi) Figure 5.20: Comparison to Values from ACI 318 and AASHTO Standard Shear Provisions over Conrete Strength Range 104

127 40 1 in = 25.4 mm L t,meas = L t,pred Bright Strand Rusted Strand Predited Transfer Length (in) Figure 5.21: Comparison of Measured Transfer Lengths to Values from AASHTO LRFD Shear Provisions l t, meas l t, pred in = 25.4 mm; 1000 psi = MPa Bright Strand Rusted Strand Conrete Strength, f ' (psi) Figure 5.22: Comparison to Values from AASHTO LRFD Shear Provisions over Conrete Strength Range Figure 5.23 and Figure 5.24 ompare the test data with the transfer length expression proposed by Bukner (1995), f pt lt = db. This expression is simply the ACI Commentary expression modified to inlude the steel stress 3 ksi immediately after transfer, rather than the steel stress after all time-dependent losses. As might be expeted, the relationship between this expression and the data is quite similar to that of the other expressions onsidered in this setion. All of these expressions effetively estimate the upper bound of the data for lower onrete strengths. However, they do not reflet the trend of the experimental transfer lengths to derease with inreasing onrete strength. 105

128 40 1 in = 25.4 mm L t,meas = L t,pred Bright Strand Rusted Strand Predited Transfer Length (in) Figure 5.23: Comparison of Measured Transfer Lengths to Values from Bukner Expression l t, meas l t, pred in = 25.4 mm; 1000 psi = MPa Bright Strand Rusted Strand Conrete Strength, f ' (psi) Figure 5.24: Comparison to Values from Bukner Expression over Conrete Strength Range Expressions That Inlude Conrete Strength The figures in this setion ompare the test data to proposed expressions that do inlude the onrete strength as a parameter. Figure 5.25 and Figure 5.26 ompare the test data to an expression proposed by Zia and Mostafa (1978), f pt l t = 1. 5 db 4. 6 in. This expression was developed on the basis of a review of published test results. However, f i results from speimens with f < 2000 psi (14 MPa) and f > 8000 psi (55MPa) were intentionally exluded. 106

129 Thus, although this expression is purported to relate transfer length to onrete strength, its effetive range is quite limited in terms of onrete strengths used in present pratie. The presene of a onstant term in the expression is not rational. As prestress levels approah zero, transfer lengths should approah zero, not a physially meaningless value suh as 4.6 in. The inadequay of this expression for higher strength speimens is apparent in Figure The expression is obviously oversensitive to the onrete strength in = 25.4 mm L t,meas = L t,pred Bright Strand Rusted Strand Predited Transfer Length (in) Figure 5.25: Comparison of Measured Transfer Lengths to Values from Zia and Mostafa Expression l t, meas l t, pred in = 25.4 mm; 1000 psi = MPa Bright Strand Rusted Strand Conrete Strength, f ' (psi) Figure 5.26: Comparison to Values from Zia and Mostafa Expression over Conrete Strength Range Figure 5.26 and Figure 5.27 exhibit a omparison between the test data and the expression developed by Lane f pj (1998), l t = 4 db 5 in. Although onsiderably more onservative than that of Zia and Mostafa, this expression f 107

130 suffers from similar faults. It is based on a statistial analysis of data from a variety of studies that primarily featured values of f less than 10,000 psi (69 MPa). Aordingly, in the same manner that the Zia and Mostafa expression was overly sensitive to f, the Lane expression beomes less onservative as onrete strength inreases. Due to a lak of data inorporation higher onrete strengths, Lane reommends that the value of f in the expression be limited to 10,000 psi. Figure 5.29 displays a omparison between the test data and the Lane expression when modified in this manner. As with the Zia and Mostafa expression, the Lane expression ontains a onstant term that annot be rationalized from a behavioral point of view. This onstant term originally resulted from aeptane of a linear regression result that featured the highest statistial orrelation oeffiient (Lane 1998, 34). A simpler, more rational expression might have been developed at the expense of a slight derease in statistial orrelation with the available test results Bright Strand Rusted Strand 1 in = 25.4 mm L t,meas = L t,pred Predited Transfer Length (in) Figure 5.27: Comparison of Measured Transfer Lengths to Values from Lane Expression l t, meas l t, pred in = 25.4 mm; 1000 psi = MPa Bright Strand Rusted Strand Conrete Strength, f ' (psi) Figure 5.28: Comparison to Values from Lane Expression over Conrete Strength Range 108

131 l t, meas l t, pred in = 25.4 mm; 1000 psi = MPa Bright Strand Rusted Strand Conrete Strength, f ' (psi) Figure 5.29: Comparison to Values from Modified Lane Expression over Conrete Strength Range The final two expressions onsidered in this setion result from a synthesis of behavioral onsiderations and experimental results. The first of these is the expression for transfer length inluded in the CEB-FIP Model Code 90 (CEB-FIP 1990, ). Formulation of the MC90 expression is explained in depth by den Uijl (1992). In the MC90 expression, transfer length is diretly proportional to the jaking stress of the tendons, f pj, as well as the tendon diameter, d b, and indiretly proportional to the tensile strength of the onrete at the time of prestress release. Thus, this relationship is quite similar to those expressed in Equation 5.5 and Equation 5.6 above. However, following the standard European pratie, MC90 diretly relates the tensile strength of the onrete at release to ( f ) i, rather than the f i of North Amerian pratie. Nonetheless, Figure 5.30 and Figure 5.31 show that, while quite onservative with respet to the test data, the MC90 expression does follow the trend of the bright strand data fairly well Bright Strand Rusted Strand L t,meas = L t,pred 1 in = 25.4 mm Predited Transfer Length (in) Figure 5.30: Comparison of Measured Transfer Lengths to Values from MC90 Expression 109

132 l t, meas l t, pred in = 25.4 mm; 1000 psi = MPa Bright Strand Rusted Strand Conrete Strength, f ' (psi) Figure 5.31: Comparison to Values from MC90 Expression over Conrete Strength Range The final expression under onsideration in this setion is that put forward by Mithell et al. (1993), -1 3 ksi lt = ksi f ptdb. Beause this expression is pratially idential to the expression f i f 0. 5 pt lt = ksi db, it also serves as an exellent upper bound to the data in this study. The Mithell et al. f i expression results from an experimental study involving 3 / 8, ½, and 0.6 in (9.5, 12.7, and 15.7 mm) strand embedded in onrete with strengths at release ranging from 3050 to 7250 psi (21 to 50 MPa). The prestress fore was transferred to the onrete gradually in = 25.4 mm L t,meas = L t,pred Bright Strand Rusted Strand Predited Transfer Length (in) Figure 5.32: Comparison of Measured Transfer Lengths to Values from Mithell et al. Expression 110

133 l t, meas l t, pred in = 25.4 mm; 1000 psi = MPa Bright Strand Rusted Strand Conrete Strength, f ' (psi) Figure 5.33: Comparison to Values from Mithell et al. Expression over Conrete Strength Range 5.6 RECOMMENDED EXPRESSION FOR TRANSFER LENGTH f pt As disussed in Setion 5.4, the expression lt = α db may be used to alulate transfer length, so long as the f hosen value of α reflets the effets of variables other than the prestress level, the strand diameter, and the onrete strength. Figure 5.11 illustrates that seleting a value of α equal to 0.57 ksi -0.5 results in an expression that serves as a onservative upper bound for the long-term transfer lengths for the bright strand used in this study. In developing a design expression, it is ritial to inorporate test results from a variety of soures. For this reason, data were olleted from other studies fousing on transfer lengths in large-sale prestressed beams. The additional data were obtained from the following test programs: 1. FHWA Phase II (Lane 1998) Transfer lengths measured on AASHTO Type II I-beams at an age of 28 days. Beams were prestressed with 0.5 in (12.7 mm) or 0.6 in (15.2 mm) strand. Thirty transfer lengths are inluded. 2. Florida DOT (Shahawy, Issa, and dev. Bathelor 1992) Transfer lengths measured on AASHTO Type II I-beams after release. Beams were prestressed with 0.5 in (12.7 mm) or 0.6 in (15.2 mm) strand. Twentysix transfer lengths are inluded. 3. Auburn University (Simmons 1995) Transfer lengths measured on 22 in (560 mm) deep T-beams after release. Beams were prestressed with 0.5 in (12.7 mm) strand. Twenty-seven transfer lengths are inluded. 4. University of Colorado (Shing et al. 1997) Transfer lengths measured on three in (550 mm) deep box girders after release. Beams were prestressed with 0.6 in (15.2 mm) strand. Only average value of the six transfer lengths is reported. 5. Tulane/CTL (Brue et al. 1994) Transfer lengths measured on three 54 in (1370 mm) bulb-tee girders at an age of 28 days. Beams were prestressed with 0.5 in (12.7 mm) strand. Six transfer lengths are inluded. 6. University of Virginia (Ozyildrium, Gomez, and Elhanal 1996) Transfer lengths measured on two AASHTO Type II I-beams after release. Four transfer lengths are inluded. 7. University of Minnesota (Ahlborn, Shield, and Frenh 1996) Transfer lengths measured on two MnDOT 45M I-beams. Beams were prestressed with 0.6 in (15.2 mm) strand. Maximum and minimum values of the four transfer lengths were reported. 111

134 8. The University of Texas at Austin (Russell and Burns 1993) Transfer lengths measured on 22 in (560 mm) and 23.5 in (595 mm) I-beams after release. Beams were prestressed with 0.5 in (12.7 mm) or 0.6 in (15.2 mm) strand. Twenty-eight transfer lengths are inluded. 9. The University of Texas at Austin (Gross and Burns 1995) Transfer lengths measured on two 42 in (1065 mm) retangular beams after release. Beams were prestressed with 0.6 in (15.2 mm) strand. Four transfer lengths are inluded. 10. The University of Texas at Austin (Cordova 1996) Transfer lengths measured on four AASHTO Type III I-beams at ages ranging from one to six months after release. Beams were prestressed with 0.6 in (15.2 mm) strand. Eight transfer lengths are inluded. Four of these transfer lengths are as yet unpublished. Figure 5.34 depits these data along with the bright strand data from this researh study. The experimentally f pt determined transfer lengths are plotted against the quantity db orresponding to eah speimen. The f i f 5 pt relationship lt = 0.57 ksi 0. d b, whih serves as an upper bound for the data from this study, is plotted for f i omparative purposes in = 25.4 mm; 1 ksi = MPa l t = ksi f pt f i d b f pt db f i Figure 5.34: Transfer Lengths from Various Studies It is evident from Figure 5.34 that the transfer lengths obtained from other studies are, on average, signifiantly larger than those obtained in this study. Rather than serving as an upper bound, the expression f 5 pt lt = 0.57 ksi 0. d b underestimates roughly half of the transfer lengths. f i The same data are plotted again in Figure 5.35, but differentiated aording to strand manufaturer. Aside from the speimens for whih the strand manufaturer is not known, the two largest groups of speimens are those ontaining strands from Manufaturer A (inluding the speimens of this study) and Manufaturer B (inluding the speimens of the other large UT study). Only a few data represent strands from Manufaturers C and D. On average, the transfer lengths of speimens ontaining strands from Manufaturer B are more than twie as long as those of speimens ontaining strands from Manufaturer A. This apparent disparity in performane lends redene to the theory (disussed in Chapter 4) that strands produed by different strand manufaturers may have signifiantly different bond harateristis. 112

135 Manufaturer A Manufaturer B Manufaturer C Manufaturer D Unknown Manufaturer 1 in = 25.4 mm; 1 ksi = MPa l t = 1.25 ksi 0. 5 f pt d f i b f pt db f i Figure 5.35: Transfer Lengths of Strands from Various Manufaturers f 5 pt While the expression lt = 0.57 ksi 0. d b still serves as an effetive upper bound expression for long-term f i transfer lengths of bright strand produed by Manufaturer A, a larger value of α is required to effetively bound the transfer lengths of strands from all produers. Based on the data presented here, the expression f 5 pt lt = 1.25 ksi 0. db is reommended for providing an upper bound estimate of the transfer length for design f i purposes. This expression, depited in Figure 5.35, yields a transfer length value nearly twie that of the urrent ACI Commentary expression when onrete with a release strength, f i, equal to 4 ksi (28 MPa) is employed. This differene is not out of line onsidering the signifiant disrepanies between the original PCA test data and the ACI Commentary expression for transfer length. These disrepanies are disussed in Chapter 2. Figure 2.2 indiates that if the ACI Commentary expression were doubled, it would have bounded approximately 90 perent of the PCA data. When designing to satisfy allowable onrete stresses, onservative design pratie usually requires that a lower bound estimate of the transfer length be used to alulate onrete stresses in the anhorage region. A lower bound expression for transfer length ould also be developed that inorporates the prestress level, strand diameter, and onrete strength. However, onsidering the short transfer lengths measured in many of the speimens of this study, it seems quite pratial to simply assume a transfer length of 6 in (150 mm) or less for this purpose. Assuming a value of zero would be safe, simple, and probably not result in signifiant extra ost. In this study and previous studies, surfae weathering of strand has served to shorten average transfer lengths. This effet is far from onsistent however. Depending upon a speifi degree of surfae weathering to improve bond performane is impratial. The upper bound relationship proposed above reflets the fat that sudden prestress release was employed for many of the test speimens in the studies listed. Thus, the expression need not be amplified if sudden prestress release is expeted. Until the apparent signifiant disparity in bond performane among strands produed by different manufaturers is redued or at least better understood, attempting to refine the transfer length expression to reflet the influene of prestress release method is impratial. The apparent differene in transfer length attributable to differenes in manufaturing proesses an largely outweigh the differene resulting from varying the release method. 113

136 Further researh is neessary to verify and/or quantify the top bar effet on the transfer length of pretensioned strands. Until suh researh has been performed and suitable onlusions reahed, onservatism suggests that the transfer lengths of tendons satisfying the ACI Code definition of top bars be inreased by at least 30 perent. 5.7 SUMMARY AND CONCLUSIONS Transfer lengths were experimentally determined for thirty-six plant-ast AASHTO Type I I-beams. Conrete ompressive strains were measured at the surfae of eah beam. Initial and long-term transfer lengths were determined by analyzing the orresponding ompressive strain profiles. The influene of onrete ompressive strength, strand surfae ondition, prestress release method, and time were investigated. On average, transfer lengths were found to be indiretly proportional to f i. Previous researh has established that transfer length is proportional to the strand prestress at release, f pt, and the diameter of the strand, d b. Transfer lengths were found to inrease approximately 10 to 20 perent over time, on average. Inreases in a few speimens exeeded 50 perent. Average transfer lengths of rusted strands were shorter than average transfer lengths of bright strands, partiularly for speimens onstruted with normal strength onrete. However, the dispersion of rusted strand results was signifiantly larger than that of bright strands. In some ases, rusted strands exhibited longer transfer lengths than those of bright strands in omparable speimens. In short, surfae weathering annot be relied upon to redue transfer lengths. In this test program, the method of prestress release was only varied for speimens with onrete release strengths larger than 7000 psi (48 MPa). For these speimens, the method of prestress release had no signifiant influene on transfer length of bright strand speimens. For rusted strands, the use of sudden prestress release resulted in transfer lengths 30 to 50 perent larger than those assoiated with more gradual release. The experimental results of this study as well as others (Russell and Burns 1993; Shahawy, Issa, and dev. Bathelor 1992) indiate that transfer lengths of debonded strands are no longer than those of similar fully bonded strands. The measured ompressive strain profiles depited in Figure 5.6 and Appendix C indiate the effetiveness of using staggered debonding of strands to redue the intensity of onrete stresses in the end regions of beams. These results indiate that partial debonding of strands may be used as a viable alternative to draping for effetively tailoring onrete stresses to satisfy allowable stress limitations immediately after prestress release. A lower bound estimate of the transfer length should be used when heking allowable stresses. For simpliity and safety, the transfer length may be estimated as zero for this purpose. The data olleted from this test program indiate that long-term transfer lengths an be onservatively estimated f 5 pt from the upper bound expression lt = 0.57 ksi 0. d b. Study of transfer length results from other test programs f i reveals that this expression underestimates the transfer lengths of speimens reinfored with strand produed by other manufaturers. A more onservative transfer length expression was developed based on data olleted from a variety of researh studies on strands from various manufaturers. The following expression is proposed for onservatively estimating long-term transfer length: l t = ksi 4 This expression takes into aount unertainties that exist during design suh as: strand manufaturing proess, method of prestress release, and strand surfae ondition. f pt f i d b 114

137 CHAPTER 6: DRAW-IN TEST PROGRAM 6.1 INTRODUCTION In order to evaluate the effetiveness of using draw-in measurements to predit transfer and flexural bond behavior, a program of draw-in testing was performed in tandem with the transfer length test program desribed in Chapter 5. Draw-in, often referred to as free end slip or suk-in, is the displaement of the prestressing tendon, resulting from the release of prestress, relative to the end of the member. In this study, the term draw-in is used to prevent possible onfusion with the term end slip, whih is used to desribe movement of the strand resulting from external loads applied during development length testing. 6.2 BACKGROUND Anderson and Anderson (1976) desribe the theoretial basis for a diret relationship between strand draw-in and transfer length. Figure 6.1 illustrates the derivation that follows in the next few paragraphs. Guyon (1953, 195) gives a omparable derivation. Beause there is no displaement of the steel relative to the onrete at the end of the transfer length, the draw-in length may be alulated as: where: l = draw-in length draw in pt t ldraw in = pt = ontration of the tendon along the transfer length, and = ontration of the onrete along the transfer length. The values of steel and onrete ontration may be alulated by integrating strains that result from prestress release along the transfer length, l t : = pt ε pdx and = t ε dx lt lt where: ε p = hange in steel strain that results from prestress release, and Thus, ε = hange in onrete strain that results from prestress release. Equation 6.1 ldraw in = ( ε p ε ) At the start of the transfer length (point of initiation of bond), alulated as: * f p f pj ε p = = E p E p where: f p = hange in steel stress that results from prestress release, l t dx t ε is zero, and the hange in steel strain may be * f pj = stress in the steel immediately prior to transfer (the jaking stress, f pj, minus losses due to relaxation between stressing and release), and E p = modulus of elastiity of the tendon. 115

138 ε f * pj E p ε p ( x) ε ( x) ε p (x) ε (x) f * pj E ff E pt pt p p f pt x lt ldraw-in = Shaded Area = f * pj 2E p l t Figure 6.1: Relationship between Draw-In and Transfer Length At the end of the transfer length, the onrete and steel strains are ompatible, and the residual steel stress is f pt. Thus, * f p f pj f pt ε = ε p = = E p E p where: f pt = stress in prestressing steel immediately after transfer. If both the steel and onrete strains are assumed to vary linearly along the transfer length, then the integrand in f * pj Equation 6.1 varies linearly from a value of at the start of the transfer length to a value of zero at the end of the E p transfer length. Therefore, Equation 6.2 results as an expression that diretly relates draw-in to transfer length. Equation 6.2 l draw in f = 2E * pj p l t Equation 6.3 results from inverting this expression. Given values of E p and estimate transfer lengths based on measured draw-in values. Equation 6.3 2E p t = * f pj l l draw in f * pj, Equation 6.3 may be used to Anderson and Anderson further propose that draw-in, in addition to indiating the atual transfer length, may indiate the flexural bond apaity of a member. They onduted a series of repeated load tests on hollow-ore produts from five manufaturers. Three different proesses were used to manufaturer the hollow-ore units. Both enter-point and third-point loading onfigurations were used. The test results indiate a strong orrelation between exessive free end slip and premature bond failure. The results were used to develop an expression for a 116

139 limiting value of draw-in. If the measured draw-in is less than this limiting value, the ACI 318 development length is adequate to ensure flexural failure. Otherwise, Anderson and Anderson propose apaity redution fators to be used based on the measured draw-in. Brooks, Gerstle, and Logan (1988) report a strand draw-in theory developed by Robert Mast. Mast s theory, a refinement of the ideas of Anderson and Anderson, assumes that the initial draw-in serves as a diret indiation of the bond quality of the onrete. Beause low-slump onrete is typially used in the prodution of hollow-ore units, onsolidation of the onrete around the strand presents more diffiulty than in pretensioned produts, suh as bridge girders, that are ast with higher-slump onrete. Thus, bond behavior may be poorer than indiated by the ACI 318 expression for development length. Mast s draw-in theory aepts measured draw-in as a diret indiator of the transfer and flexural bond apaity of the strand. Instead of Equation 6.2 above, the theory is based on the similar expression: f pt ldraw in = lt 2E p f pe in whih the prestress immediately after release is used. Substitution of the expression lt = db from the ACI 3 ksi 318 Commentary results in an allowable draw-in value, δ all, that orresponds to a transfer length equal to that implied in the Commentary: f pe f pt δ all = d b (6 ksi) E p The theory maintains that the atual transfer and flexural bond lengths of a member are in the same proportion to the ACI 318 Commentary expressions as the measured draw-in value is to δ all. If ldraw in > δ all, the resulting magnified transfer and flexural bond lengths are then used to ompute the bond apaity of the tendon. The results of an experimental program desribed by Brooks, Gerstle, and Logan support the validity of this theory when l > δ. Bond apaity alulations based on the ACI Code expression for development length, draw in l d = f ps all 2 f 3 pe d, overestimate the ultimate apaities of test speimens that displayed exessive draw-in. b Draw-in measurements were taken as part of the Stresson test program (Logan 1997) desribed in Setion Mast s theory provided exellent orrelation with the results of development length tests performed on simplysupported and antilever beam speimens pretensioned with strands from a variety of manufaturers. Measurements were onduted up to an age of 21 days, and signifiant draw-in growth ourred with time. Thus, Logan onludes that draw-in values obtained immediately upon release of prestress might not serve as an adequate indiator of bond quality or apaity. Logan also reports that the NCSU test speimens (Cousins, Johnston and Zia 1990) that exhibited extremely poor transfer and flexural bond behavior and resulted in the FHWA moratorium featured measured draw-in values signifiantly longer than draw-in values measured for hollow-ore slabs at the Stresson plant. This observation reinfores the link between draw-in and bond quality. Rose and Russell (1997) report results of a study aimed at assessing the usefulness of several proposed bond quality test methods. Measured values of draw-in were ompared with measured transfer lengths. Considering data from several transfer length studies, Rose and Russell found very good orrelation for the relationship expressed in Equation 6.3 above. They onlude that draw-in measurements provide the best orrelation with transfer length when ompared to all other test methods. More detail about this study is provided in Setion Rose and Russell ite the possible growth of draw-in with time as a potential shortoming to the use of draw-in measurements as a method of assessing bond quality. 6.3 TEST PROCEDURE Two different tehniques were used for measuring the strand draw-in in this study. For the first two speimen pairs fabriated (L0B and M0B), a small C-shaped, aluminum alignment braket was seured to eah strand by means of a hose lamp. These brakets, shown in Figure 6.2, were used to arefully align a digital depth gauge that was used to measure the distane from eah braket to the end fae of eah beam. The depth gauge featured a preision of in (0.006 mm), and the dual arms of the alignment brakets were utilized to improve the auray of repeated readings. 117

140 Figure 6.2: Alignment Brakets for Measuring Strand Draw-In One set of measurements was reorded prior to the release of prestress. Immediately after the tendons were ut, another round of measurements was performed in order to provide data for the alulation of initial strand draw-in. Long-term draw-in results were alulated using another set of measurements taken at a later date. The use of these alignment brakets proved largely ineffetive beause the strands were flame-ut. The shok from the sudden prestress release jarred most of the brakets loose thereby terminating their effetiveness as benhmarks for subsequent measurements. Of the brakets that appeared to have remained seurely fastened, areful visual inspetion revealed that some had obviously translated relative to the strand. This ast doubt on the validity of the readings obtained from brakets that appeared snugly attahed. Attempts to remedy the situation by attahing extra hose lamps to the strands of the M0B speimen pair were ineffetive. Thus, few of the draw-in results are reported for the L0B beam pair, and none are reported for the M0B pair. Use of the alignment brakets was abandoned after these two pairs of beams were ast. Although this system was ineffetive with sudden prestress release, it has proven quite suessful in other researh involving gradual release methods. A simpler, more robust tehnique was utilized to obtain draw-in data for the remaining speimens. As shown in Figure 6.3, researhers spray-painted eah strand to provide a benhmark for measurements. Masking tape was used to provide a straight line for making aurate measurements. A steel rule, graduated in inrements of 0.01 in (0.25 mm) was used for measuring the distane from the strand to the beam end. In order to redue error, only one researher performed all draw-in measurements. Measurements were reorded to the nearest in (0.13 mm). Swithing to this system resulted in measurements that were more reliable but less preise. 118

141 Figure 6.3: Strands Painted to Provide Referenes for Draw-In Measurements As is evident in Figure 6.4, the shok resulting from the flame-utting proedure was intense, partiularly for the partially debonded strands. It was ommon for the various wires omposing a single partially debonded strand to exhibit different values of draw-in. Beause it was impossible to measure the displaement of all seven wires per strand (the enter wire in partiular would have presented a unique hallenge). The displaements of the three topmost strands were reorded and later averaged during the alulation proess. The extreme unwrapping deformations experiened by some of the debonded strands (suh as Strands A2 and A3 in Figure 6.4) made it diffiult to obtain aurate readings after prestress release. This was one of several fators that hindered the estimation of true draw-in for partially debonded strands. Other fators will be disussed in the next setion. A2 A3 Figure 6.4: Flame-Cut Strands after Release of Prestress 119

142 6.4 DETERMINATION OF DRAW-IN VALUE Determination of the draw-in of the strand relative to the onrete was relatively simple for the fully bonded strands. The initial draw-in value was alulated as the differene between the distane measured immediately after prestress release and the distane measured prior to prestress release. A final refinement involved the subtration of the free ontration of the tendon ourring between the measurement benhmark and the end of the beam. The free f * pj ontration of the strand along this length was alulated as 0, where 0 is the distane from the benhmark E p to the end of the beam prior to prestress release. Thus, for fully bonded strands, * f pj Equation 6.4 ldraw in, t = t 0 0 E where: l draw in, t = draw-in value at time t, t = distane from benhmark to end of beam at time t, 0 = distane from benhmark to end of beam prior to prestress release, f * pj = stress in tendon immediately prior to prestress release, and E p = modulus of elastiity of tendon. Calulation of the draw-in along the transfer length of partially debonded strands is more omplex. For these strands, the displaement of the tendon relative to the onrete at the end of the beam is only an indiation of the relative displaement at the point of initiation of bond. In order to onvert the reorded measurements to a useful estimate of atual draw-in along the transfer length, an aurate piture of the relative displaement of the onrete and steel along the debonded length is required. The draw-in along the transfer length may be formulated as follows: where: p, db, t, db, t p * pj draw in, t = ( t 0 ) ( p, db, t, db, t ) 0 E p l = total ontration of the tendon along the debonded length at time t, and = total ontration of the onrete along the debonded length at time t. The alulation of the first of these terms, p, db, t, is relatively simple if the fritional resistane transferred from the onrete to the tendon along the debonded length, l db, is insignifiant. If so, may be aurately estimated as f * pj ldb E. p On the other hand, the aurate omputation of, db, t is fraught with diffiulty, partiularly at any time other than immediately after prestress release. Calulation of this quantity requires integration of the onrete strains along the debonded length. After prestress release, these strains are not uniform. The onrete stresses and strains aumulate along the debonded length due to the influene of other strands that are bonded along either all or a portion of this length. Aurate integration requires knowledge of the stress level indued by the bonded strands, the transfer length of eah strand, and the stiffness of the onrete. Integrated over long debonded lengths, small errors in estimating these quantities an result in signifiant errors in, db, t. In the ase of long-term measurements, reep and shrinkage deformations an elipse the elasti deformations within a few weeks. This ontinued ontration of onrete along the debonded length of strands has led some preasters to marvel at the tendeny of debonded strands to push out of the beam. Compounding these deformation unertainties with the dubious auray assoiated with f p, db, t 120

143 measuring the movement of strands suh as A3 and A4 in Figure 6.4 leaves the validity of the alulated draw-in values for debonded strands in doubt. Nonetheless, every attempt was made to aurately estimate the elasti and time-dependent strains along the debonded length so as to alulate a value for draw-in. Time-dependent deformations were alulated using proedures desribed by Collins and Mithell (1991). 6.5 DISCUSSION OF RESULTS Values of the initial and long-term draw-in for all speimens were alulated aording to the proedure outlined in the previous setion. The results are presented graphially in Appendix D. Some of the results for partially debonded strands, suh as those shown in Figure 6.5, agree fairly well with those of the fully bonded strands in the same speimen. However, the results shown in Figure 6.6 are harateristi of the poor results more ommonly obtained. Often, the draw-in results for one debonded length of strands varied onsiderably ompared to those of other debonded strand lengths and those of the fully bonded strands in the same speimen. The negative draw-in values alulated for some of the debonded strands indiate that some fritional fore was transferred through the strand jaketing along the debonded length. However, the various measurement and alulation diffiulties assoiated with debonded strands severely damage any ertitude regarding this matter. Signifiant transfer of prestress along the debonded length of the strands should have been evident from the surfae strain profiles, and there is no lear evidene that this ourred. Beause of the lak of onfidene assoiated with the results obtained from partially debonded strands, the omparisons and disussions that onstitute the remainder of this setion onsider only those results obtained from fully bonded strands Initial at 138 Days Debonded 36 in Debonded 72 in Debonded 108 in 0.10 Fully Bonded A1 A6 G3 G4 E3 E4 A3 A4 B3 B4 Strand ID Figure 6.5: L6B-B Strand Draw-In Results Bright Strand, Simultaneous Flame Release (1 in = 25.4 mm) 121

144 A1 A6 G4 E3 E4 G3 A3 A4 A2 A5 B3 B4 Fully Bonded Initial at 26 Days Debonded 36 in Debonded 72 in Debonded 108 in Strand ID Figure 6.6: M9B-C Strand Draw-In Results Bright Strand, Live End of Flame Release (1 in = 25.4 mm) The number of draw-in readings assoiated with eah fully bonded strand transfer length at eah event (initial or long-term) range from three to eight depending on the number of strands. Thus, it is not immediately lear what value of ldraw in should be used to alulate the transfer length, l t, predited from these draw-in data by means of Equation 6.3. In the omparisons that follow, two methods are used. One value, denoted l t, avg, is alulated by substituting the average draw-in value in Equation 6.3. Another value, l t, max, is alulated by substituting the maximum draw-in value. The transfer length predited on the basis of draw-in is denoted l t to distinguish it from l t, the transfer length obtained by the proedure desribed in Chapter 5. If a value of 170 ksi (1170 MPa) is assumed for tendon prestress after all losses, f pe, the ACI 318 Commentary f pe Setion R12.9 indiates a transfer length of d b = 34 in (860 mm) for these speimens. Substitution of this 3 ksi value into Equation 6.2 results in a value of ldraw in = 0.12 in (3.1 mm) that orresponds to the Commentary transfer length. All of the long-term draw-in values obtained from fully bonded strands in this study are less than 0.12 in. Hene, appliation of Mast s draw-in theory (Brooks, Gerstle, and Logan 1988) suggests that both the transfer and flexural bond lengths of the speimens in this study are less than predited by the Commentary expressions. Aordingly, Figure 5.17 and Figure 5.18 illustrate that the measured transfer lengths do not exeed the values predited by the Commentary expression. Flexural bond behavior of the test speimens is disussed in Chapter 7. The subsequent four figures, Figure 6.7 through Figure 6.10, show relationships between measured transfer lengths and strand draw-in values obtained in this study. The dashed line in eah figure represents the relationship * expressed in Equation 6.3. Using values harateristi of these speimens, E p = 28,000 ksi (193 GPa) and f pj = 200 ksi (1380 MPa), this relationship redues to lt = 280 l draw in. None of these four figures exhibits a orrelation between transfer length and draw-in that is nearly as good as that reported by Rose and Russell (1997). This weaker orrelation may be partly due to the fat that neither the transfer length nor draw-in measurements were performed under laboratory onditions as in other studies. The Rose and Russell speimens featured a retangular ross setion prestressed with just two strands eah. The speimen ross setion used in this study was more omplex and more than twie as large. In addition, the transfer zones of the fully bonded strands ontained up to eight strands in a variety of patterns. These omplexities may have ontributed to the variability of the results. 122

145 l t 2E = ldraw in = 280l f p * pj draw in 1 in = 25.4 mm Average Strand Draw-In at Release (in) Figure 6.7: Measured Initial Transfer Length vs. Average Draw-In Value at Release l t 2E = ldraw in = 280l f p * pj draw in 1 in = 25.4 mm Maximum Strand Draw-In at Release (in) Figure 6.8: Measured Initial Transfer Length vs. Maximum Draw-In Value at Release 123

146 Measured Long-Term Transfer Length (in) E lt = ldraw in = 280l f p * pj draw in Average Long-Term Strand Draw-In (in) 1 in = 25.4 mm Figure 6.9: Measured Long-Term Transfer Length vs. Average Long-Term Draw-In Value Measured Long-Term Transfer Length (in) E lt = ldraw in = 280l f p * pj draw in Maximum Long-Term Strand Draw-In (in) 1 in = 25.4 mm Figure 6.10: Measured Long-Term Transfer Length vs. Maximum Long-Term Draw-In Value Figure 6.7 and Figure 6.9 illustrate that Equation 6.3 results in an underestimation of the majority of initial and longterm transfer lengths when the average value of draw-in at the orresponding time is used. This is likely beause the full transfer length depends on the bond performane of all the strands. The total prestress fore for the transfer zone annot be transferred until the worst-performing strand has transferred its prestress. Beause it is impossible to determine exatly where the full prestress fore is ahieved, tehniques suh as the 95% AMS Method are used to evaluate the transfer length. If some of the strands transfer prestress to the onrete more rapidly than others, 95 perent of the aggregate prestress fore will be transferred over a length shorter than 95 perent of the length required by the strands with poorer bond performane. Thus, the transfer length obtained for a group of strands should lie between the average transfer length of the individual strands and the transfer length of the worst- 124

147 performing strand. This idea is also supported by Figure 6.8 and Figure 6.10 whih indiate that Equation 6.3 overestimates the majority of measured transfer lengths when the maximum draw-in value is used. Figure 6.11 through Figure 6.14 represent histograms of various ratios of the transfer length predited from Equation 6.3 to the transfer length alulated from surfae strain measurements. Figure 6.11 and Figure 6.12 inlude the data obtained immediately after prestress release; Figure 6.13 and Figure 6.14 show the relationship between the longterm observations. The first figure of eah pair represents the use of the average draw-in value to predit the transfer length, while the seond represents use of the maximum draw-in value for eah group of strands. The histograms an be thought of as representing the frequeny of ourrene of errors of different relative magnitudes when trying to predit the transfer length by means of Equation 6.3. The average tendeny of average draw-in lengths to underestimate the transfer lengths is readily disernible in these figures, as is the average tendeny of maximum draw-in values to overestimate the transfer lengths. The relationship of long-term draw-in values to long-term transfer lengths is better behaved than that between the initial values. The values represented in Figure 6.13 and Figure 6.14 are more normally distributed and exhibit a smaller of degree of relative dispersion (as measured by the oeffiients of variation noted in the figures) than those shown in Figure 6.11 and Figure This may indiate that the steel and onrete strain profiles beome more linear as assumed in the derivation of Equation 6.3 with time. In other words, if the stress/strain gradient does vary initially along the transfer length, the derease over time of the larger strain gradients where the bond stress is more intense may be more pronouned than that of the smaller strain gradients where the bond stress is less intense. Thus, the linearity of the stress/strain profile may inrease with time. Frequeny Mean = 0.93 s = 0.35 C. of V. = 37% 100% 80% 60% 40% 20% Cumulative Frequeny More l t, initial, avg l t, initial 0% Figure 6.11: Histogram Ratio of Transfer Length Calulated from Average Initial Draw-In to Measured Initial Transfer Length 125

148 Frequeny Mean = 1.23 s = 0.46 C. of V. = 38% 100% 80% 60% 40% 20% Cumulative Frequeny More l t, initial,max l t, initial % Figure 6.12: Histogram Ratio of Transfer Length Calulated from Maximum Initial Draw-In to Measured Initial Transfer Length 12 Mean = % Frequeny 8 4 s = 0.26 C. of V. = 27% 80% 60% 40% 20% Cumulative Frequeny More l t, long term, avg l t, long term 0% Figure 6.13: Histogram Ratio of Transfer Length Calulated from Average Long-Term Draw-In to Measured Long-Term Transfer Length 126

149 Frequeny C. of V. = 23% Mean = 1.24 s = % 80% 60% 40% 20% Cumulative Frequeny More l t, long term,max l t, long term 1.8 0% Figure 6.14: Histogram Ratio of Transfer Length Calulated from Maximum Long-Term Draw-In to Measured Long-Term Transfer Length Based on these histograms, it an be argued that appliation of Equation 6.3 using the average value of draw-in results in the best estimate of the atual long-term transfer length. Use of the maximum value of draw-in results in the safest (i.e. least probability of underestimation) estimate of the long-term transfer length. However, the relative dispersion evident from these results indiates that implementation of draw-in measurements for quality ontrol purposes must be done prudently. For example, use of the maximum long-term draw-in measurement is attrative from a safety point-of-view beause it appears to result in underestimation of the transfer length by more than 20 perent in less than 5 perent of ases. The preast produer, on the other hand, would be less than satisfied with this method beause it results in overestimation of the transfer length in 80 perent of ases. In fat, it results in overestimation by more than 25 perent in roughly half of the ases. Use of the average draw-in length brings the average predited transfer length loser to the atual transfer length, but is not effetive in resolving the problem presented by the dispersion of the data. Thus, for a quality ontrol program based on draw-in measurements to be implemented fairly and effetively, a proper database inluding a large number of results must be developed and maintained. In the long run, the use of the average draw-in result to estimate a partiular transfer length will probably prove to be more dependable than the use of the maximum draw-in result. Dependene on a single measurement, partiularly when that measurement is performed under field onditions, is more prone to signifiant error than dependene on an average value. The dispersion of the data must be properly onsidered; rejetion of a single produt should only our when the average draw-in reading for a transfer zone is signifiantly larger than that expeted to meet an established transfer length limitation. The size of draw-in disrepany neessary to indiate a high probability of poor bond performane would depend upon the variane of results from a signifiantly large sample of similar produts. One potential obstale to the implementation of a quality ontrol program involving draw-in measurements is the issue of time. Draw-in measurements were originally proposed as a relatively simple and immediate method of estimating the bond behavior of partiular preast produts. Implementation of a quality ontrol program that involves long-term draw-in measurements on atual preast produts (as opposed to test speimens) will be diffiult. Although most studies have indiated that signifiant transfer length and draw-in growth only ours in the first month after release, this may still prove to be an exorbitantly long time period for the preaster to keep produts in storage before being able to ut the strand extensions and/or dress the beam ends prior to shipping. In light of this onern, Figure 6.15 and Figure 6.16 indiate the ability of Equation 6.3 to predit the long-term transfer length when initial values of draw-in are onsidered. 127

150 Frequeny Mean = 0.81 s = 0.26 C. of V. = 33% 100% 80% 60% 40% 20% Cumulative Frequeny More l t, initial,avg l t, long term 0% Figure 6.15: Histogram Ratio of Transfer Length Calulated from Average Initial Draw-In to Measured Long-Term Transfer Length 12 Mean = % Frequeny 8 4 s = 0.35 C. of V. = 33% 80% 60% 40% 20% Cumulative Frequeny More l t, initial,max l t, long term 1.8 0% Figure 6.16: Histogram Ratio of Transfer Length Calulated from Maximum Initial Draw-In to Measured Long-Term Transfer Length It is not surprising that neither of the distributions is as well behaved as those that use the long-term values of drawin (Figure 6.13 and Figure 6.14). On the other hand, the oeffiients of variation are slightly better than those for the initial transfer length distributions shown in Figure 6.11 and Figure Although the distributions shown in Figure 6.15 and Figure 6.16 are less than ideal, it appears that the initial draw-in might serve as an adequate quality ontrol parameter with the development of an adequate database and statistially determined orretion fators. Of ourse, ompanion long-term draw-in measurements would still have to be sampled on a periodi basis to ensure that the relationship between long-term and initial behavior remains statistially unhanged. 128

151 In this study, the average growth of the long-term draw-in values relative to the initial draw-in values refleted the average growth of the measured transfer lengths of the orresponding fully bonded strands. The average growth of these measured transfer lengths was 15 perent. The average growth of the maximum transfer draw-in values was 16 perent, while the average growth of the average draw-in values was 19 perent. 6.6 SUMMARY AND CONCLUSIONS In order to evaluate the effiay of using measured draw-in values to quantify bond behavior in pretensioned members, both initial and long-term draw-in measurements were performed on the test speimens in this researh study. The sudden method of prestress release resulted in instrumentation diffiulties, and may have resulted in signifiantly erroneous readings for the partially debonded strands in the study. Conversion of measured values to atual draw-in values along the transfer length of partially debonded strands also introdues a signifiant level of unertainty into the values alulated for these strands. Thus, although the relative magnitudes of the measured values of draw-in obtained from the debonded strands indiates that the strands transferred little or no prestress fore to the onrete over the debonded length, the use of measured draw-in values to aurately estimate the atual transfer or development length of partially debonded strands was judged impratial. The more reliable values of draw-in measured for fully bonded strands were ompared to the orresponding transfer lengths obtained as desribed in the previous hapter. Aording to Mast s draw-in theory, the long-term draw-in values obtained indiate that all of the tendons should exhibit transfer and flexural bond behavior that omplies with the urrent ACI development length provisions (Setions 12.9 and R12.9). This agrees with the transfer length results reported in Chapter 5, whih do not exeed values predited by the expression provided in the ACI 318 Commentary. Equation 6.3 was derived as a means of prediting the transfer length for a strand given its draw-in value. It was found that using the average value of the long-term draw-in for a group of strands most aurately predited the measured long-term transfer length for that group of strands. However, on average, the value predited by this method tends to slightly underestimate the transfer length. A more onservative estimate may be obtained by using the maximum draw-in value for the group of strands. The average proportional inrease of draw-in values with time did not vary signifiantly from the average proportional inrease of the orresponding measured transfer lengths with time. Correlation between the measured draw-in values and the measured transfer lengths was signifiantly poorer than found in previous studies onduted on laboratory speimens. The dispersion of the data from this study was suh that it would be diffiult to implement a quality ontrol program based on this data alone. A single average draw-in value on the order of two to three times the expeted value might indiate a bond defiieny in a preast produt. On the other hand, a single average value in the range of one to one-and-a-half times the expeted value would hardly justify the produt s rejetion, but repeated observations in this range might indeed indiate a problem. The sope and size of the olleted data is insuffiient to serve as a basis for presribing quality ontrol riteria at this time. Conlusions regarding the ability of measured draw-in values to indiate flexural bond behavior are reserved until the next hapter. 6.7 RECOMMENDATIONS The use of draw-in measurements to predit the bond behavior of partially debonded strands is impratial and therefore not reommended. Draw-in measurements may be used to indiate trends in transfer bond behavior. Historial evidene suggests that gross defiienies in bond quality may be effetively indiated by this test method. However, the use of small sample sizes an be unreliable, and any inferenes onstruted from draw-in measurements should reflet the onsiderable degree of dispersion evidened by this test program. A detailed, statistial study of the relationship between draw-in and transfer length should be performed prior to instituting a quality ontrol system involving draw-in measurements. Suh a study should be performed on a statistially signifiant number of speimens produed by a variety of preasters using the full range of prodution methods urrently in use (suh as the various methods of prestress release). Partiular attention should be paid to the growth of transfer length with time and how this growth is refleted in both the initial and long-term draw-in measurements. If the long-term transfer length an be reliably predited by the average initial draw-in value, this 129

152 presents the ideal quality ontrol situation. Any attempt to develop suh a quality ontrol program should involve the ooperation of inspetors, building offiials and preast produers. Consultation with speialists experiened with anhorage of pretensioned reinforement and the appliation of statistial theory for quality ontrol would be prudent. 130

153 CHAPTER 7: DEVELOPMENT LENGTH TEST PROGRAM 7.1 INTRODUCTION After ast-in-plae dek slabs were added to eah pair of I-beam speimens, preparation for development length testing ommened. The two beams of eah pair were designed to be idential with the exeption of the horizontal web reinforement present in one end (End C) of one beam of the pair. Eah beam pair featured a unique ombination of the three primary variables under investigation: onrete strength, strand surfae ondition, and debonding pattern. One development length test was performed on eah end of eah beam. Thus, for eah ombination of variables, a total of four tests was performed one of whih inluded the horizontal web reinforement desribed in Setion This hapter inludes an explanation of the development length testing onfiguration and instrumentation. General testing proedure is desribed, and results are presented and disussed. 7.2 TEST APPROACH Development length annot be determined diretly from a single experiment. For this test program, an indiret approah was employed. Eah test onsisted of loading the beam speimen to failure. The resulting failure type indiated whether the bonded length of strand provided is adequate to develop the steel stress, f ps, neessary for nominal flexural strength at the ritial setion. The ritial setion is defined as the setion losest to the end of the member expeted to develop full strength when subjeted to the applied loading. The bonded length anhoring the strand at the ritial setion is referred to as the embedment length, l e. The ultimate moment resisted at the ritial setion and the behavior of the strands during eah test an be used to evaluate whether the embedment length provided is greater than or less than the neessary development length. A series of tests, eah featuring a different loading onfiguration (and therefore embedment length), an be used to establish bounds for the development length harateristi of eah ombination of primary variables. For eah pair of beams in this test program, three tests (on Beam Ends A, B, and D) were used to evaluate the development length orresponding to the ombination of primary variables represented. The fourth test, onduted on End C, was used to evaluate the potential benefit of horizontal web reinforement on the anhorage behavior of the beam. In order to allow a diret omparison with the anhorage behavior without horizontal web reinforement, this fourth test usually featured a loading onfiguration idential to one of the other three tests. As explained in Chapter 3, the final term in eah test designation represents the embedment length tested (in inhes). For speimens with partially debonded strands, there are atually multiple embedment lengths for eah test. The embedment length for eah strand depends upon the debonded length of strand. If the speimen ontains debonded strands, the designated embedment length refers to the shortest embedded length of strand at the ritial setion, i.e. that of the group of strands with the longest debonded length. This group of strands is subjeted to the highest average bond stress under the test loading onfiguration. 7.3 TEST CONFIGURATION During development length testing, the I-beam speimen was supported so that the beam end not under investigation was free from the diret effets of applied load. One support was plaed beneath the beam end being tested; the other support was plaed in the interior region of the beam to limit damage to the far end of the beam. Therefore, the beam end not being tested was antilevered and isolated from the shear and moment resulting from the applied load. The beam was diretly supported on heavily reinfored, neoprene bearing pads of 3 in (76 mm) thikness whih rested on reinfored onrete pedestals. Eah pad was 11 in by 18 in (270 mm by 457 mm) in plan. Under the loads and deformations reorded during the test program, the pads were inapable of developing a horizontal thrust large enough to signifiantly affet either the applied moment or the moment resistane of the beam. The use of these bearing pads resulted in a gradual shortening of the effetive span length during eah development length test. Due to amber, the beam was effetively supported at the exterior of eah bearing pad prior to load appliation. As the beam deformed under the applied load, the setions at eah support rotated, and the effetive enter of support moved inward (in relation to the span). Due to the large rotations experiened after yielding at the 131

154 ritial setion, the beam was supported near the interior edge of eah bearing pad at the end of the test. The resulting shortening of the span length was somewhat offset by the outward shearing of the pads, but its magnitude was signifiant nonetheless. These effets an be seen in Figure 7.1. Aordingly, measurements were reorded during eah test and inorporated into moment alulations. Approximate Loation of Resultant Bearing Fore Outward Shearing of Neoprene Bearing Figure 7.1: Rotation of Beam Setion at Support and Shearing of Neoprene Bearing Pad Test L0B-A-96 at Final Load The test loading resulted from piston displaement of a hydrauli ylinder with a apaity of 2000 kips (8.9 MN). This ylinder was installed in the movable loading frame that an be seen in Figure 7.3. The resulting load was transferred to a steel spreader beam, whih in turn distributed the load to two steel ylinders spaed 36 in (305 mm) apart in the diretion of the span. These ylinders transferred the load to steel plates mounted on the dek of the omposite beam. These omponents of the load appliation system may be seen in Figure 7.2. The roller losest to the anhorage zone under investigation was plaed at the setion orresponding to the test embedment length. The hydrauli ram was positioned so that the region of the beam between the two rollers was subjeted to a nearly onstant maximum moment. The beam s weight preluded attainment of a perfetly onstant moment in this region. A shemati of the test geometry is presented in Figure 7.4. Figure 7.5 shows a test speimen under loading. Table 7.1 and Table 7.2 summarize the test onfigurations for all sixty development length tests performed at the Phil M. Ferguson Strutural Engineering Laboratory. 132

155 Figure 7.2: Load Appliation Components Test H0R-D-66 Hydrauli Cylinder Figure 7.3: Loading Frame and Hydrauli Cylinder Used to Apply Test Loads 133

156 l debond represents the longest jaketed length of strand; if no strands are debonded, l debond = 0, and l e is measured from the end of the beam l debond l e x P = Applied Load 36 Maximum Moment Region 6 l span (measured enter-to-enter of bearing pads) Figure 7.4: Configuration of Supports and Applied Load for Development Length Tests (1 in = 25.4 mm) Figure 7.5: Test H9R-C-96H under Load 134

157 Table 7.1: Test Configurations for Speimens Containing Bright Strand (1 in = 25.4 mm) Test I.D. Beam Length (in) l span (in) l debond (in) l e (in) x (in) L0B-A L0B-B L0B-C-54H L0B-D M0B-A M0B-B M0B-C-54H M0B-D H0B-A H0B-B H0B-C-54H H0B-D L4B-A (36, 0) L4B-B (36, 0) L4B-C-48H (36, 0) L4B-D (36, 0) M4B-A (36, 0) M4B-B (36, 0) M4B-C-56H (36, 0) M4B-D (36, 0) H4B-A (36, 0) H4B-B (36, 0) H4B-C-62H (36, 0) H4B-D (36, 0) L6B-A (72, 36, 0) L6B-B (72, 36, 0) L6B-C-84H (72, 36, 0) L6B-D (72, 36, 0) M9B-A (72, 36, 0) M9B-B (72, 36, 0) M9B-C-96H (72, 36, 0) M9B-D (72, 36, 0) H9B-A (72, 36, 0) H9B-B (72, 36, 0) H9B-C-96H (72, 36, 0) H9B-D (72, 36, 0)

158 Table 7.2: Test Configurations for Speimens Containing Rusted Strand (1 in = 25.4 mm) Test I.D. Beam Length (in) l span (in) l debond (in) l e (in) x (in) M0R-A (0) M0R-B (0) M0R-C-46H (0) M0R-D (0) H0R-A (0) H0R-B (0) H0R-C-46H (0) H0R-D (0) M4R-A (36, 0) M4R-B (36, 0) M4R-C-78H (36, 0) M4R-D (36, 0) H4R-A (36, 0) H4R-B (36, 0) H4R-C-72H (36, 0) H4R-D (36, 0) M9R-A (72, 36, 0) M9R-B (72, 36, 0) M9R-C-96H (72, 36, 0) M9R-D (72, 36, 0) H9R-A (72, 36, 0) H9R-B (72, 36, 0) H9R-C-96H (72, 36, 0) H9R-D (72, 36, 0) INSTRUMENTATION This setion onsists of a desription of the instruments used to measure the response of eah beam speimen to the applied deformation. Both primary and bakup systems are detailed below Measurement of Applied Load The load resulting from the applied deformation was measured between the hydrauli ylinder and the spreader beam by means of a 1000-kip (4.45 MN), shear-type load ell. This load ell was attahed to the piston of the hydrauli ylinder. A 5000 psi (34.5 MPa) pressure transduer served as a bakup instrument. The pressure transduer monitored the hydrauli pressure supplied to the ylinder by the air-powered pump. The load ell readings were later used in the alulation of setional moments and the resulting member stresses. 136

159 7.4.2 Measurement of Displaements The primary system of measuring speimen displaements onsisted of linear potentiometers. Shown in Figure 7.6, these potentiometers were used to measure the displaement of the beam relative to the floor in the maximum moment region. Vertial and horizontal support defletions were also measured with linear potentiometers. The displaement of the beam relative to the supports was alulated based on these olleted values. This alulated value was verified by means of the tension-wire system shown in Figure 7.7. This system featured a tensioned piano wire strung between anhor bolts at eah support, and a steel rule affixed to the beam midway between the two load points. The displaement of the beam relative to the supports was measured by reading the position of the piano wire relative to the rule with a preision of 0.01 in (0.25 mm). A mirror was employed to improve the onsisteny of readings. Unless otherwise noted defletions reported in this report represent the defletion, relative to a straight line onneting the supports, at the setion midway between the two points of load appliation. Figure 7.6: Linear Potentiometers Used to Measure Beam Defletion Steel Rule Wire = 4.33 in Original Position of Wire Relative to Beam Figure 7.7: Tension-Wire System for Measuring Beam Defletions Test H4R-C-72H at Final Load 137

160 7.4.3 Measurement of Strand Slip Strand slip was measured by means of linear potentiometers attahed to eah strand at the end of the beam. These potentiometers are shown in Figure 7.8 and Figure 7.9 along with potentiometers used to measure support deformations. The slips were measured relative to the end of the beam. For partially debonded strands, the strand slip relative to the beam end is not equivalent to the slip ourring at the end of the bonded length. The widths of raks opening along the jaketed length of strand are refleted in the potentiometer measurement, as well as the elasti elongation of the onrete along this length. In order to obtain an estimation of the true strand slip along the bonded length these quantities must be subtrated from the potentiometer reading. Crak widths in this region were reorded, and onrete strains along the debonded length were alulated and integrated to obtain an estimate of the onrete elongation. These values were subtrated from the potentiometer readings to obtain the values of strand end slip reported in this report. a b Figure 7.8: Linear Potentiometers Used to Measure a) Strand Slip and b) Horizontal Bearing Pad Deformation a b Figure 7.9: Linear Potentiometers Used to Measure a) Strand Slip, b) Horizontal Bearing Pad Deformation, and ) Vertial Support Displaement 138

161 7.4.4 Measurement of Strains at the Extreme Compression Fiber Compressive strains at the dek surfae were monitored throughout eah test in an effort to foresee the onset of dek onrete rushing prior to failure. These strains were measured with Eletrial Resistane Strain Gauges (ERSG s) with a 2.36 in (60 mm) gauge length. Originally, eight ERSG s were used in the maximum moment region of eah test. The gauges were arranged along the length and aross the width of the beam. Half of the gauges for one test are shown in Figure One it was verified that the ompressive strain was being reasonably well distributed aross the full width of the dek slab, only six gauges were used. These six gauges were arranged in three pairs along the length of the speimen between the load points. Spreader Beam Strain Gauges Figure 7.10: Four Strain Gauges Bonded to Conrete Dek for Measurement of Extreme Compression Fiber Strains Data Aquisition Upon operator demand, signal voltages from the eletroni instruments were read by a Hewlett Pakard HP3852A Data Aquisition/Control Unit. The voltage readings were then transmitted to a miroomputer, where they were reorded and onverted to engineering units. A hard opy of the data was printed during the ourse of the test as a bakup. An X-Y plotter was also used to graphially display the relationship between the applied load and the beam defletion during the test. 7.5 TEST PROCEDURE Prior to the start of eah test, the speimen was subjeted to several yles of load to verify that the eletroni instruments and data aquisition system were funtioning properly. The load applied during these yles was limited to approximately 25 perent of the antiipated flexural raking load. One the instruments were heked out and initial readings were reorded, testing ommened with the appliation of the first load inrement. Load was applied in regular inrements of 10 to 20 perent of the applied load antiipated to initiate flexural raking of the beam. At the end of eah predetermined load inrement, the displaement of the hydrauli ylinder was halted, and measurements were aquired from the various instruments, both manual and eletroni. One the data were aquired, appliation of load ommened again. As the applied load neared the antiipated flexural raking load, the load inrement was redued to 5 kips (22 kn) in an effort to aurately pinpoint this load. Observation of the first flexural rak signaled the end of the load inrement in progress. The orresponding load and defletion were reorded, and the rak pattern was photographed. These and all subsequent raks were marked with felt-tipped markers at the termination of eah load inrement. The raks were labeled with the orresponding ausative load level. Other observed events for whih the ongoing load inrement eased inluded the initiation of web shear raking, flexure-shear (or shear-flexure) raking, or raking within any strand transfer 139

162 zone. These events were also reorded photographially. In some of the speimens featuring short shear spans, web shear raking preeded flexural raking as expeted. Beyond the initiation of raking, regular inrements of load (usually on the order of 5 to 10 kips [22 to 44 kn]) were applied until attainment of a load level approximately orresponding to yield of the tensile reinforement in the maximum moment region. Beyond this load level, regular displaement inrements were utilized until the end of testing. Figure 7.11 depits a test speimen after signifiant yielding of tension reinforement. Load Cell Spreader Beam Figure 7.11: Test H4B-D-62 after Yield of Tension Reinforement In most ases, testing eased after the dek slab suffered a loal ompression failure. In a few instanes, testing eased prior to rushing of the slab. This usually ourred beause the beam had already exhibited the expeted flexural strength and further defletion was onstrained by the test setup. In other instanes, testing eased beause the researhers judged that the potential safety risk outweighed the value of any information yet to be gleaned from the test. After the ompletion of testing of one end of a beam, the beam supports were moved into position to test the strand anhorage at the opposite end of the beam. Every effort was made to position the supports for eah test so that the damage from the first test would not extend into the span of the seond test. Due to pratial limits on the total length of beam speimens and the desire for eah test to have a span long enough to ensure flexural behavior, this was often impossible. For the speimens with perent of strands debonded, some flexural raking from the first test extended into the span of the seond test. This appeared to have no effet on the results of the seond test other than the expeted dereased stiffness evidened by the load-defletion behavior. 7.6 ANALYSIS PROCEDURES Stresses and strains present in the test speimens prior to development length testing were omputed from analysis assuming elasti unraked response. Transformed setion properties were used rather than gross setion properties. Stress-strain relationships were based on the results of tests onduted on the materials used to fabriate the speimens. Relaxation of the prestressing steel was modeled as desribed by Collins and Mithell (1991; 90 92) for low-relaxation strand. Creep and shrinkage were addressed aording to the provisions of Artiles and of the AASHTO LRFD speifiations. Stresses and strains in the onrete and steel were alulated for eah speimen immediately prior to release, immediately after release, prior to asting the dek onrete, after the removal of dek shores, after the movement of supports, and immediately prior to development length testing. Differential shrinkage of the dek and beam onrete was onsidered in alulating all stresses and strains ourring after asting of the dek onrete. 140

163 Stress and moment-urvature analysis of the omposite beam during development length testing were performed using the layer-by-layer approah desribed by Collins and Mithell (1991; , ). The omposite beam ross setion was disretized into thin layers whih were analyzed individually as members subjeted to axial load. The relative deformations of these layers were onstrained by the plane setions remain plane hypothesis. The dek was subdivided into thirteen layers eah with a thikness of 0.5 in (12.7 mm). The preast beam setion was subdivided into twenty-eight layers eah with a thikness of 1.0 in (25.4 mm). Eah horizontal row of mild steel reinforement and prestressing strand was represented as an additional layer. Initial stresses and strains in eah layer were determined from the elasti unraked analysis desribed above. For eah assumed value of strain at the top fiber of the setion, the resulting urvature was alulated from equilibrium onditions, i.e. when the sum of the layer fores equaled the applied axial load of zero. One eah urvature was established, the orresponding moment was alulated by summing the individual moments resulting from the layer axial fores. By repeating this proess for a series of top fiber strains, the full raked setion moment-urvature response was obtained. The omplete ompressive stress-strain response of onrete was modeled aording to the generalized Thorenfeldt, Tomaszewiz, and Jensen expression (1987) desribed by Collins and Mithell (1991; 61 64). The ompressive strength and modulus of elastiity of onrete were obtained from ylinder tests and are reorded in Appendix B. The omplete stress-strain response of the prestressing steel was modeled aording to an expression developed from tensile tests of representative strand samples. The expression is given and plotted in Setion Aording to the general proedure given by Collins and Mithell (1991; ), tension stiffening was onsidered for prediting the load-defletion response of the omposite beam. After raking, onrete fibers loated within 7.5d b of reinforement were assigned average tensile stresses aording to the following relationship: f α = 1+ 1 f r 500ε where f = average stress in onrete α 1 = 1.0 for deformed reinforing bars α 1 = 0.7 for bonded strands f r = onrete raking stress = 7.5 f ε = onrete strain For members with partially debonded strands, moment-urvature analyses were performed for eah pattern of bonded reinforement present in the beam. The defletion response of the beam was then alulated from the urvatures orresponding to eah level of applied load. Appendix E ontains omparisons of the predited loaddefletion response and the experimentally obtained response for eah development length test. The load is plotted in terms of the moment at the ritial setion normalized with respet to the alulated moment apaity of the member. 7.7 PRESENTATION AND DISCUSSION OF TEST RESULTS This setion inludes the results of the sixty development length tests performed at the Ferguson Laboratory at the The University of Texas at Austin (UT). For purposes of disussion, the tests are divided into four groups depending upon the amount of debonding harateristi of eah speimen: 1. speimens with all strands fully bonded (L0B, M0B, H0B) 2. speimens with four strands partially debonded over the support (M0R, H0R) 3. speimens with 50% of bottom flange strands partially debonded (x4x) 4. speimens with more than 50% of strands partially debonded (x6x, x9x). Eah test is briefly desribed, and relevant quantitative results are tabulated. The behavioral response of the test speimens are ompared with existing ode provisions. Eah transfer length referred to in the test desriptions 141

164 below orresponds to the atual value obtained in the transfer length test program desribed in Chapter 5. Results of the development length tests performed at Texas Teh University (TTU) are disussed after eah set of orresponding UT tests Speimens with All Strands Fully Bonded Twelve development length tests were onduted at the Ferguson Laboratory on speimens ontaining only fully bonded strands. All of these speimens ontained bright strand. Four of these tests (those ast with L Series onrete) orresponded diretly with four tests onduted at Texas Teh University on speimens with rusted strands. This setion inludes brief desriptions of eah of these tests. Test results are tabulated in Table 7.3. The value of maximum slip reported in Table 7.3 is the largest strand end slip orresponding to the maximum moment resisted at the ritial setion. The value of ε max,al represents the alulated strain in the bottom row of strands at the alulated nominal moment resistane of the beam. This value was alulated using the analysis proedures desribed in Setion 7.6. For all speimens in whih no slip ourred, the apparent depth of the neutral axis (estimated from the depth of raking) and measured extreme fiber onrete strains indiated that the atual bottom row strand elongation was at least as large as the alulated value. For tests in whih end slip ourred, it is impossible to aurately alulate the atual strand strain beause little is known about the magnitude of the strand slip at the ritial setion. Thus, eah tabulated value serves as an indiation of the strand strain required to ahieve the full flexural apaity of eah speimen. Table 7.3: Development Length Test Results for Speimens with All Strands Fully Bonded (1 in = 25.4 mm) Test I.D. l l e M M test d, ACI al Failure Type Max. Slip (in) ε max,al L0B-A Flexural L0B-B Flex. w/ Slip L0B-D Flex. w/ Slip L0B-C-54H Flex. w/ Slip M0B-A Flexural M0B-B Flexural M0B-D Flex. w/ Slip M0B-C-54H Flex. w/ Slip H0B-A Flexural H0B-B Flexural H0B-D Flex. w/ Slip H0B-C-54H Flex. w/ Slip L0B-A-96 The embedment length, l e, for this test was 1.05 times the development length, l d,aci, alulated with the ACI/AASHTO expression. The speimen failed in a flexural manner. The maximum moment resisted, M test, was equivalent to the nominal moment resistane alulated based on strain ompatibility analysis, M al. No strand end slip was deteted during the test. At maximum load, no raks rossed the strands loser than 32 in (0.81 m) from the end of the transfer length (as obtained from the transfer length testing desribed in Chapter 5). First flexural raking ourred at a moment equal to 94 perent of the alulated raking moment. The pattern of raking orresponding to the maximum load is depited in Figure This rak pattern is typial of all the tests in this group that exhibited flexural failure with no bond slip. 142

165 l t 12 in l e = 1.05l d,aci Figure 7.12: Crak Pattern for Test L0B-A-96 at Flexural Failure L0B-B-72 For this test, l e = 0.78l d,aci. The beam failed in a flexural manner. A small slip of in (0.08 mm) ourred in one strand at an applied load greater than the alulated failure load. This slip initiated with the opening of a flexural rak 12 in (305 mm) from the transfer length. Web shear raks extended to the level of the strands at the enter of the support at peak load. The maximum moment resisted was 4 perent greater than the alulated nominal moment strength. First flexural raking ourred at a moment equal to 95 perent of the alulated raking moment L0B-D-54 This test exhibited a flexural failure with strand end slip in the exterior two strands only. This slip was initiated as shear raks extended to the beam soffit in front of the support (within the transfer length). The maximum slip at ultimate strength was in (0.20 mm). Figure 7.13 depits the anhorage region of the beam at the peak load. The maximum moment resisted was 2 perent greater than the alulated nominal moment strength. First flexural raking ourred at a moment equal to 97 perent of the alulated raking moment. For both this test and Test L0B-C-54H, l e = 0.58l d, ACI. Figure 7.14 illustrates the pattern of raking for this test at final load. This rak pattern is typial of all the tests in this group that exhibited a flexural failure with strand end slip. 143

166 Crak Corresponding to Initiation of Strand End Slip Transfer Length Figure 7.13: Test L0B-D-54 at Final Load l t 12 in l e = 0.58l d,aci Figure 7.14: Crak Pattern for Test L0B-D-54 at Flexural Failure with Strand Slip L0B-C-54H This test inluded horizontal web reinforement and also exhibited a flexural failure with strand end slip in the exterior two strands only. As in the ompanion test without horizontal web reinforement (L0B-D-54), slip was initiated by shear raks extending through the transfer length of the strands. Maximum slip was in (0.13 mm) at flexural failure. The maximum moment resisted was 4 perent greater than the alulated nominal moment strength. First flexural raking ourred at a moment equal to 97 perent of the alulated raking moment Corresponding Texas Teh Tests (L0R Series) Four of the development length tests onduted at Texas Teh University (TTU) orresponded to the four L0B Series tests summarized above, exept the TTU speimens featured rusted strand rather than bright strand (Burkett and Kose 1999). All four of the TTU tests exhibited flexural failures, and no strand end slip was deteted during any of the four tests. The strand end slips were measured manually, and the effetive preision of the measurements may have preluded the observation of slips as small as those ourring in the orresponding UT tests. Thus, it appears that the rusted strand speimens appeared to perform at least as well as the bright strand speimens. 144

167 M0B-A-96 This speimen, with l e = 1.05l d,aci, failed in a flexural manner. The maximum moment resisted was 2 perent greater than the alulated nominal moment resistane. No strand end slip was deteted during the test. At maximum load, no raks rossed the strands loser than 43 in (1.09 m) from the end of the transfer length. First flexural raking ourred at a moment equal to 99 perent of the alulated raking moment. Web shear raks extended to just above the strand depth at the support M0B-B-72 This speimen, with l e = 0.78l d,aci, also failed in a flexural manner. The maximum moment resisted was 2 perent greater than the alulated nominal moment resistane. No strand end slip was deteted during the test. At maximum load, no raks rossed the strands loser than 19 in (0.48 m) from the end of the transfer length. First flexural raking ourred at a moment 1 perent greater than the alulated raking moment. Web shear raks extended to the strand depth at the support M0B-D-54 M0B-D-54 and M0B-C-54H behaved similarly to L0B-D-54 and L0B-C-54H. This speimen, with l e = 0.58l d,aci, failed in a flexural manner with a maximum slip of in (0.38 mm). Slip ourred only in the two exterior strands of the bottom row and both the strands of the seond row. This end slip was initiated by shear raks at the support and shear raks extending through strands at a distane of 5 in from the transfer length. The maximum moment resisted was equal to the alulated nominal moment resistane. First flexural raking ourred at a moment 5 perent greater than the alulated raking moment M0B-C-54H This speimen, also with l e = 0.58l d,aci but ontaining horizontal web reinforement, failed in a flexural manner with a maximum slip of in (0.38 mm). Slip ourred only in the two strands of the seond row. This end slip was initiated by shear raks extending through the transfer length at the support. The maximum moment resisted was 3 perent greater than the alulated nominal moment resistane. First flexural raking ourred at a moment 5 perent greater than the alulated raking moment H0B-A-96 This speimen, with l e = 1.08l d,aci, failed in a flexural manner. The maximum moment resisted was 2 perent greater than the alulated nominal moment resistane. No strand end slip was deteted during the test. At maximum load, no raks rossed the strands loser than 45 in (1.14 m) from the end of the transfer length. First flexural raking ourred at a moment equal to 93 perent of the alulated raking moment. Web shear raks extended to the strand depth at the support H0B-B-72 This speimen, whih behaved muh like M0B-B-72, also failed in a flexural manner. The maximum moment resisted was 4 perent greater than the alulated nominal moment resistane. No strand end slip was deteted during the test. At maximum load, no raks rossed the strands loser than 28 in (0.71 m) from the end of the transfer length. First flexural raking ourred at a moment equal to 95 perent of the alulated raking moment. Web shear raks extended to the strand depth at the support H0B-D-54 This speimen, with l e = 0.60l d,aci, failed in a flexural manner with a maximum slip of in (0.38 mm). Slip ourred only in the strands of the seond row. Shear raks passed through the strands at the support prior to strand end slip. End slip initiated with flexural raking 20 in (0.51 m) from the end of the transfer length. The maximum 145

168 moment resisted was 1 perent greater than the alulated nominal moment resistane. First flexural raking ourred at a moment equal to 96 perent of the alulated raking moment H0B-C-54H This speimen, although reinfored with horizontal web steel in the anhorage region, failed in a manner similar to H0B-D-54. Failure was flexural with a maximum strand end slip of in (0.38 mm). Slip ourred only in the strands of the seond row. Shear raks passed through the strands at the support prior to strand end slip. End slip initiated with flexural raking 15 in (0.38 m) from the end of the transfer length. The maximum moment resisted was 2 perent greater than the alulated nominal moment resistane. First flexural raking ourred at a moment equal to 92 perent of the alulated raking moment Summary of Tests Performed on Speimens with All Strands Fully Bonded All speimens in this group failed in a flexural manner at moments equal to or exeeding the predited nominal moment. For the L-Series tests, general bond slip ourred for speimens with embedment lengths less than 0.8l d,aci. In the higher strength beams, general bond slip did not our in the tests with embedment lengths approximately equal to 0.8l d,aci, but did our in tests with embedment lengths approximately equal to 0.6l d,aci. No intermediate embedment lengths were tested. In the L0B and M0B tests, general bond slip was a diret result of raking in or near (within 20d b ) the transfer length. In addition to large flexural bond stresses, shear raking at the support may have ontributed to the general bond slip that ourred in the H0B tests. From these tests, it is apparent that the neessary development length for these speimens is less than that predited by the ACI/AASHTO expression for development length of fully bonded 0.6 in (15.2 mm) diameter strands. In order to more aurately assess the flexural bond performane of these speimens, it is helpful to ompare the flexural bond lengths tested to the flexural bond length from the ACI Code. This is done in an attempt to isolate the flexural bond behavior from the transfer bond behavior. In Figure 7.15, data are plotted from the tests in whih slip ourred. The ordinate of eah point represents f p, slip f pe. The numerator in this expression is the differene between the alulated tendon stress at the ritial f ps f pe setion when slip ours, f p,slip, and the effetive prestress prior to appliation of load, f pe. This numerator represents the portion of the tendon stress developed by flexural bond stresses at the ourrene of end slip. For equitable omparison with other speimens, this value is normalized with respet to f ps f pe, whih represents the inrease in strand stress that would be developed by flexural bond stresses at nominal flexural strength given adequate anhorage. The absissa of eah point represents the flexural bond length provided, le lt, normalized with respet to the flexural bond length implied by the ACI/AASHTO expression for the development length of fully bonded strands, l fb, ACI = ( f ps f pe ) db. The solid line represents the flexural bond length expression from Commentary Setion R12.9 of ACI if general bond slip is the aepted performane riterion. Thus, data above and to the left of the line indiate that the existing expression is a onservative preditor of the flexural bond length required to prevent general bond slip. Aordingly, the data from this group of tests indiate that the ACI Commentary expression is onservative with respet to general bond slip. 146

169 f p, slip f ps f f pe pe l e l t =, ( f p slip f pe ) d b L0B M0B H0B l l l e t fb, ACI Figure 7.15: Flexural Bond Performane of Fully Bonded Speimens Normalized Flexural Tendon Stress at Slip vs. Normalized Flexural Bond Length Provided In a manner similar to Figure 7.15, Figure 7.16 illustrates the onservatism of the Commentary expression for flexural bond length if ahievement of alulated nominal strength is the performane riterion. In this hart, the ordinate represents the portion of the tendon stress developed by flexural bond stresses at the maximum moment resisted during testing. The solid line represents the flexural bond length expression from Commentary Setion R12.9 of ACI with ahievement of the full nominal strength of the member (assuming adequate bond) as the performane riterion. All the tests of the group are represented in this hart, regardless of whether or not slip ourred. Beause the full flexural strength was obtained in all of these tests, the data indiate that the Commentary expression is quite onservative with respet to attainment of the nominal apaity alulated with the assumption of adequate bond. 1 1 This method of evaluating the effetiveness of the Commentary expression for flexural bond length is similar to the method applied by Mattok to the PCA data when developing this expression (Tabatabai and Dikson 1993). 147

170 f p,max f ps f f pe pe l l = e t ( f p pe ), max f d b L0B M0B H0B l l l e t fb, ACI Figure 7.16: Flexural Bond Performane of Fully Bonded Speimens Normalized Flexural Tendon Stress at Ultimate Strength vs. Normalized Flexural Bond Length Provided It should be noted that shear fores were extremely high in these speimens. In all speimens in whih general bond slip ourred, the slip initiated at levels of shear beyond that allowed by ACI , Setion (assuming a shear resistane fator, φ v, of unity). In other words, the shear demand in the anhorage region exeeded the onrete shear resistane, V, by more than 8 f bwd. Nonetheless, in the most shear-ritial of these tests, the alulated shear resistane provided aording the ACI/AASHTO Standard method, V n,aci, was approximately 13 perent larger than the maximum shear demand during testing, V max (φ v = 1). The shear resistane provided aording to the AASHTO LRFD setional method, V n,lrfd, was approximately 6 perent larger than V max. Thus, these speimens, partiularly those with the shortest embedment lengths, did not have an exess of shear reinforement. All strand end slips were limited to approximately in. Based on the limited number of tests performed, no definite orrelation between onrete strength and flexural bond resistane was evident. Based on a omparison with the orresponding Texas Teh tests, speimens with rusted strand behaved similarly to those with bright strand. Aside from reduing rak widths, the horizontal web reinforement did not appear to signifiantly enhane resistane to general bond slip Speimens with Four Strands Partially Debonded over Support Beause no bond failures ourred in the tests onduted on speimens ontaining only fully bonded strands, it was hypothesized that the large vertial support reation was preventing signifiant slip of the strands. Beause the moment resistane is approximately onstant for eah series of tests, the size of this lamping fore inreases with dereasing embedment length. In an effort to partially disount the benefiial effets of this fore, the four interior strands (A2, A3, A4, and A5) of the bottom row were debonded over a length of 12 in (305 mm) at the support in the speimens subjeted to the eight tests desribed in this setion. This short debonding was not performed to redue the stresses in the girder, but to redue the influene of the onfining pressure due to the large reation fore at the support. These eight tests were performed on the speimens ontaining rusted strands and ast with either M or H Series onrete. Table 7.4 inludes the results of these tests. 148

171 Table 7.4: Development Length Test Results for Speimens with Four Strands Partially Debonded over the Support (1 in = 25.4 mm) Test I.D. l l e M M test d, ACI al Failure Type Max. Slip (in) ε max,al M0R-A Flexural M0R-B Flex. w/ Slip M0R-D Flex. w/ Slip M0R-C-46H Bond H0R-A Flexural H0R-D Flexural H0R-B Bond H0R-C-46H Flex. w/ Slip M0R-A-96 This speimen behaved similarly to the fully bonded speimens with the same embedment length (l e = 1.04l d,aci ). The beam failed in a flexural manner with no strand end slip. The losest rak rossing the tendons was loated 40 in (1.02m) from the transfer length. No web shear raks extended into the bottom flange in the viinity of the transfer length. The maximum moment resisted was 4 perent greater than the alulated nominal moment resistane. First flexural raking ourred at a moment 4 perent greater than the alulated raking moment M0R-B-54 This speimen also exhibited a flexural type of failure, although end slip ourred in the four debonded strands (A3 and A4). This slip appeared to initiate with the opening of a flexural rak 11 in (0.28 m) from the transfer length of these strands. The two outer debonded strands (A2 and A5) slipped less than in (0.25 mm) prior to ahievement of flexural failure. The innermost strands (A3 and A4) gradually slipped up to approximately in (0.8 mm) at a load orresponding to a moment at the ritial setion 1 perent greater than the alulated nominal strength of the beam. At this point, an additional rak formed at the end of the transfer length, and the strands ontinued to slip with little inrease in moment resistane. The maximum moment ahieved was 2 perent greater than the alulated nominal moment resistane. Loss of apaity resulted from rushing of the dek onrete. The maximum strand slip at the maximum load was in (2.8 mm). No strand slip was reorded in the fully bonded strands, whih had an embedment length approximately equal to 0.7l d,aci. First flexural raking ourred at a moment 5 perent greater than the alulated raking moment M0R-D-46 The embedment length for this test (approximately half of the ACI/AASHTO development length for fully bonded strands) was shorter than any in the group of tests on speimens with only fully bonded strands. Although the failure type has been lassified above as a flexural failure with strand end slip, it might also be desribed as a dutile bond failure that ourred at the nominal flexural strength of the member. All four of the debonded strands slipped during the test. Initiation of slip orresponded to the extension of a shear rak to the soffit of the beam within the transfer length of the debonded strands. At an applied load orresponding to a moment within 0.5 perent of the alulated nominal strength of the beam, one of the innermost strands (A3) began to slip more rapidly than the rest. This strand slipped as muh as in (5.5 mm) prior to ahievement of maximum moment at the ritial setion with rushing of the dek. The other debonded strands slipped approximately in (1.0 mm). No end slip of the fully bonded strands was observed. The maximum moment was equal to the alulated nominal strength of the member. First flexural raking ourred at a moment 3 perent greater than the alulated raking moment. 149

172 M0R-C-46H This beam end was idential to that tested in M0R-D-46 exept for the addition of horizontal web reinforement. In this test, however, bond failure aused premature flexural failure. End slip of the four debonded strands initiated with flexural raking 40 in (1.02 m) from the end of the transfer length. A shear rak had already passed through the transfer length of the strands at a lower load. As in the previous test, the debonded strands slipped up to a maximum of in (1.0 mm) exept for one strand. This one strand (A4), began to slip more rapidly than the others at a moment approximately 10 perent less than the alulated nominal strength of the member. One the slip of this strand exeeded in (2.5 mm), no signifiant inrease in moment resistane was ahieved. The strand slipped a total of in (4.2 mm) at whih point a sudden slip of approximately in (1.3 mm) resulted in a drop in moment apaity. The peak moment (immediately prior to the sudden slip) was equal to 95 perent of the alulated moment apaity. After the sudden slip, the beam resisted a moment equal 92 perent of the alulated moment apaity before dek rushing. No slip of fully bonded strands was deteted. First flexural raking ourred at a moment equal to 99 perent of the alulated raking moment. Figure 7.17 shows the pattern of raking in the anhorage region at the end of the test. Transfer Length Debonded Length Figure 7.17: Craking in the Anhorage Region of M0R-C-46H at Final Load H0R-A-96 This test was very similar to M0R-A-96. Flexural failure ourred with no strand slip. The losest rak rossing the strands was loated 39 in (0.99 m) from the transfer length. The maximum moment resisted was 1 perent greater than the alulated nominal moment resistane. First flexural raking ourred at a moment equal to 95 perent of the alulated raking moment H0R-D-66 This test, whih featured an embedment length approximately equal to 0.7l d,aci, also exhibited a flexural failure with no strand slip. The losest rak rossing the strands was loated 14 in (0.36 m) from the transfer length. Two web shear raks extended to the depth of the strands over support. The maximum moment equaled the alulated moment apaity. Flexural raking ommened at a moment equal to 97 perent of the alulated raking moment. 150

173 H0R-B-46 Muh like M0R-C-46H, this test exhibited a premature flexural failure aused by a lak of bond apaity. End slip of all four debonded strands was initiated when a shear rak extended through the transfer length of the strands. Slip in these strands progressed slowly up to a magnitude of approximately in (0.9 mm) at a moment equal to 0.92M n,al. Slip of strands A3 and A4 then inreased rapidly with little inrease in resisted moment. The resisted moment remained fairly onstant throughout an additional defletion of approximately 0.6 in (15 mm) until rushing of the dek onrete ourred. Slip of strands A3 and A4 at rushing was approximately 0.50 in (13 mm). The maximum moment resisted was equal to 93 perent of the alulated moment apaity. First flexural raking ourred at a moment orresponding to 99 perent of the alulated raking moment. No slip of fully bonded strands was deteted. Figure 7.18 shows the pattern of raking in the anhorage region at ultimate strength. Transfer Length Debonded Length Figure 7.18: H0R-B-46 Anhorage Region after Final Load H0R-C-46H This speimen experiened a flexural failure aompanied by relatively small end slip of the debonded strands. This end slip initiated with a shear rak rossing the transfer length of the strands. The slip gradually inreased to a maximum of in (0.4 mm) at flexural failure. The maximum moment was equivalent to the alulated moment apaity of the beam. First flexural raking ourred at a moment orresponding to 97 perent of the alulated raking moment. No slip of fully bonded strands was deteted. Figure 7.19 shows the pattern of raking in the anhorage region of the beam at ultimate load. 151

174 Transfer Length Debonded Length Figure 7.19: H0R-C-46H Anhorage Region after Final Load Note that the rak pattern is quite similar to that of the previous test (Figure 7.18) despite the fat that H0R-B-46 failed due to inadequate bond strength. A omparison of these two tests seems to indiate that the horizontal web reinforement was effetive in preventing premature failure of H0R-C-46H, despite the influene of raking within the transfer length. The behavior of M0R-C-46H (depited in Figure 7.17) preludes this onlusion however. That test, whih exhibited raking very similar to that of both H0R-B-46 and H0R-D-46H, suffered a premature failure due to insuffiient bond apaity despite the presene of horizontal web reinforement. Its ompanion speimen without horizontal web reinforement, M0R-D-46, did not suffer a loss of apaity due to inadequate bond. Thus, the amount of horizontal web reinforement provided did not onsistently improve the anhorage behavior in these tests Summary of Tests Performed on Speimens with Four Strands Partially Debonded over Support For the strands debonded for 12 in (305 mm) over the support, general bond slip ourred in the tests where the provided embedment length was less than 70 perent of the ACI/AASHTO development length for debonded strands. No slip was deteted in any of fully bonded strands, whih had embedment lengths as short as 0.58l d,aci. This appears to indiate that the performane of the fully bonded rusted strands was better with respet to prevention of general bond slip than that of the fully bonded bright strands. The strand slip response of M0R-B-54 indiates that the rusted strands debonded over the support slipped signifiantly more than their bright, fully bonded ounterparts in Tests M0B-D-54 and M0B-C-54H. This is likely due to the large lamping fore present above the support that inreased the bond resistane of the strands bonded along this additional 12 in (305 mm) length. All strands appeared to be able to slip up to in ( mm) and still support inreases in strand stress. Beyond this level, strands tended to slip without inrease in load. Even if strands did slip, moment resistane only dropped slightly after slip (less than 3 perent of the nominal moment apaity) until the slab rushed. Figure 7.20 and Figure 7.21 depit the flexural bond behavior of these eight speimens with respet to ACI Commentary expression for development length. Figure 7.20 represents the addition of the data from this group of tests to the hart originally presented in Figure This hart indiates the onservatism of the Commentary expression if prevention of general bond slip is the performane riterion. Here again, these tests indiate that the expression onservatively predits the flexural bond length required to prevent general bond slip, even though the four strands were debonded for 12 in (305 mm) over the support. 152

175 f p, slip f ps f f pe pe l e l t =, ( f p slip f pe ) d b M0R H0R L0B M0B H0B l l l e t fb, ACI Figure 7.20: Flexural Bond Performane of Speimens with Four Strands Partially Debonded over Support Normalized Flexural Tendon Stress at Slip vs. Normalized Flexural Bond Length Provided Figure 7.21 is analogous to Figure 7.16 inluded in the disussion of the fully bonded test speimens. The results of this group of tests also indiate that the Commentary expression is very onservative if strength redution due to inadequate bond is the failure riterion. Although half of the primary tension reinforement was partially debonded, premature failures only ourred for speimens with less than half the flexural bond length for fully bonded strands aording to the ACI Commentary expression f p,max f ps f f pe pe l l = e t ( f p pe ), max f d b M0R H0R L0B M0B H0B l l l e t fb, ACI Figure 7.21: Flexural Bond Performane of Speimens with Four Strands Partially Debonded over Support Normalized Flexural Tendon Stress at Ultimate Strength vs. Normalized Flexural Bond Length Provided Exept for larger strand end slips in some speimens, the speimens with four strands debonded over the support exhibited flexural bond behavior quite similar to the speimens with all strands fully bonded. All of these speimens performed at least as well as the bond performane indiated by the ACI/AASHTO expression for development 153

176 length of fully bonded strands. Based on these results, it an be onluded that the anhorage performane of speimens reinfored with both fully bonded and partially debonded strands does not simply depend upon the perentage of strands debonded. Examining Figure 7.20 and Figure 7.21, it appears that onrete strength does not play a signifiant role in the flexural bond resistane of pretensioned strand. The influene of onrete strength on the overall development length seems effetively limited to the portion of the development length represented by the transfer length. Any influene of strand surfae ondition on the flexural bond behavior is also unlear. Strand end slips may have been slightly smaller for rusted strands than for the orresponding bright strands, but the surfae ondition did not seem to signifiantly affet the overall behavior of the member. As disussed above, the presene of horizontal web reinforement did not onsistently improve anhorage performane. In one ase, a speimen ontaining H-bars suffered a bond failure while the orresponding speimen without H-bars did not Speimens with 50 Perent of Bottom Flange Strands Partially Debonded This group of tests featured speimens with four partially debonded strands out of the eight strands in the bottom flange. Two fully bonded strands were required at the top of some of the beams in order to satisfy allowable stress requirements. The partially debonded strands lay in the bottom row. Two were debonded for 36 in (914 mm); two were debonded for 72 in (1829 mm). The two exterior strands of the bottom row and the two strands of the seond row were fully bonded. Further details regarding these speimens are reorded in Chapter 3. As disussed in Setion 3.3.1, these girders violated the provisions of the AASHTO LRFD Speifiation (1998) Artile beause 1) more than 25 perent of the strands were partially debonded, and 2) more than 40 perent of the strands in the bottom row were debonded. Test results for speimens with bright strands are tabulated in Table 7.5. Test results for speimens with rusted strands are tabulated in Table 7.6. In eah of these tables, there are two rows of data orresponding to eah test. The first row of the pair ontains data pertaining to the pair of strands debonded for 72 in (1829 mm); the seond ontains data pertaining to the pair of strands debonded for 36 in (914 mm). The fully bonded strands in these speimens did not exhibit end slip. The shortest embedment length of fully bonded strands in this group of tests ourred in Tests L4B-A-48 and L4B-C-48H. The 120 in (3.05 m) embedment length of fully bonded strands in these tests was approximately equal to 1.25l d,aci. The fat that no slip ourred in these strands agrees with the results obtained from tests on speimens ontaining only fully bonded strands, in whih slip only ourred in strands with an embedment length onsiderably less than l d,aci. 154

177 Table 7.5: Development Length Test Results for Speimens with 50% of Bottom Flange Strands Partially Debonded Bright Strands (1 in = 25.4 mm) Test I.D. L4B-B-96 L4B-D-60 L4B-A-48 L4B-C-48H M4B-A-60 M4B-D-56 M4B-C-56H M4B-B-48 H4B-D-62 H4B-C-62H H4B-A-56 H4B-B-50 Debonded Length (in) l e (in) l l e M M test d, ACI al Failure Type Max. Slip (in) Flexural Flex. w/ Slip Bond Bond Flex. w/ Slip Bond Flex. w/ Slip Bond Flex. w/ Slip Flex. w/ Slip Flex. w/ Slip Bond ε max,al

178 Table 7.6: Development Length Test Results for Speimens with 50% of Bottom Flange Strands Partially Debonded Rusted Strands (1 in = 25.4 mm) Test I.D. M4R-A-96 M4R-D-90 M4R-C-78H M4R-B-56 H4R-A-82 H4R-D-78 H4R-B-72 H4R-C-72H Debonded Length (in) l e (in) l l e M M test d, ACI al Failure Type Max. Slip (in) Flexural Flexural Flex. w/ Slip Bond Flexural Flexural Flex. w/ Slip Flex. w/ Slip ε max,al L4B-B-96 The shortest embedment length, l e, for this test was 1.02 times the development length, l d,aci, alulated with the ACI/AASHTO expression. Although the maximum moment resisted, M test, was slightly less than the alulated moment resistane, the speimen failed in a flexural manner, and no strand end slip was deteted. At maximum load, no raks rossed the strands loser than 22 in (0.56 m) from the end of the transfer length of the strands debonded for 72 in (1.83 m). Web shear raks opened above the transfer length of these strands, but these raks did not extend into the bottom flange of the beam. First flexural raking ourred at a moment equal to 98 perent of the alulated raking moment L4B-D-60 The shortest embedment length, l e, for this test was 0.64 times the development length, l d,aci, alulated with the ACI/AASHTO expression. The embedment length of the strands debonded 36 in (0.91 m) was 1.05l d,aci. The beam failed in a flexural manner, but both pairs of debonded strands slipped prior to ahieving the maximum moment resistane. The maximum moment resisted was 1 perent greater than the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 98 perent of the alulated raking moment. The first strands to slip were those with the shortest embedment length. The slip of these strands initiated with the opening of a shear-flexure rak within their transfer length when the moment at the ritial setion was 77 perent of the alulated failure moment. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 1.0 f ; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 5.3 f. Shear at the setion was equal to 1.04 times the web shear resistane of the onrete, V w, aording to ACI As more raks opened within the transfer length, the end slip of these strands inreased gradually to a magnitude of approximately 0.40 in (10 mm) under the maximum load. The transfer length raking is shown in Figure

179 72 in Debonded Length (to end of Beam) Transfer Length Figure 7.22: Test L4B-D-60 Shear-Flexure Craks within Transfer Length of Strands Debonded for 72 in (1.83 m) The strands with a debonded length of 36 in (0.91 m) began to slip when two shear-flexure raks opened within their transfer length. These raks ourred when the moment at the ritial setion was equal to the alulated moment strength of the beam. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 0.6 f ; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 7.2 f. Shear at the setion was equal to 1.44V w,aci. These strands slipped less than in (0.4 mm) prior to flexural failure of the beam L4B-A-48 The shortest embedment length, l e, for this test was 0.50 times the development length, l d,aci, alulated with the ACI/AASHTO expression. The embedment length of the strands debonded 36 in (0.91 m) was 0.90l d,aci. The beam failed prematurely due to insuffiient bond apaity, with end slip ourring in both pairs of debonded strands. The maximum moment resisted was equal to 94 perent of the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 94 perent of the alulated raking moment. The first strands to slip were those with the shortest embedment length. The slip of these strands initiated with the opening of a shear-flexure rak within their transfer length when the moment at the ritial setion was 72 perent of the alulated failure moment. At the rak loation, the alulated stress in the bottom fiber was equal to 49 psi (0.34 MPa) of ompression; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 5.1 f. Shear at the setion was equal to 1.02V w,aci. The end slip of these strands inreased gradually to a magnitude of approximately 0.50 in (13 mm) prior to ahievement of the maximum load. The beam held this load through an additional defletion of approximately 1 in (25 mm) prior to essation of testing. At the end of this additional defletion, the total slip of these strands was approximately 0.95 in (24 mm). The strands with a debonded length of 36 in (0.91 m) began to slip when a shear-flexure rak opened 12 in (305 mm) from their transfer length. This rak ourred when the moment at the ritial setion was equal to 82 perent of the alulated moment strength of the beam. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 5.3 f ; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 7.6 f. Shear at the setion was equal to 1.23V w,aci. These strands slipped gradually up to in 157

180 (1.0 mm) prior to ahievement of the maximum load. At the end of the test, these strands had slipped a total of in (1.5 mm) L4B-C-48H This speimen was idential to L4B-A-48 exept for the presene of horizontal web reinforement. The shortest embedment length, l e, for this test was 0.50 times the development length, l d,aci, alulated with the ACI/AASHTO expression. The embedment length of the strands debonded 36 in (0.91 m) was 0.90l d,aci. This speimen also failed prematurely due to insuffiient bond apaity, with end slip ourring in both pairs of debonded strands. The maximum moment resisted was equal to 98 perent of the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 96 perent of the alulated raking moment. The first strands to slip were those with the shortest embedment length. Just as in Test L4B-A-48, the slip of these strands initiated with the opening of a shear-flexure rak within their transfer length when the moment at the ritial setion was 72 perent of the alulated failure moment. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 2.2 f ; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 5.6 f. Shear at the setion was equal to 1.07V w,aci. The end slip of these strands inreased gradually to a magnitude of approximately 0.15 in (3.8 mm) orresponding to a defletion of approximately 2 in (50 mm) and a ritial setion moment equal to 96 perent of the alulated strength. The strands then slipped an additional 0.15 in (3.8 mm) while the beam defleted approximately 0.4 in (10 mm) without a signifiant inrease in moment resistane. The load then began to inrease again with inreasing strand slip and beam defletion until the maximum moment was reahed at a defletion of 3.8 in (97 mm) and a orresponding strand slip of 0.87 in (22 mm). A very slight derease in the resisted load ourred over the next 0.2 in (5 mm) of defletion at whih point the test was ended. The final strand slip was approximately 0.98 in (25 mm). The strands with a debonded length of 36 in (0.91 m) began to slip when a shear-flexure rak opened within their transfer length. This rak ourred when the moment at the ritial setion was equal to 85 perent of the alulated moment strength of the beam. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 2.3 f ; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 7.1 Shear at the setion was equal to 1.33V w,aci. These strands slipped gradually up to in (1.1 mm) prior to ahievement of the maximum load and the end of testing. Figure 7.23 depits the extent of raking in the anhorage region at the end of the test. f. l t of Strands Debonded 36 in l t of Strands Debonded 72 in Figure 7.23: Test L4B-C-48H Craking within Strand Transfer Lengths at Final Load 158

181 Corresponding Texas Teh Tests (L4R Series) The L4R pair of beams was tested at Texas Teh (Burkett and Kose 1999). These speimens were designed to be idential to the L4B pair exept that they were prestressed with rusted strand. The results of these four development length tests are summarized in Table 7.7. Table 7.7: Summary of Texas Teh Development Length Test Results for Speimens with 50% of Bottom Flange Strands Partially Debonded Rusted Strands (1 in = 25.4 mm) Test I.D. L4R-114 L4R-96 L4R-96H L4R-60 Debonded Length (in) l e (in) l l e d, ACI Failure Type Max. Slip (in) Flexural Flexural Flexural >1.0 Bond The results largely agree with those obtained from the L4B tests onduted at the Ferguson Laboratory. All tests featuring a shortest embedment length, l e, of 96 in (2.44 m) or more failed in a flexural manner with no strand end slip. The only differene between the two groups of tests is that the L4R-60 test failed prematurely due to a lak of bond apaity while the orresponding bright strand test (L4B-D-60) exhibited less strand slip and ahieved the alulated moment apaity. In this ase, rusted strand performed slightly worse than bright strand in terms of anhorage apaity. It is impossible to draw any onlusions regarding the effetiveness of the horizontal web reinforement from these tests beause both L4R-96 and L4R-96H were flexural failures with no strand slip M4B-A-60 The shortest embedment length, l e, for this test was 0.66 times the development length, l d,aci, alulated with the ACI/AASHTO expression. The embedment length of the strands debonded 36 in (0.91 m) was 1.07l d,aci. The beam failed in a flexural manner, but the pair of strands debonded for 72 in (1.83 m) slipped prior to ahieving the maximum moment resistane. The maximum moment resisted was 4 perent greater than the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 90 perent of the alulated raking moment. Strand end slip initiated with the opening of a shear-flexure rak within the transfer length when the moment at the ritial setion was 83 perent of the alulated failure moment. Figure 7.24 depits the extent of the rak immediately after it opened. At the rak loation, the alulated ompressive stress in the bottom fiber was equal to 120 psi = 1.1 f ; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 475 psi = 4.6 f. Shear at the setion was equal to 1.26V 2 w,aci. The end slip of these strands inreased gradually to a magnitude of approximately 0.47 in (12 mm) when the dek onrete rushed at the ritial setion under the maximum load. 2 Aording to the provisions of ACI , the value of f used in this alulation is limited to 100 psi for values of f greater than 10,000 psi. 159

182 The strands with a debonded length of 36 in (0.91 m) did not slip. No raks rossed these strands loser than 16 in (0.41 m) from the end of the transfer length. Web shear raking did not extend into the bottom flange in this region. Aording to unraked setion analysis, the bottom fiber of the beam was not yet in tension within this transfer length at maximum load. l t of Strands Debonded 72 in Figure 7.24: Test M4B-A-60 Shear-Flexure Crak within Transfer Length of Strands Debonded 72 in (1.83 m) M4B-D-56 The shortest embedment length, l e, for this test was 0.60 times the development length, l d,aci, alulated with the ACI/AASHTO expression. The embedment length of the strands debonded 36 in (0.91 m) was 1.01l d,aci. The beam failed prematurely due to insuffiient bond apaity, with end slip ourring in both pairs of debonded strands. The maximum moment resisted was equal to 97 perent of the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 87 perent of the alulated raking moment. The first strands to slip were those with the shortest embedment length. The slip of these strands initiated with the opening of two shear-flexure raks within their transfer length when the moment at the ritial setion was 77 perent of the alulated failure moment. At the rak loation, the alulated stress in the bottom fiber was approximately equal to 110 psi (0.76 MPa) of ompression; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 455 psi = 4.4 f. Shear at the setion was equal to 1.22V w,aci. The end slip of these strands inreased gradually to a magnitude of approximately 0.39 in (10 mm) prior to ahievement of the maximum load. The beam held this approximate load through an additional defletion of slightly more than 1 in (25 mm) prior to essation of testing. At the end of this additional defletion, the total slip of these strands was approximately 0.95 in (24 mm). The strands with a debonded length of 36 in (0.91 m) began to slip when a shear-flexure rak opened within their transfer length. This rak ourred when the moment at the ritial setion was equal to 91 perent of the alulated moment strength of the beam. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 240 psi (1.65 MPa) of ompression; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 530 psi = 5.1 f. Shear at the setion was equal to 1.54V w,aci. These strands slipped gradually up to in (2.5 mm) prior to ahievement of the maximum load and the slip then remained virtually onstant until the end of the test. 160

183 M4B-C-56H This speimen was idential to M4B-D-56 exept for the presene of horizontal web reinforement. The shortest embedment length, l e, for this test was 0.60 times the development length, l d,aci, alulated with the ACI/AASHTO expression. The embedment length of the strands debonded 36 in (0.91 m) was 1.01l d,aci. The beam failed in a flexural manner, with end slip ourring in both pairs of debonded strands. The maximum moment resisted was 1 perent greater than the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 87 perent of the alulated raking moment. The first strands to slip were those with the shortest embedment length. The slip of these strands initiated with the opening of a shear-flexure rak within their transfer length when the moment at the ritial setion was 74 perent of the alulated failure moment. At the rak loation, the alulated stress in the bottom fiber was approximately equal to 15 psi (0.09 MPa) of ompression; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 475 psi = 4.6 f. Shear at the setion was equal to 1.21V w,aci. The end slip of these strands inreased gradually to a magnitude of approximately 0.75 in (19 mm) prior to ahievement of the maximum load at the end of testing. The strands with a debonded length of 36 in (0.91 m) began to slip when a shear-flexure rak opened within their transfer length. This rak ourred when the moment at the ritial setion was equal to 86 perent of the alulated moment strength of the beam. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 440 psi (3.03 MPa) of ompression; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 450 psi = 4.4 f. Shear at the setion was equal to 1.44V w,aci. These strands slipped gradually up to in (0.8 mm) prior to the end of testing M4B-B-48 The shortest embedment length, l e, for this test was 0.52 times the development length, l d,aci, alulated with the ACI/AASHTO expression. The embedment length of the strands debonded 36 in (0.91 m) was 0.93l d,aci. The beam failed prematurely due to insuffiient bond apaity, with end slip ourring in both pairs of debonded strands. The maximum moment resisted was equal to 96 perent of the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 86 perent of the alulated raking moment. The first strands to slip were those with the shortest embedment length. The slip of these strands initiated with the opening of a shear-flexure rak within their transfer length when the moment at the ritial setion was 73 perent of the alulated failure moment. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 20 psi (0.14 MPa); the prinipal tensile stress at the juntion of the web and bottom flange was equal to 490 psi = 4.7 f. Shear at the setion was equal to 1.24V w,aci. The end slip of these strands inreased gradually to a magnitude of approximately 0.38 in (10 mm) at a beam defletion of 2.2 in (55 mm) orresponding to a ritial setion moment equal to 95 perent of the alulated moment apaity. The beam defleted an additional 2.0 in (50 mm) prior to rushing of the onrete dek. During this additional defletion, the moment resisted remained relatively onstant as the strands slipped an additional 0.63 in (16 mm). The peak moment orresponded to a umulative strand slip of 0.73 in (18.5 mm). The strands with a debonded length of 36 in (0.91 m) began to slip when a shear-flexure rak opened within their transfer length. This rak ourred when the moment at the ritial setion was equal to 90 perent of the alulated moment strength of the beam. At the rak loation, the alulated stress in the bottom fiber was equal to 140 psi (1.0 MPa) of ompression; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 580 psi = 5.6 f. Shear at the setion was equal to 1.63V w,aci. These strands slipped gradually up to in (1.0 mm) prior to ahievement of the maximum load. The slip then remained onstant until the end of testing H4B-D-62 The shortest embedment length, l e, for this test was 0.66l d,aci. The embedment length of the strands debonded 36 in (0.91 m) was 1.05l d,aci. The beam failed in a flexural manner, with end slip ourring in both pairs of debonded strands. The maximum moment resisted was 2 perent greater than the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 95 perent of the alulated raking moment. 161

184 The first strands to slip were those with the shortest embedment length. The slip of these strands initiated with the opening of two shear-flexure raks within their transfer length when the moment at the ritial setion was 88 perent of the alulated failure moment. These raks are shown in Figure At the rak loation, the alulated tensile stress in the bottom fiber was approximately equal to 160 psi = 1.5 f ; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 560 psi = 5.3 f. Shear at the setion was equal to 1.43V w,aci. The end slip of these strands inreased gradually to a magnitude of approximately 0.25 in (6.4 mm) prior to ahievement of the maximum load at a defletion of 4.0 in (100 mm). The beam defleted an additional 1.2 in (30 mm) without a signifiant loss in apaity prior to the end of the test. At the end of the test, the umulative strand slip was 0.70 in (17.8 mm). l t of Strands Debonded 72 in Figure 7.25: Test H4B-D-62 Shear-Flexure Craking within Transfer Length of Strands Debonded for 72 in (1.83 m) The strands with a debonded length of 36 in (0.91 m) began to slip when a shear-flexure rak opened within their transfer length. This rak ourred when the moment at the ritial setion was equal to 96 perent of the alulated moment strength of the beam. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 245 psi (1.69 MPa) of ompression; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 525 psi = 5.0 f. Shear at the setion was equal to 1.65V w,aci. These strands slipped gradually up to in (0.3 mm) prior to the end of testing. This shear-flexure rak an be seen at the far right of Figure 7.26, whih depits the extent of raking at the end of the test (for the beam fae opposite that shown in Figure 7.25). 162

185 Figure 7.26: Test H4B-D-62 Extent of Craking at End of Test H4B-C-62H The shortest embedment length, l e, for this test was 0.65l d,aci. The embedment length of the strands debonded 36 in (0.91 m) was 1.05l d,aci. The beam failed in a flexural manner, with end slip ourring in both pairs of debonded strands. The maximum moment resisted was 6 perent greater than the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 96 perent of the alulated raking moment. The first strands to slip were those with the shortest embedment length. The slip of these strands initiated with the opening of two shear-flexure raks within their transfer length when the moment at the ritial setion was 88 perent of the alulated failure moment. At the rak loation, the alulated tensile stress in the bottom fiber was approximately equal to zero; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 525 psi = 4.9 f. Shear at the setion was equal to 1.32V w,aci. The end slip of these strands inreased gradually to a magnitude of approximately 0.33 in (8.4 mm) prior to ahievement of the maximum load at a defletion of 4.5 in (113 mm). The beam defleted an additional 1.3 in (33 mm) without a signifiant loss in apaity prior to the end of the test. At the end of the test, the umulative stand slip was 0.65 in (16.5 mm). The strands with a debonded length of 36 in (0.91 m) began to slip when a shear-flexure rak opened within their transfer length. This rak ourred when the moment at the ritial setion was equal to 95 perent of the alulated moment strength of the beam. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 175 psi (1.21 MPa) of ompression; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 535 psi = 5.0 f. Shear at the setion was equal to 1.52V w,aci. These strands slipped gradually up to in (0.3 mm) prior to the end of testing. Despite the additional horizontal web reinforement present in this speimen, its behavior was very similar to that of H4B-D-62 desribed above H4B-A-56 The shortest embedment length, l e, for this test was equal to 0.60l d,aci. The embedment length of the strands debonded 36 in (0.91 m) was equal to 1.00l d,aci. The beam failed in a flexural manner, with end slip ourring only in the pair of strands debonded for 72 in (1.83 m). The maximum moment resisted was 1 perent greater than the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 91 perent of the alulated raking moment. Strand end slip initiated with the opening of a shear-flexure rak within the transfer length when the moment at the ritial setion was 83 perent of the alulated failure moment. At the rak loation, the alulated tensile stress 163

186 in the bottom fiber was approximately equal to 50 psi = 0.5 f ; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 540 psi = 5.1 f. Shear at the setion was equal to 1.38V w,aci. The end slip of these strands inreased gradually to a magnitude of approximately 0.46 in (12 mm) prior to ahievement of the load at the end of the test. The strands with a debonded length of 36 in (0.91 m) did not slip. At the final load, the nearest rak rossing the strands was loated 16 in (0.41 m) from the transfer length. Aording to unraked setion analysis, the bottom fiber of the beam was not yet in tension within this transfer length at maximum load H4B-B-50 The shortest embedment length, l e, for this test was equal to 0.54l d,aci. The embedment length of the strands debonded 36 in (0.91 m) was equal to 0.94l d,aci. The beam failed prematurely due to insuffiient bond apaity, with end slip ourring in both pairs of debonded strands. The maximum moment resisted was equal to 99 perent of the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 95 perent of the alulated raking moment. The first strands to slip were those with the shortest embedment length. The slip of these strands initiated with the opening of two shear-flexure raks within the transfer length when the moment at the ritial setion was 82 perent of the alulated failure moment. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 70 psi = 0.7 f ; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 560 psi = 5.3 f. Shear at the setion was equal to 1.41V w,aci. The end slip of these strands inreased gradually to a magnitude of approximately 0.20 in (5 mm) at a beam defletion of 2.0 in (50 mm) orresponding to a ritial setion moment equal to 98 perent of the alulated moment apaity. The beam defleted an additional 1.5 in (38 mm) until the test was stopped. During this additional defletion, the moment resisted remained relatively onstant as the strands slipped an additional 0.65 in (17 mm). The peak moment orresponded to a umulative strand slip of 0.40 in (10 mm). The strands with a debonded length of 36 in (0.91 m) began to slip when a shear-flexure rak opened within their transfer length. This rak ourred when the moment at the ritial setion was equal to 90 perent of the alulated moment strength of the beam. At the rak loation, the alulated stress in the bottom fiber was equal to 300 psi (2.07 MPa) of ompression; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 540 psi = 5.1 f. Shear at the setion was equal to 1.64V w,aci. These strands slipped gradually up to in (1.0 mm) prior to ahievement of the maximum load plateau. The slip then remained onstant until the end of testing M4R-A-96 The shortest embedment length, l e, for this test was equal to 1.05l d,aci. The maximum moment resisted was 3 perent greater than the alulated moment resistane. The speimen failed in a flexural manner, and no strand end slip was deteted. At maximum load, no raks rossed the strands loser than 29 in (0.74 m) from the end of the transfer length of the strands debonded for 72 in (1.83 m). Although the shear demand at maximum load was as high as 1.28V w,aci, there were no web shear raks in the anhorage region. First flexural raking ourred at a moment equal to 97 perent of the alulated raking moment M4R-D-90 The shortest embedment length, l e, for this test was equal to 0.97l d,aci. The maximum moment resisted was 1 perent greater than the alulated moment resistane. The speimen failed in a flexural manner, and no strand end slip was deteted. At maximum load, no raks rossed the strands loser than 27 in (0.69 m) from the end of the transfer length of the strands debonded for 72 in (1.83 m). Although the shear demand at maximum load was as high as 1.33V w,aci, there were no web shear raks in the anhorage region. First flexural raking ourred at a moment equal to 94 perent of the alulated raking moment. 164

187 M4R-C-78H The shortest embedment length, l e, for this test was equal to 0.84l d,aci. The embedment length of the strands debonded 36 in (0.91 m) was equal to 1.25l d,aci. The beam failed in a flexural manner, with end slip ourring only in the pair of strands debonded for 72 in (1.83 m). The maximum moment resisted was 3 perent greater than the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 91 perent of the alulated raking moment. Strand end slip initiated with the opening of a shear-flexure rak within the transfer length when the moment at the ritial setion was 99 perent of the alulated failure moment. At the rak loation, the alulated tensile stress in the bottom fiber was approximately equal to 335 psi = 3.2 f ; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 610 psi = 5.8 f. Shear at the setion was equal to 1.31V w,aci. The end slip of these strands inreased gradually to a magnitude of approximately in (2.2 mm) at the maximum load orresponding to rushing of the dek onrete. The strands with a debonded length of 36 in (0.91 m) did not slip. At the final load, the nearest rak rossing the strands was loated 27 in (0.69 m) from the transfer length. Aording to unraked setion analysis, the bottom fiber of the beam was not yet in tension within this transfer length at maximum load M4R-B-56 The shortest embedment length, l e, for this test was equal to 0.61l d,aci. The embedment length of the strands debonded 36 in (0.91 m) was equal to 1.03l d,aci. The beam failed prematurely due to insuffiient bond apaity, with end slip ourring only in the pair of strands debonded for 72 in (1.83 m). The maximum moment resisted was equal to 98 perent of the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 96 perent of the alulated raking moment. Strand end slip initiated with the opening of two shear-flexure raks within the transfer length when the moment at the ritial setion was equal to 84 perent of the alulated failure moment. At the rak loation, the alulated tensile stress in the bottom fiber was approximately equal to 205 psi = 2.0 f ; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 525 psi = 5.0 f. Shear at the setion was equal to 1.24V w,aci. The end slip of these strands inreased gradually to a magnitude of approximately in (6.4 mm) at a beam defletion of 2.45 in (62 mm) orresponding to a ritial setion moment equal to 98 perent of the alulated moment apaity. The beam defleted an additional 1.55 in (39 mm) until the test was stopped when the dek onrete began to rush. During this additional defletion, the moment resistane remained almost onstant as the strands slipped an additional 0.66 in (17 mm). The pair of strands with a debonded length of 36 in (0.91 m) did not slip. At the final load, the nearest rak rossing the strands was loated 8 in (0.20 m) from the transfer length. Aording to unraked setion analysis, the bottom fiber of the beam was not yet in tension within this transfer length at maximum load H4R-A-82 The shortest embedment length, l e, for this test was equal to 0.88l d,aci. Although the maximum moment resisted was slightly less than the alulated moment resistane, the speimen failed in a flexural manner, and no strand end slip was deteted. At maximum load, no raks rossed the strands that were debonded for 72 in (1.83 m) loser than 24 in (0.61 m) from the end of the transfer length. Although the shear demand at maximum load was as high as 1.47V w,aci, there were no web shear raks in the anhorage region. First flexural raking ourred at a moment equal to 89 perent of the alulated raking moment H4R-D-78 The shortest embedment length, l e, for this test was equal to 0.83l d,aci. The maximum moment resisted was equal to the alulated moment resistane, and the speimen failed in a flexural manner. No strand end slip was deteted. At maximum load, no raks rossed the strands that were debonded for 72 in (1.83 m) loser than 22 in (0.56 m) from the end of the transfer length. Although the shear demand at maximum load was as high as 1.51V w,aci, there were 165

188 no web shear raks in the anhorage region. First flexural raking ourred at a moment equal to 93 perent of the alulated raking moment H4R-B-72 The shortest embedment length, l e, for this test was equal to 0.77l d,aci. The embedment length of the strands debonded 36 in (0.91 m) was equal to 1.17l d,aci. The beam failed in a flexural manner, with end slip ourring only in the pair of strands debonded for 72 in (1.83 m). The maximum moment resisted was 1 perent less than the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 89 perent of the alulated raking moment. Strand end slip initiated with the opening of a shear-flexure rak within the transfer length when the moment at the ritial setion was 95 perent of the alulated failure moment. At the rak loation, the alulated tensile stress in the bottom fiber was approximately equal to 175 psi = 1.6 f ; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 555 psi = 4.8 f. Shear at the setion was equal to 1.37V w,aci. The end slip of these strands inreased gradually to a magnitude of approximately in (1.4 mm) at the maximum load orresponding to rushing of the dek onrete. The strands with a debonded length of 36 in (0.91 m) did not slip. At the final load, the nearest rak rossing these strands was loated 18 in (0.69 m) from the transfer length. Aording to unraked setion analysis, the bottom fiber of the beam was not yet in tension within this transfer length at maximum load H4R-C-72H The shortest embedment length, l e, for this test was equal to 0.77l d,aci. The embedment length of the strands debonded 36 in (0.91 m) was equal to 1.17l d,aci. The beam failed in a flexural manner, with end slip ourring only in the pair of strands debonded for 72 in (1.83 m). The maximum moment resisted was 2 perent greater than the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 88 perent of the alulated raking moment. Strand end slip initiated with the opening of a shear-flexure rak within the transfer length when the moment at the ritial setion was equal to the alulated failure moment. At the rak loation, the alulated tensile stress in the bottom fiber was approximately equal to 225 psi = 2.0 f ; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 590 psi = 5.1 f. Shear at the setion was equal to 1.39V w,aci. The end slip of these strands inreased gradually to a magnitude of approximately in (1.4 mm) at the maximum load orresponding to rushing of the dek onrete. The strands with a debonded length of 36 in (0.91 m) did not slip. At the final load, the nearest rak rossing these strands was loated 28 in (0.71 m) from the transfer length. Aording to unraked setion analysis, the bottom fiber of the beam was not yet in tension within this transfer length at maximum load Summary of Tests Performed on Speimens with 50 Perent of Bottom Flange Strands Partially Debonded Speimens in this group exhibited all three types of failures: flexural, flexural with strand slip, and bond. Loss of adequate anhorage strength resulting from inadequate bond only ourred in strands with a bonded embedment length of approximately 0.6 times the ACI development length for fully bonded strands. All strands with embedment lengths greater than 0.61l d,aci exhibited the required anhorage strength to develop the full flexural strength of the beam. For strand with a debonded length of 72 in (1.83 m), general bond slip only ourred when the bonded embedment length was less than 0.85l d,aci. For strand with a debonded length of 36 in (0.91 m), general bond slip only ourred when the bonded embedment length was less than or equal to 1.05l d,aci. Among strands with bonded embedment lengths between 0.85l d,aci and 1.0l d,aci, strands debonded 36 in (0.91 m) exhibited general bond slip, while strands debonded 72 in (1.83 m) did not. Regardless of performane riterion (prevention of slip or adequate strength), these results indiate that the neessary development length for these speimens is less than or approximately equal to l d,aci for fully bonded 166

189 strands. In order to remove the influene of the transfer length portion of the development length, the flexural bond performane of these speimens is illustrated in the next four figures. These graphs are formulated in the same manner desribed in Setion above for Figure 7.20 and Figure Figure 7.27 depits the flexural bond performane of the strands debonded for 72 in (1.83 m) in these speimens relative to the ACI Commentary expression when prevention of general bond slip is the assumed performane riterion. The Commentary expression appears to be a good indiator of the embedment length required to prevent general bond slip of these strands. The graph also indiates that neither strand surfae ondition nor onrete strength seems to signifiantly alter the flexural bond length required to prevent general bond slip f p, slip f ps f f pe pe l e l t =, ( f p slip f pe ) d b L4B M4B H4B M4R H4R l l l Figure 7.27: Flexural Bond Performane of Speimens with 50 Perent of Strands Partially Debonded Normalized Flexural Tendon Stress at Slip vs. Normalized Flexural Bond Length Provided Strands Debonded 72 in (1.83 m) Figure 7.28 shows the flexural bond performane of the strands debonded for 72 in (1.83 m) in these speimens relative to the ACI Commentary expression when adequate anhorage strength is the assumed performane riterion. For these strands, a flexural bond length equal to 75 perent of that alulated from the Commentary expression appears adequate to provide the anhorage strength that will result in a flexural failure mode. It is diffiult to draw any onlusions from these data regarding the influene of strand surfae ondition or onrete strength on the postslip behavior. e t fb, ACI 167

190 f p,max f ps f f pe pe l l = e t No slip ( f p pe ), max f d b L4B M4B H4B M4R H4R l l Figure 7.28: Flexural Bond Performane of Speimens with 50 Perent of Strands Partially Debonded Normalized Flexural Tendon Stress at Ultimate Strength vs. Normalized Flexural Bond Length Provided Strands Debonded 72 in (1.83 m) Figure 7.29 shows the flexural bond performane of the strands debonded for 36 in (0.91 m) relative to the ACI Commentary expression when prevention of general bond slip is the assumed performane riterion. One again, the strand surfae ondition and the onrete strength appear to have little influene on the flexural bond length required to prevent general bond slip. Unlike the 72 in (1.83 m) debonded strands, these strands appear to require a flexural bond length to prevent bond slip greater than that resulting from the ACI Commentary expression. Figure 7.30 indiates that the Commentary expression provides a flexural bond length adequate for development of the full flexural strength for the strands debonded 36 in (0.91 m) l e t fb, ACI f p, slip f ps f f pe pe l e l t =, ( f p slip f pe ) d b L4B M4B H4B M4R H4R l l l Figure 7.29: Flexural Bond Performane of Speimens with 50 Perent of Strands Partially Debonded Normalized Flexural Tendon Stress at Slip vs. Normalized Flexural Bond Length Provided Strands Debonded 36 in (0.91 m) e t fb ACI 168

191 f p,max f ps f f pe pe l l = e t No Slip ( f p pe ), max f d b L4B M4B H4B M4R H4R l l Figure 7.30: Flexural Bond Performane of Speimens with 50 Perent of Strands Partially Debonded Normalized Flexural Tendon Stress at Ultimate Strength vs. Normalized Flexural Bond Length Provided Strands Debonded 36 in (0.91 m) In this group of speimens, only a slight improvement in anhorage behavior resulted from the addition of horizontal web reinforement. Considering the pair of L4B speimens with l e = 48 in (1.22 m), both exhibited bond failures, but the speimen with horizontal web reinforement ahieved 98 perent of the alulated flexural strength ompared to 94 perent for the speimen without the H-bar. Test M4B-D-56 resulted in a bond failure at 97 perent of the flexural apaity while the ompanion test, M4B-C-56H, resulted in a ahievement of the flexural apaity with strand end slip. However, horizontal web reinforement was ineffetive as a means of inreasing the resistane to general bond slip in this group of tests. Beause of the larger shear spans that were harateristi of this group of tests, the shear demand was less than that in the tests on fully bonded speimens. In the most shear-ritial of these tests, V n,aci was approximately equal to 1.8V max throughout the anhorage region. V n,lrfd was approximately equal to 1.8V max near the support, and dereased to 1.4V max at the end of the 72 in (1.83 m) debonded length, where the ritial strand slip ourred. l e t fb ACI Speimens with More than 50 Perent of Strands Partially Debonded The speimens in this group had either 60 perent (L6x speimens) or 75 perent (M9x and H9x speimens) of the total strands debonded. The L6x speimens had only four fully bonded strands out of a total of ten. The M9x and H9x speimens had only three fully bonded strands out of a total of twelve. Three different debonding lengths, 36, 72, and 108 in (0.91, 1.83, and 2.74 m), were used in eah speimen. Further details regarding these speimens are reorded in Chapter 3. These girders violated the provisions of the AASHTO LRFD Speifiation (1998) Artile in the following ways: 1. More than 25 perent of the total number of strands were partially debonded. 2. More than 40 perent of the strands in several horizontal rows were partially debonded. 3. The debonding pattern was not symmetri in the M9x and H9x speimens. 4. Exterior strands in several of the rows were partially debonded. Test results for speimens with bright strands are tabulated in Table 7.8. Test results for speimens with rusted strands are tabulated in Table 7.9. In eah of these tables, there are two rows of data orresponding to eah test. The first row of the pair ontains data pertaining to the pair of strands debonded for 108 in (2.74 m); the seond ontains data pertaining to the pair of strands debonded for 72 in (1.83 m). 169

192 Neither the fully bonded strands or those with a debonded length of 36 in (0.91 m) exhibited signifiant end slip in these tests. The embedment length of these strands was not less than 1.6l d,aci in any of these tests. Based on the results of the previous groups of tests, no end slip was expeted for these strands, nor was it noted in the tests. Table 7.8: Development Length Test Results for Speimens with More than 50% of Bottom Flange Strands Partially Debonded Bright Strands (1 in = 25.4 mm) Test I.D. L6B-B-114 L6B-A-96 L6B-D-84 L6B-C-84H M9B-A-180 M9B-D-114 M9B-B-96 M9B-C-96H H9B-A-180 H9B-D-114 H9B-B-96 H9B-C-96H Debonded Length (in) l e (in) l l e M M test d, ACI al Failure Type Max. Slip (in) Flexural Flex. w/ Slip Flex. w/ Slip Flex. w/ Slip Flexural Flexural Flex. w/ Slip Flex. w/ Slip Flexural Flexural Bond Flex. w/ Slip ε max,al

193 Table 7.9: Development Length Test Results for Speimens with More than 50% of Bottom Flange Strands Partially Debonded Rusted Strands (1 in = 25.4 mm) Test I.D. M9R-A-180 M9R-D-114 M9R-B-96 M9R-C-96H H9R-A-180 H9R-D-114 H9R-B-96 H9R-C-96H Debonded Length (in) l e (in) l l e M M test d, ACI al Failure Type Max. Slip (in) Flexural Flexural Flex. w/ Slip Flex. w/ Slip Flexural Flexural Flex. w/ Slip Flex. w/ Slip ε max,al L6B-B-114 The shortest embedment length, l e, for this test was equal to 1.21l d,aci (for the strands with a debonded length of 108 in [2.74 m]). The maximum moment resisted was equal to the alulated moment resistane. The speimen failed in a flexural manner, and no strand end slip was deteted. First flexural raking ourred at a moment 2 perent greater than the alulated raking moment. No raking ourred in the anhorage region of the beam until the moment at the ritial setion was equal to 93 perent of the alulated moment apaity of the member. At this point, the shear-flexure rak shown in Figure 7.31 opened. This rak rossed through the bottom flange at the point where jaketing ended for the strands debonded 108 in (2.74 m). Therefore, this rak did not exert any anhorage demand on these strands. This rak rossed the strands at a distane of 24 in (0.61 m) from the transfer length of the strands that were jaketed for 72 in (1.83 in). Aordingly, this rak did not result in end slip of either group of debonded strands. 171

194 To support Maximum moment region Transfer length of strands debonded 108 in Figure 7.31: Test L6B-B-114 Crak Passing Aross Strands at End of 108 in (2.74 m) Debonded Length This rak is partiularly noteworthy beause of its position relative to the other raks present at the time it opened. As an be seen in Figure 7.31, the rak opened at a onsiderable distane from the flexural raks that were progressing out from the region of maximum moment. The rak opened where it did beause of the redued level of prestress fore present at that setion. Aordingly, the onrete resistane to flexural and shear raking was signifiantly less at this setion than at setions loser to the maximum moment region. Just prior to raking, the tensile stress in the bottom fiber was approximately equal to 415 psi = 5.0 f. The shear at the setion was only equal to 0.78V w,aci. However, the prinipal tensile stress due to ombined flexure and shear at the juntion of the web and the bottom flange was equal to 330 psi = 4.0 f. This level of stress is apable of ausing raking of onrete subjeted to a biaxial state of stress. This type of raking, whih begins at the juntion of the web and the bottom flange due to the interation of flexure and shear, ourred repeatedly in the test speimens of this group. However, resistane to this type of raking is not expliitly addressed in ACI or AASHTO ode provisions. In the formulation of the expression for onrete resistane to web shear raking, V w, raking is assumed to initiate due to shear when the prinipal tensile stress exeeds 4 f at the entroid of the omposite setion (or at the juntion of the web and the top flange if the entroid lies within the top flange). In the formulation of the expression for onrete resistane to flexure-shear raking, V i, raking is assumed to initiate at the extreme tensile fiber when the tensile stress exeeds 6 f. Neither of these expressions would have indiated the opening of the shear-flexure rak in this speimen beause the ritial loation in terms of prinipal tensile stress ourred at the bottom of the web due to shear-moment interation. Figure 7.32 shows the beam under the final test load. 172

195 Figure 7.32: Test L6B-B-114 Craks at Final Load L6B-A-96 The shortest embedment length, l e, for this test was equal to 1.03l d,aci. The embedment length of the strands debonded 72 in (1.83 m) was 1.43l d,aci. The beam failed in a flexural manner, but both pairs of debonded strands slipped prior to ahieving the maximum moment resistane. The maximum moment resisted was 6 perent greater than the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 99 perent of the alulated raking moment. The first strands to slip were not those with the shortest embedment length. The strands that were debonded for 72 in (1.83 m) started to slip with the opening of a shear-flexure rak within their transfer length when the moment at the ritial setion was equal to 90 perent of the alulated failure moment. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 145 psi = 1.7 f ; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 295 psi = 3.6 f. Shear at the setion was equal to 0.84V w,aci,. The end slip of these strands inreased gradually to a magnitude of approximately in (0.8 mm) under the maximum load. The strands with a debonded length of 108 in (2.74 m) began to slip when several shear-flexure raks opened within and near their transfer length. These raks ourred when the moment at the ritial setion was equal to 95 perent of the alulated moment strength. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 555 psi = 6.7 f ; the alulated prinipal tensile stress at the juntion of the web and bottom flange was equal to 410 psi = 4.9 f. Shear at the setion was equal to 0.85V w,aci. These strands slipped approximately in (0.8 mm) prior to flexural failure of the beam L6B-D-84 The shortest embedment length, l e, for this test was equal to 0.88l d,aci. The embedment length of the strands debonded 72 in (1.83 m) was 1.27l d,aci. The beam failed in a flexural manner, but both pairs of debonded strands slipped prior to ahieving the maximum moment resistane. The maximum moment resisted was 1 perent less than the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 96 perent of the alulated raking moment. The first strands to slip were those with the shortest embedment length. The strands with a debonded length of 108 in (2.74 m) began to slip when a shear-flexure rak opened within their transfer length. These raks ourred when the moment at the ritial setion was equal to 80 perent of the alulated moment strength. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 380 psi = 4.6 f ; the alulated prinipal 173

196 tensile stress at the juntion of the web and bottom flange was equal to 335 psi = 4.1 f. Shear at the setion was equal to 0.77V w,aci. These strands slipped approximately in (1.5 mm) prior to flexural failure of the beam. The strands that were debonded for 72 in (1.83 m) started to slip with the opening of a shear-flexure rak within their transfer length when the moment at the ritial setion was equal to 89 perent of the alulated failure moment. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 355 psi = 4.3 f ; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 375 psi = 4.5 f. Shear at the setion was equal to 0.89V w,aci,. The end slip of these strands inreased gradually to a magnitude of approximately in (2.0 mm) under the maximum load. The shear-flexure raks that initiated the strand slip of the two groups of debonded strands disussed above are shown in Figure The raking pattern of the beam at flexural failure is depited in Figure Transfer length of strands debonded 108 in Transfer length of strands debonded 72 in Figure 7.33: Test L6B-D-84 Shear-Flexure Craks within Transfer Lengths of Debonded Strands Figure 7.34: Test L6B-D-84 Craks at Final Load 174

197 L6B-C-84H The shortest embedment length, l e, for this test was equal to 0.88l d,aci. The embedment length of the strands debonded for 72 in (1.83 m) was 1.28l d,aci. The beam failed in a flexural manner, but both pairs of debonded strands slipped prior to ahieving the maximum moment resistane. The maximum moment resisted was 1 perent greater than the alulated moment resistane of the beam. First flexural raking ourred at a moment equal to 97 perent of the alulated raking moment. The strands with a debonded length of 108 in (2.74 m) began to slip when a shear-flexure rak opened within their transfer length. These raks ourred when the moment at the ritial setion was equal to 81 perent of the alulated moment strength. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 300 psi = 3.6 f ; the alulated prinipal tensile stress at the juntion of the web and bottom flange was equal to 310 psi = 3.8 f. Shear at the setion was equal to 0.73V w,aci. These strands slipped approximately in (1.9 mm) prior to flexural failure of the beam. The strands that were debonded for 72 in (1.83 m) also started to slip with the opening of a shear-flexure rak within their transfer length when the moment at the ritial setion was equal to 81 perent of the alulated failure moment. At the rak loation, the alulated tensile stress in the bottom fiber was equal to 265 psi = 3.2 f ; the prinipal tensile stress at the juntion of the web and bottom flange was equal to 315 psi = 3.8 f. Shear at the setion was equal to 0.81V w,aci,. The end slip of these strands inreased gradually to a magnitude of approximately in (1.0 mm) under the maximum load Corresponding Texas Teh Tests (L6R Series) The L6R pair of beams was tested at Texas Teh (Burkett and Kose 1999). These speimens were designed to be idential to the L6B pair exept that they were prestressed with rusted strand. The four development length tests onduted on these speimens orresponded exatly with the four L6B tests desribed above. The results of the TTU tests mathed those of the ompanion bright strand speimens very losely. The same failure mode was observed for eah orresponding test, and strand end slip values were approximately the same. These results indiate no signifiant differene in the anhorage performane of bright and rusted strands M9B-A-180 The shortest embedment length, l e, for this test was equal to 1.99l d,aci (for the strands with a debonded length of 108 in [2.74 m]). The maximum moment resisted was 1 perent greater than the alulated moment resistane. The speimen failed in a flexural manner, and no strand end slip was deteted. No rak rossed any strands within 79 in (2.01 m) of the transfer length. First flexural raking ourred at a moment equal to 99 perent of the alulated raking moment. In the transfer regions of debonded strands, tensile stresses at the bottom fiber were limited to approximately 3 f, and prinipal tensile stresses at the juntion of the web and the bottom flange were limited to less than 3 f at the maximum load. Figure 7.35 depits the raking pattern at the end of the test. l e = 1.99l d,aci # of Bonded Strands 12 in Figure 7.35: Crak Pattern for Test M9B-A-180 at Flexural Failure 175

198 M9B-D-114 This test, along with the other tests in this group featuring a shortest embedment length of 114 in (2.90 m), was fairly similar to Test L6B-B-114. The shortest embedment length was equal to 1.25l d,aci (for the strands with a debonded length of 108 in [2.74 m]). The embedment length of the strands that were debonded for 72 in (1.83 m) was equal to 1.66l d,aci. The maximum moment resisted was 1 perent greater than the alulated moment resistane. The speimen failed in a flexural manner, and no strand end slip was deteted. First flexural raking ourred at a moment equal to 99 perent of the alulated raking moment. At a load orresponding to a ritial setion moment equal to 84 perent of the alulated moment apaity, a shearflexure rak opened at the end of the 108 in (2.74 m) debonded length. This rak was very similar to the rak shown in Figure 7.31 above for Test L6B-B-114. As in that test, the rak did not ross the transfer length of any strands, and there was no aompanying strand slip. When this rak ourred, the alulated tensile stress in the bottom fiber at that loation was equal to 615 psi = 5.5 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 415 psi = 3.7 f. The shear fore was equal to 0.77V w,aci. Unlike Test L6B-B-114, a similar rak also opened at the end of the 72 in (1.83 m) debonded length at a load orresponding to a ritial setion moment equal to 91 perent of the alulated moment apaity. This rak also did not ross the transfer length of any strands, and there was no aompanying strand slip. The alulated tensile stress in the bottom fiber at that loation was equal to 580 psi = 5.2 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 445 psi = 4.0 f. The shear fore was equal to 0.86V w,aci M9B-B-96 The shortest embedment length was equal to 1.05l d,aci (for the strands with a debonded length of 108 in [2.74 m]). The embedment length of the strands that were debonded for 72 in (1.83 m) was equal to 1.49l d,aci. The maximum moment resisted was equal to the alulated moment resistane. The speimen failed in a flexural manner, and some strand end slip ourred in the debonded strands. First flexural raking ourred at a moment 2 perent greater than the alulated raking moment. At a load orresponding to a ritial setion moment equal to 82 perent of the alulated moment apaity, a shearflexure rak opened at the end of the 108 in (2.74 m) debonded length. The rak did not ross the transfer length of any strands, and there was no aompanying strand slip. When this rak ourred, the alulated tensile stress in the bottom fiber at that loation was equal to 735 psi = 6.6 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 460 psi = 4.2 f. The shear fore was equal to 0.79V w,aci. A similar rak also opened at the end of the 72 in (1.83 m) debonded length at a load orresponding to a ritial setion moment equal to 91 perent of the alulated moment apaity. This rak also did not ross the transfer length of any strands, and there was no aompanying strand slip. The alulated tensile stress in the bottom fiber at the initial rak loation was equal to 720 psi = 6.5 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 520 psi = 4.7 f. The shear fore was equal to 0.92V w,aci. At a load orresponding to a ritial setion moment equal to 93 perent of the alulated moment apaity, a shearflexure rak opened within the transfer length of the strands that were debonded for 108 in (2.74 m). These strands then proeeded to slip as muh as in (4.7 mm) prior to ahievement of the peak load. At the initiation of these transfer length raks, the alulated tensile stress in the bottom fiber at the initial rak loation was equal to 430 psi = 3.9 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 435 psi = 3.9 f. The shear fore was equal to 0.85V w,aci. At a load orresponding to a ritial setion moment equal to 96 perent of the alulated moment apaity, a shearflexure rak opened within the transfer length of the strands that were debonded for 72 in (1.83 m). These strands then proeeded to slip as muh as in (1.9 mm) prior to ahievement of the peak load orresponding to rushing of the dek onrete. At the initiation of these transfer length raks, the alulated tensile stress in the 176

199 bottom fiber at the initial rak loation was equal to 525 psi = 4.7 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 485 psi = 4.4 f. The shear fore was equal to 0.95V w,aci. Figure 7.36 depits the raking pattern at the end of this test. This pattern of raking was typial of the other tests in this group with l e = 96 in (2.44 m). l e = 1.05l d,aci # of Bonded Strands 12 in Figure 7.36: Crak Pattern for Test M9B-B-96 at Flexural Failure with Strand Slip M9B-C-96H The shortest embedment length was equal to 1.04l d,aci (for the strands with a debonded length of 108 in [2.74 m]). The embedment length of the strands that were debonded for 72 in (1.83 m) was equal to 1.46l d,aci. The maximum moment resisted was 3 perent greater than the alulated moment resistane. The speimen failed in a flexural manner, and some strand end slip ourred in the debonded strands. First flexural raking ourred at a moment 1 perent less than the alulated raking moment. At a load orresponding to a ritial setion moment equal to 80 perent of the alulated moment apaity, a shearflexure rak opened at the end of the 108 in (2.74 m) debonded length. The rak did not ross the transfer length of any strands, and there was no aompanying strand slip. When this rak ourred, the alulated tensile stress in the bottom fiber at that loation was equal to 700 psi = 6.3 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 450 psi = 4.1 f. The shear fore was equal to 0.77V w,aci. A similar rak also opened at the end of the 72 in (1.83 m) debonded length at a load orresponding to a ritial setion moment equal to 87 perent of the alulated moment apaity. This rak also did not ross the transfer length of any strands, and there was no aompanying strand slip. The alulated tensile stress in the bottom fiber at the initial rak loation was equal to 670 psi = 6.1 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 490 psi = 4.4 f. The shear fore was equal to 0.88V w,aci. At a load orresponding to a ritial setion moment equal to 94 perent of the alulated moment apaity, a shearflexure rak opened within 8 in (0.20 m) of the transfer length of the strands that were debonded for 72 in (1.83 m). These strands then proeeded to slip as muh as in (2.0 mm) prior to ahievement of the peak load orresponding to rushing of the dek onrete. At the initiation of these transfer length raks, the alulated tensile stress in the bottom fiber at the initial rak loation was equal to 530 psi = 4.8 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 460 psi = 4.1 f. The shear fore was equal to 0.92V w,aci. At a load orresponding to a ritial setion moment equal to 96 perent of the alulated moment apaity, a shearflexure rak opened within the transfer length of the strands that were debonded for 108 in (2.74 m). These strands then proeeded to slip as muh as in (1.3 mm) prior to ahievement of the peak load. At the initiation of these transfer length raks, the alulated tensile stress in the bottom fiber at the initial rak loation was equal to 177

200 755 psi = 6.8 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 545 psi = 4.9 f. The shear fore was equal to 0.90V w,aci H9B-A-180 The shortest embedment length, l e, for this test was equal to 1.95l d,aci (for the strands with a debonded length of 108 in [2.74 m]). Although the maximum moment resisted was 1 perent less than the alulated moment resistane, the speimen failed in a flexural manner, and no strand end slip was deteted. No rak rossed any strands within 74 in (1.88 m) of the transfer length. First flexural raking ourred at a moment equal to 94 perent of the alulated raking moment. In the transfer regions of debonded strands, tensile stresses at the bottom fiber were limited to less than 3 f, and prinipal tensile stresses at the juntion of the web and the bottom flange were limited to less than 3 f at the maximum load H9B-D-114 This speimen behaved very muh like M9B-D-114. The shortest embedment length was equal to 1.23l d,aci (for the strands with a debonded length of 108 in [2.74 m]). The embedment length of the strands that were debonded for 72 in (1.83 m) was equal to 1.67l d,aci. The maximum moment resisted was 2 perent greater than the alulated moment resistane. The speimen failed in a flexural manner, and no strand end slip was deteted. First flexural raking ourred at a moment equal to 97 perent of the alulated raking moment. At a load orresponding to a ritial setion moment equal to 82 perent of the alulated moment apaity, a shearflexure rak opened at the end of the 108 in (2.74 m) debonded length. As in previous tests with this embedment length, the rak did not ross the transfer length of any strands, and there was no aompanying strand slip. When this rak ourred, the alulated tensile stress in the bottom fiber at that loation was equal to 630 psi = 5.3 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 390 psi = 3.3 f. The shear fore was equal to 0.71V w,aci. A similar rak also opened at the end of the 72 in (1.83 m) debonded length at a load orresponding to a ritial setion moment equal to 92 perent of the alulated moment apaity. This rak also did not ross the transfer length of any strands, and there was no aompanying strand slip. The alulated tensile stress in the bottom fiber at that loation was equal to 675 psi = 5.7 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 465 psi = 3.9 f. The shear fore was equal to 0.83V w,aci. Figure 7.37 depits these raks, whih are typial of all the M9x and H9x tests with an embedment length of 114 in (2.90 m), at the final test load. 178

201 End of 108 in debonded length End of 72 in debonded length Figure 7.37: Test H9B-D-114 Craks at End of Strand Debonded Lengths (at Final Load) H9B-B-96 The shortest embedment length was equal to 1.04l d,aci (for the strands with a debonded length of 108 in [2.74 m]). The embedment length of the strands that were debonded for 72 in (1.83 m) was equal to 1.48l d,aci. The maximum moment resisted was equal to 97 perent of the alulated moment resistane. The speimen failed due to a loss of bond apaity. First flexural raking ourred at a moment approximately equal to the alulated raking moment. At a load orresponding to a moment at the ritial setion equal to 75 perent of the alulated moment apaity, a shear-flexure rak opened at the end of the 108 in (2.74 m) debonded length. The rak did not ross the transfer length of any strands, and there was no aompanying strand slip. When this rak ourred, the alulated tensile stress in the bottom fiber at that loation was equal to 610 psi = 5.2 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 390 psi = 3.3 f. The shear fore was equal to 0.69V w,aci. At a load orresponding to a moment at the ritial setion equal to 81 perent of the alulated moment apaity, a shear-flexure rak opened within the transfer length of the strands that were debonded for 72 in (1.83 m). Slip of these strands initiated with this rak. When this rak ourred, the alulated tensile stress in the bottom fiber at that loation was equal to 610 psi = 5.2 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 410 psi = 3.5 f. The shear fore was equal to 0.79V w,aci. The resulting slip inreased gradually with inreasing load resistane up to a magnitude of in (3.8 mm) when the maximum load was reahed (97 perent of the alulated beam apaity). At this point, two more raks opened within the transfer length, and this pair of strands began to slip very rapidly. The load resisted by the beam dereased immediately, and further appliation of defletion to the beam resulted in a larger redution in resistane as the slip ontinued to inrease. The maximum strain at the extreme ompression fiber was less than two-thirds of the typial value at whih rushing of the dek ourred in tests that failed in a flexural manner. Thus, the maximum resistane of the beam was ontrolled by the bond apaity of the strands rather than the deformation apaity of the dek onrete as it would have been in a flexural failure. The strands debonded for 108 in (2.74 m) began to slip when a shear-flexure rak opened within their transfer length at a load orresponding to a moment at the ritial setion equal to 92 perent of the alulated moment apaity. When this rak ourred, the alulated tensile stress in the bottom fiber at that loation was equal to 600 psi = 5.1 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 445 psi 179

202 = 3.8 f. The shear fore was equal to 0.83V w,aci. These strands slipped up to 0.040in (1.0 mm) prior to the maximum load, whih orresponded to the sudden slip of the strands debonded for 72 in (1.83m) H9B-C-96H The shortest embedment length was equal to 1.03l d,aci (for the strands with a debonded length of 108 in [2.74 m]). The embedment length of the strands that were debonded for 72 in (1.83 m) was equal to 1.47l d,aci. The maximum moment resisted was 2 perent higher than the alulated moment resistane. The speimen failed in a flexural manner, and some strand end slip ourred in the debonded strands. First flexural raking ourred at a moment approximately equal to the alulated raking moment. At a load orresponding to a ritial setion moment equal to 77 perent of the alulated moment apaity, a shearflexure rak opened at the end of the 108 in (2.74 m) debonded length. The rak did not ross the transfer length of any strands, and there was no aompanying strand slip. When this rak ourred, the alulated tensile stress in the bottom fiber at that loation was equal to 710 psi = 6.1 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 425 psi = 3.6 f. The shear fore was equal to 0.71V w,aci. A similar rak also opened at the end of the 72 in (1.83 m) debonded length at a load orresponding to a ritial setion moment equal to 80 perent of the alulated moment apaity. This rak also did not ross the transfer length of any strands, and there was no aompanying strand slip. The alulated tensile stress in the bottom fiber at the initial rak loation was equal to 620 psi = 5.3 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 420 psi = 3.6 f. The shear fore was equal to 0.77V w,aci. At a load orresponding to a ritial setion moment equal to 92 perent of the alulated moment apaity, a shearflexure rak opened within 2 in (50 mm) of the end of the transfer length of the strands that were debonded for 72 in (1.83 m). These strands then proeeded to slip as muh as in (1.5 mm) prior to ahievement of the peak load orresponding to rushing of the dek onrete. At the initiation of these transfer length raks, the alulated tensile stress in the bottom fiber at the initial rak loation was equal to 520 psi = 4.4 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 435 psi = 3.7 f. The shear fore was equal to 0.86V w,aci. At a load orresponding to a ritial setion moment equal to 96 perent of the alulated moment apaity, a shearflexure rak opened within the transfer length of the strands that were debonded for 108 in (2.74 m). These strands then proeeded to slip as muh as in (1.3 mm) prior to ahievement of the peak load. At the initiation of these transfer length raks, the alulated tensile stress in the bottom fiber at the initial rak loation was equal to 590 psi = 5.0 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 450 psi = 3.8 f. The shear fore was equal to 0.83V w,aci M9R-A-180 The shortest embedment length for this test was equal to 1.95l d,aci (for the strands with a debonded length of 108 in [2.74 m]). Although the maximum moment resisted was 1 perent less than the alulated moment resistane, the speimen failed in a flexural manner, and no strand end slip was deteted. No rak rossed any strands within 92 in (2.01 m) of the transfer length. First flexural raking ourred at a moment equal to 99 perent of the alulated raking moment. In the transfer regions of debonded strands, tensile stresses at the bottom fiber were limited to approximately 3.5 f, and prinipal tensile stresses at the juntion of the web and the bottom flange were limited to less than 3 f at the maximum load. 180

203 M9R-D-114 This speimen behaved very muh like M9B-D-114 and H9B-D-114. The shortest embedment length was equal to 1.23l d,aci (for the strands with a debonded length of 108 in [2.74 m]). The embedment length of the strands that were debonded for 72 in (1.83 m) was equal to 1.67l d,aci. The maximum moment resisted was 1 perent greater than the alulated moment resistane. The speimen failed in a flexural manner, and no strand end slip was deteted. First flexural raking ourred at a moment equal to the alulated raking moment. At a load orresponding to a ritial setion moment equal to 81 perent of the alulated moment apaity, a shearflexure rak opened at the end of the 108 in (2.74 m) debonded length. As in previous tests with this embedment length, the rak did not ross the transfer length of any strands, and there was no aompanying strand slip. When this rak ourred, the alulated tensile stress in the bottom fiber at that loation was equal to 530 psi = 4.6 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 365 psi = 3.2 f. The shear fore was equal to 0.71V w,aci. A similar rak also opened at the end of the 72 in (1.83 m) debonded length at a load orresponding to a ritial setion moment equal to 97 perent of the alulated moment apaity. This rak also did not ross the transfer length of any strands, and there was no aompanying strand slip. The alulated tensile stress in the bottom fiber at that loation was equal to 715 psi = 6.3 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 500 psi = 4.4 f. The shear fore was equal to 0.80V w,aci M9R-B-96 The shortest embedment length was equal to 1.04l d,aci (for the strands with a debonded length of 108 in [2.74 m]). The embedment length of the strands that were debonded for 72 in (1.83 m) was equal to 1.48l d,aci. The maximum moment resisted was 1 perent greater than the alulated moment resistane. The speimen failed in a flexural manner, and some strand end slip ourred in the debonded strands. First flexural raking ourred at a moment 3 perent larger than the alulated raking moment. At a load orresponding to a ritial setion moment equal to 75 perent of the alulated moment apaity, a shearflexure rak opened within transfer length of the strands that were debonded for 72 in (1.83 m). A small slip of these strands began with the opening of this rak. This strand slip gradually inreased to a magnitude of in (1.3 mm) at the final load. When this rak ourred, the alulated tensile stress in the bottom fiber at that loation was equal to 780 psi = 6.8 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 615 psi = 5.4 f. The shear fore was equal to 0.88V w,aci. At a load orresponding to a ritial setion moment equal to 83 perent of the alulated moment apaity, a shearflexure rak opened at the end of the 108 in (2.74 m) debonded length. The rak did not ross the transfer length of any strands, and there was no aompanying strand slip. When this rak ourred, the alulated tensile stress in the bottom fiber at that loation was equal to 785 psi = 6.9 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 480 psi = 4.2 f. The shear fore was equal to 0.79V w,aci. A similar rak also opened at the end of the 72 in (1.83 m) debonded length at a load orresponding to a ritial setion moment equal to 99 perent of the alulated moment apaity. This rak also did not ross the transfer length of any strands, and there was no aompanying strand slip. The alulated tensile stress in the bottom fiber at the initial rak loation was equal to 875 psi = 7.7 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 610 psi = 5.3 f. The shear fore was equal to 0.99V w,aci. At a load orresponding to a ritial setion moment equal to 98 perent of the alulated moment apaity, a shearflexure rak opened within the transfer length of the strands that were debonded for 108 in (2.74 m). These strands then proeeded to slip as muh as in (1.4 mm) prior to ahievement of the peak load. At the initiation of these transfer length raks, the alulated tensile stress in the bottom fiber at the initial rak loation was equal to 181

204 465 psi = 4.1 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 460 psi = 4.0 f. The shear fore was equal to 0.93V w,aci M9R-C-96H The shortest embedment length was equal to 1.04l d,aci (for the strands with a debonded length of 108 in [2.74 m]). The embedment length of the strands that were debonded for 72 in (1.83 m) was equal to 1.48l d,aci. The maximum moment resisted was 2 perent greater than the alulated moment resistane. The speimen failed in a flexural manner, and some strand end slip ourred in the debonded strands. First flexural raking ourred at a moment approximately equal to the alulated raking moment. At a load orresponding to a ritial setion moment equal to 78 perent of the alulated moment apaity, a shearflexure rak opened at the end of the 108 in (2.74 m) debonded length. The rak did not ross the transfer length of any strands, and there was no aompanying strand slip. When this rak ourred, the alulated tensile stress in the bottom fiber at that loation was equal to 720 psi = 6.3 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 440 psi = 3.8 f. The shear fore was equal to 0.76V w,aci. A similar rak also opened at the end of the 72 in (1.83 m) debonded length at a load orresponding to a ritial setion moment equal to 83 perent of the alulated moment apaity. This rak also did not ross the transfer length of any strands, and there was no aompanying strand slip. The alulated tensile stress in the bottom fiber at the initial rak loation was equal to 620 psi = 5.4 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 440 psi = 3.8 f. The shear fore was equal to 0.83V w,aci. At a load orresponding to a ritial setion moment equal to 97 perent of the alulated moment apaity, a shearflexure rak opened within the transfer length of the strands that were debonded for 108 in (2.74 m). These strands then proeeded to slip as muh as in (1.1 mm) prior to ahievement of the peak load. At the initiation of these transfer length raks, the alulated tensile stress in the bottom fiber at the initial rak loation was equal to 810 psi = 7.0 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 550 psi = 4.8 f. The shear fore was equal to 0.89V w,aci. At a load orresponding to a ritial setion moment equal to 101 perent of the alulated moment apaity, a shear-flexure rak opened within the transfer length of the strands that were debonded for 72 in (1.83 m). These strands then proeeded to slip as muh as in (1.8 mm) prior to ahievement of the peak load orresponding to rushing of the dek onrete. At the initiation of these transfer length raks, the alulated tensile stress in the bottom fiber at the initial rak loation was equal to 530 psi = 4.7 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 510 psi = 4.5 f. The shear fore was equal to 1.00V w,aci H9R-A-180 The shortest embedment length, l e, for this test was equal to 1.92l d,aci (for the strands with a debonded length of 108 in [2.74 m]). The maximum moment resisted was equal to the alulated moment resistane. The speimen failed in a flexural manner, and no strand end slip was deteted. No rak rossed any strands within 82 in (2.08 m) of the transfer length. First flexural raking ourred at a moment equal to 99 perent of the alulated raking moment. In the transfer regions of debonded strands, tensile stresses at the bottom fiber were limited to approximately 4.5 f, and prinipal tensile stresses at the juntion of the web and the bottom flange were limited to less than 3.2 f at the maximum load. 182

205 H9R-D-114 This speimen behaved very muh like M9B-D-114, H9B-D-114, and M9R-D-114. The shortest embedment length was equal to 1.23l d,aci (for the strands with a debonded length of 108 in [2.74 m]). The embedment length of the strands that were debonded for 72 in (1.83 m) was equal to 1.67l d,aci. The maximum moment resisted was 1 perent greater than the alulated moment resistane. The speimen failed in a flexural manner, and no strand end slip was deteted. First flexural raking ourred at a moment equal to the alulated raking moment. At a load orresponding to a ritial setion moment equal to 79 perent of the alulated moment apaity, a shearflexure rak opened at the end of the 108 in (2.74 m) debonded length. As in previous tests with this embedment length, the rak did not ross the transfer length of any strands, and there was no aompanying strand slip. When this rak ourred, the alulated tensile stress in the bottom fiber at that loation was equal to 530 psi = 4.4 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 360 psi = 3.0 f. The shear fore was equal to 0.72V w,aci. A similar rak also opened at the end of the 72 in (1.83 m) debonded length at a load orresponding to a ritial setion moment equal to 85 perent of the alulated moment apaity. This rak also did not ross the transfer length of any strands, and there was no aompanying strand slip. The alulated tensile stress in the bottom fiber at that loation was equal to 505 psi = 4.2 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 415 psi = 3.4 f. The shear fore was equal to 0.81V w,aci H9R-B-96 The shortest embedment length was equal to 1.02l d,aci (for the strands with a debonded length of 108 in [2.74 m]). The embedment length of the strands that were debonded for 72 in (1.83 m) was equal to 1.46l d,aci. The maximum moment resisted was 1 perent greater than the alulated moment resistane. The speimen failed in a flexural manner, and some strand end slip ourred in the debonded strands. First flexural raking ourred at a moment equal to the alulated raking moment. At a load orresponding to a ritial setion moment equal to 83 perent of the alulated moment apaity, a shearflexure rak opened at the end of the 108 in (2.74 m) debonded length. The rak did not ross the transfer length of any strands, and there was no aompanying strand slip. When this rak ourred, the alulated tensile stress in the bottom fiber at that loation was equal to 815 psi = 7.3 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 500 psi = 4.5 f. The shear fore was equal to 0.79V w,aci. A similar rak also opened at the end of the 72 in (1.83 m) debonded length at a load orresponding to a ritial setion moment equal to 101 perent of the alulated moment apaity. This rak also did not ross the transfer length of any strands, but three more raks immediately followed whih rossed the transfer length of the strands that were debonded for 72 in (18.3 m). The alulated tensile stress in the bottom fiber at the initial rak loation was equal to 935 psi = 8.4 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 635 psi = 5.7 f. The shear fore was equal to 1.00V w,aci. Strand slip of these strands aompanied the opening of these raks. The strand slip inreased with the transfer length raking up to a magnitude of in (4.1 mm) prior to ahievement of the maximum load when rushing of the dek onrete ourred. The strands that were debonded 108 in (2.74 m) may have slipped a small amount (less than in [0.4 mm]). Beause of the number of raks that rossed the jaketed portion of these strands, more preise alulation of the true slip values based on values measured at the end of the beam is diffiult H9R-C-96H The shortest embedment length was equal to 1.03l d,aci (for the strands with a debonded length of 108 in [2.74 m]). The embedment length of the strands that were debonded for 72 in (1.83 m) was equal to 1.46l d,aci. The maximum moment resisted was equal to the alulated moment resistane. The speimen failed in a flexural manner, and 183

206 some strand end slip ourred in the debonded strands. First flexural raking ourred at a moment approximately equal to the alulated raking moment. At a load orresponding to a ritial setion moment equal to 75 perent of the alulated moment apaity, a shearflexure rak opened at the end of the 108 in (2.74 m) debonded length. The rak, whih is shown in Figure 7.38, did not ross the transfer length of any strands, and there was no aompanying strand slip. When this rak ourred, the alulated tensile stress in the bottom fiber at that loation was equal to 630 psi = 5.2 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 400 psi = 3.3 f. The shear fore was equal to 0.72V w,aci. End of 108 in debonded length Figure 7.38: Test H9R-C-96H Crak at End of 108 in (2.74 m) Debonded Length A similar rak also opened at the end of the 72 in (1.83 m) debonded length at a load orresponding to a ritial setion moment equal to 84 perent of the alulated moment apaity. This rak also did not ross the transfer length of any strands, and there was no aompanying strand slip. The alulated tensile stress in the bottom fiber at the initial rak loation was equal to 660 psi = 5.4 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 470 psi = 3.9 f. The shear fore was equal to 0.84V w,aci. Both this rak and the rak at the end of the 108 in (2.74 m) debonded length are shown in Figure Note how isolated they are from the region of flexural raking in the onstant moment portion of the beam. This illustration indiates how the redution in effetive prestress fore that results from strand debonding an signifiantly redue raking resistane. 184

207 End of 72 in debonded length Flexural Craking in Constant Moment Region End of 108 in debonded length Figure 7.39: Test H9R-C-96H Craks at Ends of 72 (1.83 m) and 108 in (2.74 m) Debonded Lengths At a load orresponding to a ritial setion moment equal to 99 perent of the alulated moment apaity, shearflexure raking began within the transfer length of the strands that were debonded for 72 in (1.83 m). These strands began to slip and three raks rapidly formed in this transfer region. These strands slipped as muh as in (1.5 mm) prior to ahievement of the peak load orresponding to rushing of the dek onrete. At the initiation of these transfer length raks, the alulated tensile stress in the bottom fiber at the initial rak loation was equal to 600 psi = 4.9 f ; the prinipal tensile stress at the juntion of the web and the bottom flange was equal to 515 psi = 4.2 f. The shear fore was equal to 0.96V w,aci. Immediately after the opening of these raks and the aompanying strand slip, a rak opened within the transfer length of the strands that were debonded for 108 in (2.74 m). These strands also began to slip. The total slip in these strands was approximately in (0.9 mm) at the ahievement of the maximum load. The raking pattern at the end of the test is depited in Figure The general progression of raking and strand slip desribed here was typial of all the speimens in this group featuring embedment lengths of 96 in (2.44 m) or less. 185

208 End of 72 in debonded length End of 108 in debonded length Figure 7.40: Test H9R-C-96H Craks at Final Load (Flexural Failure with Strand Slip) Summary of Tests Performed on Speimens with More than 50 Perent of Strands Partially Debonded As for the previous group of tests, the anhorage behavior of the strands varied aording to the debonded length. For strand with a debonded length of 108 in (2.74 m), anhorage strength was adequate in all of the tests. For strand with a debonded length of 72 in (1.83 m), anhorage strength was adequate in all tests exept one, whih featured an embedment length equal to approximately 1.5l d,aci. Other speimens with embedment lengths as short as 1.3l d,aci resulted in flexural failures however. For strand with a debonded length of 108 in (2.74 m), general bond slip only ourred for strand with bonded embedment lengths less than or equal to 1.05l d,aci. For strand with a debonded length of 72 in (1.83 m), general bond slip ourred for embedment lengths up to 1.5l d,aci. Among strands with bonded embedment lengths between 1.05l d,aci and 1.5l d,aci, strands debonded 72 in (0.91 m) exhibited general bond slip, while strands debonded 108 in (2.74 m) did not. Figure 7.41 depits the flexural bond performane of the strands debonded for 96 in (2.74 m) relative to the ACI Commentary expression for fully bonded strands when prevention of general bond slip is the performane riterion. The Commentary expression appears to be slightly unonservative when used to predit the flexural bond length required to prevent general bond slip of these strands. Strand surfae ondition and onrete strength appear to have no signifiant influene on the required flexural bond length. 186