reliability validation of highway bridges designed by lrfd

158 Pages·2002·2.4 MB·English

FINAL REPORT

RELIABILITY VALIDATION OF
HIGHWAY BRIDGES DESIGNED BY
LRFD

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Technical Report Documentation Page

1. Report No. 2. Government Accession No. 3. 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
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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

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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.

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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.

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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
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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

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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

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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

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