Analysis of isolated girder and bearing movement on Lowndes County bridge

GEORGIA DOT RESEARCH PROJECT 18-21 FINAL REPORT
ANALYSIS OF ISOLATED GIRDER AND BEARING MOVEMENT ON LOWNDES COUNTY BRIDGE
Office of Perfomance Based Management and Research
ONE GEORGIA CENTER, 5TH FLOOR 600 W. PEACHTREE STREET N.W.
ATLANTA, GA 30308

TECHNICAL REPORT DOCUMENTATION PAGE

1. Report No.:
FHWA-GA-19-1821

2. Government Accession No.:

3. Recipient's Catalog No.:

4. Title and Subtitle:
Analysis of Isolated Girder and Bearing Movement on Lowndes County Bridge

5. Report Date:
August 2019
6. Performing Organization Code:

7. Author(s):
D.W. Scott, D.W. White, and F. Chung

8. Performing Organ. Report No.:
18-21

9. Performing Organization Name and Address:
Georgia Institute of Technology

10. Work Unit No.:

School of Civil and Environmental Engineering 790 Atlantic Drive NW

11. Contract or Grant No.: 00

Atlanta, GA 30332

12. Sponsoring Agency Name and Address:
Georgia Department of Transportation

13. Type of Report and Period Covered:
Final; May 2018August 2019

Office of Performance-based Management 14. Sponsoring Agency Code: and Research

600 W. Peachtree Street Atlanta, GA 30308

15. Supplementary Notes:
Performed in cooperation with the U.S. Department of Transportation, Federal Highway

Administration.

16. Abstract:

A 2018 routine inspection of a Georgia Department of Transportation (GDOT) bridge located

in Lowndes County revealed that the expansion bearing for an exterior plate girder on one of the simply supported end spans at the southeast corner of the bridge had experienced a movement of approximately 5 inches, with the steel girder itself also translating and rotating.

A detailed field inspection and document review of the bridge was combined with analytical and numerical analyses to investigate the potential causes for the observed damage and to

estimate the residual capacity of the bridge in the damaged condition. The shift in the bearing and girder was most likely caused by a combination of thermal effects that led to the shear failure of the anchor bolts, followed at a later time by a temporary removal of dead load due to

some unknown dynamic event. The bridge was subsequently repaired. The analysis of the residual capacity of the shifted girder demonstrates that the system was still more than

adequate to carry the expected service loads on the bridge. As such, heat straightening the end of the girder and installing a new anchored bearing is a more economical and appropriate remediation approach compared to girder replacement. This validation can be used to facilitate

future repairs in similar situations on Georgia bridges.

17. Key Words:

inspection, plate girders, in-service evaluation

19. Security Class (this report):
Unclassified

20. Security Class (this page):
Unclassified

Form DOT 1700.7 (8-69)

18. Distribution Statement:
21. Number of Pages: 22. Price:
144

GDOT Research Project 18-21
Final Report
ANALYSIS OF ISOLATED GIRDER AND BEARING MOVEMENT ON LOWNDES COUNTY BRIDGE
By David Scott, Associate Professor
Donald White, Professor Frederick Chung, Graduate Research Assistant
Georgia Tech Research Corporation Atlanta, Georgia Contract with
Georgia Department of Transportation
In cooperation with U.S. Department of Transportation Federal Highway Administration
August 29, 2019
The contents of this report reflect the views of the authors who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the Georgia Department of Transportation or the Federal Highway Administration. This report does not constitute a standard, specification, or regulation.

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................. vi

LIST OF FIGURES .......................................................................................................... vii

EXECUTIVE SUMMARY ............................................................................................... xi

ACKNOWLEDGEMENTS.............................................................................................. xv

INTRODUCTION AND BACKGROUND ........................................... 1

1.1

Problem Statement ................................................................................. 1

1.2

Project Objectives................................................................................... 3

1.3

Previous Work ........................................................................................ 4

INSPECTION AND DOCUMENT REVIEW ....................................... 6

2.1

Detailed Field Inspection Prior to Bridge Repair ................................... 6

2.2

Field Inspection After Bridge Repair ................................................... 10

2.3

Document Review ................................................................................ 13

2.4

Review of Similar Incident on Another GDOT Bridge ....................... 13

POTENTIAL CAUSES OF THE BEARING SHIFT .......................... 17

3.1

Shearing of Anchor Bolts Prior to Bearing Shift ................................. 18

3.2

Bearing Shifted by an External Force .................................................. 27

3.3

Bearing Shift Due to Initial Conditions and Service Environment ...... 43

RESIDUAL CAPACITY ANALYSIS ................................................. 45

4.1

Load & Resistance Factor Rating Analysis.......................................... 46

4.2

Component Dead and Wearing Surface Dead Load for the

Southeast Exterior Girder of the Lowndes County Bridge .................. 50

4.3

Inventory and Operating Level Rating Factors Corresponding to

the Flexural Resistance of the Southeast Exterior Girder of the

Lowndes County Bridge....................................................................... 52

4.4

Inventory Level Rating Factor Corresponding to the Resistance of

the Bearing Stiffeners at the Displaced Bearing .................................. 57

4.5

Inventory Level Rating Factor Corresponding to the Shear

Resistance of the Girder Web End Panel Adjacent to the

Displaced Bearing ................................................................................ 60

4.6

Inventory Level Rating Factor based on Full Nonlinear Shell

Finite Element Analysis ....................................................................... 64

CONCLUSIONS AND RECOMMENDATIONS ............................... 82

5.1

Conclusions .......................................................................................... 82

5.2

Recommendations ................................................................................ 84

iv

REFERENCES ..................................................................................... 86 APPENDIX A BRIDGE DESIGN DRAWINGS ....................................................... A-1 APPENDIX B FIELD INSPECTION PRIOR TO REPAIR PHOTOS ................... B-1 APPENDIX C FIELD INSPECTION AFTER REPAIR PHOTOS ........................ C-1 APPENDIX D SUMMARY OF DOCUMENTS REVIEWED .................................. D-1 APPENDIX E DEAD LOAD CALCULATIONS.......................................................E-1 APPENDIX F LIVE LOAD DISTRIBUTION FACTOR CALCULATIONS...........F-1
v

LIST OF TABLES

Table

Page

1. Steel Material Properties .......................................................................................... 28

vi

LIST OF FIGURES

Figure

Page

1. Bridge Location in Lowndes County, Georgia .......................................................... 1
2. Bearing Movement at End of Girder on Lowndes County Bridge ............................ 2
3. Bearing Rotation at End of Girder on Lowndes County Bridge................................ 3
4. Snooper Truck Setup for Bridge Inspection: (a) Exterior; (b) Interior ...................... 6
5. Bearing Shift at End of Plate Girder .......................................................................... 7
6. Curvature in Girder at Shifted Bearing ...................................................................... 8
7. Measured Rotation in Girder at Shifted Bearing ....................................................... 9
8. Concrete Edge Beam: (a) View of Framing into the Girder at the Bearing Location; (b) Closeup of Damage to Edge Beam .................................................... 10
9. Section of Repaired Girder Subjected to Heat Straightening (note freshly painted sections): (a) Interior; (b) Exterior .............................................................. 11
10. Repaired Bearing: (a) Interior Side of Girder; (b) Exterior Side of Girder ............. 12
11. Repaired Concrete Edge Beam ................................................................................ 12
12. Bridge 309-0014-0 Located Approximately 75 miles SE of Macon ....................... 13
13. Inspection Report for Bridge 309-0014-0 Noting Twisted Girder and Detailing Repairs Completed ................................................................................... 15
14. Twisted Girder Observed on Bridge 309-0014-0: (a) Exterior View; (b) Interior View ...................................................................................................... 16
15. Repaired Girder on Bridge 309-0014-0 ................................................................... 16
16. Sheared Anchor Bolt in Pier Cap at Shifted Bearing Location................................ 19
17. Repaired Girder Bearing Showing Original Expansion Bearing Slot...................... 20
18. Deformed Girder due to Uniform Temperature Change (Increase in Temperature) with Zero Relative Movement Between the Bearings at the Bottom of the Girder ................................................................................................ 22
19. Girder Subjected to Uniform Temperature Change and Restrained at its Top and Bottom ............................................................................................................... 24

vii

20. Damaged Girder from Underneath the Bridge Highlighting the Bearing Stiffeners at the Pier and the Bottom Flange of the Girder Used in the Simplified Model ..................................................................................................... 30
21. Illustration of Upper-bound Idealized Model of the Girder Bottom Flange............ 31
22. Illustration of Upper-bound Idealized Model of the Bearing Stiffeners .................. 32
23. Displaced Shape of Upper-bound Model at 5-in. Displacement of the Bearing and Corresponding Development of the Model's Maximum Load in MASTAN2 [12] ....................................................................................................... 32
24. Photos from Underneath the Bridge Highlighting the Diaphragms and the Connection Plates..................................................................................................... 34
25. Embedment of the Bearing Stiffeners into the Damaged Concrete Edge Beam ..... 34
26. Illustration of Lower-bound Idealized Model of the Girder .................................... 35
27. Displaced Shape of Lower-bound Model in MASTAN2 [12] at 5-in. Displacement of the Bearing.................................................................................... 36
28. Finite Element Model of the Exterior Girder System and Concrete Edge Beam in ABAQUS [14] ..................................................................................................... 37
29. Physical Elements Assumed as Restraints in the Finite Element Model: (a) Diaphragm Connected to the Exterior and the Adjacent Interior Girder; (b) Fixed Bearing at the Abutment; (c) Concrete Deck and Haunch at the Top Flange of the Girder; (d) Bearing Stiffeners Embedded in Concrete Edge Beam ........................................................................................................................ 39
30. Displaced Bearing: (a) Detail; (b) Corresponding ABAQUS Finite Element Model [14]................................................................................................................ 40
31. Deformed Finite Element Model at Load of 32.6 kips, Corresponding to a Shift of the Bearing by 5 .......................................................................................... 41
32. Scaffolding Details: (a) Common Scaffolding Used by Painting Contractors on GDOT Bridges; (b) Support Cables for Scaffolding Running Parallel to Girders...................................................................................................................... 42
33. Factored 1.25 DC + 1.5 DW: (a) Free-body; (b) Shear; and (c) Moment Diagrams for the Exterior Girder of the Lowndes County Bridge .......................... 51
34. Unfactored HL-93: (a) Free-body; (b) Shear; and (c) Moment Diagrams Producing the Maximum Moment Within the Exterior Girder of the Lowndes County Bridge, Including 33% Dynamic Load Allowance on the Design Truck and Based on a Flexural Live Load Distribution Factor of g = 0.66............. 54
35. Unfactored HL-93: (a) Free-body; (b) Shear; and (c) Moment Diagrams Associated with the Maximum Live Load Reaction at the Subject Bearing of the Exterior Girder of the Lowndes County Bridge, Including 33% Dynamic
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Load Allowance and Based on a Shear Live Load Distribution Factor of g = 0.82........................................................................................................................... 57
36. Unfactored HL-93: (a) Free-body; (b) Shear; and (c) Moment Diagrams Associated with the Critical Shear in the Web End Panel Adjacent to the Subject Bearing of the Exterior Girder of the Lowndes County Bridge, Including 33% Dynamic Load Allowance and Based on a Shear Live Load Distribution Factor of g = 0.82................................................................................. 61
37. Finite Element Model of the Exterior Girder System in ABAQUS [14]................. 64
38. Beam Multi-point Constraint Pattern Applied at the Patch Where HL-93 Axle (Except the Rear Axle) Loads Were Applied .......................................................... 67
39. First Buckling Mode from an Elastic Linear Buckling Analysis of the Exterior Girder (U Indicates the Magnitude of the Out-of-plane Displacement) .................. 68
40. Out-of-plane Displacement (in.) at the Shear Capacity of the Plumb Girder (RF = 2.44) of: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface ..................................................................................................................... 71
41. Equivalent Plastic Strain at the Shear Capacity of the Plumb Girder (RF = 2.44) on: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface..... 72
42. Out-of-plane Displacement (in.) at Post-peak Load of the Plumb Girder of: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface .................... 73
43. Equivalent Plastic Strain at Post-peak Load of the Plumb Girder on: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface................................... 74
44. Out-of plane Displacement (in.) at the Shear Capacity of the Girder with Displaced Bearing (RF = 2.05) of: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface.................................................................................. 75
45. Equivalent Plastic Strain at the Shear Capacity of the Girder with Displaced Bearing (RF = 2.05) on: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface ................................................................................................ 76
46. Out-of-plane Displacement (in.) at the Bearing Capacity of the Girder with Displaced Bearing (RF = 2.60) of: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface.................................................................................. 77
47. Equivalent Plastic Strain at the Bearing Capacity of the Girder with Displaced Bearing (RF = 2.60) on: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface ................................................................................................ 78
48. Out-of-plane Displacement (in.) at Post-peak Load of the Girder with Displaced Bearing of: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface ............................................................................................................. 79
ix

49. Equivalent Plastic Strain at Post-peak Load of the Girder with Displaced Bearing on: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface ..................................................................................................................... 80
x

EXECUTIVE SUMMARY
The bridges in GDOT's inventory include one in Lowndes County that is specifically located at county road station 416 + 87.52. The structure is a four-span steel plate girder bridge with two spans continuous over traffic and two simply supported end spans that are not located over traffic. A 2018 routine inspection of this bridge revealed that the expansion bearing for the fascia girder located at the pier on the simply supported end span at the southeast corner of the bridge had experienced a movement of approximately 5 in., with the steel girder itself also translating and rotating. This condition was not observed in the bridge inspection completed two years prior, and as such is presumed to have occurred at some point in the previous 24 months.
The objective of this research project was to perform an assessment and analysis of the plate girder and bearing that had moved on this Lowndes County bridge. The first series of tasks performed for this research program involved a detailed field inspection of the subject bridge prior to repairs. In addition to the field inspection, previous inspection reports and photos were reviewed to ascertain any history of the bridge that might be related to the observed bearing movement and girder translation/rotation. The next set of tasks focused on the evaluation of potential causes for the observed bearing shift. A simplified model was used to estimate the force required to translate the bearing/girder 5 in.. A series of numerical simulations was performed to determine the types of actions that could cause the bearing/girder to shift in the observed manner. Finally, the residual capacity of the shifted girder was compared with the capacity of the girder in its original undamaged configuration. American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Rating (LRFR) calculations and numerical
xi

simulations were performed to determine the rating factor of the plate girder in both the shifted and the original undamaged configuration.
The bearing displacement on the Lowndes County bridge occurred subsequent to a shear failure of the anchor bolts at the expansion bearing. However, it is impossible to state with any certainty exactly when this anchor bolt failure occurred. The most likely cause for the failure in the anchor bolts was excessive restraint at the expansion joint location coupled with thermal loading from the service environment. If thermal expansion was adequately restrained at the bearing, a temperature rise of approximately 29F could result in forces that would exceed the shear capacity of the anchor bolts.
Based on the field inspection, document review, analytical/numerical analyses performed, and anecdotal information about the behavior of the shifted girder during the repair process, the research team developed a potential scenario to account for the shift at the bearing observed on this Lowndes County bridge. This scenario postulates that the girder was initially curved, and forced into position and held via the anchor bolts and friction due to dead loading after the initial bridge construction was completed. At some point, the anchor bolts failed due to thermal loading with excessive unaccounted-for restraint in the expansion bearing. However, the friction force on the girder continued to hold it in place. Some inciting event led to a short-term reduction in the vertical reaction at the bearing, relieving the frictional force at the bearing and allowing the girder to shift back to its original configuration prior to construction. This scenario appears to fit most of the observations from the bridge both pre- and post-repair. However, this sequence of events is purely speculative in the absence of more compelling evidence.
xii

The residual capacity analysis in Chapter 4 indicates some reduction in the girder web end panel shear resistance, as well as the resistance of the bearing stiffeners at the subject bearing due to the bearing displacement. Based on a refined full nonlinear finite element analysis, the inventory level rating factor based on the girder web end panel shear resistance is estimated to be reduced from 2.44 to 2.05 and the corresponding rating factor based on the bearing stiffeners at the displaced bearing is estimated to be reduced from 2.90 to 2.60. The exterior girder has sufficient inventory level capacity with respect to these strength limit states in spite of the bearing lateral displacement. Furthermore, it is noted that the girder would actually reach its flexural capacity before the above limit states are achieved, due to flexural yielding combined with minor flange and web local buckling, even for the loadings that maximize the web end panel shear or the subject end bearing vertical reaction. The girder flexural capacity is achieved at locations along its length that are significantly removed from the "damaged" portions of the girder, both for the critical loadings maximizing the web end panel shear and the vertical reaction supported by the bearing stiffeners, as well as for the live load position maximizing the girder major-axis bending moment. Therefore, the flexural resistance of the girder in essence protects the girder against failure involving the strength limit states influenced by the bearing displacement. Regarding its flexural capacity, the exterior girder is found to approximately satisfy the AASHTO LRFR first-level design-load operating level requirements.
The analysis performed in this project shows that the girder still has excess capacity to resist expected service loading even in its shifted configuration. As such, total girder replacement is not needed. If future occurrences of bearing and associated steel girder end shifts are observed on Georgia bridges, detailed analysis will not be needed unless the
xiii

altered geometry is significantly different than the as-built configuration. The methodology for repair used the previous two times that steel girder bearing shifts were observed is appropriate and should be used for any future occurrences on Georgia bridges. This repair methodology includes heat-straightening the rotated/shifted girder and installing a new bearing and anchor bolts.
xiv

ACKNOWLEDGEMENTS Mr. Bill Duvall, State Bridge Engineer; Mr. Clayton Bennett, State Bridge Maintenance Engineer; Mr. David Jared, Assistant Office Head/Research Section Head; and Mrs. Supriya Kamatkar, Research Engineer, at GDOT provided many valuable suggestions throughout this study. Special thanks go to Mr. Ryan Beasley, GDOT Bridge Inspection Supervisor, and his crew who provided the snooper truck and traffic control for the field inspections on the subject bridge. At the Georgia Institute of Technology, Mr. Jeremy Mitchell provided invaluable help with the field inspections. The authors express their profound gratitude to all of these individuals for their assistance and support during the completion of this research project.
xv

INTRODUCTION AND BACKGROUND 1.1 Problem Statement
The bridges in GDOT's inventory include one in Lowndes County that is specifically located at county road station 416 + 87.52. The general location of the bridge is shown in Figure 1. The structure is a four-span steel plate girder bridge with two spans continuous over traffic and two simply supported end spans that are not located over traffic.
FIGURE 1 Bridge Location in Lowndes County, Georgia A 2018 routine inspection of the bridge revealed that the expansion bearing for the fascia girder located at the pier on the simply supported end span at the southeast corner of the bridge had experienced a movement of approximately 5 in., with the steel girder itself also translating and rotating. Figure 2 is a photo of the translation. In addition to the lateral
1

movement, the end of the steel girder was rotated at the bearing plates as shown in Figure 3. This condition was not observed in the bridge inspection completed two years prior, and as such is assumed to have occurred at some point in the previous 24 months.
FIGURE 2 Bearing Movement at End of Girder
on Lowndes County Bridge
2

FIGURE 3 Bearing Rotation at End of Girder on Lowndes County Bridge
1.2 Project Objectives The objective of this research project was to perform an assessment and analysis of the
plate girder and bearing that had moved on the Lowndes County bridge. The first series of research tasks involved a detailed field inspection of the subject bridge prior to repairs. With support from GDOT personnel, the research team was able to inspect the translated bearing and rotated girder, as well as the other structural components of the bridge. In addition to the field inspection, previous inspection reports and photos were reviewed to ascertain any history of the bridge that might be related to the observed bearing movement and girder translation/rotation. The bridge drawings provided by GDOT for this purpose can be found in Appendix A. Once repairs were completed on the bridge, a second inspection was performed.
3

The next set of tasks related to an evaluation of potential causes for the observed bearing shift. This evaluation necessitated estimation of the forces required to generate the movement at the bearing and rotate the steel girder. A simplified model was used to estimate the force required to translate the bearing/girder 5 in.. Then, a series of numerical simulations were performed to determine the types of actions that could cause the bearing/girder to shift in the observed manner.
The final task of the project focused on determining the residual capacity of the shifted girder and comparison with the capacity of the girder in its original undamaged configuration. American Association of State Highway and Transportation Officials (AASHTO) Load Resistance Factor Rating (LRFR) [1] calculations were performed to determine the governing rating factor for the plate girder. Then, refined finite element simulations were performed to verify the rating factor for both the shifted and the original undamaged configuration of the bridge girder.
1.3 Previous Work There has been a limited amount of published work focused on the evaluation and
analysis of damaged plate girder bridges. Urban [2] used field measurements and finite element analysis to evaluate the fatigue performance of damaged steel bridge girders and the efficacy of heat-straightening techniques to make field repairs. Al Badran [3] performed a structural reliability assessment of a corroded steel girder bridge considering both ultimate and serviceability limit states. Czarnecki [4] created a series of system reliability models to evaluate steel girder bridges. Khurram et al. [5] performed an experimental and numerical evaluation of the bearing capacity of steel plate girders affected by end panel corrosion. The authors in that study determined that minimum thickness within any damage
4

height may be used to simulate the corrosion damage in a finite element analysis (FEA). They further proposed empirical relationships to estimate the bearing strength of a plate girder affected by the local corrosion damage at its end. Stuir and Earls [6] developed a methodology to rapidly assess bridges with damage to the superstructure, caused by overheight trucks or lower-than-average overhead clearance. Terrestrial laser scanning and image processing techniques were combined with the finite element method to develop a suitable analytical model. Kuawa and Bien [7] developed a comprehensive methodology of numerical nonlinear analysis of the consecutive phases in the structural behavior of bridge plate girders with deformations. These previous works indicate that no single tool or methodology is applicable in the evaluation and repair of plate girder bridges, and that case-by-case assessments must be performed based on the particular geometric, environmental, and service load conditions.
5

INSPECTION AND DOCUMENT REVIEW
2.1 Detailed Field Inspection Prior to Bridge Repair The research team visited the bridge in Lowndes County on June 6, 2018, and
performed a detailed inspection of the girder and bearing that had experienced movement. The other structural components in the area adjacent to the incident location were also examined to identify any damage or deterioration that may have been related to the subject bearing movement. With support from experienced GDOT personnel, the research team was able to inspect the translated bearing and rotated girder closely using a snooper truck to examine the structural elements in detail. Figure 4 shows the snooper truck setup that the research team used to perform the detailed inspection of the bridge.

(a)

(b)

FIGURE 4 Snooper Truck Setup for Bridge Inspection: (a) Exterior; (b) Interior

The research team first confirmed that the dimensions of the plate girder were the same as the dimensions shown in the bridge plans. The shifted bearing was then examined in detail, confirming the initial report of an end translation of approximately 5 in., as shown

6

in Figure 5. In addition, the research team noted the obvious curvature and rotation in the girder, as shown in Figure 6. Based on field measurements, the girder appeared to have rotated torsionally by approximately 7 degrees, as shown in Figure 7.
FIGURE 5 Bearing Shift at End of Plate Girder
7

FIGURE 6 Curvature in Girder at Shifted Bearing
8

FIGURE 7 Measured Rotation in Girder at Shifted Bearing A concrete edge beam framed into the top of the girder at the location of the shifted bearing. This edge beam exhibited clear damage, as shown in Figure 8. While it is not possible to say exactly when the edge beam was damaged, it should be noted that the type of damage observed is consistent with torsional loading on a reinforced concrete beam. In addition, a portion of the edge beam that had spalled off was found on the shoulder of the
9

highway next to the pier. As such, a reasonable inference is that the rotation of the girder accompanying the bearing shift is the likely cause of the damage to the concrete edge beam.

(a)

(b)

FIGURE 8
Concrete Edge Beam: (a) View of Framing into the Girder at the Bearing Location; (b) Closeup of Damage to Edge Beam

One important observation from the inspection performed prior to repair of the bridge was that none of the structural elements adjacent to the shifted bearing appeared to have been impacted or damaged from external forces. In fact, no signs of impact damage were found on any of the bridge substructure or superstructure elements. An expanded set of photos and details from the pre-repair field inspection is given in Appendix B.

2.2 Field Inspection After Bridge Repair The research team returned to the Lowndes County bridge site on March 29, 2019, to
inspect the bridge after contractors had completed their repairs to the shifted girder. Based on discussions with the GDOT District 4 engineer, the following basic steps were taken to complete the repair:

10

1. The dead load was removed from the girder using hydraulic jacks. When the load was removed, the girder shifted part of the way back to its original position on the pier cap. The specific amount of movement was not recorded.
2. The end of the girder from the location of the closest diaphragm to the bearing location was heat straightened to bring the girder back to its original position. The heat-straightened section is shown in Figure 9.
3. New anchor bolts were installed in the pier cap and a wider (compared to the original) bearing was installed. The repaired bearing is shown in Figure 10.
4. The concrete edge beam framing in to the top of the girder was repaired, as shown in Figure 11.

(a)

(b)

FIGURE 9
Section of Repaired Girder Subjected to Heat Straightening (note freshly painted sections): (a) Interior; (b) Exterior

11

(a)

(b)

FIGURE 10 Repaired Bearing: (a) Interior Side of Girder; (b) Exterior Side of Girder

FIGURE 11 Repaired Concrete Edge Beam An expanded set of photos and details from the post-repair field inspection is given in Appendix C.
12

2.3 Document Review Previous inspection reports and photos were examined, but no clear history related to
the observed bearing movement and girder translation was found. Documents reviewed can be found in Appendix D. 2.4 Review of Similar Incident on Another GDOT Bridge
While investigating the observed damage on the Lowndes County bridge, the research team was made aware of a similar incident that had occurred previously on another bridge in GDOT's inventory. Bridge 309-0014-0 traversed the Oconee River on State Road 280 approximately 75 miles southeast of Macon, Georgia. The general location of the bridge was as shown in Figure 12.
FIGURE 12 Bridge 309-0014-0 Located Approximately 75 miles SE of Macon
13

This bridge was originally constructed in 1930 and widened in 1956. A 2008 routine inspection of the bridge noted a girder that was described as "twisted" by inspectors, as described in the portion of the inspection report shown in Figure 13. The shifted/twisted bridge girder is shown in Figure 14. The inspection report noted that during the repair of this bridge, "....the crew jacked up on the beam and it came back into place on the cap." This is similar to the girder movement observed when dead loads were removed during repairs on the Lowndes County bridge, as noted in Section 2.2. The girder for Bridge 3090014-0 was repaired by installing new anchor bolts and steel retaining plates as shown in Figure 15. The bridge functioned normally after these repairs were completed, until it was replaced with a new bridge.
14

15

FIGURE 13 Inspection Report for Bridge 309-0014-0 Noting Twisted Girder and Detailing Repairs Completed

FIGURE 14 Twisted Girder Observed on Bridge 309-0014-0: (a) Exterior View; (b) Interior View
FIGURE 15 Repaired Girder on Bridge 309-0014-0
16

POTENTIAL CAUSES OF THE BEARING SHIFT
The research team considered two potential causes for the bearing shift observed on the Lowndes County bridge. The first scenario involved the application of a horizontal force on the girder near the bearing that would have caused the bearing to shift laterally. This is the most straightforward scenario given the observed movement in the bearing. However, the research team's conclusion is that it is very unlikely that an external force was the cause of the girder shift. A simple structural analysis indicates that a relatively high force would be needed to overcome friction and other resistance to translation and rotation at the end of the girder. A scenario causing the application of that force to the girder without resulting in additional observable damage to the girder is difficult to envision.
The second potential scenario considered by the research team involved a series of interconnected circumstances originating when the bridge was first constructed and considering the bridge service environment and a significant short-term loading event. While this scenario requires multiple stages to occur over time, the research team believes this scenario is the most likely one to cause the bearing shift observed in the bridge. Each of these scenarios is explored in more detail in this chapter.
One important factor in evaluating the potential causes for the observed bearing shift is the realization that the anchor bolts installed at the bearing during initial construction must have failed at some point during the bridge's service life to allow the lateral movement to take place. After extensive discussions with GDOT personnel, the research team identified the most likely cause for the anchor failure as restrained thermal expansion causing the buildup of excess force, and resulting in shear rupture of the bolts at the interface of the bearing with the concrete pier cap. This failure would have occurred at
17

some time during the bridge's service life; it is impossible to identify with any certainty when this occurred. A rational analysis of the service conditions and thermal effects needed to cause the anchor bolt failure is presented in Section 3.1.

3.1 Shearing of Anchor Bolts Prior to Bearing Shift As shown on Drawing Sheet 5 (see Appendix A), an expansion bearing was specified
at the end of the damaged girder supported by the pier in the original design. This bearing was designed to allow longitudinal expansion of the girder; anchor bolts installed in the pier cap passed through slots in the girder bottom flange at this location. The two anchor bolts were 1 in. in diameter. During the initial damage inspection of the bridge by GDOT, the failure surface of one of the anchor bolts was photographed as shown in Figure 16. The corrosion on the failure surface of the bolt indicates that the anchor failure most likely occurred some time before the bearing shift occurred.
Given the nature of the observed failure in the anchor bolts, it is critical to determine the shear capacity of the anchorage system. The shear capacity of the anchor bolts is calculated based on American Concrete Institute (ACI) 318-14 Design Provisions [8]. Equation 17.5.1.2b from the ACI 318 code is used to calculate the shear capacity of the anchor bolt:

= 0.6,

(3-1)

where,

,

= Shear capacity of a bolt = Bolt area = 0.785 in2

= Steel tensile strength (estimated as 58 ksi from code provisions)

18

Using this equation, the shear capacity of a single anchor bolt is found to be approximately 27 kips; for the two-bolt configuration, the nominal shear capacity is accordingly 54 kips.
FIGURE 16 Sheared Anchor Bolt in Pier Cap at Shifted Bearing Location As noted previously, the bearing in question on the Lowndes County bridge was designed as an expansion bearing; with such bearings, axial expansion due to thermal effects is allowed by placing the anchor bolt within a slot in the girder flange rather than using a standard hole diameter. In theory, this configuration should allow thermal expansion of the girder without significant restraint. However, the degree of expansion allowed may have been much less than called for in the design. Figure 17 shows the original bearing slot in the repaired girder at the bearing. Measurements of the slot indicate that there may not have been sufficient clearance to allow the girder to expand without generating large forces at the bearing. That is, it appears that the width of the slot in the
19

direction perpendicular to the slot length may not have been sufficient to accommodate the 1-in.-diameter anchor bolts and allow free movement in the longitudinal direction. If that was, in fact, the case, then thermal effects could have caused the buildup of sufficient forces to exceed the shear capacity of the anchor bolts.
FIGURE 17 Repaired Girder Bearing Showing Original Expansion Bearing Slot The research team estimated the required uniform temperature change to generate the reaction force that would rupture the anchor bolts if the girder was restrained against thermal expansion. Article 3.12.2 of the AASHTO Load and Resistance Factor Design (LRFD) Bridge Design Specifications [9] specifies the consideration of the effects of uniform temperature change during the service life of a bridge. Article 3.12.3 also specifies an optional additional temperature gradient effect. For the steel girder under consideration, the AASHTO temperature gradient profile suggests a larger temperature change in the deck concrete, but a corresponding uniform temperature change in the steel girder. Since the
20

girders in the Lowndes County bridge are noncomposite, the temperature gradient profile would suggest vertical bending deformations of the bridge deck different from those of the steel girder. Concomitant bending of the steel girder would require composite interaction with the deck. Whether incidental composite interaction (due to friction, etc.) is assumed between the girders and the deck or not, the temperature gradient loading would suggest that vertical forces would be required between the deck and the steel girder to force the deck and the girder to have the same vertical displacements. This would likely result in some vertical separation between the deck and the steel girder, reducing the incidental composite interaction. If the steel girders are assumed to have no composite interaction with the steel deck, then the corresponding uniform temperature change in the steel girder associated with the AASHTO temperature gradient profile would cause additional movement comparable to that associated with a basic uniform temperature change in the steel. Therefore, for the noncomposite girder under consideration in this study, only the AASHTO requirement for the accommodation of a larger uniform temperature change (discussed below) is considered.
Using the above assumptions, two different boundary conditions are considered to estimate the upper and lower bounds for the uniform temperature change needed to exceed the shear capacity in the anchor bolts. The following additional assumptions are made in performing the thermal analyses:
1. Plane sections remain plane in the girder upon bending. 2. The girder stress is below yield, such that the steel girder behaves elastically. 3. The anchor bolts are not deteriorated and maintain their full capacity.
21

4. Only a temperature increase, relative to the initial conditions when the bearings were set during the initial construction of the bridge, is considered. A comparable decrease in temperature relative to the initial conditions could be considered; the results would be equal and opposite.
3.1.1 Upper-bound Analysis Based on the Assumption of Zero Relative Movement Between the Bearings at the Ends of the Girder
The first set of boundary conditions considered for the thermal analysis is based on the assumption of full restraint by the anchor bolts against longitudinal displacement at the bottom of the girder, while the top of the girder is assumed to be free to expand. Composite action of the noncomposite steel girders with the concrete deck, e.g., due to friction between the deck and the girder top flange, is neglected as a simplification. The corresponding deformed configuration of the girder is shown schematically in Figure 18.

T

F

F

47.5 ft
FIGURE 18 Deformed Girder due to Uniform Temperature Change (Increase in Temperature) with
Zero Relative Movement Between the Bearings at the Bottom of the Girder
Because the relative longitudinal displacement between the bearings at the ends of the girder is assumed to be zero until the anchor bolts rupture, the relative displacement due to

22

the thermal expansion and that due to the reaction forces, F, at the bottom of the girder, must be equal in magnitude but opposite in direction. This condition is expressed as:

T + = 0

(3-2)

where, T

= Displacement due to thermal expansion = Displacement due to force exerted at the anchor bolts

The reaction force, F, not only compresses the girder, but also induces uniform moment throughout the length of the girder due to the eccentricity of the bearings with respect to the girder centroid. The corresponding bending deformations cause additional relative longitudinal displacement between the bearings. The total relative displacement between the bearings at the ends of the girder can be estimated as:

T

-



-





2



2



2



2

=

0

(3-3)

where, L T F A E d I

= Length of the girder = 47.5 ft = Coefficient of thermal expansion = 6.5E-6 in./in./ [10] = Change in temperature (solution variable) = Force required to rupture two anchor bolts in shear = 54 kips = Cross sectional area of the girder = 30.38 in.2 = Elastic modulus of steel = 29,000 ksi [10] = Depth of the girder = 61 in. = Moment of inertia of the girder with respect to the horizontal axis (major-
axis bending = 14,156 in.4)

23

From Equation 3-3, the temperature change required to rupture the two anchor bolts is estimated to be approximately 29.
3.1.2 Lower-bound Analysis Based on the Assumption of Zero Relative Movement Between the Girder Ends at the Bottom and at the Top of the Girder
The second set of boundary conditions considered to estimate the lower-bound temperature change needed to rupture the anchor bolts is based on the assumption that both the girder top and bottom are restrained against expansion. The scenario in this case is that the top of the girder is also restrained against expansion by the concrete deck, including potential conditions causing longitudinal restraint at the deck joints. The ends of the girder are embedded in concrete edge beams at the girder top flange; therefore, this would potentially provide some ability to restrain the tops of the girder by the deck. This analysis neglects any concomitant elongation of the bridge deck between the bearing locations. The corresponding girder condition is shown schematically in Figure 19.

F2

T

F2

F1

F1

47.5 FIGURE 19 Girder Subjected to Uniform Temperature Change and Restrained at its Top and Bottom

Similar to the analysis of the girder using the previous boundary conditions, the sum of the relative displacements between the girder ends due to thermal expansion and due to the
24

reaction forces must equal zero, based on the above idealization, until the anchor bolts rupture. There are no girder bending deformations in this analysis, since it is assumed that the forces F1 and F2 in Figure 19 are equidistant from the girder centroid. The magnitudes of the reaction forces at the top and bottom of the girder are assumed to be equal given a uniform temperature change in the girder and the boundary condition assumptions. Therefore, the total girder relative end displacements can be expressed as:

T + 1 + 2 = 0 or

(3-4)

T

-

1

-

2

=

0

(3-5)

where, T 1 1 1 2

= Displacement due to thermal expansion = Displacement due to force exerted at the anchor bolts = Displacement due to force exerted at the concrete edge beam = Force required to rupture two anchor bolts in shear = 54 kips = Restraint force at the top of the girder, equal in magnitude to F1

From Equation 3-5, the temperature change required to rupture two anchor bolts was estimated to be approximately 19.
The maximum and minimum design temperatures for steel girder bridges with concrete decks in South Georgia are given as 110 and 20, using the contour maps for Procedure B in Figures 3.12.2.2-3 and 3.12.2.2-4 of Article 3.12.2.2 of the AASHTO LRFD Specifications. Procedure B provides more accurate estimates of the uniform temperature changes that should be considered for design compared to the more traditional

25

Procedure A. As such, it is certainly plausible that a temperature change of the magnitudes noted in the analysis above could occur in the expected service environment for the Lowndes County bridge. If the longitudinal displacement were constrained at the expansion bearing, it would be possible for the bearing anchor bolts to fail in shear due to thermal effects.

3.1.3 Other Sources of Bearing Longitudinal Force One additional source of potential large longitudinal force at the bearing location, if the
longitudinal expansion were constrained at the expansion bearing, would be the tendency for relative longitudinal expansion between the girder bearings when vertical loads are applied to the bridge. To approximately quantify these longitudinal forces, one can calculate the relative longitudinal movement in a general doubly-symmetric beam subjected to uniformly distributed load. If the maximum simply supported moment is set equal to the girder yield moment, the girder end rotations are calculated due to the corresponding loading, and the relative longitudinal expansion between the girder ends is then taken equal to the end rotations times one-half the girder depth, one obtains the following:

= 2
3

(3-6)

where Fy is the specified minimum yield strength, taken as 36 ksi for this bridge, and the other variables have been defined above. This equation indicates that, at the development of the yield moment in the girder, the relative longitudinal displacement--if the girder is free to expand--is 0.471 in. If the relative longitudinal movement between the bearings is

26

prevented due to unintended restraint at the expansion bearing, a force equal to 243 kips is obtained using the second and third expressions in Eq. (3-3).
Under the expected service conditions, the live load moments in the girder would tend to be smaller than the girder yield moment. However, live load moments that are a significant fraction of the girder yield moment are certainly possible. The corresponding live load longitudinal forces at the constrained bearings would combine with the corresponding forces due to thermal expansion, thereby potentially rupturing the anchor bolts at an even smaller uniform temperature change.
3.2 Bearing Shifted by an External Force Assuming the anchor bolts had failed previously, a scenario where an external load
caused the shift of the bearing was considered first. To estimate the force that could cause the observed shift in the girder bearing, a simple approach based on fundamental application of strength of materials and structural mechanics concepts was initially employed. After estimating the force required to shift the bearing analytically, more detailed numerical analyses were performed to verify that the estimates were reasonable. These analyses required knowledge of the material properties of the steel girder; however, the specific steel type and associated properties were not listed in the bridge drawings or the maintenance documentation discovered during this investigation. Based on commonly used steel types for bridge girders fabricated in the time period the bridge was constructed, the research team selected standard A36 steel for use in the analyses [10, 11]. The properties of the steel were taken from the American Institute of Steel Construction (AISC) Steel Construction Manual (SCM) [10], and are given in Table 1. The AASHTO Manual for Bridge Evaluation (MBE) [1] Article 6A.6.3.2 suggests the use of Fy = 33 ksi and Fu =
27

66 ksi for bridges constructed between 1936 and 1963 when the specification and grade of steel are unknown. The latest date of notes on the engineering drawings is 1961. The Lowndes County bridge was constructed at a time of transition to A36 as the predominant steel employed in construction.

TABLE 1 Steel Material Properties

Properties
Elastic Modulus, E
Poisson's Ratio, Specified Minimum Yield
Strength, Fy Minimum Tensile
Strength, Fu

Values 29,000 ksi
0.3 36 ksi 58 ksi

3.2.1 Idealized Models and Analytical Solutions The first step in the bearing shift analysis was to estimate the force required to shift the
bearing horizontally by 5 in., assuming a simple transverse force applied at the bottom flange of the girder near the bearing location. The analytical models used to represent the girder and its bracing system were developed using the original bridge drawings provided by GDOT, supplemented by observations and measurements made during the detailed field inspection. Two idealized models were used in this first-stage analysis: (1) an "upperbound" model that assumes stiff boundary conditions and structural interaction of the girder elements, and (2) a "lower-bound" model that assumes more flexibility in the system.
28

3.2.1.1 Upper-bound Idealized Model In the upper-bound idealized model, the girder bottom flange, the bearing stiffeners at
the shifted bearing, and the connection plates at the diaphragm locations are assumed to provide the structural resistance to lateral translation of the end of the girder. The components of this model are identified in Figure 20. The contribution of the girder web and girder top flange to the transverse stiffness is neglected. The girder bottom flange is modeled as a simply supported continuous beam with lateral displacement constraints at the location of the diaphragms, as shown in Figure 21. The bearing stiffeners at the end of the girder are modeled separately as a cantilever beam extending from a rigid connection at the bottom of the edge beam down to a pinned connection at the bottom flange, as shown in Figure 22. While this basic model is clearly a dramatic over-simplification of the actual girder system, it provides a useful first-stage upper-bound estimate of the forces required.
The total force required to translate the bearing by 5 in. is calculated by adding the force required to cause a 5-in. displacement in the bottom flange "continuous beam" and the force needed to produce a similar displacement in the "cantilever" bearing stiffener:

= 1 + 2

(3-7)

where P1 is designated as the "beam force" and P2 is designated as the "cantilever force." Basic structural analysis indicates that both structural elements must form a plastic hinge at the supports adjacent to the bearing location to reach the required horizontal displacement at the bearing. The forces required to generate the 5-in. displacement in the bottom flange (P1) and in the bearing stiffeners (P2) are estimated to be about 2.9 kips and 12.9 kips, respectively. As such, the total force, Ptotal, required to shift the bearing is estimated to be about 15.8 kips using the upper-bound idealized model. This analytical

29

solution is validated by building the same model in a simple matrix structural analysis program. The program MASTAN2 [12] provides basic capabilities for three-dimensional (3D) truss and/or frame element modeling of structures. A snapshot of the upper-bound model in MASTAN2 [12] at a 5-in. displacement of the bearing, also associated with the maximum load capacity of the model, is shown in Figure 23.
Diaphragm Connection Plates
Bearing Stiffeners Bottom Flange
FIGURE 20 Damaged Girder from Underneath the Bridge Highlighting the Bearing Stiffeners at the
Pier and the Bottom Flange of the Girder Used in the Simplified Model
30

FIGURE 21 Illustration of Upper-bound Idealized Model of the Girder Bottom Flange
31

FIGURE 22 Illustration of Upper-bound Idealized Model of the Bearing Stiffeners
FIGURE 23 Displaced Shape of Upper-bound Model at 5-in. Displacement of the Bearing and
Corresponding Development of the Model's Maximum Load in MASTAN2 [12]
32

3.2.1.2 Lower-Bound Idealized Model The upper-bound idealized model provides a reasonable estimate of the required force
to shift the bearing, but this significantly simplified representation of the girder and its boundary conditions result in what is expected to be an overly stiff structural system. Boundary conditions preventing any lateral displacement at the locations of the diaphragms and restraining both lateral displacement and torsional rotation at the top of the bearing stiffeners are likely to be very conservative in terms of estimating the restraint provided to the bearing lateral movement by the physical girder. To develop a corresponding lowerbound idealized model, displacement constraints at the diaphragm locations on the bottom flange are replaced with elements representing the connection plates and the bridge diaphragms at the diaphragm locations highlighted in Figure 24. The connection plates are assumed to be pin-supported at the top flange of the girder, and the diaphragms are assumed to be pin-supported at the adjacent bridge girder. Moreover, the fixed support at the top of the bearing stiffeners is replaced with a rigid connection to a frame model of the concrete edge beam highlighted in Figure 25. The edge beam is assumed to be pin-supported at the locations of the steel girders along its length.
33

Diaphragm

Diaphragm

Connection Plate

Connection Plate

FIGURE 24
Photos from Underneath the Bridge Highlighting the Diaphragms and the Connection Plates

Bearing stiffeners embedded in concrete edge beam
FIGURE 25 Embedment of the Bearing Stiffeners into the Damaged Concrete Edge Beam
34

A schematic illustration of the lower-bound model is shown in Figure 26. The MASTAN2 [12] model formulated based on these assumptions is shown in Figure 27. Similar to the upper-bound analysis, the total force required to cause a 5-in. displacement at the bearing is the sum of the "beam force," P1, developed in the girder bottom flange and the "cantilever force," P2, developed in the bearing stiffeners. The force required to displace the bearing 5 in. is estimated using MASTAN2 [12] to be approximately 10.5 kips.
FIGURE 26 Illustration of Lower-bound Idealized Model of the Girder
35

FIGURE 27 Displaced Shape of Lower-bound Model in MASTAN2 [12] at 5-in. Displacement of the
Bearing
3.2.1.3 Frictional Restraint at Bearing from Concrete Pier Any externally applied force has to overcome the lateral frictional restraint induced
from the contact between the bearing and the concrete pier, in addition to the force estimated from the upper- and lower-bound models to displace the bearing by 5 in. The frictional force is calculated by multiplying the estimated vertical dead load supported by the bearing with the static coefficient of friction between steel and concrete. The dead load carried by the bearing is estimated to be 29.4 kips. A detailed description of the dead load calculations is provided in Appendix E. Assuming the static coefficient of friction between the concrete and steel surfaces is 0.57 [13], the force required to overcome friction is estimated to be approximately 16.8 kips. Adding this to the upper- and lower-bound forces calculated previously, the external lateral force required to shift the bearing by 5 in. is estimated to be in the range of 27.3 to 32.6 kips.
3.2.2 Finite Element Analysis To provide a more rigorous estimate of the external force required to shift the girder
bearing, the bridge girder was modeled using the FEA program ABAQUS [14]. To simplify
36

the finite element analysis, the research team explicitly modeled only the girder itself, the bearing experiencing the 5-in. movement, the girder diaphragms, and the concrete edge beam connected to the girder top flange above the subject bearing. The influence of the other components of the bridge were accounted for with the selection of appropriate boundary conditions. Figure 28 shows the model used in the simulation and its overall displacement boundary conditions.
FIGURE 28 Finite Element Model of the Exterior Girder System and Concrete Edge Beam in
ABAQUS [14] The exterior girder, including its transverse stiffeners and diaphragms were modeled using the four-node quadrilateral general-purpose S4R shell element. The sole plate and bearing plate, and a plate that represents the top of the pier cap were modeled using the C3D8R element, an eight-node general-purpose three-dimensional solid element. The concrete edge beam was modeled using the B31 element, a two-node linear beam element. The material properties of A36 steel taken from the AISC SCM [10] were used in the simulations, with yield strength of 36 ksi and modulus of elasticity of 29,000 ksi. The material was modeled as a bilinear material with a tangent modulus within the inelastic
37

range of 110 ksi for numerical stability. The concrete was modeled to have a compressive strength of 4500 psi and a unit weight of 150 pcf, so that the modulus of elasticity was calculated to be 4070 ksi [8]. The von Mises yield condition was used to capture the yielding response within the simulation models. The small inelastic stiffness was represented using an isotropic hardening idealization.
The displacement boundary conditions of the above model are as follows. The top flange of the girder is constrained against movement in the lateral direction to represent the effect of a continuous lateral restraint from the concrete deck and haunch at the top flange of the girder. Also, displacement constraints in lateral and vertical directions are applied to the bottom flange at the abutment location on the opposite end of the girder from the displaced bearing. The lateral displacement and the rotations in the plane of the cross section are constrained at the ends of the diaphragms opposite from their connection to the exterior girder to represent the connection between the diaphragms and the adjacent interior girder. The concrete edge beam is pin-supported along its length at the locations of the intersecting girders and assumed to be rigidly connected to the girder top flange at the location of the bearing stiffeners. The components of this model are highlighted in Figure 29. Figure 30(a) shows a close-up view of the girder bearing. A sole plate is attached to the bottom of the girder on top of the bearing plate. As shown in Figure 30(b), a plate representing the top of the pier cap is modeled, which is constrained in all directions. To account for the frictional force induced between the contact surfaces, the same static coefficient of friction used in the simplified analytical solutions is applied between the contact surfaces of the bearing and the plate representing the top of the pier cap.
38

Diaphragm

Interior Girder

Exterior Girder

(a)

Concrete Deck

Haunch

Top Flange

Fixed Bearing (b)
Concrete Edge Beam

Bearing Stiffeners

(c)

(d)

FIGURE 29
Physical Elements Assumed as Restraints in the Finite Element Model: (a) Diaphragm Connected to the Exterior and the Adjacent Interior Girder; (b) Fixed Bearing at the Abutment; (c) Concrete Deck and Haunch at the Top Flange of the Girder; (d) Bearing
Stiffeners Embedded in Concrete Edge Beam

39

(a)

(b)

FIGURE 30 Displaced Bearing: (a) Detail; (b) Corresponding ABAQUS Finite Element Model [14]

The dead load of the steel components is applied as a body load given the weight density of steel, 490 pcf. The dead load of the concrete edge beam is applied as a body load given the weight density of concrete, 150 pcf. The concentrated load due to additional loads from details at the north end girder bearing is applied as a uniform pressure to the surface of the top flange of the girder between the bearing stiffeners at this location. The remainder of the dead loads are applied as a uniform surface pressure to the top flange of the girder. Then, a concentrated load in the lateral direction is applied on the bottom flange at the location of subject bearing.
The finite element analysis indicates that a lateral force of approximately 32.6 kips is required to shift the bearing by 5 in.; this result is close to the predicted required load from the upper-bound model. Figure 31 shows the configuration of the girder when an external force of 32.6 kips is applied in the lateral direction on the bottom flange at the bearing location. The magnitude of lateral displacement, U, indicated in the figure legend is in units of inches.

40

FIGURE 31 Deformed Finite Element Model at Load of 32.6 kips, Corresponding to a Shift of the
Bearing by 5 in.
It is difficult for the research team to identify a scenario where a lateral force of this magnitude would be specifically applied to the girder bearing without any evidence of significant damage to the girder. One potential cause investigated was the attachment of support scaffolding used by contractors when the girders are periodically repainted. This scaffolding may be attached to the girders, and as such could potentially cause lateral forces on a girder near a bearing. However, when the research team visited a painting site on a bridge similar to the one investigated on this project, it was noted that the scaffolding was attached parallel to the girders as opposed to transversely. This connection detail is shown in Figure 32. GDOT personnel have noted that painting contractors use a variety of connection and support methods for their scaffolding, and that some setups would result in lateral forces being introduced to the girder. However, even if this is the case, it seems highly unlikely that contractor scaffolding could result in a force of over 30 kips on the girder at a single location, as appears necessary from the analysis in the previous sections.
41

As such, the research team does not believe that the bearing shift was caused by a single external force.
Another possible scenario was that a number of distributed lateral loads was applied to the girder, resulting in a total bearing force that overcame the friction at the bearing and displaced the fascia girder by 5 in. at the support. However, a total applied load larger than 30 kips would be necessary to generate the 5-in. movement at the bearing if the load were distributed along the girder length. The movement may have been caused by distributed loads from the attachment of scaffolding, but would require an unexpectedly large total lateral force. Furthermore, given that the lateral movement of the fascia girder was dominated by the lateral displacement at the bearing, and the girder lateral deformations were predominantly concentrated at the bearing, any lateral forces from the attachment of scaffolding would necessarily have been concentrated mainly in the vicinity of the bearing.

Direction of primary support cables

(a)

(b)

FIGURE 32
Scaffolding Details: (a) Common Scaffolding Used by Painting Contractors on GDOT Bridges; (b) Support Cables for Scaffolding Running Parallel to Girders

42

3.3 Bearing Shift Due to Initial Conditions and Service Environment Once the analysis outlined in Section 3.2 was completed, it became clear that the
bearing shift on the Lowndes County bridge was most likely not the result of an externally applied force on the girder. As such, the research team considered other events that could have led to the damage observed on the bridge. Eventually, a scenario was envisioned that a girder with a significant initial geometric imperfection had been straightened during its original installation, and kept in place by anchor bolts and a frictional force generated from the dead load once the bridge deck and remaining superstructure elements were installed. At some point during the bridge's service life, in that scenario, the bearing anchor bolts failed--most likely due to a combination of thermal effects plus the effects of live load as discussed in Section 3.1. The frictional force generated by the sustained dead loads kept the girder in its installed position, overcoming any restoring force generated as the girder attempted to re-align to its "natural" imperfect geometry.
The next event leading to the shift in the girder bearing would have been something that temporarily relieved the dead load over the end of the girder, releasing the frictional restraint on the bearing and allowing the girder restoring force to swing the girder back toward its original (preconstruction) position. It is unclear what might have led to the release of the dead load on the system. One potential cause envisioned by the research team would be a heavy vehicle very abruptly stopping on the bridge over the girder area. Anecdotal information indicates that this kind of emergency stop by a heavy vehicle in motion can cause the vehicle braking system to lock, making the vehicle "bounce" as the wheels slide over the roadway and causing a very short-duration load reversal of the bridge superstructure. The research team readily acknowledges that this is only speculation--
43

during the field inspection, no evidence of such an event was found in the roadway leading up to or on the bridge. However, if the girder had been straightened and locked into position at the bearing, the bearing would be transferring a lateral force to the pier necessary to hold the girder in its "unnatural" position. Therefore, the dead load reaction need not be reduced to zero, but would only need to be reduced a sufficient amount so that the internal lateral force at the bearing overcame the friction.
If the scenario of the temporary release of the dead loads over the girder is accepted, then it is very conceivable that the girder was attempting to return to its initial imperfect geometry. If simple harmonic motion is assumed in the girder end after the frictional force was overcome by the girder restoring force, then the girder would have swung past its original configuration. If at this point the dead loads (and resulting frictional restraint) were restored on the system, the girder would have been locked in its "shifted" configuration. While this scenario might seem overly complex, it aligns with observations reported to the research team by contractors during the bridge repair discussed in Chapter 2. At some point during the repair process, the dead load on the girder was removed using load jacks. During this process, the girder moved back in the direction of its anchored configuration. However, it did not return completely to the plumb position. Therefore, the scenario outlined above does fit the limited observations available to the research team. As such, this is considered to be the most likely scenario to cause the bearing shift on the bridge among several potential scenarios considered.
44

RESIDUAL CAPACITY ANALYSIS
Detailed analyses were conducted to determine the influence of the subject bearing displacement on the capacity of the southeast exterior girder on the Lowndes County bridge. These analyses were conducted as factored Strength I live load capacity evaluations using the LRFR provisions of the AASHTO MBE [1], considering the factored dead load conditions within the girder. The factored live load capacity of the girder is evaluated based on its "undamaged" configuration prior to the bearing movement, as well as in its "damaged" state given the lateral displacement of the bearing.
The research team conducted a first-level design-load rating evaluation of the exterior girder by LRFR to determine inventory and operating level rating factors associated with the base AASHTO [1, 9] HL-93 live load. The research team first utilized routine AASHTO LRFD [9] equations to characterize the resistances associated with the key potential failure modes (or limit states) of the girder. A design-level rating was conducted considering:
1. the girder's flexural resistance, 2. the girder's resistance associated with the local transfer of the end reactions
between the girder and the bridge pier at the subject bearing by the bearing stiffeners, and 3. the girder's shear capacity adjacent to the subject bearing.
The girder's live load capacity was assessed considering these limit states for the plumb girder prior to the bearing lateral displacement, and for the deformed girder after the subject bearing was displaced laterally. These calculations were followed by a refined full
45

nonlinear shell finite element evaluation of the girder bearing and shear live load capacity at and adjacent to the subject bearing in the "undamaged" and "damaged" condition of the girder.
In summary, it was determined that even for the live load configuration producing the maximum reaction at the subject bearing, the southeast exterior girder capacity in the Lowndes County bridge is governed by the flexural resistance within the span, at a location where there is no substantive impact from the subject bearing lateral displacement. The girder shear capacity adjacent to the end corresponding to the subject bearing is impacted by a small extent due to the bearing lateral displacement, but the girder still has ample shear capacity at the subject bearing to accommodate the inventory level live load. The research team concludes that the bearing lateral displacement has a small effect on the ability of the bearing stiffeners to transfer vertical reactions to the subject bearing. Furthermore, the flexural capacity limit of the girder "protects" against the small degradation of the girder end shear or bearing capacity, since the girder will fail in flexure well before the end shear or bearing capacity is reached, even for the "damaged" girder. The criticality of the design conditions for flexure versus for shear is common for bridge girders composed of rolled Isections, but depends on the specifics of the shear design versus the flexural design for built-up I-girders. The following sections summarize the LRFR calculations and explain these attributes of the southeast exterior girder behavior.
4.1 Load & Resistance Factor Rating Analysis Load rating is the evaluation of highway bridges subjected primarily to permanent
loads and vehicular loads to determine the governing "rating factor," RF, which is the
46

multiple of a selected live load that can be safely supported by the bridge. The fundamental equation for the rating factor can be expressed as:

RF = C - DL LL

(4-1)

where, C
DL LL

= Resistance associated with the failure mode (i.e., limit state) under consideration
= Demand from the bridge dead load associated with this resistance = Critical live load demand associated with this resistance

In the context of LRFR [1], this equation becomes:

RF

=

csRn

- DC DC - DW DW
LL ( LL + IM )



PP

(4-2)

where, c

= Condition factor, which is intended to account for the uncertainty associated with the assessment of member deterioration due to natural causes (e.g., atmospheric corrosion). The AASHTO [1] Article 6A.4.2.3 commentary states that "damage caused by accidents is specifically not considered" by this factor. This factor is taken equal to 1.0 for members in good or satisfactory condition, 0.95 for members in "fair" condition, and 0.85 for members in poor condition [1]. This factor is specifically tied to the uncertainty associated with the in-condition assessment of the structure for bridges in these different conditions; the engineer still performs calculations to estimate the in-condition nominal resistance. The AASHTO commentary

47

provides an approximate conversion between the NBI (National Bridge

Inventory) superstructure condition rating and the above definitions of good

or satisfactory, fair, and poor. Based on the field assessment by the research

team, the girder was in good condition with respect to any deterioration of

its cross section; therefore, c is taken equal to 1.0 in all of the following

assessments.

s

= System factor, intended to reflect the level of redundancy corresponding to

the complete superstructure system. The Lowndes County bridge has four

girders with a girder spacing greater than 4 ft. Therefore, it is classified as

having a s = 1.0 according to Article 6A.4.2.4 of the MBE [1]. The product

cs is limited to a minimum value of 0.85 in all cases; this product is equal

to 1.0 for the Lowndes County bridge.



= Resistance factor for the limit state under consideration, from the AASHTO

LRFD Specifications [9], equal to 1.0 for flexure and for shear, and equal to

0.95 for the resistance of the bearing stiffeners.

Rn = Nominal resistance from the limit state under consideration, evaluated from

the AASHTO LRFD Specifications [9] when conducting a routine

assessment, and, in this study, evaluated by full nonlinear finite element

analysis when conducting a refined analysis assessment.

DC = Load factor associated with the component dead load, equal to 1.25 for the

Strength I assessment.

DW = Load factor associated with the wearing surface dead load, equal to 1.50 for

the Strength I assessment.

48

LL = Live load factor, equal to 1.75 for the inventory level rating and 1.35 for

operating level rating for the Strength I assessment.

P

= LRFD load factor for permanent loads other than the dead load, equal to

1.0.

DC = Component dead load; since the girders are noncomposite by design in the

Lowndes County bridge, these loads are calculated in this study based on

the tributary width of the exterior girder, and they are assumed to be resisted

entirely by the noncomposite steel girder section. These loads include the

concrete dead load from the deck; the overhang and the girder haunch; the

barrier rail attached to the overhang and the concrete edge beam along the

deck joint at the subject bearing; the steel girder self-weight, including the

miscellaneous steel weight from the transverse stiffeners; and the self-

weight from the tributary length of the steel diaphragms.

DW = The wearing surface dead load. This load is calculated using a 30 psf

wearing surface allowance in this study, as indicated for wearing surface

loads in the Georgia DOT Bridge and Structures Design Manual [15].

Assuming 145 pcf for normal weight concrete, this corresponds to a 2.6-in.-

thick concrete wearing surface.

P

= Permanent load other than dead load, taken equal to zero in this study.

LL = AASHTO LRFD [1, 9] HL-93 notional live load effect.

IM = AASHTO LRFD [1, 9] dynamic load allowance, taken equal to 0.33LL.

At the inventory level (i.e., rating with the use of LL = 1.75) for Strength I, RF > 1.0 indicates that the bridge has adequate capacity for all AASHTO legal loads and for state

49

legal loads that fall within the exclusion limits described within the AASHTO LRFD Bridge Design Specifications [9]. That is, the bridge has adequate capacity to handle live loads routinely permitted on highways of various states and grandfather exclusions to federal weight laws. At the operating level (i.e., rating with the use of LL = 1.35) for Strength I, RF > 1.0 indicates that the bridge has adequate capacity for AASHTO legal loads and for state legal loads that comply with federal weight limits and Formula B [1]. Satisfaction of RF = 1.0 at the inventory level rating corresponds to a target reliability index of 3.5, consistent with the target reliability for members in new bridges designed according to the AASHTO LRFD Specifications, whereas satisfaction of RF = 1.0 at the operating level corresponds to a target reliability index of 2.5 [16]. As indicated by the National Highway Institute (NHI), "For evaluation, a lower bound on acceptable reliability is more appropriate as the cost impact due to bridge strengthening or traffic restrictions could be quite significant. [16]"
4.2 Component Dead and Wearing Surface Dead Load for the Southeast Exterior Girder of the Lowndes County Bridge
Appendix E presents in detail the dead load calculations for the southeast exterior girder of the Lowndes County bridge. The dead loads are uniformly distributed along the girder length based on the deck and overhang tributary widths, including the barrier rail load. It is common in many designs to distribute the barrier rail load equally to all the girders in the bridge cross section for a line girder analysis. In addition, in many cases, engineers will distribute the bridge dead load equally to all the girders of the bridge cross section for line girder analysis. However, within the end spans of the Lowndes County bridge, the two exterior girders are substantially deeper than the two interior girders.
50

Furthermore, the diaphragms within the end span are of relatively shallow depth and are located near the top of the girder cross sections. Therefore, the opinion of the research team is that distribution of the dead loads based on tributary width is a more realistic representation of the actual bridge conditions for the Lowndes County bridge. The dead load from the concrete edge beam at the deck joint over the pier at the subject bearing the and dead load from the extension of the bridge girder and the deck beyond the centerline of the bearing are calculated as a concentrated load at the bearing location.
Figure 33 shows the free-body, shear, and moment diagrams for 1.25 DC + 1.5 DW for the above simply supported girder.

2.4 kip (a)
37.8 kip

47.5 ft

1.49 klf 35.4 kip

(b)

35.4 kip

-35.4 kip

420 kip-ft (c)

FIGURE 33
Factored 1.25 DC + 1.5 DW: (a) Free-body; (b) Shear; and (c) Moment Diagrams for the Exterior Girder of the Lowndes County Bridge

51

4.3 Inventory and Operating Level Rating Factors Corresponding to the Flexural Resistance of the Southeast Exterior Girder of the Lowndes County Bridge
Calculation of the design-load rating factors corresponding to the flexural resistance of the southeast exterior girder of the Lowndes County bridge requires the evaluation of the girder nominal flexural resistance. As stated previously, the girders are noncomposite in the Lowndes County bridge. The subject exterior girder has 10 in. in. top and bottom flanges and a 61 in. in. web. As such, the girder moment of inertia is Ix = 14,156 in4 and the elastic section modulus is Sx = 458.5 in3. Taking the minimum specified yield strength of the steel as Fy = 36 ksi as discussed in Section 3.2, the girder yield moment is estimated as My = 1,380 kip-ft.
Given the above dimensions, the slenderness ratio of the web is D/tw = 163. The corresponding AASHTO noncompact web limit for an I-girder is rw = 5.7 E / Fy = 162 . Therefore, the girder web classifies as slender according to the AASHTO LRFD Specifications; however, the web is very close to the noncompact web limit. Upon substituting these values into the AASHTO equation for the web load-shedding factor, Rb, it yields Rb = 0.998, which may be rounded to 1.0.
The bottom of the haunch of the girders in the Lowndes County bridge is flush with the bottom of the girder top flanges. Therefore, the girder top flanges are taken to be continuously restrained against lateral translation by the deck concrete. As such, the girder flexural resistance is not influenced by lateral-torsional buckling. However, the flanges have a bf /2tf = 13.3, which classifies them as noncompact. Therefore, the flexural resistance is impacted slightly by flange local buckling, and the factored flexural capacity of the girder in terms of bending moment, based on AASHTO LRFD [9] Article 6.10.8.2.2, is
52

csMn = (1.0)(1.0)(1.0)(0.909My) = 1250 kip-ft. Although the top flanges are restrained on three sides by the girder haunches, the AASHTO LRFD Specifications do not account for any enhancement of the flange local buckling resistance due to this restraint unless the girder is composite. The noncompact flanges can buckle locally in the direction outward from the bottom of the deck.
Calculation of the design-load rating factors corresponding to the flexural resistance also requires calculation of the maximum HL-93 live load effect. Figure 34 shows the freebody, shear, and moment diagrams for the unfactored live load causing the maximum bending moment in the subject exterior girder. These diagrams include a dynamic load allowance of 33% on the design truck and are based on a governing exterior girder flexural live load distribution factor of g = 0.66. Appendix F contains the detailed calculation of the exterior girder live load distribution factors.
53

28.1 kip

28.1 kip

7.0 kip

0.42 klf

(a)

45.1 kip

38.0 kip

11.75 ft

14 ft

14 ft

7.75 ft

40.2

(b)

45.1

12.1

Units: kip 6.2

-21.9

-27.8 -34.8

-38.0

501 kip-ft

630 kip-ft

456 kip-ft

(c)

FIGURE 34
Unfactored HL-93: (a) Free-body; (b) Shear; and (c) Moment Diagrams Producing the Maximum Moment Within the Exterior Girder of the Lowndes County Bridge, Including 33% Dynamic Load Allowance on the Design Truck and Based on a Flexural Live Load
Distribution Factor of g = 0.66

The engineer can utilize Table E6A-1 of the MBE [1] to determine the maximum HL-93 live load moment for simply supported girders. Interpolating between the rows for a 46 and 48 ft span in that table, and multiplying by g = 0.66, it yields 954 kip-ft 0.66 = 630 kip-ft for the maximum unfactored live load moment. The design truck is actually positioned in the direction opposite to the flow of traffic at the southeast corner of the bridge.
Given the above live load result, the inventory level rating factor is calculated as:

= RF (1= 12.7550)-(643108) 0.75

(4-3)

and the operating level rating factor is computed as:

54

= RF (1= 12.3550)-(643108) 0.98

(4-4)

where 418 kip-ft is the factored dead load moment from Figure 33 at the position of the maximum HL-93 live load moment (with a design truck 14 ft axle spacing) in Figure 34.
Given that both of the above rating factors are less than 1.0, there are a number of options to evaluate the sufficiency of the exterior girder in the Lowndes County bridge. These include:

1. The wearing surface load, DW, was based on an allowance of 30 psf on the roadway area between the curbs in the calculation of the factored dead load in Section 4.2. Table 6A.4.2.2-1 of the MBE [1] indicates that the load factor for DW at the strength limit state may be taken as 1.25 instead of 1.50 where the thickness of the wearing surface has been field measured. Measurement of the wearing surface on the Lowndes County bridge may result in a smaller factored dead load moment, increasing the value of the above rating factors.
2. A grid or 3D finite element analysis could be conducted on the simply supported end span of this skewed I-girder bridge. Such an analysis would likely give a smaller effective live load distribution to the exterior girder, thus reducing the unfactored live load moment and increasing the value of the above rating factors.
3. A legal load rating analysis could be conducted with the AASHTO or state legal loads and generalized load factors to determine whether RF is greater than 1.0.
4. The material properties of the steel in the Lowndes County bridge could be verified by coupon tests. The nominal values for the yield and tensile strength are typically taken as the mean test value minus 1.65 standard deviation to provide a 95%

55

confidence limit. Guidance on material sampling for bridge evaluation is provided in Article 5.3 of the MBE [1]. 5. The bridge girders could be made composite by using post-installed shear connectors. This type of operation has been employed with some success for strengthening existing steel bridge girders in Texas [17]. For composite girders, the AASHTO LRFD Specifications do not require consideration of any degradation in the flexural resistance due to flange local buckling for the flange connected to the concrete deck; furthermore, the live load stresses in the girders are significantly reduced if they are composite with the concrete deck.
The focus of this report is not on the rating factors for flexure of the exterior girder of the Lowndes County bridge in themselves, but rather it is on the influence of the lateral displacement at the subject bearing. It can be stated that the exterior girder on the Lowndes County bridge approximately satisfies the AASHTO LRFR operating level design-load rating requirements, given the estimated operating level rating factor of RF = 0.98 and given that the wearing surface load employed in this study is likely to be a conservative estimate. The maximum moments in the Lowndes County bridge are far removed from the displaced bearing. The first diaphragm within the span is located at 9.7 ft from the centerline of the displaced bearing. From the field inspection discussed in Chapter 2 and documented in detail in Appendix B, the lateral displacements are on the bottom flange and these displacements are effectively negligible once one reaches this diaphragm. The envelope of the live load moment on the exterior girder has significantly smaller ordinates within the 9.7 ft length between the centerline of the subject bearing and the first diaphragm. The critical HL-93 moment diagrams associated with other positions of the
56

design truck, maximizing the reaction at the displaced bearing or the shear in the web end panel adjacent to this bearing, are presented in the following sections.
4.4 Inventory Level Rating Factor Corresponding to the Resistance of the Bearing Stiffeners at the Displaced Bearing
Figure 35 shows the free-body, shear, and moment diagrams for the unfactored HL-93 live load producing the maximum reaction at the displaced bearing on the southeast exterior girder of the Lowndes County bridge. Similar to the above case producing the maximum live load moment within the span, the HL-93 design truck is oriented in the direction opposite from the flow of traffic at the southeast corner of the bridge. The rear axle is located over the top of the bearing, and the second heavy axle is located 14 ft away from the bearing.

34.9 kip (a)

34.9 kip

8.7 kip

75.4 kip

14 ft

14 ft

0.52 klf

19.5 ft

27.8 kip

(b)

40.5

33.2 -1.7

-9.0 -17.7

Units: kip

-27.8

516 kip-ft

444 kip-ft

(c)

FIGURE 35
Unfactored HL-93: (a) Free-body; (b) Shear; and (c) Moment Diagrams Associated with the Maximum Live Load Reaction at the Subject Bearing of the Exterior Girder of the
Lowndes County Bridge, Including 33% Dynamic Load Allowance and Based on a Shear Live Load Distribution Factor of g = 0.82

57

The subject bearing is at the obtuse corner of the skewed simply supported end span, and the bearing reaction is closely tied to the girder end shear. Therefore, the shear live load distribution factor of g = 0.82 is employed along with the 33% dynamic load allowance on the design truck to estimate the maximum live load bearing reaction. Appendix F provides the detailed calculations behind the live load distribution factor for shear. The maximum unfactored live load reaction at the subject bearing is 75.4 kip.
The girder had two 4.5 in. double-sided full-depth bearing stiffeners, spaced at 6 in. apart center-to-center, at the subject bearing. The centerline of the first bearing stiffener was located at 2 in. from the end of the steel girder. The AASHTO LRFD Specifications [9] give a width of the web of 2 in. + 6 in. + 9( in.) = 11.4 in. that is considered to participate with the two bearing stiffeners as an effective column section resisting the bearing reaction. The area of this section is A = 11.0 in.2, and the moment of inertia about a horizontal axis at the mid-thickness of the web is I = 51.5 in.4, giving a radius of gyration = of r = I / A 2.16 in. The effective length, KL, of the effective column is taken as 0.75D = 0.75(61 in.) = 45.8 in., and therefore KL/r = 21.2. The yield load of the effective column is Ry = (11.0 in2)(36 ksi) = 396 kip and the corresponding factored effective column capacity of the bearing stiffeners is c s Rn = (1.0)(1.0)(0.95)(0.977Ry) = 368 kip.
Given the above capacity, the maximum unfactored bearing live load reaction from Figure 35, and the factored dead load reaction from Figure 33, the inventory level rating factor corresponding to the bearing stiffeners and the transfer of the reaction to the subject bearing is found as:

= RF (= 13.6785)-(3775..84) 2.50

(4-5)

58

The above calculation is performed without the consideration of any impact of the bearing lateral displacement on the resistance of the bearing stiffeners. It is expected that this impact is relatively small. This is because the bearing reaction is rapidly transferred from the stiffeners to the web of the I-section to develop the web shear force. Furthermore, the torsional stiffness of the girder helps resist any eccentricity effects from the bearing reaction at the displaced bearing. These expectations are tested via full nonlinear shell finite element analysis in Section 4.6.
As noted at the beginning of this chapter, the flexural capacity limit of the girder "protects" against the small degradation of the girder end bearing capacity, since the girder will fail in flexure well before the end bearing capacity is reached. This can be understood by calculating the inventory rating factor given the factored girder moment capacity, the maximum unfactored live load moment in Figure 35, and the corresponding maximum factored dead load moment from Figure 33:

= RF (1= 12.7550)-(531560) 1.00

(4-6)

Therefore, for the HL-93 live load shown in Figure 35, causing the maximum live load reaction at the subject bearing, the girder live load capacity is actually limited by the girder flexural resistance (within the portion of the girder length between the two intermediate diaphragm locations) well before the capacity of the bearing stiffeners is reached at the subject bearing.

59

4.5 Inventory Level Rating Factor Corresponding to the Shear Resistance of the Girder Web End Panel Adjacent to the Displaced Bearing
Figure 36 shows the free-body, shear, and moment diagrams for the unfactored HL-93 live load producing the critical shear in the web end panel adjacent to the subject bearing on the southeast exterior girder of the Lowndes County bridge. Interestingly, if the girder web were sufficiently stocky such that its shear resistance was governed by the plastic shear capacity, the critical live load for the girder end shear would be essentially the same as that shown in Figure 35, which maximizes the end reaction. This is because if the axle load over the bearing in Figure 35 is moved an infinitesimal distance into the span, the girder web has to be able to support an end shear that is essentially equal to the maximum end reaction. While this statement is true for any case--that is, the web must be able to resist the end shear associated with the maximum end reaction within a small length adjacent to the bearing--the critical shear loading for the thin web panel adjacent to the subject bearing in the Lowndes County bridge, which can buckle in shear at a relatively small load compared to the plastic shear capacity, is with the design truck rear axle placed over the top of the first intermediate transverse stiffener within the span. This is because, considering Figure 35, the shear force within the girder web reduces substantially once the design truck rear axle load is transferred to the girder (e.g., note that while the reaction at the subject bearing is 75.4 kip in Figure 35, the corresponding shear at the end of the girder is only 40.5 kip). The first intermediate transverse stiffener is located 4.9 ft from the centerline of the subject end bearing.
60

34.9 kip

34.9 kip

8.7 kip

(a)

67.3 kip

4.9 ft

14 ft

14 ft

0.52 klf

14.6 ft

35.9 kip

64.8

(b)

29.9 67.3

22.6

Units: kip

-19.6

-12.3

-28.3

-27.8

691 kip-ft
324 kip-ft (c)

468 kip-ft

FIGURE 36
Unfactored HL-93: (a) Free-body; (b) Shear; and (c) Moment Diagrams Associated with the Critical Shear in the Web End Panel Adjacent to the Subject Bearing of the Exterior
Girder of the Lowndes County Bridge, Including 33% Dynamic Load Allowance and Based on a Shear Live Load Distribution Factor of g = 0.82

Although shear influence lines for the simply supported exterior girder would suggest that the girder shear at the first intermediate transverse stiffener is maximized by stopping the lane load at the transverse stiffener, continuing the lane load throughout the span maximizes the overall shear within the web end panel adjacent to the subject bearing.
The girder web end panel adjacent to the subject bearing had a length do = 55.3 in. Given the web depth D = 61 in., the aspect ratio of this panel is do/D = 0.907. As such, the AASHTO shear buckling coefficient is calculated as k = 5 + 5 / (do/D)2 = 11.1. By comparing the web slenderness D/tw = 163 to the limit 1.40 Ek / Fyw = 132 , one can conclude that the web shear buckling resistance is governed by elastic shear buckling.

61

Therefore, the ratio of the web buckling resistance to the web plastic shear capacity is calculated as:

=C (= D1./5t7w )2 FEykw 0.529

(4-7)

Therefore, given the web plastic shear strength Vp = 0.58 Fyw D tw = 478 kip, the factored shear capacity is obtained as c s Vn = (1.0)(1.0)(1.0)(0.529Vp) = 253 kip. This results in an inventory level rating factor of:

= RF (= 12.5735)-(3657..43) 1.85

(4-8)

It is important to recognize that the AASHTO LRFD characterization of the shear resistance of web end panels can be rather conservative in many cases. The traditional idealization is that web end panels and unstiffened webs are never able to develop shear postbuckling resistance. The recent 2016 AISC specification [10] has introduced enhanced shear strength equations that account for web shear postbuckling resistance in both of these cases. The new AISC equations are based on the rotated stress field theory (RSFT) proposed by Hoglund [18]. The implementation of these equations is very simple. For webs that fail within the inelastic shear buckling range, the RSFT strength is the same as the traditional inelastic shear buckling strength. However, for webs that fail by elastic shear buckling, the RSFT equations simply continue to use the traditional inelastic shear buckling equation for all girder web slenderness values. The resulting AISC calculation for the ratio of the nominal shear capacity to the plastic shear capacity of the end panel in the Lowndes County bridge is:

62

=C 1= .10 Ek / Fyw 1.10 (29000 ksi)(= 11.1) / 36 ksi 0.638

D / tw

163

(4-9)

Given the AISC calculation of the plastic web shear resistance as Vp = 0.6Fyw dtw = 0.6 (36 ksi)(61.75 in.)( in.) = 500 kip, the factored shear capacity becomes csVn = (1.0)(1.0) (1.0)(0.638Vp) = 319 kip. The corresponding inventory level rating factor is:

= RF (= 13.1795)-(3657..43) 2.41

(4-10)

The above calculations are performed without the consideration of any impact of the bearing lateral displacement on the shear resistance. It is expected that this impact is relatively small. This is because of the stable postbuckling behavior of web panels in shear. These expectations are tested via full nonlinear shell finite element analysis in Section 4.6.
As noted at the beginning of this chapter, the flexural capacity limit of the girder "protects" against any small degradation of the girder end panel shear capacity, since the girder will fail in flexure well before the end panel shear capacity is reached. This can be understood by calculating the inventory rating factor given the factored girder moment capacity, the maximum unfactored live load moment in Figure 36, and the corresponding maximum factored dead load moment from Figure 33:

= RF (1= 12.7550)-(649013) 0.70

(4-6)

Therefore, for the HL-93 live load shown in Figure 36, causing the critical live load shear in the end panel adjacent to the subject bearing, the girder live load capacity is actually limited by the girder flexural resistance (within the portion of the girder length between the two intermediate diaphragm locations) well before the capacity of the end

63

panel is reached. Note that the live load moment demand within the span based on Figure 36 (690 kip-ft) is actually larger than the live load moment demand within the span based on Figure 34 (630 kip-ft). This is because the diagrams in Figure 36 are based on the shear live load distribution factor, g = 0.82, whereas the diagrams in Figure 34 are based on the flexural live load distribution factor, g = 0.66. 4.6 Inventory Level Rating Factor based on Full Nonlinear Shell Finite Element
Analysis 4.6.1 Full Nonlinear Shell Finite Element Analysis Model
To determine how the translation of the bearing affects the inventory level rating factor pertaining to the end shear and bearing capacities of the girder, full nonlinear analyses were conducted of the southeast exterior on the Lowndes County bridge using the ABAQUS [14] finite element analysis software. Figure 37 shows the model used in the simulations and its overall displacement boundary conditions.
FIGURE 37 Finite Element Model of the Exterior Girder System in ABAQUS [14]
64

The exterior girder, including its transverse stiffeners and diaphragms were modeled using the four-node quadrilateral general-purpose S4R shell element. The sole plate and bearing plate, and a plate that represents the top of the pier cap were modeled using the C3D8R element, an eight-node general-purpose three-dimensional solid element.
The displacement boundary conditions of the above model were as follows. To model the fixed bearing support at the south end of the girder, the lateral and vertical displacement degrees of freedom were restrained at the bottom flange. The center of the top flange along the length of the girder was continuously constrained against lateral translation to account for the restraint from the haunch. The lateral displacement and the rotations in the plane of the cross section were constrained at the ends of diaphragms opposite from their connection to the exterior girder to represent the connection between the diaphragms and the adjacent interior girder. The sole plate at the girder north end support was attached continuously to the bottom flange to represent the welded connection between the sole plate and the bottom flange. The sole plate was placed on top of the bearing plate with frictional contact surfaces. The bearing plate was placed on top of a plate that represents the top surface of the pier cap with frictional contact surfaces. The plate representing the top of the pier cap was constrained in all directions.
The material properties of A36 steel taken from the AISC SCM [10] were used in the simulations, with a yield strength of 36 ksi and a modulus of elasticity of 29,000 ksi. The material was modeled as a bilinear material with a tangent modulus within the inelastic range of 110 ksi for numerical stability. The von Mises yield condition was used to capture the yielding response within the simulation models. The small inelastic stiffness was represented using an isotropic hardening idealization.
65

The application of loads to the above model was divided into two steps. First, the factored dead loads were applied. Second, the factored dead loads were held constant and the factored live load was applied as a reference load using the modified Riks method, which allowed the prediction of the collapse load and post-peak response of the structure [14]. The largest load proportionality factor for the applied live load determined from the nonlinear finite element analysis was effectively the rating factor, RF, predicted by the nonlinear analysis.
The total factored dead loads applied to the exterior girder are shown in Figure 33(a). The factored dead load of the steel components was applied as a body load given the weight density of steel, 490 pcf, multiplied by the dead load factor, 1.25. The concentrated load at the north end girder bearing in Figure 33(a) was applied as a uniform pressure to the surface of the top flange of the girder between the bearing stiffeners at this location. The remainder of the dead loads were applied as a uniform surface pressure to the top flange of the girder. The live loads shown in Figure 35(a) and Figure 36(a) were multiplied by the live load factor corresponding to the inventory level (1.75) to obtain the reference load corresponding to an FEA RF = 1.0 in the following finite element studies. The factored lane load was applied as a uniformly distributed pressure to the top flange of the girder. The factored HL-93 design truck rear axle load was applied as a line load at the juncture of transverse stiffeners and top flange at the locations of this load. This approximated the actual application of this load to the girder through the concrete deck, and avoided false modeling of local bending of the top flange that would occur if these loads were modeled as a uniform pressure on the top flange. The other two factored HL-93 axles were applied as a uniform pressure on patches that were 20 in. long and 10 in. wide. A beam multi-point
66

constraint was applied to the nodes within this patch, which forced the nodes within the patch to deflect as if they were attached to the centroid of the patch by a rigid bar [14]. Figure 38 shows the pattern of the beam MPC used in the simulations. This modeling approach was not employed at the rear axle of the design truck, since the beam MPC may overly constrain the shell finite element model at the locations near the sites where the strength of the girder was being evaluated.
FIGURE 38 Beam Multi-point Constraint Pattern Applied at the Patch Where HL-93 Axle (Except the Rear Axle) Loads Were Applied A representative girder geometric imperfection pattern was specified as the first elastic buckling mode from an elastic linear buckling analysis, with the girder subjected to the live load shown in Figure 36(a), multiplied by 0.1. This gave a web out-of-flatness equal to 0.1 in. where the contour of the buckling displacements shown in Figure 39 is equal to 1.0. This imperfection magnitude was representative of the out-of-flatness of the girder web
67

estimated in locations other than the location of the displaced bearing during the field inspection of the bridge, and was significantly smaller than the out-of-flatness of D/110 = 0.6 in. permitted in fascia girder web panels with double-sided transverse stiffeners by the American Welding Society (AWS) Bridge Welding Code [19]. Figure 39 shows the displacement contours on the girder model corresponding to the first buckling mode.
As explained in Sections 4.4 and 4.5, the girder would fail in flexure before the end panel shear or bearing stiffener capacities at its north bearing were reached. Therefore, to avoid flexural failure and allow study of the impact of the bearing displacement on the end panel shear and bearing stiffener resistances, the simulation model was modified to prevent the girder from failing in flexure. These modifications were as follows: (1) rotational restraints were applied about the longitudinal and vertical axes to all the nodes on the top flange from the northern-most intermediate diaphragm within the span to the south end of the girder to prevent the girder failing from flange local buckling; (2) additionally, the steel was modeled to behave only as a linear elastic material from the northern-most intermediate transverse stiffener within the span to the south end of the girder.
FIGURE 39 First Buckling Mode from an Elastic Linear Buckling Analysis of the Exterior Girder
(U Indicates the Magnitude of the Out-of-plane Displacement)
68

4.6.2 Full Nonlinear Shell Finite Element Analysis Results 4.6.2.1 Analysis of Shear Capacity of the Plumb Girder
In this analysis, the rating factor for the shear capacity of the plumb girder web end panel was analyzed. As discussed previously, the factored dead loads shown in Figure 33(a) were applied in the first step of the loading procedure. Then, the live loads shown in Figure 36(a), which maximize the girder end panel shear, were applied after being factored by the inventory level live load factor (1.75). The rating factor for the shear capacity of the plumb girder web end panel was found to be 2.44, which is close to the value of 2.41 calculated manually using the AISC [10] rotated stress field theory idealization. Figure 40 and Figure 41 show the response of the model at the peak load capacity (RF = 2.44) and Figure 42 and Figure 43 show the post-peak response.
The results indicate that the end panel failed in shear after developing significant postbuckling strength. The figures showing equivalent plastic strain indicate the formation of a yielded diagonal tension band (or tension field) in the web due to the shear loads.
4.6.2.2 Analysis of Shear Capacity of the Girder with an Initially Displaced Bearing This analysis was performed similarly to the previous analysis, but an additional initial
analysis step was included to displace the bearing laterally by 5 in. after applying the factored dead loads and before applying the live load. The rating factor for the shear capacity of the "damaged" girder was found to be RF = 2.05. Figure 44 and Figure 45 show the analysis results of the model at RF = 2.05.
The shear capacity of the girder was influenced measurably due to the displacement of bearing. The rating factor was reduced from 2.44 to 2.05. However, clearly the girder still had substantial additional shear capacity above that required to satisfy the inventory level
69

rating. Also, as discussed previously, the girder would actually fail in flexure well before this strength limit state was achieved.
Upon examining Figure 44 and Figure 45 in detail, it is apparent that measurable yielding occurred at the bottom of the bearing stiffeners. This may have had some influence on the maximum resistance. Therefore, although the rating factor for the bearing stiffeners discussed in Section 4.4 was larger than that for the web end panel discussed in Section 4.5, the bearing stiffeners may experience some reduction in their capacity for the live load in Figure 35, causing the maximum reaction at the girder's north end bearing. Therefore, a separate finite element analysis was conducted to evaluate the bearing capacity of the girder with a displaced bearing, and these results are presented below.
4.6.2.3 Analysis of Bearing Stiffener Capacity for the Case with the Displaced Bearing In this analysis, the rating factor of the girder bearing stiffeners, given the initial 5 in.
bearing lateral displacement, was analyzed. The factored dead loads shown in Figure 33(a) were applied in the first step of the loading procedure. Then, the live loads shown in Figure 35(a), which maximize the end reaction at the subject bearing, were applied after being factored by the inventory level live load factor (1.75). A step to displace the bearing was added after applying the factored dead loads and before applying the factored live loads. The rating factor of the bearing capacity of the girder with displaced bearing was found to be 2.60. Figure 46 and Figure 47 show the response of the model at the maximum live load capacity (RF = 2.60), and Figure 48 and Figure 49 show the post-peak load response.
70

(a)
(b)
(c) FIGURE 40 Out-of-plane Displacement (in.) at the Shear Capacity of the Plumb Girder (RF = 2.44) of: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface
71

(a)
(b)
(c) FIGURE 41 Equivalent Plastic Strain at the Shear Capacity of the Plumb Girder (RF = 2.44) on: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface (light colored contours indicating locations where the plates are yielded on one of the surfaces)
72

(a)
(b)
(c) FIGURE 42 Out-of-plane Displacement (in.) at Post-peak Load of the Plumb Girder of: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface
73

(a)
(b)
(c) FIGURE 43 Equivalent Plastic Strain at Post-peak Load of the Plumb Girder on: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface
74

(a)
(b)
(c) FIGURE 44 Out-of plane Displacement (in.) at the Shear Capacity of the Girder with Displaced Bearing (RF = 2.05) of: (a) West Side Surface; (b) Girder End Surface; (c) East Side
Surface 75

(a)
(b)
(c) FIGURE 45 Equivalent Plastic Strain at the Shear Capacity of the Girder with Displaced Bearing (RF = 2.05) on: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface
76

(a)
(b)
(c) FIGURE 46 Out-of-plane Displacement (in.) at the Bearing Capacity of the Girder with Displaced Bearing (RF = 2.60) of: (a) West Side Surface; (b) Girder End Surface; (c) East Side
Surface 77

(a)
(b)
(c) FIGURE 47 Equivalent Plastic Strain at the Bearing Capacity of the Girder with Displaced Bearing (RF = 2.60) on: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface
78

(a)
(b)
(c) FIGURE 48 Out-of-plane Displacement (in.) at Post-peak Load of the Girder with Displaced Bearing of: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface
79

(a)
(b)
(c) FIGURE 49 Equivalent Plastic Strain at Post-peak Load of the Girder with Displaced Bearing on: (a) West Side Surface; (b) Girder End Surface; (c) East Side Surface
80

The inventory level rating factor of the bearing stiffeners with the displaced bearing determined from the finite element analysis was found to be higher than the rating factor of bearing capacity of the plumb girder calculated manually. The researchers expect that this is because the AASHTO LRFD Specifications [9] provide a more conservative estimate than the actual capacity of the "undamaged" bearing. To verify the results, a finite element analysis was conducted to determine the rating factor for the bearing stiffeners in the plumb girder. This analysis gives RF = 2.90. The analysis results indicate that the displacement of the bearing causes a measurable reduction in the bearing stiffener capacity. However, the rating factors corresponding to the shear and bearing capacities determined from the girder with a displaced bearing are still significantly larger than the rating factor of the flexural capacity. As a result, the flexural capacity limit of the girder "protected" against small degradation of the girder end shear or bearing capacity, since the girder would fail in flexure well before the end shear or bearing capacity was reached, even for the "damaged" girder.
81

CONCLUSIONS AND RECOMMENDATIONS
5.1 Conclusions The following observations and conclusions can be drawn from this research project:
1. The displaced bearing on the Lowndes County bridge occurred subsequent to shear failure in the anchor bolts in the expansion bearing. The corrosion present on the failure surface of the anchor bolt indicates that the broken bolts had been exposed to the bridge service environment for an extended period. However, it is impossible to state with any certainty exactly when this anchor bolt failure occurred.
2. The most likely cause for the failure in the anchor bolts was excessive restraint at the expansion joint location coupled with thermal loading from the service environment. The bearing slots in the original bearing (refer to Figure 17) may have lacked sufficient clearance around the anchor bolts to allow thermal expansion under uniform temperature increases. If thermal expansion was adequately restrained at the bearing, a temperature rise of approximately 30 could result in forces that would exceed the shear capacity of the anchor bolts.
3. No signs of external impact loading or other damage were found on the bridge girder or other bridge structural elements in the vicinity of the shifted bearing. Analytical and numerical analysis of the girder and bearing indicate that a concentrated lateral force of approximately 32 kips would be necessary to shift the bearing 5 in. as observed. The research team considered several possibilities, but was unable to envision a scenario where that magnitude of lateral load would be applied to the girder without causing significant visible damage.
82

4. During repairs on the bridge, the girder appeared to shift back toward its original position when dead loads were removed. The girder did not completely return to its original position. This action was very similar to the behavior of a twisted girder on another bridge in the state of Georgia in 2008.
5. Based on the field inspection, document review, analytical/numerical analyses performed, and anecdotal information about the behavior of the shifted girder during the repair process, the research team developed a potential scenario to account for the shifted bearing observed on the Lowndes County bridge. This scenario postulates that the girder was initially curved, and forced into position and held via the anchor bolts and friction due to dead loading after the initial bridge construction was completed. At some point, the anchor bolts failed due to thermal loading with excessive unaccounted for restraint in the expansion bearing. However, the friction force on the girder continued to hold it in place. Some inciting event-- such as abrupt stopping on the bridge by a very heavy vehicle--lead to a short-term load reversal, relieving the frictional force at the bearing and allowing the girder to shift back to its original configuration prior to construction. The girder underwent dynamic harmonic motion, oscillating beyond its original position. The dead load and associated friction force returned to the girder and bearing, holding the girder in a new location. When the dead loads were removed during the repair process, the girder shifted back to its original preconstruction geometry.
6. The previously described scenario appears to fit most of the observations from the bridge both pre- and post-repair. However, this sequence of events is purely speculative in the absence of more compelling evidence.
83

7. Although measurable reductions are estimated in the exterior girder web end panel shear capacity and the capacity of the bearing stiffeners in transferring the end reaction to the subject bearing due to the bearing lateral displacement, the inventory level rating factors for these components estimated by full nonlinear finite element analysis are still significantly larger than 1.0. Therefore, the exterior girder has sufficient inventory level capacity with respect to these strength limit states in spite of the bearing lateral displacement.
8. The exterior girder rating is actually governed by its flexural capacity at locations along its length that are significantly removed from the "damaged" portions of the girder. Therefore, flexural yielding and minor flange and web local buckling in essence protect the girder against failure involving the strength limit states influenced by the bearing displacement.
9. Regarding its flexural capacity, the exterior girder is found to approximately satisfy the AASHTO LRFR first-level design-load operating level requirements.
5.2 Recommendations Based on these conclusions, the following recommendations are made to GDOT: 1. The analysis shows that the girder still has excess capacity to resist expected service loading even in its shifted configuration. As such, total girder replacement is not needed. 2. If future occurrences of bearing and associated steel girder end shifts are observed on Georgia bridges, detailed analysis will not be needed unless the altered geometry is significantly different than the as-built configuration.
84

3. The methodology for repair used the previous two times that steel girder bearing shifts were observed is appropriate and should be used for any future occurrences on Georgia bridges. This repair methodology includes heatstraightening the rotated/shifted girder and installing a new bearing and anchor bolts.
85

REFERENCES
1. American Association of State Highway and Transportation Officials (AASHTO). Manual for Bridge Evaluation, 2nd Edition. Washington, D.C., 2011.
2. Urban, M. J. Effects of Residual Damage on the Fatigue Performances of Steel Bridge Girders. Lehigh University, Bethlehem, Pennsylvania, 2005.
3. Al Badran, M. S. Structural Reliability Analysis of Corroded Steel Girder Bridge. University of Nebraska-Lincoln, Lincoln, Nebraska, 2013.
4. Czarnecki, A. A. System Reliability Models for Evaluation of Corroded Steel Girder Bridges. University of Nebraska-Lincoln, Lincoln, Nebraska, 2006.
5. Khurram, N., et al. Experimental and Numerical Evaluation of Bearing Capacity of Steel Plate Girder Affected by End Panel Corrosion. International Journal of Steel Structures, 2014.
6. Stuir, C. J. , and C. J. Earls. A Rapid Assessment Methodology for Bridges Damaged by Truck Strikes. Steel and Composite Structures, 2009.
7. Kuawa, M., and J. Bie. Experimentally Validated Nonlinear Analysis of Bridge Plate Girders with Deformations. Studia Geotechnica et Mechanica, 2015.
8. American Concrete Institute (ACI). 318-14 Building Code Requirements for Structural Concrete and Commentary. 11, Farmington Hills, Michigan, 2014.
9. American Association of State Highway and Transportation Officials (AASHTO). LRFD Bridge Design Specifications, 8th Edition. Washington, D.C., 2017.
10. American Institute of Steel Construction (AISC). Steel Construction Manual, 15th Edition. Chicago, Illinois, 2017.
11. Gustafson, K. Evaluation of Existing Structures. Steel Wise, 2007.
12. Ziemian, R., and W. McGuire. MASTAN 2. bhttp://www.mastan2.com/.
13. Rabbat, B. G. , and H. G. Russell. Friction Coefficient of Steel on Concrete or Grout. Journal of Structural Engineering, 2008.
14. Simulia. ABAQUS/STANDARD. Simulia, Inc, Providence, Rhode Island, 2013.
15. Georgia Department of Transportation. Bridge and Structures Design Manual. 2019. http://www.dot.ga.gov/PartnerSmart/DesignManuals/BridgeandStructure/GDOT_B ridge_and_Structures_Policy_Manual.pdf.
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16. National Highway Institute (NHI). Fundamentals of LRFR and Applications of LRFR for Bridge Structures, Participant Work Book. Federal Highway Administration, National Highway Institute, 2013.
17. Engelhardt, M. D., and R. E. Klingner. Developing Composite Action in Existing Non-Composite Steel Girder Bridges. Devils Thumb Ranch, Tabernash, Colorado, 2008.
18. Hglund, T. Shear Buckling Resistance of Steel and Aluminum Plate Girders. ThinWalled Structures, 2002.
19. AASHTO/AWS. Bridge Welding Code. A Joint Publication of AASHTO and American Welding Society. AASHTO, Washington D.C. and AWS, Miami, Florida, 2002.
20. White, D. W., A. Kamath, J. A. Heath., B. K. Adams, and A. Anand. (2019). Straight Steel I-Girder Bridges with Skew Index Approaching 0.3, Report to Florida Department of Transportation, Tallahassee, Florida, September (to appear).
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APPENDIX A

BRIDGE DESIGN DRAWINGS

Figure A-1. Bridge Drawing Sheet 1 A-1

Figure A-2. Bridge Drawing Sheet 2 A-2

Figure A-3. Bridge Drawing Sheet 3 A-3

Figure A-4. Bridge Drawing Sheet 4 A-4

Figure A-5. Bridge Drawing Sheet 5 A-5

Figure A-6. Bridge Drawing Sheet 6 A-6

Figure A-7. Bridge Drawing Sheet 7 A-7

Figure A-8. Bridge Drawing Sheet 8 A-8

Figure A-9. Bridge Drawing Sheet 9 A-9

Figure A-10. Bridge Drawing Sheet 10 A-10

Figure A-11. Bridge Drawing Sheet 11 A-11

Figure A-12. Bridge Drawing Sheet 12 A-12

Figure A-13. Bridge Drawing Sheet 13 A-13

Figure A-14. Bridge Drawing Sheet 14 A-14

APPENDIX B FIELD INSPECTION PRIOR TO REPAIR PHOTOS

(a)

(b)

Figure B-2. Snooper Truck Setup: (a) Truck; (b) Inspection Platform

(a)

(b)

(c)

(d)

Figure B-1. Shifted Girder: (a) South Side (Exterior); (b) South Side (Exterior; Closer View); (c) Research Team Viewing North Side (Interior); (d) North Side (Interior)

B-1

(a)

(b)

(c)

(d)

(e)

(f)

Figure B-3. Shifted Girder: (a) Bearing Shift; (b) Underside Showing Curvature; (c) Girder and Concrete Edge Beam; (d) Bearing Stiffeners; (e) Measuring Web Shift; (f) Measuring Web Shift (Closeup)

B-2

(a)

(b)

(c)

(d)

(e)

(f)

Figure B-4. Shifted Bearing: (a) View Showing Adjacent Bearing on Pier Cap; (b) Measuring Shift of Bearing Plate; (c) Relative Shift of Bearing Plate and Sole Plate (Exterior); (d) Relative Shift
of Bearing Plate and Sole Plate (Interior); (e) Plate Lifted Off Pier Cap; (f) Temporary Shoring of Bearing Plate in Shifted Position

B-3

(a)

(b)

(c)

(d)

(e)

(f)

Figure B-5. Concrete Edge Beam: (a) Connection to Plate Girder; (b) Edge Beam Spanning Between Parallel Girders;
(c) Closeup of Damage; (d) Closeup of Damage; (e) Measuring Spall Area; (f) Spalled Sections of Edge Beam Found Underneath Bridge

B-4

(a)

(b)

Figure B-7. Diaphragms: (a) Diaphragm Located 10.3 ft from Shifted Bearing; (b) Diaphragm Located 28.4 ft from Shifted Bearing

(a)

(b)

(c)

(d)

Figure B-6. Abutment: (a) North (Interior) View of Abutment for Shifted Girder; (b) Top of Girder at Abutment; (c) South (Exterior) View of Abutment for Shifted
Girder; (d) Bottom of Girder at Abutment

B-5

(a)

(b)

Figure B-9. Broken Anchor Bolts: (a) Shift of Bearing Relative to the Ruptured Anchor Bolt; (b) Expansion Slot for Anchor in Girder at Bearing Location

(a)

(b)

(c)

(d)

Figure B-8. Undamaged Girder on the Opposite End of the Bridge (Northeast Corner): (a) Exterior View; (b) Bearing Details at Pier Cap; (c) Undamaged
Concrete Edge Beam; (d) Bearing Stiffeners

B-6

APPENDIX C FIELD INSPECTION AFTER REPAIR PHOTOS

(a)

(b)

Figure C-2. Repaired Exterior Girder:

(a) South (Exterior) View; (b) North (Interior) View

(a)

(b)

Figure C-1. Heat-straightened Section of Girder (note fresh paint): (a) South (Exterior) View; (b) North (Interior) View

(a)

(b)

Figure C-3. Repaired Bearing:

(a) South (Exterior) Side View; (b) North (Interior) Side View

C-1

(a)

(b)

Figure C-4. Repaired Sole Plate: (a) Width; (b) Length

(a)

(b)

Figure C-5. Repaired Bearing Plate: (a) Width; (b) Length

(a)

(b)

Figure C-6. New Anchor Bolts Installed: (a) Diameter; (b) Length

C-2

(a)

(b)

Figure C-4. Repaired Concrete Edge Beam: (a) Connection to Repaired Girder; (b) View of Beam Span Between Parallel Girders

C-3

APPENDIX D SUMMARY OF DOCUMENTS REVIEWED

Table D-1. Summary of Bridge Inspection Report (4/15/1998)

Date Substructure Superstructure
Deck

4/15/1998 Consists of two 36 35 concrete columns per bent with 36 48 concrete caps. Some minor cracks in the caps Jersey-type barrier rail have been placed next to the columns and guardrail has been added to the barrier rails on north- and southbound lanes. Consists of four steel I-beams. The outside beams are 10 62. The inside beams are 12 36 with cover plates on the beams on bents 2 and 5. All beams have steel "x" bracing except spans 1 and 4; they have steel lateral bracing. All bracing and lateral bracing are welded. Consists of 7 concrete deck. Deck has deflection cracks throughout. Some exposed rebar on the handrails left side on span 3. Wingwall has cracking present on both abutments. Efflorescence cracks are present in the sidewalk on the underside. Some efflorescence along the outside beams span 3 let side. Guardrails are attached to the structure. All deck joints were sealed. Armored joint on bent 3. Bent 2 joint needs to be resealed.

Table D-2. Summary of Bridge Inspection Report (3/8/2000)

Date Substructure Superstructure
Deck
General

3/8/2000 Two 36 35 concrete columns per bent with 36 48 concrete caps. Some minor cracks in the caps. Columns have spread footings. Two 61 10 plate girders and two W36 150 plate girders on the approaches. Four 64 14 plate girders on the main spans. All beams have steel "x" bracing, except spans 1 and 4; they have steel lateral bracing. All bracing and lateral bracing are welded; 24 movable bearing, 8 fixed bearing. 7 concrete deck. Armored joint on bent 3 has been replaced with XJS joint. Moderate transverse and minor map cracking in deck. Some exposed rebar on the handrails left side on span 3. Wingwall has cracking present on both abutments. Efflorescence cracks are present in the sidewalk on the underside. Some effloresce along the outside beams span 3 left side. Deck joints are beginning to leak. Bent 2 joint needs to be resealed. Map cracking in curb and handrail. Built in 1961 331 26.3 H15 Design. Note: bridge is on a skew. Jersey-type barrier rails have been placed next to the columns and guardrail has been added to the barrier rails on north- and southbound lanes.

D-1

Table D-3. Summary of Bridge Inspection Report (1/3/2002)

Date Substructure Superstructure
Deck

1/3/2002
Two 36 35 concrete columns per bent with 36 48 concrete caps. Some minor cracks in the caps. Minor spall at bent 2 on column 1. Columns have spread footings. Two 61 10 plate girders and two W36 150. plate girders on the approaches. Four 64 14 plate girders on the main spans. All beams have steel "x" bracing, except spans 1 and 4; they have steel lateral bracing. All bracing and lateral bracing are welded; 24 moveable bearing, 8 fixed bearing. 7 concrete deck. Armored joint on bent 3 has been replaced with XJS joint. Heavy transverse and heavy map cracking in deck. Some exposed rebar on the handrails left side on span 3. Wingwall has cracking present on both abutments. Efflorescence cracks are present in the sidewalk on the underside. Some efflorescence along the outside beams span 3 left side. Map cracking in curb and handrail. Deck joints are leaking-- should be cleaned and sealed.

Table D-4. Summary of Bridge Inspection Report (1/10/2004)

Date Substructure Superstructure
Deck
General

1/10/2004
Two 36 35 concrete columns per bent with 36 48 concrete caps. Minor cracks are present in the caps. Minor spall is present at bent 2 on column 1. Columns have spread footings. Two 61 10 and 2 W36 150 plate girders are present on the approaches. Four 64 14 plate girders are present on the main spans. All beams have steel lateral bracing present. All bracing and lateral bracing are welded. 7 concrete deck. Armored joint on bent 3 has been replaced with XJS joint. Heavy transverse and heavy map cracking in deck. Some exposed rebar on the handrails left side on span 3. Wingwall have minor cracking present on both abutments. Efflorescence cracks are present in the sidewalk on the underside. Minor random cracking is present in curb and handrail. Deck joints are leaking--should be cleaned and sealed. Built in 1961. 331 26.3 H15 Design. Note: Bridge is on a skew. Deficiencies: Erosion is present under the left enroll area next to column 1--should be repaired. Deck joints are leaking--should be cleaned and sealed.

D-2

Table D-5. Summary of Bridge Inspection Report (2/7/2006)

Date Substructure Superstructure
Deck

2/7/2006
Two 36 35 concrete columns per bent with 36W 48H concrete caps. Minor cracks are present in the caps. Minor spall is present at bent 2 on column 1. Columns have spread footings. Two 62 10 and two W36 150 plate girders are present on spans 1 and 4. Four 64 14 plate girders are present on span 3. All beams have steel lateral bracing present. All bracing and lateral bracing are welded. 7 concrete deck. Armored joint on bent 3 has been replaced with XJS joint. Heavy transverse and random cracking in deck. Minor exposed rebar on the handrails left side on span 3--no repairs needed at this time. Wingwalls have minor cracking present on both abutments. Efflorescence cracks are present in the sidewalk on the underside. Minor random cracking is present in curb and handrail. Deck joints are leaking--should be cleaned and sealed. 2/04

Table D-6. Summary of Bridge Inspection Report (2/13/2008)

Date Substructure Superstructure
Deck

2/13/2008
Two 36 35 concrete columns per bent with 36W 48H concrete caps. Substructure = H-26 Calculated 2006 by Central Office (Load Factor). Bent 3 at column 1 has a minor shear crack. Minor cracks are present in the caps. Minor spall is present at bent 2 on column 1. Columns have spread footings. Two 62 10 and two W36 150 plate girders are present on spans 1 and 4. Four 64 14 plate girders are present on spans 2 and 3. All beams have steel lateral bracing present. All bracing and lateral bracing are welded. Superstructure = H-21 Calculated 2006 by Central Office (Load Factor). 7 concrete deck. Heavy transverse and random cracking in deck. Minor exposed rebar on the handrails left side on span 3--no repairs needed at this time. Wingwalls have minor cracking present on both abutments. Efflorescence cracks are present in the sidewalk on the underside.

D-3

Table D-7. Summary of Bridge Inspection Report (2/20/2010)

Date Substructure Superstructure
Deck

2/20/2010
Foundation: Piers 2, 3, and 4 each have two concrete 36 35 columns with concrete 36 wide 48 high caps. Columns have spread footings (not visible). Substructure = H-26 Calculated in 2006 by Central Office (Load Factor). Abutments: The joint is not sealed between the abutment backwalls and the retaining walls allow rain water to penetrate the abutment caps and exterior steel bearings. The west and east ends of the abutment caps under the retaining walls have up to 1 long 1/32 wide horizontal cracks with efflorescence leakage. Both abutments have up to 22 long 1/32 wide vertical cracks under beams 1 and 4 and at the step downs for beams 2 and 3. Abutment 5 backwall in Bay 4-2 has three spalls up to 8 diameter deep with exposed rebar due to lack of concrete cover. Abutment 5 cap has a 4.5 long 1/32 wide vertical crack under beams 2 and 3. Random concrete slope panels have up to 3 wide vertical cracks at both abutment slopes. Abutment 5 concrete slope has a 10 8 2 settled/displaced at west side of beam 1. Refer to photo 4. Caps: The underside of Pier 4 cap on the east side of column 2 has a 6 long piece of exposed rebar due to lack of concrete cover. The south face of pier 3 cap on east side of column 1 has a 4 long 1/32 wide shear crack. Columns: The north face of column 2-1 at the cap has a 16 10 1 spall with no exposed steel. Column 4-2 has an 8 3 1 spall with no exposed steel at the southeast corner at the crash barrier.
The two exterior beams are 62 10 and two W36 150 plate girders are present in spans 1 and 4. There are four 64 14 plate girders in spans 2 and 3. All beams have steel lateral bracing present. All bracing and lateral bracing are welded. Superstructure = H-21 Calculated 2006 by Central Office (Load Factor). Beams: The -thick bottom flanges of beams 1 and 4 (62 10) in spans 1 and 4 have deformations up to 14 long 6 wide high, adjacent to most of the vertical web stiffeners. Refer to photo 5.
7-thick concrete deck with silicone sealed expansion joints. Resealed in 2008. Bridge rails are reinforced concrete post and beam bridge rails. Deck Top: The deck top of spans 1 and 4 has up to 26 long 1/16 wide transverse and diagonal cracks which coincide with the cracks noted in the underside. Refer to photo 6. Deck Underside: The deck underside near the abutments has diagonal cracks up to 7 long 1/32 wide in all three bays. The undersides of the sidewalks have up to 1/32 wide cracks with efflorescence. There is 1/32 wide transverse and vertical cracking in the curbs. The left overhang in span 3 at pier 3 has a 14 8 delamination under the steel expansion joint plate. Refer to photo 7. Bridge Rails: The left side beam rails in span 3 have a few pop-outs with exposed rebar. Joints: Pier 2 joint sealant has two areas of adhesion loss up to 1 long in the northbound lane/shoulder. Refer to photo 8.

D-4

General

Four-span structure built in 1961 at 331 long 32.0 wide on a H15 Design. Calculations were determined by the Central Office in May 2006. Equipment Used: Hand Tools, Ladder and Binoculars. Inspected by Kisinger Campo and Associates Team Leader: Charles Elliott (FLA - CBI#00363) Team Member: Andre Favreau Repairs: Repair spalls with rebar in Abutment 5 backwall in Bay 4-2. Repair delamination in left overhang in span 3. Clean and seal pier 2 expansion joint.

Table D-8. Summary of Bridge Inspection Report (2/5/2016)

Date Substructure Superstructure
Deck

2/5/2016
Two 36 36 concrete columns. Columns have spread footings (not visible). 36W 48H concrete caps. Minor cracking is present in the abutments under the beams. Spalls with exposed rebar are present in the abutments. Minor cracking and spalls with exposed rebar is present in the caps over the columns. Minor spalls are present in the columns. Two exterior beams are 62 10 and two W36 150 plate girders are present in spans 1 and 4. There are four 64 14 plate girders in spans 2 and 3. All beams have steel lateral bracing present. All bracing and lateral bracing are welded. The -thick bottom flanges of beams 1 and 4 (62 10) in spans 1 and 4 have deformations up to 14 long 6 wide high, adjacent to most of the vertical web stiffeners. Refer to photo. 7-thick concrete deck with silicone expansion joints. Moderate cracking is present throughout the deck top. Minor spalls are present at the deck joints. Minor pop-outs are present in the deck. Minor scaling is present on the deck top. Cracking with minor efflorescence is present throughout bottom of the deck. Cracking is present throughout the curbs. Deck joints are leaking.

D-5

Table D-9. Summary of Bridge Inspection Report (2/5/2018)

Date Substructure
Superstructure
Deck

2/5/2018
NBIS Condition 6 Satisfactory Condition, two 36 36 concrete columns. Columns have spread footings (not visible). 36W 48H concrete caps. Minor cracking is present in the abutments under the beams. Spalls with exposed rebar are present in the abutment back walls. Minor cracking and spalls with exposed rebar are present in the caps. (See photo) Minor spalls are present in the columns. NBIS Condition 4 Poor Condition. Two exterior girders are 62 10 and two interior beams are W36 150 at spans 1 and 4. There are four 64 14 girders in spans 2 and 3. All beams and girders have steel lateral bracing present. All bracing and lateral bracing are welded. The -thick bottom flanges of girders 1 and 4 (62 10) in spans 1 and 4 have deformations up to 14 long 6 wide high, adjacent to most of the vertical web stiffeners. Refer to photo. Span 1, girder 4 has distortion present in approximately the last 10 over bent 2. The deformity is in a northward direction approximately 6 from the original bearing area. This distortion has also caused the bearing to move with it and creating the bearing plate to rest near the rear of the cap and causing a reduction in bearing area. District 4 Bridge Headquarters has been notified on 2/5/2018 (see photos). 7-thick concrete deck with silicone and compression expansion joints. New 0.375-thick polymer overlay has been affixed to the approach slabs and deck surface. Cracking with efflorescence is present throughout bottom of the deck. Cracking is present throughout the curbs. The deck joints are sealed.

D-6

APPENDIX E DEAD LOAD CALCULATIONS

The analyses of the bearing shift and the residual capacity require the estimate of the dead load supported by the subject fascia girder. The components considered in estimating this dead load are the girder itself, the diaphragms, the concrete deck and overhang, the concrete edge beam, and the bridge barrier rails. All the dead loads located outside of the fascia girder on the bridge cross section plus the dead loads within the interior tributary width (one-half the spacing to the adjacent interior girder) are considered to be applied to the fascia girder.

i) Self-Weight of the Structural Steel
The weight of the steel girder is calculated by using the weight density of steel, 490 pcf, times the volume of the web, top and bottom flange plates, nine pairs of intermediate transverse stiffeners attached on the web within the span, and the diaphragms. Only half the weight of the diaphragms is included based on the tributary width relative to the adjacent interior girder. The weight of each component of the steel girder is shown in Table E-1. The total weight of the structural steel is found to be approximately 5,590 lb.

Table E-1. Volumes and Weights of the Exterior Girder Components

Parts Web Plate

Volume (cu. ft.) 61 0.375 47.5 = 7.55

Weight (lb)
3,700

Top Flange Plate

10 0.375 47.5 = 1.24

610

Bottom Flange Plate

10 0.375 47.5 = 1.24

610

Stiffeners Diaphragms

4 0.375 61 18 = 0.95

470

7.34 in.2 4 2 = 0.41

200

E-1

ii) Weight of the Concrete
The tributary volume associated with the exterior girder is calculated to estimate the weight of the concrete deck. The portion of the concrete deck, the overhang, and the haunch considered supported by the exterior girder are highlighted by the rectangle in Figure E-1. The weight of the barrier rail attached to the overhang is also estimated.
The volume of the concrete deck, the overhang, and the haunch are calculated by using the dimensions specified in the bridge drawings. These dimensions were verified at several locations, where practical, during the field inspection. The weight of the concrete excluding the barrier rail is calculated by multiplying the unit weight of the concrete of 150 pcf by the above volume of concrete, and is found to be 34,700 lb. The weight of each concrete component is shown in Table E-2.

Table E-2. Volumes and Weights of the Concrete Deck Components

Parts Deck

Volume (cu. ft.) 67.5 6.5 47.5 = 144.7

Weight (lb)
21,700

Overhang (14 (6+7.5) /2 + 30 (5 + 6)/2) 47.5 = 85.6 12,800

Haunch

(4 0.375 + 14.5 0.375 1/2) 47.5 = 1.4

200

iii) Weight of the Concrete Edge Beam The weight of the concrete edge beam connected to the top of the girder at the location
of the bearing is also included in the estimation of the dead load. A view of the concrete edge beam from undeneath the deck is shown in Figure E-2.

E-2

E-3

4 ft.
Figure E-1. Concrete Structures Carried by the Exterior Girder

Only the weight of one-half the length of the concrete edge beam between the exterior girder and the interior girder is considered based on tributary width. With the crosssectional area of 1.35 sq. ft. and a length of 6.33 ft, the weight of the concrete edge beam is found to be 1,280 lb.
Figure E-2. Concrete Edge Beam Connected to the Top of the Bearing Stiffeners
iv) Weight of the Bridge Barrier Rail The dimensions of the bridge barrier rail are estimated based on Figure E-3 by
comparing the dimensions of the barrier rail to the height of the exterior girder. The weights of each component of the barrier rail are shown in Table E-3.
E-4

Figure E-3. Bridge Barrier Rail Supported by the Exterior Girder

Table E-3. Volumes and Weights of the Bridge Barrier Components

Parts Posts Horizontal Rails

Volume (cu. ft.) 10 10 30 6 = 10.4 8 8 (50 - 10 6) 2 = 40

Weight (lb) 1,600 6,000

v) Weight of the Wearing Surface
The tributary width used for calculating the weight contribution from the wearing surface is 5 ft based on one-half the spacing between the girders plus 1 ft dimension from the centerline of the exterior girder to the curb as shown in Figure E-2. The weight of the wearing surface is calculated by multiplying the area of the wearing surface by 30 psf, which is specified in the Bridge and Structures Design Manual published by GDOT [15]. The weight contribution from the wearing surface is found to be 7,130 lb over the total 47.5 ft length of the girder.

E-5

vi) Additional Loads from Details at Bearing
Additional contributions to the bearing reaction from the details at the bearing are calculated to account for the loads carried by the portion of the girder and the deck extending beyond the bearing support. The length of the concrete structure and the wearing surface beyond the centerline of the support is 0.5 ft, and the length of the girder beyond the centerline of the support is 0.42 ft. The weight of the bearing stiffeners at the support is also included here. The summation of the additional loads is calculated to be 605 lb. The weight of each additional load component is shown in Table E-4.

Table E-4. Weights of the Additional Loads from Details at Bearing

Parts Concrete Structures
Wearing Surface Steel Structures Bearing Stiffeners

Weight Calculations (21,700 lb +12,800 lb + 200 lb) 0.5 / 47.5
7,130 lb 0.5 / 47.5 (3,700 lb + 610 lb + 610 lb) 0.42 / 47.5
4 0.375 4.5 61 490 pcf

Weight (lb) 365 75 45 120

vii) Summary of the Dead Load
The weight of the structural components except the concrete edge beam and the additional loads from details at the bearing is assumed to be uniformly distributed along the girder length for the structural analyses, while the additional loads from the concrete edge beam and other details at bearing are applied directly at the bearing location. The unfactored dead loads are summarized in Table E-5 and the factored dead loads are summarized in Table E-6.

E-6

Table E-5. Summary of Unfactored Dead Loads

Unfactored Component Dead Load (DC)

47,890 lb

Unfactored Wearing Surface Dead Load (DW)

7,130 lb

Unfactored Additional Load Transfer to the Subject Bearing 1,890 lb

Table E-6. Summary of Factored Dead Loads

Factored Component Dead Load (DC) (DC = 1.25)

59,860 lb

Factored Wearing Surface Dead Load (DW) (DW = 1.5)

10,700 lb

Factored Additional Load Transfer to the Subject Bearing (LL = 1.25) 2,360 lb

E-7

APPENDIX F LIVE LOAD DISTRIBUTION FACTOR CALCULATIONS
The girder residual capacity analyses conducted in this research are focused on the assessment of the fascia girder on the southeast corner of the bridge. In conducting these analyses, the dead and wearing surface loads are distributed to the fascia girder as discussed in Appendix E. For the analysis of the live load shear and bearing capacities, the live load distribution factor (LLDF) for shear from AASHTO LRFD [9] Article 4.6.2.2.3 is applied to the AASHTO HL-93 live load model to assign the live loads to the subject fascia girder. For the evaluation of the live load flexural capacity of the girder, the AASHTO LLDF for flexure is calculated from AASHTO LRFD [9] Article 4.6.2.2.2.
Shear Live Load Distribution to the Exterior Girder on the Lowndes County Bridge Based on AASHTO LRFD [9] Article 4.6.2.2.3b, one estimate of the shear LLDF for
the subject exterior girder is obtained from Table 4.6.2.2.3b-1. In addition, this article specifies that Article 4.6.2.2.2d applies for bridges with diaphragms, which is the case for the Lowndes County bridge. Article 4.6.2.2.2d requires that the LLDF for the exterior beam of a steel beamslab bridge with diaphragms shall not be taken to be less than the reaction found from a rigid cross-section analysis. It is determined that the rigid cross-section analysis for one lane loaded, multiplied by the multiple presence factor of 1.2 for this case, generates the largest LLDF. The calculations from Table 4.6.2.2.3b-1 [9] are presented first and then the rigid cross-section analysis is summarized in the following.
Table 4.6.2.2.3b-1 [9] requires the use of the lever rule for calculation of the LLDF for the one lane loaded case. This LLDF is calculated to be 0.5 by the lever rule since the exterior steel girder is located 1 ft inside the curb for the roadway, the critical location of
F-1

the lane closest to the exterior girder is with its outside edge along the curb, and the critical

location of the resultant for the lane load and the design vehicle load are both located at 5 ft from the outside edge of the lane. As such, the resultant for the live load is 4 ft inside

the exterior girder. Since the girders are spaced at 4 ft, the single lane LLDF by the lever

rule is 0.5, one-half to the exterior girder and one-half to the adjacent interior girder. For consideration of the case with two design lanes loaded, Table 4.6.2.2.3b-1 specifies

the following equations (Equation F-1 is specified by reference to Table 4.6.2.2.3a-1):



=

0.2

+

12

-

35 2

(F-1)



=

0.6

+

10

(F-2)

=

(F-3)

where,

= Distribution factor of the adjacent interior girder

= Distribution factor of the subject exterior girder

S

= Spacing between exterior and interior girders = 8 ft



= Horizontal distance from the centerline of the exterior girder to the

interior edge of the curb or traffic barrier, taken as positive if the exterior

girder is inboard of the curb or traffic barrier, which is the case for the

Lowndes County bridge = 1 ft

Upon substituting the values listed above into Eqs. (F-1) to (F-2), the LLDF for the two lanes loaded case is found to be 0.57.

F-2

Next, the LLDF is calculated from a rigid cross-section analysis using AASHTO LRFD [9] Equation C4.6.2.2.2d-1. AASHTO LRFD Article 3.6.1.1.2 [9] also requires that the multiple presence factor must be applied to the reaction determined from the rigid crosssection analysis. The resulting equation for the LLDF from the rigid cross-section analysis model is:



=




+

2





(F-4)

where, LLDF e
x
mpf

= Reaction (distribution factor) on exterior beam = Number of loaded lanes under consideration, one and two for the
Lowndes County bridge = Eccentricity of a design truck or a design lane load from the center of
gravity of the pattern of girders = 8 ft and -4 ft for the lane closest to the subject exterior girder and for the lane farther from this girder, respectively = Horizontal distance from the center of gravity of the pattern of girders to each girder = 12 ft, 4 ft, -4 ft, and -12 ft for the four girders in the Lowndes County bridge = Horizontal distance from the center of gravity of the pattern of girders to the exterior girder = 12 ft for the Lowndes County bridge = Number of beams or girders = 4 for the Lowndes County bridge = Multiple presence factor, equal to 1.2 for the one lane loaded case and 1.0 for the two lanes loaded case

F-3

Upon substituting the above-listed values into Equation F-4, the LLDFs for the one lane loaded and two lanes loaded cases are found to be 0.66 and 0.65, respectively, from the rigid cross-section model.
The LLDF of 0.66 is the largest value, and thus the governing value, among the distribution factors calculated based on the requirements of AASHTO LRFD [9] Article 4.6.2.2.3b.
The Lowndes County bridge has a 53 degree parallel skew of its bearing lines. Therefore, AASHTO LRFD [9] requires one additional modification to the above skew correction factor. AASHTO LRFD [9] Article 4.6.2.2.3c specifies a "correction factor" for skew, when calculating the shear at the obtuse corner of a skewed bridge span (implied, a span with parallel bearing lines set at a skew). Recent studies by White et al. [20] show that the AASHTO skew correction factor for shear has very limited accuracy at best for straight skewed steel I-girder bridges. However, the AASHTO skew correction factor does properly account for the tendency for an increase in the reactions at the obtuse corners of a bridge span with a parallel skew.
The applicable AASHTO LRFD [9] skew correction factor is given by the equation:

1.0

+

0.20



12.0Lts3 Kg

0.3

tan



(F-5)

AASHTO

LRFD

allows

the

use

of

an

approximate

value

of

0.97

for



12.0Lts3 Kg

0.3

"with

the owners' concurrence" in the case of steel I-girder bridges. Given the characteristics of

the Lowndes County bridge, with signficantly deeper fascia girders compared to the

interior girders, the research team concludes that the detailed calculations suggested by the

F-4

above expression are not merited. Therefore, using the approximation of 0.97 for the complex factor in Equation F-5, and 50.7 degrees for the skew angle, the skew correction factor is calculated as 1.24.
Upon applying the skew correction factor of AASHTO LRFD [9] Article 4.6.2.2.3c to the LLDF calculated based on Article 4.6.2.2.3b, the LLDF for the subject exterior girder of the Lowndes County bridge is determined to be (0.66)(1.24) = 0.82.

Flexural Live Load Distribution to the Exterior Girder on the Lowndes County Bridge

The estimates of flexural live load distribution for the subject exterior girder are obtained from Table 4.6.2.2.2.d-1[9] based on the AASHTO LRFD [9] Article 4.6.2.2.2. It is specified to use the lever rule for calculating LLDF for the one lane loaded case in Table. 4.6.2.2.2.d-1[9]. The value corresponding to the ratio of reaction force due to lane load and the design vehicle load was previously found to be 0.5 for the exterior girder. By multiplying the value of 0.5 by the multiple presence factor of 1.2 for the one lane loaded case, the LLDF for the one lane loaded case is calculated to be 0.6. For consideration of the case with two design lanes loaded, Table 4.6.2.2.2.d-1 [9] specifies the following equations (Equation F-6 is specified by reference to Table 4.6.2.2.2b-1):

= 0.075 + 9.5 0.6 L0.2 12.03 0.1



=

0.77

+

9.1

=

where,

= Distribution factor of the adjacent interior girder

(F-6) (F-7) (F-8)

F-5

= Distribution factor of the subject exterior girder

S

= Spacing between exterior and interior girders = 8 ft

L

= Span length of the girder = 47.5 ft



= Horizontal distance from the centerline of the exterior girder to the

interior edge of the curb or traffic barrier, taken as positive if the exterior

girder is inboard of the curb or traffic barrier, which is the case for the

Lowndes County bridge = 1 ft



= Depth of concrete slab = 6.5 in.

Upon substituting the value of 1.02 for 12.03 0.1and the values listed above into Eqs. F-6 to F-7, the LLDF for the two lanes loaded case is found to be 0.63. Based on the

AASHTO LRFD [9] Article 4.6.2.2.d, the LLDF of 0.66 determined from the rigid cross-

section analysis governs.

F-6