Recommended LRFD Minimum Flexural Reinforcement Requirements (2010)

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ACKNOWLEDGMENT This work was sponsored by the American Association of State Highway and Transportation Officials (AASHTO), in cooperation with the Federal Highway Administration, and was conducted in the National Cooperative Highway Research Program (NCHRP), which is administered by the Transportation Research Board (TRB) of the National Academies. COPYRIGHT PERMISSION Authors herein are responsible for the authenticity of their materials and for obtaining written permissions from publishers or persons who own the copyright to any previously published or copyrighted material used herein. Cooperative Research Programs (CRP) grants permission to reproduce material in this publication for classroom and not-for-profit purposes. Permission is given with the understanding that none of the material will be used to imply TRB, AASHTO, FAA, FHWA, FMCSA, FTA, Transit Development Corporation, or AOC endorsement of a particular product, method, or practice. It is expected that those reproducing the material in this document for educational and not-for-profit uses will give appropriate acknowledgment of the source of any reprinted or reproduced material. For other uses of the material, request permission from CRP. DISCLAIMER The opinion and conclusions expressed or implied in the report are those of the research agency. They are not necessarily those of the TRB, the National Research Council, AASHTO, or the U.S. Government. This report has not been edited by TRB.

i   CONTENTS Contents ............................................................................................................................................ i  Author Acknowledgements ............................................................................................................ iv  Abstract ........................................................................................................................................... v  Summary ......................................................................................................................................... 1  Chapter 1 Introduction and Research Approach ............................................................................ 6  1.1 Problem Statement............................................................................................................... 6  1.2 Research Objectives ............................................................................................................ 8  1.3 Research Tasks .................................................................................................................... 8  1.4 Research Work Plan .......................................................................................................... 10  1.4.1 Refine the Modified LRFD Method ........................................................................... 10  1.4.2 Perform the Parametric Study .................................................................................... 10  1.4.3 Evaluate the Statistical Parameters of Minimum Flexural Reinforcement ................. 10  1.5   Key Definitions .................................................................................................................. 11  Chapter 2   Findings ....................................................................................................................... 12  2.1   Observed Response of Lightly Reinforced Concrete and Prestressed Concrete Members 12  2.2   Flexural Tensile Strength ................................................................................................... 16  2.2.1   Direct Testing of Concrete Fracture in Tension ......................................................... 16  2.2.2   Modulus of Rupture .................................................................................................... 17  2.2.3   Size Effects on the Flexural Cracking Strength .......................................................... 19  2.3 Statistical Analysis of Concrete Flexural Strength ............................................................ 22  2.3.1 Analysis Methods ....................................................................................................... 22  2.3.3 Modulus of Rupture .................................................................................................... 22  2.3.3 Full-Size Member Cracking Strength ......................................................................... 24  2.3.4 Prestressed Variability ................................................................................................ 25 

ii   2.3.5 Summary of Statistical Analysis of Flexural Cracking Strength ................................ 26  2.4   Methods and Procedures for Developing Minimum Reinforcement ................................. 26  2.4.1 AASHTO LRFD ......................................................................................................... 27  2.4.2 AASHTO Segmental Guide Specifications ................................................................ 31  2.4.3 ACI 318 ...................................................................................................................... 32  2.4.4 Freyermuth and Aalami—CEB-FIP ........................................................................... 34  2.4.5 International Practice .................................................................................................. 36  2.4.6 Leonhardt’s Method ................................................................................................... 39  2.4.7 Modified LRFD Method ............................................................................................. 42  2.4.8   Comparison of Minimum Flexural Reinforcement Provisions ................................... 46  Chapter 3   Interpretation, Appraisal and Application ................................................................... 48  3.1 Parametric Study of Minimum Reinforcement Provisions ................................................ 48  3.1.1 Concrete Structures Database ..................................................................................... 49  3.1.2 Minimum Flexural Reinforcement ............................................................................. 56  3.1.3 Cracking Moment (Mcr) .............................................................................................. 61  3.1.4   Nominal Moment at Overstrength (Mo) ...................................................................... 61  3.1.5   Parametric Study Results ............................................................................................ 61  3.1.6   Recommendations ....................................................................................................... 63  3.2   Proposed Revisions to the AASHTO LRFD Specifications .............................................. 64  3.3 Design Examples ............................................................................................................... 68  3.3.1 Multi-Span Precast Concrete Girder Made Continuous with Composite Deck ......... 68  3.3.2 Cast-in-Place Concrete Box Girder ............................................................................ 69  3.3.3 Span-by-Span Segmental Bridge with External Tendons .......................................... 71  3.3.4 Balanced Cantilever Bridge with Internal Tendons .................................................... 73  3.3.5 Cap Beam ................................................................................................................... 75  Chapter 4 Conclusions and Suggested Research ......................................................................... 77 

iii   4.1   Conclusions ........................................................................................................................ 77  4.1.1 Conclusions on the Observed Response of Lightly Reinforced and Prestressed Concrete Members ................................................................................................................ 77  4.1.2 Conclusions on the Review of US and International Practice .................................... 78  4.1.3   Conclusions on the Parametric Study ......................................................................... 79  4.2 Suggested Research ........................................................................................................... 79  References ..................................................................................................................................... 80  Appendix A Parametric Study Results Appendix B Design Examples