Calibration of AASHTO LRFD Concrete Bridge Design Specifications for Serviceability (2014)

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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 INFORMATION 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 opinions and conclusions expressed or implied in this report are those of the researchers who performed the research. They are not necessarily those of the Transportation Research Board, the National Research Council, or the program sponsors. The information contained in this document was taken directly from the submission of the author(s). This material has not been edited by TRB.

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TABLE OF CONTENTS LIST OF FIGURES ..................................................................................................................... x LIST OF TABLES .................................................................................................................... xiii ACKNOWLEDGMENTS ........................................................................................................... xv ABSTRACT ............................................................................................................................. xvi EXECUTIVE SUMMARY ............................................................................................................ 1 1 BACKGROUND AND RESEARCH APPROACH ................................................................ 3 1.1 Background ................................................................................................................... 3 1.2 Special Challenges Related to Service Limit States ................................................... 3 1.3 Problem Statement and Research Objective ............................................................... 4 1.4 Scope of the Study ........................................................................................................ 4 1.5 Relationship to Project SHRP R19B ............................................................................. 6 1.6 Research Approach ....................................................................................................... 6 2 SERVICE LIMIT STATES IN CURRENT PRACTICES AND AVAILABLE LITERATURE ... 7 2.1 State-of-the-Art Summary ............................................................................................. 7 2.1.1 Questionnaire of Bridge Owners .......................................................................... 7 2.1.2 Literature Review ................................................................................................. 9 2.1.3 Overarching Characteristics of Other Specifications ............................................ 9 2.1.3.1 Reversible versus Irreversible Limit States .......................................... 9 2.1.3.2 Load-Driven versus Non-Load-Driven Limit States ........................... 10 2.1.4 Lessons Learned from Review of Existing Design Specifications ....................... 10 2.1.5 Search for Concrete SLSs Not Yet Implemented ............................................... 10 2.1.6 SLSs to be Considered in this Report ................................................................ 11 3 OVERVIEW OF CALIBRATION PROCESS .......................................................................12 3.1 Introduction ................................................................................................................. 12 3.2 Calibration by Determination of Reliability Indices ................................................... 13 3.2.1 Basic Framework ............................................................................................... 13 3.2.2 Closed-form Solutions ........................................................................................ 18 3.2.3 Using Monte Carlo Simulation in the Calibration Process ................................... 19 3.2.4 Statistical Parameters for Resistance and Other Loads (Excerpted from Kulicki, et al. 2007) ......................................................................................................... 19 3.2.4.1 Resistance Models ............................................................................... 19 3.2.4.2 Statistics of Loads Other Than Live Load .......................................... 21 3.3 “Deemed to Satisfy” .................................................................................................... 21 iv

4 Live Load for Calibration ..................................................................................................22 4.1 Development of Live Load Models for Service Limit States ..................................... 22 4.1.1 Introduction ........................................................................................................ 22 4.1.2 WIM Database ................................................................................................... 23 4.1.3 WIM Data Filtering ............................................................................................. 25 4.2 Initial Data Analysis ..................................................................................................... 31 4.2.1 Gross Vehicle Weight (GVW) ............................................................................. 31 4.2.2 Moments from the WIM Data ............................................................................. 32 4.2.3 Filtering of Presumed Illegal Overloads and Special Permit Loads .................... 35 4.2.4 Multiple Presence Analysis ................................................................................ 37 4.2.5 Project Guidelines Regarding Live Load ............................................................ 40 4.3 Statistical Parameters for Service Limit States Other Than Fatigue ........................ 41 4.3.1 Maximum Moments for Different Time Periods .................................................. 41 4.3.2 Statistical Parameters of Live Load .................................................................... 45 4.3.3 Reactions ........................................................................................................... 46 4.3.4 Axle Loads ......................................................................................................... 47 4.4 Development of Statistical Parameters of Fatigue Load .......................................... 54 4.4.1 Objective ............................................................................................................ 54 4.4.2 WIM Data Used for Fatigue Calculation ............................................................. 55 4.4.3 Fatigue Limit State II – Finite Fatigue Life .......................................................... 56 4.4.4 Fatigue Limit State I – The Maximum Moment Range Ratio .............................. 56 4.4.5 Statistical Parameters of Fatigue Live Load ....................................................... 61 4.4.6 Recommendations ............................................................................................. 63 4.5 Development of Overload and Permit Load Parameters .......................................... 64 4.5.1 Based on WIM Data ........................................................................................... 64 4.5.1.1 Load Model ........................................................................................... 64 4.5.2 Based on Louisiana Permit Load Citations ......................................................... 70 4.5.3 Conclusions Regarding Overloads and Permit Loads ........................................ 82 5 CALIBRATION RESULTS ..................................................................................................83 5.1 Cracking of Reinforced Concrete Components Service I Limit State – Annual Probability .............................................................................................................. 83 5.1.1 Live Load Model ................................................................................................ 84 5.1.2 Target Reliability Index....................................................................................... 84 5.1.2.1 Limit State Function ............................................................................. 84 5.1.2.2 Statistical Parameters of Variables Included in the Design .............. 84 5.1.2.3 Database of Reinforced Concrete Decks ............................................ 85 5.1.2.4 Selection of the Target Reliability Index ............................................. 86 v

5.1.3 Calibration Result............................................................................................... 88 5.1.3.1 Step 1: Formulate the Limit State Function and Identify Basic Variables ............................................................................................... 88 5.1.3.2 Step 2: Identify and Select Representative Structural Types and Design Cases ........................................................................................ 88 5.1.3.3 Step 3: Determine Load and Resistance Parameters for the Selected Design Cases ........................................................................ 88 5.1.3.4 Step 4: Develop Statistical Models for Load and Resistance ............ 88 5.1.3.5 Step 5: Develop the Reliability Analysis Procedure ........................... 88 5.1.3.6 Step 6: Calculate the Reliability Indices for Current Design Code and Current Practice ............................................................................ 89 5.1.3.7 Step 7: Review the Results and Select the Target Reliability Index, βT ................................................................................................ 89 5.1.3.8 Step 8: Select Potential Load and Resistance Factors for Service I, Crack Control through the Distribution of Reinforcement ............. 89 5.1.3.9 Step 9: Calculate Reliability Indices .................................................... 92 5.1.3.10 Summary and Recommendations for Service I Limit State, Crack Control through the Distribution of Reinforcement ........................... 92 5.1.4 Proposed AASHTO LRFD Revisions ................................................................. 92 5.2 Tension in Prestressed Concrete Beams Service III Limit State – Annual Probability .............................................................................................................. 92 5.2.1 History of Major Relevant Design Provisions and Revisions to AASHTO LRFD Specifications ..................................................................................................... 93 5.2.1.1 Load Factor for Live Load in Service III Load Combination .............. 93 5.2.1.2 Method of Calculating Prestressing Losses....................................... 94 5.2.2 Live Load Model ................................................................................................ 95 5.2.3 Methods of Analysis for Study Bridges ............................................................... 95 5.2.4 Target Reliability Index....................................................................................... 96 5.2.4.1 Limit State Functions Investigated ..................................................... 96 5.2.4.2 Statistical Parameters of Variables Included in the Design .............. 97 5.2.4.3 Database of Existing Bridges .............................................................. 99 5.2.4.4 Estimated Reliability Index of Existing Bridges ................................. 99 5.2.4.5 Database of Simulated Bridges ......................................................... 100 5.2.4.6 Selection of the Target Reliability Index ........................................... 104 5.2.5 Calibration Result............................................................................................. 104 5.2.5.1 Step 1: Formulate the Limit State Function and Identify Basic Variables ............................................................................................. 104 5.2.5.2 Step 2: Identify and Select Representative Structural Types and Design Cases ...................................................................................... 105 vi

5.2.5.3 Step 3: Determine Load and Resistance Parameters for the Selected Design Cases ...................................................................... 105 5.2.5.4 Step 4: Develop Statistical Models for Load and Resistance .......... 105 5.2.5.5 Step 5: Develop the Reliability Analysis Procedure ......................... 105 5.2.5.6 Step 6: Calculate the Reliability Indices for Current Design Code and Current Practice .......................................................................... 106 5.2.5.7 Step 7: Review the Results and Select the Target Reliability Index βT ......................................................................................................... 106 5.2.5.8 Step 8: Select Potential Load and Resistance Factors for Service III .......................................................................................................... 106 5.2.5.8.1 Step 8a: Select Potential Load and Resistance Factors for Service III - Bridges Designed for Maximum Concrete Tensile Stress of ................................................................ 107 5.2.5.8.2 Step 8b: Select Potential Load and Resistance Factors for Service III - Bridges Designed for Maximum Concrete Tensile Stress of .................................................................... 113 5.2.5.8.3 Step 8c: Select Potential Load and Resistance Factors for Service III – Bridges Designed for Maximum Concrete Tensile Stress of ................................................................... 116 5.2.5.9 Step 9: Calculate Reliability Indices .................................................. 119 5.2.5.10 Summary of Target Reliability Indices for Different Design and Performance Levels ........................................................................... 119 5.2.5.11 Effect of Proposed Changes on Design ............................................ 120 5.2.5.12 Summary and Recommendations for Service III Limit State ........... 121 5.2.6 Results for Adjacent Box Beams, Spread Box Beams, and American Segmental Box Institute (ASBI) Boxes ............................................................................... 123 5.2.7 Sections Designed Using Other Methods of Determining Prestressing Time- Dependent Losses and/or Section Properties .................................................. 127 5.2.8 Proposed AASHTO LRFD Revisions ............................................................... 128 5.3 Fatigue Limit State – Lifetime ................................................................................... 128 5.3.1 Formulate the Limit State Function .................................................................. 128 5.3.1.1 Select Structural Types and Design Cases ...................................... 129 5.3.1.2 Determine Load and Resistance Parameters for Selected Design Cases .................................................................................................. 129 5.3.1.2.1 Steel Reinforcement in Tension .................................................. 129 5.3.1.2.2 Concrete in Compression ............................................................ 130 5.3.1.3 Develop Statistical Models for Loads and Resistances .................. 130 5.3.1.3.1 Load Uncertainties ....................................................................... 130 5.3.1.3.2 Resistance Uncertainties ............................................................. 131 0.0948t cf f ′= 0.19t cf f ′= 0.25t cf f ′= vii

5.3.1.4 Develop the Reliability Analysis Procedure ..................................... 133 5.3.1.4.1 General .......................................................................................... 133 5.3.1.4.2 Monte-Carlo simulation ................................................................ 133 5.3.1.5 Calculate the Reliability Indices for Current Design Code or Current Practice ................................................................................. 133 5.3.1.6 Select the Target Reliability Index, βT ............................................... 134 5.3.1.7 Select Potential Load and Resistance Factors ................................. 134 5.3.1.8 Calculate Reliability Indices .............................................................. 135 5.3.2 Proposed AASHTO LRFD Revisions ............................................................... 135 5.4 Service Design for Overload ..................................................................................... 136 6 PROPOSED CHANGES TO AASHTO LRFD ................................................................... 138 6.1 Cracking of Prestressed Concrete – Currently Service III ...................................... 138 6.1.1 Proposed Revisions to Section 5 ..................................................................... 138 6.2 Cracking of Prestressed Concrete ........................................................................... 139 6.2.1 Proposed Revisions to Section 3 ..................................................................... 139 6.3 Fatigue ....................................................................................................................... 142 6.3.1 Proposed Revisions to Section 3 ..................................................................... 142 6.3.2 Proposed Revisions to Section 5 ..................................................................... 143 7 CONCLUSIONS AND SUGGESTED FUTURE RESEARCH ............................................ 144 7.1 Conclusions ............................................................................................................... 144 7.1.1 General Conclusions Related to the Calibration of Service Limit States ........... 144 7.1.2 Conclusions Related to the Live Load Model for Service Limit States .............. 144 7.1.3 General Conclusions Related to the Specific Limit States Calibrated ............... 145 7.1.3.1 Cracking of Reinforced Concrete Decks through the Distribution of Reinforcement ................................................................................ 145 7.1.3.2 Tension in Prestressed Concrete Beams ......................................... 145 7.1.3.3 Fatigue of Steel Reinforcement in Tension and Concrete in Compression ...................................................................................... 146 7.2 Suggested Future Research ..................................................................................... 146 REFERENCES ...................................................................................................................... 148 LIST OF ACRONYMS ............................................................................................................ 151 Appendix A ............................................................................................................................ A-1 Appendix B ............................................................................................................................ B-1 Appendix C ............................................................................................................................ C-1 Appendix D ............................................................................................................................ D-1 Appendix E ............................................................................................................................ E-1 viii

Appendix F ............................................................................................................................ F-1 Appendix G ............................................................................................................................ G-1 ix

LIST OF FIGURES Figure 3-1 Basic calibration framework – flowchart. .................................................................. 16 Figure 3-2 Use of normal probability paper. .............................................................................. 17 Figure 4-1 Flowchart of the Filtering Process. ........................................................................... 26 Figure 4-2 CDF of GVW - FHWA Data and Ontario. ................................................................. 27 Figure 4-3 CDF of GVW – Oregon, Florida and Ontario. ........................................................... 28 Figure 4-4 CDF of GVW – Indiana, Mississippi and Ontario. ..................................................... 28 Figure 4-5 CDF of GVW – California, New York and Ontario. ................................................... 28 Figure 4-6 Legend for All Graphs. ............................................................................................. 31 Figure 4-7 CDF of Gross Vehicle Weight (GVW). ...................................................................... 32 Figure 4-8 CDFs of WIM Moment and HL-93 Moment Ratio, Span = 30 ft. ............................... 33 Figure 4-9 CDFs of WIM Moment and HL-93 Moment Ratio, Span = 60 ft. ............................... 33 Figure 4-10 CDFs of WIM Moment and HL-93 Moment Ratio, Span = 90 ft. ............................. 34 Figure 4-11 CDFs of WIM Moment and HL-93 Moment Ratio, Span = 120 ft. ........................... 34 Figure 4-12 CDFs of WIM Moment and HL-93 Moment Ratio, Span = 200 Ft. .......................... 34 Figure 4-13 Configuration of Extremely Loaded Truck. ............................................................. 35 Figure 4-14 Data Removal New York 0580 and 2680. .............................................................. 36 Figure 4-15 Data Removal New York 8280 and 8382. .............................................................. 36 Figure 4-16 Data Removal New York 9121 and Mississippi I-10. .............................................. 37 Figure 4-17 Two Cases of The Simultaneous Occurrence. ....................................................... 38 Figure 4-18 Histogram – Trucks Side by Side – Florida I-10 and New York 8382. .................... 38 Figure 4-19 Comparison of the Mean GVW and GVW of the Whole Population – Florida and New York. ................................................................................................................................. 39 Figure 4-20 Histogram – Trucks One After Another – Florida I-10 and New York 8382. ............ 39 Figure 4-21 Comparison of the Mean GVW and GVW of the Whole Population – Florida and New York. ................................................................................................................................. 40 Figure 4-22 Vertical Coordinates for Different Time Periods, ADTT = 1000 and Span = 120 ft. ........................................................................................................................... 44 Figure 4-23 CDFs of Mean Maximum Moment Ratios for ADTT = 1000 and Span Length 120 ft. ............................................................................................................................ 45 Figure 4-24 Determination of Mean Values at 1.5 σ. ................................................................. 46 Figure 4-25 Fatigue Failure on S-N Curve. ................................................................................ 54 Figure 4-26 The Threshold Stress on S-N Curve. ........................................................ 56 Figure 4-27 Moment Corresponding to the Upper 0.01%, Span = 120 ft. .................................. 57 Figure 4-28 The Maximum Moment Range Ratio (Fatigue LS I) for Simple Supported Bridges at the Mid-Span. ........................................................................................................................... 61 Figure 4-29 The Maximum Moment Range Ratio (Fatigue LS I) for Continuous Bridges at the Middle Support. ......................................................................................................................... 61 Figure 4-30 The Maximum Moment Range Ratio (Fatigue LS I) for Continuous Bridges at 0.4 of the Span Length. ....................................................................................................................... 62 Figure 4-31 Probability Density Function of the National Fatigue Load. .................................... 63 Figure 4-32 Annual Average Exceedances Versus Span. ......................................................... 67 Figure 4-33 Annual Average Exceedances Versus Ratio Truck/HL-93. ..................................... 67 ( )THF∆ x

Figure 4-34 Annual Average Events Scaled to ADTT = 2500 Versus Span. .............................. 69 Figure 4-35 Annual Average Events Scaled to ADTT = 2500 Versus Ratio Truck/HL-93. ......... 69 Figure 4-36 Gross Vehicle Weight of Louisiana Permit and WIM Trucks ................................... 76 Figure 4-37 Ratio of Axle Group Scale Weight and Permitted Axle Set Weight for Axle Sets with Different Number of Axles ......................................................................................................... 77 Figure 4-38 Ratio of GVW and Permitted GVW for Permit Vehicles .......................................... 78 Figure 4-39 Correlation of GVW to Ratio of GVW and Permitted GVW ..................................... 79 Figure 4-40 Correlation of GVW and Lane Moment for Various Span Lengths. (Laman 1993) .. 80 Figure 4-41 Histograms for NJ Permit Data and Louisiana Violation Records ........................... 82 Figure 5-1 Reliability Indices of Various Bridge Decks Designed Using a 1.0 Live Load Factor Over A 1 Year Return Period (ADTT=5000), Positive Moment Region, Class 1 Exposure ........ 90 Figure 5-2 Reliability Indices Of Various Bridge Decks Designed Using A 1.0 Live Load Factor Over A 1 Year Return Period (ADTT=5000), Negative Moment Region, Class 1 Exposure ....... 90 Figure 5-3 Reliability Indices Of Various Bridge Decks Designed Using A 1.0 Live Load Factor Over A 1 Year Return Period (ADTT=5000), Positive Moment Region, Class 2 Exposure ........ 91 Figure 5-4 Reliability Indices Of Various Bridge Decks Designed Using A 1.0 Live Load Factor Over A 1 Year Return Period (ADTT=5000), Negative Moment Region, Class 2 Exposure ....... 91 Figure 5-5 Reliability indices for bridges at decompression limit state (ADTT=5000), γLL=0.8, ( )........................................................................................................................ 109 Figure 5-6 Reliability indices for bridges at maximum allowable tensile stress limit state (ADTT=5000), γLL=0.8, ( ). ................................................................................ 109 Figure 5-7 Reliability Indices for bridges at maximum allowable crack width limit state (ADTT=5000), γLL=0.8, ( ). ................................................................................ 110 Figure 5-8 Reliability indices for bridges at decompression limit state (ADTT=5000), γLL=1.0 ( ). ........................................................................................................................ 112 Figure 5-9 Reliability indices for bridges at maximum allowable tensile stress limit state (ADTT=5000), γLL=1.0 ( ). ................................................................................... 112 Figure 5-10 Reliability indices for bridges at maximum allowable crack width limit state (ADTT=5000), γLL=1.0 ( ).................................................................................... 113 Figure 5-11 Reliability indices for bridges at decompression limit state (ADTT=5000), γLL=0.8 ( )............................................................................................................................ 113 Figure 5-12 Reliability indices for bridges at maximum allowable tensile stress limit state (ADTT=5000), γLL=0.8 ( ). ..................................................................................... 114 Figure 5-13 Reliability indices for bridges at maximum allowable crack width limit state (ADTT=5000), γLL=0.8 ( ). ..................................................................................... 114 Figure 5-14 Reliability indices for bridges at decompression limit state (ADTT=5000), γLL=1.0 ( )............................................................................................................................ 115 0.0948t cf f ′= 0.0948t cf f ′= 0.0948t cf f ′= 0.0948t cf f ′= 0.0948t cf f ′= 0.0948t cf f ′= 0.19t cf f ′= 0.19t cf f ′= 0.19t cf f ′= 0.19t cf f ′= xi

Figure 5-15 Reliability indices for bridges at maximum tensile stress limit state (ADTT=5000), γLL=1.0 ( ). ............................................................................................................. 115 Figure 5-16 Reliability indices for bridges at maximum crack width limit state (ADTT=5000), γLL=1.0 ( ). ............................................................................................................. 116 Figure 5-17 Reliability indices for bridges at decompression limit state (ADTT=5000), γLL=0.8 ( ). ........................................................................................................................ 116 Figure 5-18 Reliability indices for bridges at maximum allowable tensile stress limit state (ADTT=5000), γLL=0.8 ( ). .................................................................................... 117 Figure 5-19 Reliability indices for bridges at maximum allowable crack width limit state (ADTT=5000), γLL=0.8 ( ). .................................................................................... 117 Figure 5-20 Reliability indices for bridges at decompression limit state (ADTT=5000), γLL=1.0 ( ). ........................................................................................................................ 118 Figure 5-21 Reliability indices for bridges at maximum tensile stress limit state (ADTT=5000), γLL=1.0 ( ). ........................................................................................................... 118 Figure 5-22 Reliability indices for bridges at maximum crack width limit state (ADTT=5000), γLL=1.0 ( ). ........................................................................................................... 119 Figure 5-23- Adjacent box beams, reliability indices for bridges at decompression limit state (ADTT=5000), γLL=1.0 ( ). ............................................................................... 124 Figure 5-24 Adjacent box beams, reliability indices for bridges at decompression limit state (ADTT=5000), γLL=1.0 ( ). ................................................................................... 124 Figure 5-25 Spread box beams, reliability indices for bridges at decompression limit state (ADTT=5000), γLL=1.0 ( ). ............................................................................... 125 Figure 5-26 Spread box beams, reliability indices for bridges at decompression limit state (ADTT=5000), γLL=1.0 ( ). ................................................................................... 125 Figure 5-27 ASBI box beams, reliability indices for bridges at decompression limit state (ADTT=5000), γLL=1.0 ( ). ............................................................................... 126 Figure 5-28 ASBI box beams, reliability indices for bridges at decompression limit state (ADTT=5000), γLL=1.0 ( ). ................................................................................... 126 Figure 5-29 Normal Probability Plot of Fatigue Resistance Data for Steel Reinforcement in Tension ................................................................................................................................... 132 Figure 5-30 Normal Probability Plot of Truncated Fatigue Resistance Data with Best-Fit Line for Steel Reinforcement in Tension .............................................................................................. 132 0.19t cf f ′= 0.19t cf f ′= 0.25t cf f ′= 0.25t cf f ′= 0.25t cf f ′= 0.25t cf f ′= 0.25t cf f ′= 0.25t cf f ′= 0.0948t cf f ′= 0.19t cf f ′= 0.0948t cf f ′= 0.19t cf f ′= 0.0948t cf f ′= 0.19t cf f ′= xii

LIST OF TABLES Table 2-1 SLSs Identified for Development ...............................................................................11 Table 3-1 Statistical Parameters of Component Resistance (Used with permission of the Transportation Research Board of the National Academies) ..................................................... 20 Table 3-2 Statistical Parameters of Dead Load ......................................................................... 21 Table 4-1 Summary of State Sites and Their Traffic Data for Figure 4-2 Through Figure 4-5 .... 27 Table 4-2 WIM Locations and Number of Recorded Vehicles ................................................... 30 Table 4-3 Removal of the Heaviest Vehicles for 90 ft Spans ..................................................... 36 Table 4-4 Vertical Coordinates for the Mean Maximum Moment. .............................................. 43 Table 4-5 Statistical Parameters of Live Load Moments for ADTT 250,  λ = μ + 1.5σ .............. 48 Table 4-6 Statistical Parameters of Live Load Moments for ADTT 1,000,  λ = μ + 1.5σ ........... 48 Table 4-7 Statistical Parameters of Live Load Moments for ADTT 2,500,  λ = μ + 1.5σ ........... 49 Table 4-8 Statistical Parameters of Live Load Moments for ADTT 5,000,  λ = μ + 1.5σ ........... 49 Table 4-9 Statistical Parameters of Live Load Moments for ADTT 10,000,  λ = μ + 1.5σ ......... 50 Table 4-10 Statistical Parameters of Live Load Reactions for ADTT 250, λ = μ + 1.5σ ............. 50 Table 4-11 Statistical Parameters of Live Load Reactions for ADTT 1,000,  λ = μ + 1.5σ ....... 51 Table 4-12 Statistical Parameters of Live Load Reactions for ADTT 2,500,  λ = μ + 1.5σ ........ 51 Table 4-13 Statistical Parameters of Live Load Reactions for ADTT 5,000,  λ = μ + 1.5σ ..... 52 Table 4-14 Statistical Parameters of Live Load Reactions for ADTT 10,000,  λ = μ + 1.5σ ...... 52 Table 4-15 Statistical Parameters for Axle Loads, λ = μ + 1.5σ ................................................. 53 Table 4-16 WIM Locations and Number of Vehicles Used for Fatigue Analysis......................... 55 Table 4-17 The Maximum Moment Range for Simply Supported Bridges at the Mid-Span ....... 58 Table 4-18 The Maximum Moment Range for Continuous Bridges at the Middle Support ......... 59 Table 4-19 The Maximum Moment Range for Continuous Bridges at 0.4 of the Span Length ... 60 Table 4-20 The Maximum Moment Range Ratio for Fatigue I LS .............................................. 63 Table 4-21 Number of Times WIM Moments Exceeded a Factored HL-93 Loadings ................ 65 Table 4-22 Exceedances Per Year ............................................................................................ 66 Table 4-23 Events Per Year Scaled to ADTT = 2500 ................................................................ 68 Table 4-24 Statistics of Cited Vehicles When All Permit Vehicles are Considered .................... 71 Table 4-25 Statistics of Cited Permit Vehicles When Only Vehicles with GVW Greater Than 80,000 lbs are Considered ........................................................................................................ 72 Table 4-26 Number of GVW Violations Per Weight Class for Louisiana Permit Vehicles ........... 75 Table 4-27 Statistics for Different GVW Categories ................................................................... 81 Table 5-1 Summary of Statistical Information for Variables used in the Calibration of Service I Limit State for Crack Control ..................................................................................................... 85 Table 5-2 Summary Information of 15 Bridge Decks Designed using AASHTO LRFD Conventional Deck Design Method ........................................................................................... 86 Table 5-3 Summary of Reliability Indices for Concrete Decks Designed According to AASHTO LRFD (2012) ............................................................................................................................. 87 Table 5-4 Reliability Indices of Existing Bridges based on 1-year Return Period ....................... 88 Table 5-5 Relation Between Limiting Criteria and Reliability Index for a Given Girder ............... 97 Table 5-6 Random Variables and the Value of Their Statistical Parameters .............................. 98 Table 5-7 Summary of Reliability Indices for Existing I- and Bulb T Girder Bridges with One Lane Loaded and Return Period of 1 Year .............................................................................. 100 Table 5-8 Summary of the Reliability Indices of Simulated Bridges Designed Using AASHTO Girders with ADTT=5000 and .......................................................................... 102 Table 5-9 Summary of the Reliability Indices of Simulated Bridges Designed Using AASHTO Girders with ADTT=5000 and .............................................................................. 103 0.0948t cf f ′= 0.19t cf f ′= xiii

Table 5-10 Reliability Indices for Existing and Simulated Bridges (Return Period of 1 Year and ADTT 5000) ............................................................................................................................ 104 Table 5-11 Summary Information of Bridges Designed with γLL=0.8, ( ) ............. 108 Table 5-12 Summary Information of Bridges Designed with γLL=1.0, ( ) ............ 111 Table 5-13 Summary of Reliability Indices for Simulated Bridges Designed for . 119 Table 5-14 Summary of Reliability Indices for Simulated Bridges Designed for .... 120 Table 5-15 Summary of Reliability Indices for Simulated Bridges Designed for ... 120 Table 5-16 Comparison of number of strands required for different design assumptions ........ 122 Table 5-17 Average Reliability Indices for Different Types of Girders ...................................... 127 Table 5-18 Current Fatigue Load Factors ................................................................................ 129 Table 5-19 Load Uncertainties ................................................................................................ 131 Table 5-20 Resistance Uncertainties ....................................................................................... 133 Table 5-21 Current Reliability Indices for the AASHTO LRFD Fatigue I Limit States ............... 134 Table 5-22 Current Reliability Indices for Steel Members Using AASHTO Fatigue I and Fatigue II Limit States .......................................................................................................................... 134 Table 5-23 Proposed Fatigue I Limit-State Resistance Factors ............................................... 135 Table 5-24 Summary of Relevant Articles in AASHTO LRFD for Foundation Deformations .... 136 0.0948t cf f ′= 0.0948t cf f ′= 0.0948t cf f ′= 0.19t cf f ′= 0.25t cf f ′= xiv