FINAL REPORT RELIABILITY VALIDATION OF HIGHWAY BRIDGES DESIGNED BY LRFD RRRReeeesssseeeeaaaarrrrcccchhhh RRRReeeeppppoooorrrrtttt NNNNoooo.... FFFFLLLL////DDDDOOOOTTTT////RRRRMMMMCCCC////6666666677772222----888811114444 CCCCoooonnnnttttrrrraaaacccctttt NNNNoooo.... 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Recipient's Catalog No. FL/DOT/RMC/6672-814 4. Title and Subtitle 5. Report Date March 2002 Reliability Validation of Highway Bridges Designed by LRFD 6. Performing Organization Code 7. Author(s) 8. Performing Organization Report No. Ton-Lo Wang and Chunhua Liu 9. Performing Organization Name and Address 10. Work Unit No. Florida International University Department of Civil and Environmental Engineering 11. Contract or Grant No. University Park BC-814 Miami, Florida 33199 13. Type of Report and Period Covered 12. Sponsoring Agency Name and Address Final Report October 2000 – March 2002 Florida Department of Transportation Research Center, MS30 14. Sponsoring Agency Code 605 Suwannee Street 99700-3596-119 Tallahassee, Florida 32399-0450 15. Supplementary Notes Prepared in cooperation with the Federal Highway Administration 16. Abstract The reliability index is examined for steel girder highway bridges designed by AASHTO LRFD Strength I limit state for flexure and shear. The reliability analysis is based on the extensive stochastic finite element method (SFEM). The SFEM takes advantages of the conventional advanced first-order second- moment (AFOSM) in that it considers the mechanic connection between the critical member and other members in the whole structure. Simply supported multigirder steel bridges with span length of 30 ft to 120ft and girder spacing of 4 ft to 12 ft are designed. The bridges are modeled as grillage beam systems. The sectional and material properties as well as dead and live loads are treated as basic design variables. The results obtained in this study indicate that the reliability index is very sensitive to the lateral distribution of live loads such as HS20 truck loading. Consequently, a simplified reliability analysis method for multigirder bridges can be used in the analysis. This simplified method can avoid the complex computation in SFEM yet achieve good accuracy. Based on this study, the AASHTO LRFD specification for Strength I limit state for flexure is a conservative design of steel girder bridges. However, the design based on Strength I limit state for shear achieves the target safety level. 17. Key Words 18. Distribution Statement Reliability Analysis, Highway Bridges, Steel This document is available to the public through the Girder, Statistics, Bridge Design, LRFD National Technical Information Service, Springfield, Method, Stochastic Finite Element Method Virginia, 22161 (SFEM) 19. Security Classify. (of this report) 20. Security Classify. (of this page) 21. No. of Pages 22. Price Unclassified Unclassified 147 Form DOT F 1700.7 (8-72) Reproduction of Completed Page Authorized FFFFiiiinnnnaaaallll RRRReeeeppppoooorrrrtttt i METRIC CONVERSIONS N × 1,000 = kN ft × 0.3048 = m inch × 2.54 = cm kip (force) × 4.448 = kN kip (mass) × 454 = kg (mass) mph × 1.609 = km/h psi × 6.895 = kPa ksi × 6.895 = Mpa ii FFFFiiiinnnnaaaallll RRRReeeeppppoooorrrrtttt DISCLAIMER The opinions, findings and conclusions expressed in this publication are those of the authors and not necessarily those of the Department of Transportation or the U.S. Department of Transportation. Prepared in cooperation with the State of Florida Department of Transportation and the U.S. Department of Transportation. FFFFiiiinnnnaaaallll RRRReeeeppppoooorrrrtttt iii ACKNOWLEDGEMENTS The authors wish to express their sincere appreciation to the Florida Department of Transportation (FDOT) for funding this research. Special thanks are also extended to Mr. Marcus Ansley, Director, and Dr. Dongzhou Huang, Senior Research Scientist, Structural Research Center, FDOT for their valuable advice, suggestions, and comments during the course of this study. The help from graduate student, Mr. Benito A. Berlanga, is appreciated for his preparation for the design bridge data. iv FFFFiiiinnnnaaaallll RRRReeeeppppoooorrrrtttt TABLE OF CONTENTS LIST OF TABLES........................................................................................................................vii LIST OF FIGURES......................................................................................................................viii 1. INTRODUCTION.......................................................................................................................1 2. THEORY FOR STRUCTURAL RELIABILITY ANALYSIS..................................................3 2.1 ADVANCED FIRST ORDER SECOND MOMENT (AFOSM) METHOD...............3 2.2 STOCHASTIC FINITE ELEMENT METHOD (SFEM).............................................5 3. DESIGN OF BRIDGES BASED ON LRFD APPROACH........................................................9 3.1 DESIGN EXAMPLES BASED ON STRENGTH I LIMIT STATE FOR FLEXURE...................................................................................9 3.2 DESIGN EXAMPLES BASED ON STRENGTH I LIMIT STATE FOR SHEAR.....................................................................................19 4. FINITE ELEMENT MODELS FOR BRIDGES......................................................................22 4.1 GRILLAGE MODEL..................................................................................................22 4.2 THREE-DIMENSIONAL SLAB ON GIRDER MODEL..........................................24 5. RELIABILITY ANALYSIS FOR STEEL GIRDER BRIDGES..............................................26 5.1 DEVELOPMENT AND CALIBARTION OF THE SFEM MODELS......................26 5.2 STRENGTH I LIMIT STATE FOR FLEXURE........................................................36 5.3 STRENGTH I LIMIT STATE FOR SHEAR.............................................................42 6. SUMMARIES, RECOMMENDATIONS, AND CONCLUSIONS.........................................45 6.1 SUMMARIES.............................................................................................................45 6.2 RECOMMENDATIONS............................................................................................45 6.3 CONCLUSIONS.........................................................................................................46 REFERENCES..............................................................................................................................48 APPENDIX A USER’S MANUAL FOR THE SFEM MODEL..................................................50 FFFFiiiinnnnaaaallll RRRReeeeppppoooorrrrtttt v APPENDIX B USER’S MANUAL FOR THE DESIGN OF NONCOMPOSITE STEEL BRIDGES...............................................................67 APPENDIX C USER’S MANUAL FOR THE DESIGN OF COMPOSITE STEEL BRIDGES........................................................................69 APPENDIX D DESIGN EXAMPLES.........................................................................................71 APPENDIX E COMPUTER PROGRAMS..................................................................................93 RELI.FOR..........................................................................................................................94 NONCOMP-ME.FOR.....................................................................................................140 NONCOMP-MI.FOR.......................................................................................................142 COMP-ME.FOR..............................................................................................................144 COMP-MI.FOR...............................................................................................................146 vi FFFFiiiinnnnaaaallll RRRReeeeppppoooorrrrtttt LIST OF TABLES Table 2-1. Basic Variables for Noncomposite Steel Bridges.........................................................7 Table 2-2. Statistical Data of Loads...............................................................................................8 Table 2-3. Statistical Data of Sectional and Material Properties...................................................8 Table 5-1. Comparison of Static Moment....................................................................................27 Table 5-2. Three Design Examples..............................................................................................29 Table 5-3. Reliability Index β......................................................................................................29 Table 5-4. Basic Variables at the Design Point X*......................................................................31 Table 5-5. Basic Variables at the Design Point X*......................................................................31 Table 5-6. Design Examples........................................................................................................34 FFFFiiiinnnnaaaallll RRRReeeeppppoooorrrrtttt vii LIST OF FIGURES Figure 3-1. Typical Cross Section of the Bridges........................................................................10 Figure 3-2. Typical Beam Section...............................................................................................15 Figure 3-3. Symbols for Calculation of Plastic Moment.............................................................18 Figure 4-1. Grillage Element e.....................................................................................................22 Figure 4-2. Typical Bridge Plan and Grillage Model...................................................................23 Figure 4-3. Three Dimensional Finite Element Cross Section....................................................25 Figure 5-1. One Design Example (L = 60ft)................................................................................27 Figure 5-2. Variation of Reliability Index to the Deviation of Distributed Loads on Exterior Girder....................................................................32 Figure 5-3. Relationship between the Difference in β and Ratio of Discrepancy in Total Moment.....................................................................35 Figure 5-4. Reliability Indices for Strength Limit I for Flexure of Noncomposite Bridges (AFOSM)...........................................................37 Figure 5-5. Reliability Indices for Strength Limit I for Flexure of Noncomposite Bridges (SFEM)..............................................................38 Figure 5-6. Reliability Indices for Strength Limit I for Flexure of Composite Bridges (AFOSM).................................................................40 Figure 5-7. Reliability Indices for Strength Limit I for Flexure of Composite Bridges (SFEM)....................................................................41 Figure 5-8. Reliability Indices for Strength Limit I for Shear (AFOSM)....................................43 Figure 5-9. Reliability Indices for Strength Limit I for Shear (SFEM)........................................44 viii FFFFiiiinnnnaaaallll RRRReeeeppppoooorrrrtttt