Technical Report Documentation Page 1. Report No. 2. Government Accession No. 3. Recipient's Catalog No. FHWA/TX-07/ 0-4759-1 4. Title and Subtitle 5. Report Date Rational Shear Provisions for AASHTO LRFD Specifications: October 2006 TECHNICAL REPORT Published: January 2007 6. Performing Organization Code 7. Author(s) 8. Performing Organization Report No. Arghadeep Laskar, Jun Wang, Thomas T. C. Hsu, and Y. L. Mo Report 0-4759-1 9. Performing Organization Name and Address 10. Work Unit No. (TRAIS) Department of Civil & Environmental Engineering Cullen College of Engineering 11. Contract or Grant No. University of Houston Project 0-4759 Houston, TX 77204-4003 12. Sponsoring Agency Name and Address 13. Type of Report and Period Covered Texas Department of Transportation Technical Report: Research and Technology Implementation Office September 2003 – August 2006 P. O. Box 5080 14. Sponsoring Agency Code A ustin, Texas 78763-5080 15. Supplementary Notes Project performed in cooperation with the Texas Department of Transportation and the Federal Highway Administration Project title: Rational Shear Provisions for AASHTO LRFD Specifications URL: http:// www.egr.uh.edu/structurallab/ 16. Abstract Prestressed concrete I-beams are used extensively as the primary superstructure components in Texas highway bridges. This research intends to solve one of the most troublesome problems in prestressed concrete, namely shear. The problem arises from the lack of a rational model to predict the behavior of prestressed concrete structures under shear action and the various modes of shear failures. Because of this deficiency, all the guidelines for shear design, such as ACI Codes and AASHTO Specifications, are empirical and have severe limitations. The research work was divided into two phases: Phase One consisted of developing the constitutive laws for prestressed concrete membrane elements and developing an analytical model for predicting the shear behavior of such elements. Crack simulation tests were first performed on rectangular prestressed beams to find the same cracking pattern of post-tensioned concrete with conduits as that in pre-tensioned concrete without conduits. Ten prestressed concrete panels (two series of five panels each) were tested. The first series of five panels was tested under sequential loading. The results of these tests were used to establish the constitutive relationships of materials (concrete and prestressing tendons). The second series of panels was tested under pure shear (a special case of proportional loading) to study the shear behavior of prestressed concrete membrane elements. Finally the Softened Membrane Model for Prestressed Concrete (SMM-PC) was developed to predict the response of prestressed concrete membrane elements under shear loading. Phase Two of the research dealt with testing of full-scale prestressed concreted I-beams and developing a new simplified equation for the shear design of prestressed concrete girders. Five TxDOT Type-A beams were designed, cast and tested to study their behavior in web shear and flexural shear failures. The results of these tests, along with the constitutive laws of prestressed concrete (developed in Phase One), were used to develop a new simplified equation for shear design of prestressed girders. Results of other prestressed beams available in literature were also considered to validate the design equation. The shear capacities of all the tested and referred beams were obtained using the new design equation and compared with the shear capacities obtained using ACI and AASHTO guidelines. Four design examples were prepared to illustrate the application of the new equation for design of prestressed girders. The new design equation was thereby extended to include non-prestressed girders. An example showing the design of a non-prestressed girder using the new equation was also completed. The research findings proved that the shear capacities of prestressed beams depended mainly on the compressive strength of concrete and the shear span to depth ratio of the beams. The effect of the amount of prestressing force and the angle of the failure planes of the beams on their shear capacities is insignificant. 17. Key Words 18. Distribution Statement Beams, Constitutive Laws, Shear Provisions, Prestressed No restrictions. This document is available to the public Concrete, Membrane Elements, Full-Scale Tests, Design through NTIS: Equation National Technical Information Service Springfield, Virginia 22161. www.ntis.gov and University of Houston, Houston, Texas 77204 www.egr.uh.edu/structurallab/ 19. Security Classif.(of this report) 20. Security Classif.(of this page) 21. No. of Pages 22. Price Unclassified Unclassified 216 Form DOT F 1700.7 (8-72) Reproduction of completed page authorized Rational Shear Provisions for AASHTO LRFD Specifications: Technical Report by Arghadeep Laskar Research Assistant Jun Wang Research Assistant Thomas T. C. Hsu Moores Professor and Y. L. Mo Professor Report 0-4759-1 Project 0-4759 Project Title: Rational Shear Provisions for AASHTO LRFD Specifications Performed in cooperation with the Texas Department of Transportation and the Federal Highway Administration October 2006 Published: January 2007 Department of Civil and Environmental Engineering University of Houston Houston, Texas iv DISCLAIMER This research was performed in cooperation with the Texas Department of Transportation and the U.S. Department of Transportation, Federal Highway Administration. The contents of this report reflect the views of the authors, who are responsible for the facts and accuracy of the data presented herein. The contents do not necessarily reflect the official view or policies of the FHWA or TxDOT. This report does not constitute a standard, specification, or regulation, nor is it intended for construction, bidding, or permit purposes. Trade names were used solely for information and not product endorsement. v ACKNOWLEDGEMENTS This research, Project 0-4759, was conducted in cooperation with the Texas Department of Transportation and the U.S. Department of Transportation, Federal Highway Administration. The project monitoring committee consisted of J. C. Liu (Program Coordinator), Jon Holt (Project Director), Tim Bradberry (Project Advisor), Amy Eskridge (Project Advisor), Mark Holt (Project Advisor), John Vogel (Project Advisor), and Tom Yarbrough (Project Advisor). The researchers would like to thank the Texas Concrete Company, Victoria, Texas, for continued co-operation during this project. The researchers are grateful to Chaparrel Steel Co. of Midlothian, Texas, for supplying the steel bars for this research. vi i vi ii TABLE OF CONTENTS Page CHAPTER 1 Introduction....................................................................................................1 1.1 Overview of Research....................................................................................................1 1.2 Objectives of Research..................................................................................................4 1.3 Outline of Report...........................................................................................................4 PART I: PRESTRESSED CONCRETE ELEMENTS CHAPTER 2 Backgrounds on Shear Theories of Reinforced and Prestressed Concrete Panels............................................................................................................9 2.1 Introduction....................................................................................................................9 2.2 Shear Theories of Reinforced Concrete in Literature....................................................9 2.3 Previous Studies by Research Group at UH................................................................12 2.3.1 Rotating-Angle Softened Truss Model (RA-STM).........................................15 2.3.2 Fixed-Angle Softened Truss Model (FA-STM)..............................................17 2.3.3 Softened Membrane Model (SMM).................................................................20 2.4 Literature Survey on Shear Behavior of Prestressed Concrete Panels........................27 CHAPTER 3 Crack Simulation Tests................................................................................29 3.1 General Description.....................................................................................................29 3.2 Test Program................................................................................................................31 3.3 Test Specimens............................................................................................................33 3.3.1 Fabrication of Specimens.................................................................................33 3.3.2 Tendon Jacking System...................................................................................37 3.4 Materials......................................................................................................................40 3.4.1 Concrete ..........................................................................................................40 3.4.2 Reinforcements................................................................................................40 3.5 Loading Procedure.......................................................................................................42 3.6 Test Results..................................................................................................................42 3.7 Conclusions..................................................................................................................46 CHAPTER 4 Prestressed Concrete 0-deg Panels Under Sequential Loading...............47 4.1 Test Program (Group TE)............................................................................................47 4.2 Test Specimens (Group TE).........................................................................................48 4.2.1 Layout of Specimens........................................................................................48 4.2.2 Fabrication of Specimens.................................................................................53 4.2.3 Tendon Jacking System...................................................................................56 4.3 Materials (Group TE)...................................................................................................56 4.3.1 Concrete ..........................................................................................................56 4.3.2 Reinforcements................................................................................................57 4.4 Loading Procedure (Group TE)...................................................................................57 4.5 General Behavior of Test Panels in Group TE............................................................58 4.5.1 Applied Tensile Stress-Strain Relationships....................................................59 4.5.2 Applied Compressive Stress-Strain Relationships...........................................61 4.6 Smeared (Average) Stress-Strain Relationships of Concrete in Tension....................62 4.6.1 Decompression.................................................................................................62 ix 4.6.2 Post-Decompression Behavior.........................................................................65 4.6.3 Mathematical Modeling of Smeared (Average) Stress-Strain Curve of Concrete in Tension.....................................................................................65 4.7 Smeared (Average) Stress-Strain Relationships of Prestressing Tendons Embedded in Concrete.................................................................................................71 4.8 Smeared (Average) Stress-Strain Relationships of Concrete in Compression............76 CHAPTER 5 Prestressed Concrete 45-deg Panels Under Pure Shear (Proportional Loading) ..........................................................................................................83 5.1 Test Program (Group TA)............................................................................................83 5.2 Test Specimens (Group TA)........................................................................................84 5.2.1 Layout of Specimens........................................................................................84 5.2.2 Fabrication of Specimens.................................................................................87 5.2.3 Tendon Jacking System...................................................................................90 5.3 Materials (Group TA)..................................................................................................92 5.3.1 Concrete ..........................................................................................................92 5.3.2 Reinforcements................................................................................................92 5.4 Loading Procedure (Group TA)...................................................................................93 5.5 General Behavior of Test Panels in Group TA............................................................94 5.5.1 Cracking Behavior...........................................................................................94 5.5.2 Yielding of Steel..............................................................................................95 5.5.3 Shear Stress vs. Shear Strain Relationships (τ −γ Curves)........................97 lt lt 5.5.4 Shear Stress vs. Principal Tensile Strain Relationships (τ −ε Curves).......98 lt 1 5.5.5 Shear Stress vs. Principal Compressive Strain Relationships (τ −ε Curves)............................................................................................100 lt 2 5.6 Smeared (Average) Stress-Strain Relationships of Concrete in Compression..........102 5.6.1 Experimental Curves for Prestressed Concrete..............................................102 5.6.2 Mathematical Modeling of Smeared (Average) Stress-Strain Curve of Prestressed Concrete in Compression............................................................105 CHAPTER 6 Analytical Models of Prestressed Concrete Panels.................................115 6.1 Introduction................................................................................................................115 6.2 Fundamentals of Softened Membrane Model for Prestressed Concrete....................115 6.2.1 Equilibrium and Compatibility Equations.....................................................116 6.2.2 Biaxial Strains vs. Uniaxial Strains...............................................................117 6.2.3 Constitutive Relationships of Concrete in Prestressed Elements..................118 6.2.4 Constitutive Relationships of Reinforcements...............................................120 6.2.5 Solution Algorithm........................................................................................121 6.3 Applications of SMM-PC to Test Panels TA-1 to TA-5...........................................124 PART II: SHEAR IN PRESTRESSED CONCRETE BEAMS CHAPTER 7 Shear Tests of Prestressed Concrete Beams............................................129 7.1 Introduction................................................................................................................129 7.2 Test Program..............................................................................................................129 7.3 Test Specimens..........................................................................................................135 x