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This is to certify that the
thesis entitled

EVALUATION OF PREFABRICATED COMPOSITE STEEL
BOX GIRDER SYSTEMS FOR RAPID BRIDGE
CONSTRUCTION

presented by

Benjamin S. Pavlich

has been accepted towards fulfillment
of the requirements for the

MS. degree in Civil Engineering

 

 

 

Major l5rofessor’ Signature

2.. 445......2
/ /

7/16/20/0

Date

MSU is an Affirmative Action/Equal Opportunity Employer

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5/08 K:IProlecc&Pres/CIRCIDateDueJndd

 

 

E\

EVALUATION OF PREFABRICATED COMPOSITE STEEL BOX GIRDER
SYSTEMS FOR RAPID BRIDGE CONSTRUCTION

By

Benjamin S. Pavlich

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Civil Engineering

201.0

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ABSTRACT

EVALUATION OF PREFABRICATED COMPOSITE STEEL BOX GIRDER
SYSTEMS FOR RAPID BRIDGE CONSTRUCTION

By

Benjamin S. Pavlich

Prefabrication is a popular practice that has gained widespread use in the bridge
engineering community. Ofien certain components of a bridge are prefabricated and,
then assembled at the job site. However, this report focuses on the possibility of
prefabricating a box girder/slab unit and shipping the entire assembly to a job site, where
only placement and transverse post-tensioning would be required to complete the
construction. This could drastically reduce construction time, eliminating the need for

lengthy and costly road closures.

The objective of the project was to evaluate through numerical simulations the
feasibility of creating an entirely prefabricated composite box girder bridge system and
employing such a system for highway bridges. This included evaluating the global
response of the system, local response of the composite girder/deck units and joints, and
the vibration characteristics of the resulting bridge systems. To ensure accuracy, the

analytical models were checked against theoretical predictions and experimental data.

Results from the simulation studies of this work indicated that the prefabricated
steel/concrete composite girder/deck units are a safe and viable system for short-span
highway bridges. It was shown that acceptable joint closure could be maintained below

the AASHTO post-tensioning limits.

T 0 my grandparents — Stephen, Velna, C. Wesley, and Miriam — who would
have been very proud to see this day.

iii

ACKNOWLEDGEMENTS

This work would never have been possible without the constant guidance and help
of my advisor Dr. Rigoberto Burguefio. His knowledge and experience, coupled with
the insatiable drive to teach and instill knowledge in his students is unmatched. He has
helped me not only with my research, but also with my work ethic, my approach to
problem solving, and my overall capabilities as an engineer. For this, and many other
things over the 4+ years that I have known him, I will always be grateful.

The research described in this report was carried out under funding from the
Michigan Department of Transportation, Contract 2002-0532 — Authorization 12, MSU
APP 90038, with Mr. Steve Kahl as the project manager. The financial support of
MDOT and the coordination of Mr. Kahl throughout the execution of the experimental
program are gratefully acknowledged. Mr. Roger Till (MDOT) provided many helpful
suggestions on the direction of the present study and his help is thankfully recognized.
Also, Mr. Guy Nelson (Nelson Engineering Services) provided invaluable knowledge
and support to this research, which stemmed fiom his insightful bridge concept,
supporting the analytical effort reported in this report with much needed information on
the real construction and performance of prefabricated steel-box girder bridges.

Many of my peers at MSU deserve recognition for supporting me and helping me
think through problems in my research and schoolwork, as well as lending a hand at the
lab including Mahmood Haq, David Bendert, Janelle Musch, Megan Vivian, Zhe Li and
Xuejian Liu, among others.

Finally, I would like to thank my family and friends for encouraging me through

the times when my outlook was a bit bleak. Thanks to all.

iv

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TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................ vii
LIST OF FIGURES ......................................................................................................... viii
1. INTRODUCTION ........................................................................................................... 1
1.1 Summary .................................................................................................................. 1
1.2 Research Objectives ................................................................................................. 3
1.3 Scope and Organization ........................................................................................... 3
2. LITERATURE REVIEW ................................................................................................ 5
2.1 General ..................................................................................................................... 5
2.2 Prefabricated Superstructure Systems ...................................................................... 5
2.3. Prefabricated Steel Box Composite Superstructure Systems .................................. 8
2.3.1 Pressed-Formed Steel Box Girder Bridge System -— West Virginia
University ................................................................................................................. 8
2.3.2 Texas DOT Prefabricated Steel Tub-Girder System — University of Texas,
Austin ..................................................................................................................... 1 1
2.3.3 Inverted Steel Box Bridge System — University of Nebraska, Lincoln ........ 15
2.3.4 Composite Girders with Steel U Section — Tokai University ....................... 17
2.3.5 Con-Struct Bridge System — Nelson Engineering Services .......................... 18
2.4. Deck Systems ........................................................................................................ 21
2.5. Longitudinal Girder—Deck Shear Connections ...................................................... 22
2.6. Transverse Deck Joints ......................................................................................... 23
2.7. Longitudinal Deck Connections ........................................................................... 23
3. DESIGN AND ANALYSIS CONSIDERATIONS ....................................................... 27
3.1 General ................................................................................................................... 27
3.2 Materials ................................................................................................................ 27
3.3 Loading .................................................................................................................. 28
3.4 Design Limit States ................................................................................................ 29
3.5 AASHTO Simplified Analysis and Design Methods ............................................ 30
3.6 Refined Analysis Methods ..................................................................................... 36
3.7 Joint Performance Criteria ..................................................................................... 37
3.8 Parametric and Optimization Analyses .................................................................. 38
3.8.1 Optimization Problem ................................................................................... 38
3.8.2 Problem Formulation .................................................................................... 39
3.8.3 Implementation ............................................................................................. 43
3.8.4 Results ........................................................................................................... 43
3.4.5 Discussion ..................................................................................................... 43
4. CONCEPT EVALUATION .......................................................................................... 46
4.1 Flexural Performance of Con-Struct Bridge System ............................................. 46
4.2 Concept Evaluation and Selection ......................................................................... 52

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5. ANALYTICAL EVALUATION ................................................................................... 5 7

5.1 General ................................................................................................................... 57
5.2. Stress Analysis of Bridge Components and System ............................................. 57
5.2.1 Model Bridge Geometry ............................................................................... 58
5.2.2 Model Bridge Loading .................................................................................. 59
5.2.3 Grillage Model .............................................................................................. 60
5.2.4 Three-Dimensional Finite Element Model ................................................... 69
5.2.5 Comparison of Models .................................................................................. 70
5.2.6 Verification of Models Using Experimental Data ........................................ 73

5.3 Global Parametric Analysis ................................................................................... 79
5.3.1 Creation of 3D FE Models ............................................................................ 81
5.3.2 Selection of Model Geometries .................................................................... 83
5.3.3 System Response .......................................................................................... 86
5.3.4 Discussion of Results .................................................................................... 94

5.4 Stress Analysis and Characterization of Connection Details ................................. 96
5.4.1 General .......................................................................................................... 96
5.4.2 Approach ....................................................................................................... 96
5.4.3 Evaluation of Contact Interaction Modeling ................................................. 97
5.4.4 Model Characterization ............................................................................... 109
5.4.5 System Response ........................................................................................ 111

5.5 Vibration Characteristics ..................................................................................... 127
6. CONCLUSIONS AND RECOMMENDATIONS ...................................................... 133
6.1 Observations ........................................................................................................ 133
6.2 Recommendations for Design .............................................................................. 134
6.3 Recommendations for Future Work ..................................................................... 136
APPENDICES ................................................................................................................. 1.38
Appendix I. Comparison of Analysis Tools ............................................................ 138
Appendix 11. Bridge Case 1: FE Models Responses ................................................ 139
Appendix 111. Bridge Case 2: FE Models Responses .............................................. 141
Appendix IV. Bridge Case 3: FE Models Responses .............................................. 143
Appendix V. Bridge Case 4: FE Models Responses ................................................ 145
Appendix VI. Bridge Case 5: FE Models Responses .............................................. 147
Appendix VII. Bridge Case 6: FE Models Responses ............................................. 149
Appendix VIII. Bridge Case 7: FE Models Responses ............................................ 151
Appendix IX. Bridge Case 8: FE Models Responses .............................................. 153
Appendix X. Bridge Case 9: FE Models Responses ................................................ 155
Appendix XI. Bridge Case 10: FE Models Responses ............................................ 157
Appendix XII. Bridge Case 11: FE Models Responses ........................................... 159
Appendix XIII. Bridge Case 12: FE Models Responses .......................................... 161
REFERENCES ................................................................................................................ 165

vi

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LIST OF TABLES

Table 1. Material Properties .............................................................................................. 28
Table 2. Loading and Moment Demands for Beam Analysis ........................................... 31
Table 3. Loading and Shear Demands for Beam Analysis ............................................... 31
Table 4. Sample Results from Cross-Section Optimization Analyses .............................. 44
Table 5. Design Parameter Selection Criteria and Importance Factor .............................. 55
Table 6. Scoring and Ranking of Design Options ............................................................ 56
Table 7. Summary of limit states considered to evaluate bridge models .......................... 60
Table 8. Smnmary of grillage member properties ............................................................ 66
Table 9. Elements Used in Con-Struct 3D FE Model ....................................................... 76
Table 10. Material Properties used in 3D FE model ......................................................... 77
Table 11. Case Matrix for Global Parametric Analyses ................................................... 80
Table 12. Element Data for Parametric Models with Shell Deck Elements ..................... 82
Table 13. Original Geometries Used for Models in Parametric Study ............................. 83
Table 14. Results of ABAQUS Analysis on Original Geometries ................................... 84
Table 15. Modified Geometries to Meet AASHTO Specifications .................................. 85
Table 16. Results of ABAQUS Analysis on Original Geometries ................................... 85
Table 17. Summary of Maximum Forces in Bridge Models ............................................ 93
Table 18. Case Matrix of Post-Tensioning Levels and Loading Conditions .................. 111
Table 19. Element Data for Full Models with Solid Deck Elements .............................. 1 1 1

Table 20. Fundamental Frequencies of the First Three Bending Mode Shapes, 50’ Bridge
Model .............................................................................................................................. 128

Table 21. Fundamental Frequencies of the First Three Bending Mode Shapes, 100’
Bridge Model .................................................................................................................. 130

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LIST OF FIGURES
Images in this thesis are presented in color

Figure 1. Composite Steel Box Girder Concept ................................................................. 1
Figure 2. Schematic of Prefabricated Steel Composite Superstructure with I-Girders ...... 7

Figure 3. Press—Formed Composite Box Girder from Gangarao and Taly (Taly, 1979) 9

Figure 4. Shear Key Details for Pressed-Formed Steel Box Girders (Taly, 1979) ........... 10
Figure 5. Connection and Stiffener Details at Abutment Support (Taly, 1979) ............... 11
Figure 6. Texas DOT Steel Tub-Girder Section (Freeby, 2005) ...................................... 13

Figure 7. Typical Bridge Cross-Section using TDOT Steel Tub-Girders (Freeby, 2005) 13

Figure 8. Transverse Deck Connection Detail for Steel Tub-Girder (Freeby, 2005) ....... 14

Figure 9. Inverted Box Girder Bridge Diagram (Y akel, 2007) ......................................... 16
Figure 10. Alternate Inverted Box Girder Geometry (Azizinamini, 2006) ...................... 16
Figure 11. U-Shaped Girder Cross Sections (Nakamura, 2002) ....................................... 17
Figure 12. Preliminary Concept for Composite Steel Box Girder (Nelson, 2004) ........... 19
Figure 13. Pedestrian Bridge over Tyler Creek (MI) with Con-Struct System (Nelson,
2006) ................................................................................................................................. 21
Figure 14. Deck Connection Detail using Reinforcement in Precast Pockets (Badie, 1999)
........................................................................................................................................... 25
Figure 15. Deck Connection Detail using Confined Reinforcement in Full- Depth Key ,
(Badie,1999) ..................................................................................................................... 26
Figure 16. Deck Connection Detail using Welded Steel Plate (Badie, 1999) .................. 26
Figure 17. Design Truck Schematic ................................................................................. 29
Figure 18. Bridge Geometry Used in AASHTO Analysis ............................................... 30
Figure 19. Variables for AASHTO Nominal Plastic Moment of Composite Girders
(AASHTO, 1998) .............................................................................................................. 33
Figure 20. Composite Steel Box Girder Cross-Sectional Geometry ................................ 39

viii

Figure 21. Bridge System Profile under Beam-Line Analysis Assumption ..................... 39

Figure 22. Typical Cross-Section of Con-Struct Test Units (Nelson, 2006) .................... 47
Figure 23. Test Unit with Cast-in-Place Concrete Deck (Nelson, 2006) .......................... 48
Figure 24. Test Unit with Precast Concrete Deck System (Nelson, 2006) ....................... 49
Figure 25. General Test Setup Views — C.I.P. Test Unit .................................................. 50
Figure 26. Moment vs. Curvature Response of C.I.P. Test Unit at Mid-Span ................. 51
Figure 27. Bridge being modeled for analysis approach comparison ............................... 59
Figure 28. Schematic of grillage element cross-sections and grillage model ................... 61
Figure 29. Nomenclature of box sides .............................................................................. 62
Figure 30. Chart for distortion deflection parameter w for simply supported beams and

box without cross-bracing or diaphragms (Hambly, 1991) .............................................. 64
Figure 31. Section A geometry and associated grillage properties ................................... 65
Figure 32. Section B and C geometry and associated grillage properties ........................ 66
Figure 33. Section D geometry and associated grillage properties ................................... 66
Figure 34. Application of wheel loads to grillage model .................................................. 68
Figure 35. Completed grillage model and system transverse moment response .............. 68
Figure 36. Girder modification in 3-D FEA model .......................................................... 69
Figure 37. Completed 3-D F EA model and von Mises stress contours ............................ 70
Figure 38. Location of forces chosen for comparison ...................................................... 71

Figure 39. Comparison of analysis tools on full scale bridge model (lane load only) ..... 71

Figure 40. Comparison of analysis tools (fiill AASHTO loading) ................................... 73
Figure 41. Finite Element Model of Con-Struct System in Flexure. ................................ 77
Figure 42. Experimental Test Setup .................................................................................. 75

Figure 43. Experimental Load Displacement Response of Cast-in-Place Con-Struct
System ............................................................................................................................... 75

ix

Figure 44. Assembled 3D Model ...................................................................................... 77

Figure 45. Load Displacement Results of Experimental Model vs. FE Model ................ 78
Figure 46. Response measures of interest in parametric studies ...................................... 80
Figure 47. Typical Bridge Model Using Shell Elements .................................................. 81
Figure 48. Typical Deformed Shape and Moment Distribution. ...................................... 86
Figure 49. Typical Deformed Shape and Moment Distribution. ...................................... 87
Figure 50. Typical Location of Paths ................................................................................ 88
Figure 51. 50' Span: Transverse Moment v. Transverse Distance Comparison ............... 89
Figure 52. 50' Span: Transverse Moment v. Longitudinal Distance Comparison ............ 89
Figure 53. 50' Span: Longitudinal Moment v. Longitudinal Distance Comparison ......... 90
Figure 54. 75' Span: Transverse Moment v. Transverse Distance Comparison ............... 90
Figure 55. 75' Span: Transverse Moment v. Longitudinal Distance Comparison ............ 91
Figure 56. 75' Span: Longitudinal Moment v. Longitudinal Distance Comparison ......... 91
Figure 57. 100' Span: Transverse Moment v. Transverse Distance Comparison With and
Without Diaphragms ......................................................................................................... 92
Figure 58. 100' Span: Transverse Moment v. Longitudinal Distance Comparison With
and Without Diaphragms .................................................................................................. 92
Figure 59. 100' Span: Longitudinal Moment v. Longitudinal Distance Comparison With
and Without Diaphragms .................................................................................................. 93
Figure 60. Schematic of Cube Contact Model with Pressure Applied Normal to the
Contact Plane .................................................................................................................... 99
Figure 61. Cube model showing separation of nodes ....................................................... 99

Figure 62. Schematic of Cube Contact Model with Pressure Normal to the Contact Plane
and Vertical Pressure ...................................................................................................... 100

Figure 63. Bottom view of top-loaded model showing separation of nodes under load 100
Figure 64. Schematic of Updated Model with More Accurate Geometry ...................... 101

Figure 65. Updated Model with More Accurate Geometry ............................................ 102

X

Figure 66. (a) Top view of deformed shape of model in Figure 62 and (b) Bottom view of
model in Figure 62 showing node separation ................................................................. 102
Figure 67. Schematic of Rectangular Beams Used for Quantitative Evaluation ............ 103
Figure 68. Model of rectangular beams .......................................................................... 103
Figure 69. Deformed rectangular beam model showing no separation at midspan ........ 104
Figure 70. Stress profile in rectangular beam model ...................................................... 105
Figure 71. Schematic of Male—to-Female Joint Model ................................................... 106
Figure 72. ABAQUS Model with Male-to-Female Joint ................................................ 106
Figure 73. FE Model of Male-to-Female Joint ............................................................... 107
Figure 74. Comparison of longitudinal stress in FE model ......................... p ................... 107
Figure 75. Comparison of longitudinal stresses in models with and without joint ......... 108
Figure 76. FE Model of Shear Key Joint Opening Under Loading ................................ l 10
Figure 77. FE Model of Bridge Model 9. ....................................................................... 110
Figure 78. Parameters Studied in Models with Joints ..................................................... 113
Figure 79. FE Model with Solid Deck Elem ents and Joints Representing Model # 1 .. 113
Figure 80. Deformed Shape of Model in Figure 76. ....................................................... 114
Figure 81. Longitudinal Stress Variation by Girder (SO—ft Model, Service Loading) 115
Figure 82. Longitudinal Stress Variation by Girder (SO-ft Model, Strength Loading)... 115
Figure 83. Transverse Profile of Vertical Displacement at Midspan Under Varying Post-

tensioning Levels (SO-ft Model, Service Loading) ......................................................... 116
Figure 84. Transverse Profile of Vertical Displacement at Midspan Under Varying Post-

tensioning Levels (SO-ft Model, Strength Loading) ....................................................... 117
Figure 85. Joint 3 Opening Along Span (SO-fi Model, Service Loading) ...................... 118
Figure 86. Joint 3 Opening Along Span (SO-fi Model, Strength Loading) ..................... 118
Figure 87. Joint 4 Opening Along Span (SO-fl Model, Service Loading) ...................... 119

Figure 88. Joint 4 Opening Along Span (SO-fl Model, Strength Loading) ..................... 119

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Figure 89. FE Model with Solid Deck Elements and Joints Representing Model # 9 120
Figure 90. Deformed Shape of Model in Figure 86. ....................................................... 121
Figure 91. Longitudinal Stress Variation by Girder (100-fi Model, Service Loading) .. 122
Figure 92. Longitudinal Stress Variation by Girder(100-ft Model, Strength Loading). 122

Figure 93. Transverse Profile of Vertical Displacement at Midspan Under Varying Post-

tensioning Levels (lOO-fi Model, Service Loading) ....................................................... 123
Figure 94. Transverse Profile of Vertical Displacement at Midspan Under Varying Post-

tensioning Levels (lOO-ft Model, Strength Loading) ..................................................... 123
Figure 95. Joint 2 Opening Along Span (lOO-fi Model, Service Loading) .................... 124
Figure 96. Joint 2 Opening Along Span (lOO-ft Model, Strength Loading) ................... 125
Figure 97. Joint 3 Opening Along Span (lOO-fi Model, Service Loading) .................... 125
Figure 98. Joint 3 Opening Along Span (100-ft Model, Strength Loading) ................... 126
Figure 99. Joint 4 Opening Along Span (100-ft Model, Service Loading) .................... 126
Figure 100. Joint 4 Opening Along Span (lOO-ft Model, Strength Loading) ................. 127
Figure 101. Bending Mode Shape 1, 50’ Bridge Model ................................................. 128
Figure 102. Bending Mode Shape 2, 50’ Bridge Model ................................................. 128
Figure 103. Bending Mode Shape 3, 50’ Bridge Model ................................................. 129
Figure 104. Bending Mode 2 Cross-Section ................................................................... 129
Figure 105. Bending Mode 3 Cross-Section ................................................................... 130
Figure 106. Bending Mode Shape l, 100’ Model ........................................................... 131
Figure 107. Bending Mode Shape 2, 100’ Model ........................................................... 131
Figure 108. Bending Mode Shape 3, 100’ Model ........................................................... 132

xii

1. INTRODUCTION

1.1 Summary

In order to offer faster and, in some cases, less expensive bridge construction,
precast superstructures have recently become a topic of much interest to federal and state
highway agencies (FHWA, 2004; Shahawy, 2003). Almost any component of a bridge
can be precast or prefabricated, including girders, abutments, and decks (FHWA, 2004;
Shahawy, 2003). The focus of this research is that of completely prefabricated
composite steel box girder sections for rapid construction. While the exact geometry is
to be developed with the work from this research project, the basic concept being

investigated is presented in Figure 1 below.

     

1: Concrete Deck
2: Bent Steel Plate

3: Shear Stud

4: Longitudinal Joint
5: Transverse Joint

Figure 1. Composite Steel Box Girder Concept

As shown in Figure 1, the prefabricated steel box superstructure system consists
of a cast in place or precast deck connected to a press-formed or cold-bent steel plate by
means of shear studs. These sections could then be placed side by side and connected
transversely, utilizing a shear key or other similar mechanism. While the behavior,
design, and analysis of composite steel box girders is well established, several
outstanding issues are unresolved for implementation of prefabricated concepts. The
information needed in order to make the proposed prefabricated system viable is:

- What, if any systems are already in place
' Design of shear connection
'I Design of longitudinal deck connection

' Design and analysis modeling techniques

These topics and their applicability to a prefabricated composite steel box girder

system constitute the focus of the work performed in this project.

While the system that originally initiated the interest of the Michigan Department
of Transportation (MDOT) in this topic utilized a cold bent plate, the intention of this
project is not to limit this system to tubs that can only be press formed. The tub size
used in the longer span (100 ft) bridges being studied would require an extremely
substantial plate forming and bending operation. The author is not familiar with an
operation of such magnitude, and hence tubs for longer spans may require welded plates.
Although this would introduce additional cost into the system, it will not affect

performance, and will not be discussed further.

 

 

 

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1.2 Research Objectives

The overall goal of the project was to gain a working knowledge of the bridge
system at hand. This was considered to have been achieved when the following

objectives were met:

I Determine global system response of prefabricated composite steel box
girder systems due to loads

I Determine localized behavior of joints

I Determine the effect of reduced post-tensioning on both global behavior
and joint behavior

I Present design recommendations

The first three objectives were met by developing a hierarchical suite of finite
element analyses that could address different aspects of the bridge behavior. While
some models were conducive to global analysis, others were more suited for detailed
joint analysis. Others yet had reduced complexity that led to smaller run times, making
them more adept to parametric studies. These finite element models were meticulously

checked against theoretical and experimental results in order to ensure their accuracy.

The final objective was accomplished by analyzing the data compiled throughout
the first three objectives. These results allowed the author to make recommendations for

employing prefabricated composite steel box girder systems.

1.3 Scope and Organization

The first step toward completing the project was to compile and study existing

literature on related topics. This literature review can be found in Chapter 2 of this

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thesis. Although many similar systems were found, the exact system being investigated
here was not. Therefore, it is the belief of the author that this is the first major study of
this particular system. The design and analysis considerations for the project are listed
in Chapter 3. These included loading conditions and limit states, analysis methods, and

some preliminary optimization work.

Once the literature review was performed the possible variations of the system to
be studied were pared down using a rating system which accounted for factors such as:
cost efficiency, constructability, fatigue performance/durability, and ease of
replacement/removal. The highest ranking designs were then chosen for analysis. This

can be found in Chapter 4.

Chapter 4 also highlights information gathered from experimental testing of a_
prefabricated steel box girder system. This experimental evaluation adds credibility to

the analytical evaluations performed for this project.

The technical bulk of the work done on this project can be found in Chapter 5.
This section details the selection of analysis tools, parametric studies, and detailed
studies of joints and connections. The information found here can be used to aid in the

design of prefabricated composite box girder systems.

Lastly, design recommendations are presented in Chapter 6.

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2. LITERATURE REVIEW

2.1 General

A literature and survey review of current prefabricated complete superstructure
systems has been conducted to identify prefabricated solutions similar to the system
being studied or that address some of the issues noted in Section 1. The review
considered available information at the conceptual, research, or implementation stage.
As a reference, a brief account of concrete solutions is discussed and then more
emphasis is placed on steel composite solutions. In the discussion of connection
elements, the girder material type is not relevant and thus they are discussed as stand-

alone details.

2.2 Prefabricated Superstructure Systems

As previously mentioned, national and state highway agencies have a high interest
in using completely prefabricated bridge systems (AASHTO, 2002; FHWA, 2004;
Shahawy, 2003). Technological progress is such that almost all the different elements
composing a bridge system have had prefabricated solutions implemented in various

projects. Thus, complete superstructure elements should be no different.

The most common type of prefabricated superstructure elements are clearly the
girders, which could be prefabricated in either steel or prestressed concrete solutions and
in either I or box shapes. These prefabricated beams are usually made composite with a
cast-in-place concrete deck. Thus, complete superstructure solutions are typically

referred to as those that use prefabricated elements that integrally feature both the girder

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and the deck system. Under this defrnition, untopped adjacent prestressed box girders
could be considered a complete prefabricated system; and clearly so would be
precast/prestressed concrete segmental bridges (typically cellular box girders). Both
adjacent prestressed box girders and segmental cellular box girders are commonly and

successfully used.

Prestressed double-tee beams have also been used as complete prefabricated
superstructure solutions in several states (e.g., Colorado, New Mexico, and Wyoming)
(Shahawy, 2003). Continuity between adjacent double-tee units is achieved by
transverse post-tensioning. While this solution is aimed at highway bridges, it has been
mostly used for rural and secondary roads. Complete superstructure deck systems have
also been proposed, usually called full-depth prefabricated decks. Systems with and
without the requirement of a cast-in-place topping have been developed (FHW A, 2004).
Prefabricated prestressed and post-tensioned full-depth deck panels have also been used

for complete superstructure replacement in Europe (Shahay, 2003).

A more recent concept is the use of precast/prestressed girder elements with full
or partial deck flanges for a prefabricated superstructure element. A complete
superstructure would then be assembled by a cast-in-place deck topping or connection of
the prefabricated girder/deck elements through transverse connection of the deck flanges
(Badie, 1999; FHWA, 2004; F reeby, 2005). These systems have been developed using I-
or bulb-tee girders (FHWA, 2004), standard and modified closed box girders (Badie,
1999; Freeby, 2005), and U- or tub-shaped girders with deck flange overhangs (Badie,

1999; Freeby, 2005).

he"
L 513

3551‘?

 

F121}

 

Prefabricated steel superstructure systems are less common but several have also
been developed. Complete superstructure elements have been created by the pre-
assembly of I-girders with a composite concrete deck with partial overhangs as shown in
Figure 2. If needed, the superstructure unit is prefabricated with transverse diaphragms.
A superstructure of this type was used for the James River bridge replacement project in
Richmond, Virginia (FHWA, 2004; Ralls, 2003). The contractor used prefabricated steel
I-girder/deck units for most of the 101 bridge spans. The girder-deck units were pre-
constructed in a casting yard near the site. The old bridge was removed overnight.
Abutments were prepared for placement of the new bridge and the composite units were
then set in place. The slab joints were sealed and the slab was post-tensioned
transversely. For this project, the Virginia DOT did not consider any bids over 220 days.
The winning bid was for 179 days and the contractor finished the job in 140 days. For
each day under 179 the contractor received $30,000 bonus, and was to be charged the

same amount for each day over schedule.

 

 

 

 

 

Figure 2. Schematic of Prefabricated Steel Composite Superstructure with I-Girders

2.3. Prefabricated Steel Box Composite Superstructure Systems

Much to the surprise of the author, a literature review on prefabricated steel box
composite bridge superstructure elements showed that such a concept has been proposed
several times during the past 35 years. The concept, as discussed in Section 1, uses a
tub-shaped steel section as the girder element connected compositely to a concrete deck.
The steel tub section and the composite deck then define a box section. The
prefabricated steel composite box girders are then to be used as complete superstructure

units, placed side by side to make up the require bridge width.

2.3.1 Pressed-Formed Steel Box Girder Bridge System — West Virginia University

In reviewing the literature, the first finding of a prefabricated steel composite box
girder system was the conceptual designs of Gangarao and Taly (Taly, 1979). In the
early 19705 Gangarao and Taly developed and studied several modular bridge systems
aimed at short and medium spans. Concepts for prefabricated press-formed steel box
girder bridge superstructure elements were developed and found economical and
suitable for span ranges of 40 to 100 feet under HS20—44 loading. The proposed system
consists of a trapezoidal trough section which is press-formed from a 3/8-in. thick A36
steel plate (see Figure 3). The deck consists of 5-in. thick precast prestressed concrete
panels. The concrete deck is to be precast with the stud-plate embedded in it and then
the entire deck assembly is shop—welded to the steel trough section. The precast concrete

Planks are nominally prestressed to minimize shrinkage cracks.

no

OI'

The composite solution was an alternate to an all-steel designed proposed by the
same authors (T aly, 1979). The webs and the bottom flange are not stiffened internally
or externally. Different girder sections were suggested for different span lengths. They
envisioned the girders to be produced in two top-flange widths, 6 ft and 8 it, each having
three variations in depth: 2.5 ft, 3.0 ft, and 3.5 ft. Their studies showed that a suitable

combination of these sections results in various deck width designs at 2 ft intervals for

 

 

 

 

 

spans up to 65 ft.
H {A
5 ER STUDS SEE DETAIL ”A"
PRECAST P/S CONCRETE SLAB—\ / /_\ /
\ ' i \
,5 FM; gm; ’\\ Q /
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4|! BI‘O" 4H

 

Figure 3. Press-Formed Composite Box Girder from (Taly, 1979)

Lateral load distribution between the adjacent girder units is achieved through
shear keys with weld-ties at the junction of the two adjacent beam deck flanges as
shown in Figure 4. The ends of the girders are closed by a 3/8-in. thick plate diaphragm
welded all around the flanges and webs of the girders. Bearing stiffeners were provided .
at the beam ends (see Figure 5). Drainage holes were proposed in the bottom flange to

drain out moisture from the closed steel box section.

 

 

Fi-

Ill:

 

 

Irv

 

 

113:

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SHEAR KET

PRECAST P/S CONCRETE SLAB—\ ,_ ‘ SEE DETAIL 'A"
9 ALL ‘ .u. [-32 .m ,u, L

    

  

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Figure 4. Shear Key Details for Pressed-Formed Steel Box Girders (Taly, 1979)

Since the American Association of Highway Transportation Officials (AASHTO)
specifications did not provide any criteria for design with press-formed steel members,
the proposed girder was checked according to the 1977 American Iron and Steel
Institute specifications. Regarding the maintenance and durability of the system, the
proponents note that investigations on several steel bridges with hollow members that
had been in service for over 60 years had shown no signs of moisture or corrosion on the

inside surfaces. Accordingly, Gangarao and Taly did not suggest corrosion-protective

10

 

 

 

 

T.- .

~ j .

 

treatment for the interior of the proposed girders. For the exterior, they recommend
painting the steel surface to protect it from corrosion, unless weathering steel, such as

Corten or Mayari-R, is used for fabrication.

PLATES NIDER AT

ENDS TO PROVIDE

BEARING AREA FOR
STIFFENER

SHEAR KEY

PRECAST P/s CONCRETE SLAB—1 ,

E " (LIL? CD ,ILMJ Lu. é.
, = 1

'IA

    
 
 
 

     
   
 

 

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/,: WET—— a

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STIFFENER PLATES I

 

 
 

 

 
 

 

 

 

 

1/2' x 6" TYP.
v2" x I2" PL. 5' I WHTYP. .. d ELASTOMERIC
a: E: II 5: BEARING PAD
I ~ '~ TYP.
L 20" ABUTMENT ( )
S”—
| 1/4“ DIA. SNEDGE BOLT IN

 

I 5/8' HOLE (FIXED END)
' I 5/5" DIA. SNEDGE BOLT IN

0-0.1 SLOTTED HOLE (EXP. END)-

 

 

Figure 5. Connection and Stiffener Details at Abutment Support (Taly, 1979)

2.3.2 Texas DOT Prefabricated Steel Tub-Girder System — University of Texas, Austin
A more recent effort to develop steel box girder systems for modular
prefabricated bridge superstructures was performed at the University of Texas, Austin
for the Texas Department of Transportation (Freeby, 2005). The effort was propelled by
the pressure on the Texas DOT to upgrade and expand its on- and off-system roadways
and, in particular, the need for the rapid construction of the nearly 150 bridges that cross
1-35 in central Texas. Construction of these structures was scheduled to begin in spring

2005.
l 1

From the effort noted above, two new prefabricated bridge superstructure systems
were developed: a steel tub-girder and a prestressed concrete pre-topped U-beam
(Freeby, 2005). Both systems were developed for maximum span lengths of 115 ft and

total superstructure depth of 38 in. Only the steel solution is discussed here.

The steel tub-girder system uses a conventional pre-fabricated trapezoidal steel
girder topped with a cast-in-place concrete slab before transportation to the bridge site.
To achieve a shallow superstructure depth, the beams are shored during placement of the
concrete deck to make them composite for all loads. After slab placement, the beam is
hauled to the bridge site and erected on the piers/abutments. A cast-in-place closure pour
joins the deck girder sections after they are in place. Figure 6 shows a girder section for
a 115 fi span. The steel tub-girder has a 29.5-in. deep steel section with an 8.5-in. slab
for a total section depth of 38 in. The design used ASTM A709 Grade 50W steel. A

typical transverse cross—section of a bridge is shown in Figure 7.

As shown in Figure 6 the steel tub is formed of welded steel plates, as opposed to
the bent steel plate proposed in this project. This gives the advantage of variable widths
for the webs and flanges, but comes at the expense of requiring costly welds. However,
it should be noted that the Texas DOT opted for welded steel plates in order to avoid

introducing new bending technology, not on the basis of performance (F reeby, 2006).

12

 

 

 

 

 

 

 

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TYP.

 

 

 

 

 

 

 

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Figure 6. Texas DOT Steel Tub-Girder Section (Freeby, 2005)

 

 

 

 

 

 

 

 

 

g 40'-3" OVERALL f
L. 4C'—O" ROADWAY (NOMINAL) Al
I PERMISSIBLE NOMINAL FACE /
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TUB GIRDER SPACING
AT BOTTOM OF GIRDER

SHOWING TYP. CROSS SECTION

SHOWING THICKENED SLAB END AT ABJT.

Figure 7. Typical Bridge Cross-Section using TDOT Steel Tub-Girders (Freeby,

2005)

The girder design was developed using the AASHTO LRFD Bridge Design

Specifications with HL93 loading (AASHTO, 1998). The design of the girder element

was controlled by the Texas DOT imposed live load deflection limit of U800 and not by

13

allowable strength requirements. Due to the unusually shallow section, the girder was

proportioned so that the deck would not crush before the steel tub reached yield.

The transverse deck connections for the prefabricated systems are reported to be
undergoing testing at the University of Texas, Austin (Freeby, 2005). The concept for
the joint detail used in the steel tub-girder superstructure is shown in Figure 8.
Preliminary research results noted that the closure joint behaves as designed and
develops the predicted moment and shear capacities with failure due to yielding of the
reinforcement, exhibiting ductile behavior (Freeby, 2005). While durability of the joints
is a general issue, Texas DOT is not concerned with corrosion due to their weather but

plan to monitor the structures closely.

 

 

 

 

 

 

 

 

 

 

I'—4" NOMINAL
:71 V2" MIN. .
C_ON§T. .IOINT (TYP) 3/8" DIA. x ?" A307 CALv. BO_L_T
/"
\ 1/ 7

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DOEs NOT LEAR OUT (A, ./ ’

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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wmxjfi \_B_R_.\ \\ \\PRE§A SLBLAB
I 5

TAT—IN—PLACE FORM
—4 34‘ \PRECAST SLAB REINF

Figure 8. Transverse Deck Connection Detail for Steel Tub-Girder (Freeby, 2005)

Weathering steel was specified for durable performance without maintenance
costs. Drip tabs and other details were provided to reduce the potential for substructure

staining from the weathering steel. A flexible lifting scheme was incorporated in the

14

A '4

£01

in

of

 

 

 

design to give the contractors more options on the lifting and placement of the

prefabricated units.

The two competing prefabricated bridge designs were released for letting in
August 2004 and the winning bid was of the pretopped prestressed U-beam design. It is
felt that the recent rise in steel prices prevented the steel tub-girder design from being
competitive. It should also be noted that the steel tub-girder is composed of welded
plates, which add a considerable amount of labor. The Texas DOT anticipates that both
of the developed prefabricated bridge superstructures will be used over the next 10 years

for the rapid construction of the I-35 corridor in central Texas.

2.3.3 Inverted Steel Box Bridge System — University of Nebraska, Lincoln

A new steel configuration for prefabricated steel composite superstructure bridge
elements is currently being developed and studied at the University of Nebraska,
Lincoln under a contract from the Nebraska Department of Roads (TRB-RIP, 2006). The
concept uses an inverted steel tub/box girder connected compositely with a concrete
deck. The rationale for inverting the steel tub-girder section follows from the case that
small box sections do not permit maintenance workers inside the box for inspection.
Inverting the steel box eliminates this problem. A bridge cross section of this system is
shown in Figure 9. A United States patent from the same research team shows a
different press-formed geometry of the inverted girders, as shown in Figure 10

(Azizinamini, 2006).

15

L:\

,QQNQIEEEBECIS-

 

 

 

ML 1 .L 1.1/

\\

_______._-___.. ___. \ INVERTED BO_>_< GIRDER

Figure 9. Inverted Box Girder Bridge Diagram (Y akel, 2007)

 

 

Figure 10. Alternate Inverted Box Girder Geometry (Azizinamini, 2006)

The inverted steel box girder features are:

A girder consisting of an inverted steel box section. The web and top
flange are of the same thickness and the bottom flanges are welded to the
end of the web.

The inverted box girder could be shop-welded or made by bending a flat
plate into a U shape.

Knee braces extending from the bottom flange ends can allow longer deck
overhangs, if needed, and can provide horizontal restraint to the bottom
flanges since they will have the tendency to “kick-out” (in plan) under
flexural demands.

Initial horizontal curvature (in plan) in the flanges could reduce the
tendency of the bottom from “kicking-out” under flexural demands. This
approach can also be used to generate an initial compressive force in the

16

bottom flanges to counteract dead load stresses and increase the live load

capacity of the girder.
The wide top flange of the inverted box provides a convenient platform for
construction workers but it may need to be stiffened.

A research project sponsored by the Nebraska Department of Roads (NDOR)
published in 2007 provides extensive background on this system (Y akel, 2007) The

research suggested that such an inverted box girder system would likely be a vrable

option for bridges of less than IOO-fi span.

2.3.4 Composite Girders with Steel U Section — Tokai University

Professor Shun-ichi Nakamura of Tokai University in Japan studied the bendrng
behavior of composite steel box girders of a “U-shape” in 2002. His research Involved
testrng three different sections of such a girder. One of the sections was prestressed and

will not be discussed here. The other two sections can be seen below in Figure 11

I
I

I I

DI

450

PL-e _.
(55400) \

 

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EBA—Ow" \‘I-SO ILA

Figure 11. U-Shaped Girder Cross Sections (N akamura, 2002)

 

 

 

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The second girder configuration shown in Figure 11 is depicted upside-down to
represent a section over a support where the section would be in negative bending. The
section is filled with concrete to take the compressive forces induced by this negative
bending and to stabilize the steel against buckling.

The researchers in this project developed an analysis model that divided the
section into vertical “layers” and then analyzed the system assuming a bilinear stress-
strain curve for the steel and a parabolic stress-strain curve for the concrete. They were
able to match experimental findings closely.

Overall the researchers concluded that the U-girder system was a viable system
and could be designed using a plastic design procedure. A three-span continuous bridge
consisting of 60m (195 ft) spans was designed, with U-girders reaching heights of 2.5m

(97.5 in.) and a plate thickness of 25mm (1 in.) (Nakamura, 2002).

2.3.5 Con-Struct Bridge System — Nelson Engineering Services

Nelson Engineering Services (NBS) has developed an innovative concept for a
prefabricated composite steel box girder system with an integral road deck for shallow
prefabricated bridge superstructures (AASHTO, 1998). The Con-Struct concept is that
of a shallow girder element consisting of a cold-formed bent steel plate in the shape of a
“bath-tub” connected compositely to a reinforced concrete deck (Figure 12a). The
composite box shape is braced for placement by the prefabricated deck, which
eliminates the need for cross-frames. Prefabricated girder units can be placed side by
side and post-tensioned transversely at the deck level or at intermediate concrete

diaphragms to build up the desired superstructure width (Figure 12b).

18

6.0"

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4" DEEP 51?. / \_ Inm _ _ II J
DECKING
(CAULK EACH
SIDE AT TOP
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a) Beam-Cross Section at Intermediate Diaphragm

 

fl BARRIER PRECAST
WITH BEAM

12'0“ PRECAST DOUBLE SECTION _,
[EPOXY ADHESIVE ON

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,

 

 

 

 

 

 

 

 

 

 

 

DIAPHRAGM

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b) Partial Deck Cross-Section

Figure 12. Preliminary Concept for Composite Steel Box Girder (Nelson, 2004)

19

Unique to the Con-Struct system from Nelson Engineering is their concept to
prestress the steel plate to increase the composite girder capacity for live loads. This is
achieved by propping the steel tub section at mid-span and stabilizing it, but not
supporting it from its ends. A cast-in-place deck is then poured and a Styrofoam block or
metal decking is used to form the deck on top of the tub-girder void. The self weight of
the deck introduces negative bending on the steel plate when propped on its center. This
negative moment introduces an initial compressive state in the bottom of the tub-girder
soffit. Once cured, the concrete slab and the steel girder act compositely and the
compressive stress in the steel tub is “locked-in.” This stress can be further controlled by
using tensioning devices at the end of the steel tub-girder. The concept is to use the
initial pre-compressive stress to provide camber to the section and to counteract dead

load stresses. This also increases the service live load capacity of the section.

The Con-Struct system is built using galvanized steel for durability measures. To
the knowledge of the author, Nelson Engineering has not yet developed or validated
transverse deck connection details to connect multiple girder sections for wider bridge
solutions. The system, however, has been effectively used in several private pedestrian
bridges in Michigan. A picture of a 40 ft long pedestrian bridge using the Con-Struct

system is shown in Figure 13.

20

 

 

 

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Figure 13. Pedestrian Bridge over Tyler Creek (MI) with Con-Struct System
(Nelson, 2006)

2.4. Deck Systems

In designing a composite bridge girder system, even if it is prefabricated, a
decision must be made between decks cast-in—place, decks made of precast elements
with cast-in-place overlays, decks made of precast elements with wet joints, and totally

precast decks.

Decks cast-in-place have strong advantages. They are simple to erect and easy to
connect. However, these deck systems may suffer high tensile strains produced by
shrinkage, which is resisted by the steel beam. Slabs made from precast elements also
have advantages: low cost, fast construction, and high product quality. Connection of a
precast deck to a steel girder is achieved by distributing the connection in groups that are
anchored in pockets left in the precast deck and which, after placement, are filled with
non-shrink grout. Problems with this solution may include connector density, corrosion
between the girder and the deck, and shrinkage of the concrete in the pockets. The best

solution is to prefabricate the deck and to prestress it longitudinally before connecting it

21

to the steel girder (Virlogeux, 1999). The only concern would be creep in the concrete,
which could be reduced through prefabrication. Thus, the slab could be made of precast
elements made continuous through longitudinal joints before prestressing the deck;

leaving the connection to the steel girder last.

2.5. Longitudinal Girder-Deck Shear Connections

Shear connections in composite beams are obviously essential. The nature of
composite action induces large shear forces at the interface between the steel and
concrete. Traditionally, these shear forces are carried by means of a shear stud welded to
the steel, which is then embedded into the concrete deck. When a cast-in-place deck is
used, embedding of the shear studs is simple. Shear studs are shop-welded and the deck
is poured around them. However, if the deck is prefabricated, pockets are left in the
precast slabs that correspond to the location of the shear studs on the steel. These
pockets are then filled with a non-shrink grout, which hardens to achieve the composite
action. The design of the shear studs, as well as the properties of the grout used, can

have large effects on the response of the entire section.

Considerable information exists both in code guidelines and research findings to
guide the design of girder-deck shear connections. This research will study further the
guidelines in the AASHTO LRFD specifications. Considerable information was also
found from activities in Korea on the development of composite box girder sections with
precast decks (Chang, 2001). General guidelines on steel and concrete composite

Construction were also found (Ohelers, 1995).

22

2.6. Transverse Deck Joints

Also of consideration are the transverse connections between prefabricated deck
segments. Transverse deck joints will be less critical for the concept under investigation
here since the sections are to be used as simple spans. Therefore, negative moments, and
the associated tensile stresses will not occur at the transverse joints. Despite this,
transverse deck connections between prefabricated panels should not be ignored as they
are responsible for transferring the longitudinal shear in the deck element. An
inadequate transverse shear connection can lead to slip between adjacent precast panels

and limit the flexural and shear capacity of the overall system.

Typically, the joints connecting prefabricated panels are made by means of shear
keys of two basic types: female-to-female or tongue-and-groove type joints. After
installation, the joints are filled with high—strength non-shrink grout or with an epoxy
mortar. Longitudinal post-tensioning is sometimes necessary to provide sufficient

compression to keep the joints from opening.

Use of precast concrete panels for full depth decks has been in use since the 19703
(Taly, 1979) and new efforts closely related to steel box construction have been recently

published (Chang, 2001). Thus, extensive literature exists on the topic (Issa, 1995).

2.7. Longitudinal Deck Connections

The capacity of a deck system to distribute loads transversely between girders
deflnes the load distribution characteristics of the bridge system. Thus, the ability to

Connect the prefabricated sections transversely, at the deck flanges, will be of great

23

importance for the system under consideration. The longitudinal deck connections for
prefabricated (decks seem to be designed on a project specific basis for connecting
prefabricated double tees (Shahawy, 2003) as well as the prefabricated steel box tub-
girder concepts presented in Section 2.3.1 and Section 2.3.2. An overview of the

concepts identified follows.

In general, to maintain continuity between adjacent prefabricated deck elements
(or the flanges of prefabricated girder/deck elements), the flange edges, or sides, are
shaped to create a continuous shear key that can be filled with a non-shrink grout or

epoxy mortar. Different types of longtitudinal deck connections are feasible:

1. Grouted female-to-female shear keys. In this connection detail shear is transferred
by friction and by the creation of an internal diagonal compression strut inside the
shear key cavity.

2. Grouted tongue-and-groove shear keys. In this connection detail shear is transferred
largely by friction and by the diagonal compression transferring load between the
groove part of the key onto the tongue part in the other component.

3. Reinforced (confined or unconfined) s_hear keys blocks. This connection requires the
provision of long pockets inside the prefabricated deck system. The pockets are
asymmetrical such that the reinforcement is placed first on one side and then slid
across the joint once the adjacent member is in place — see Figure 14.

4. Reinforced (confined or unconfined) female-to-female shear keg In this
connection, a firll depth shear key is reinforced with splicing bars extending from the
adjacent panels. The reinforcement could be a simple splice or confined as shown in
Figure 15.

5. Post-tensioned grouted female-to-female shear keys. This connection concept is as
described in (1) above with additional post-tensioning forces to avoid cracking or
opening of the joint and increase its shear capacity.

6. Post-tensioned grouted tongue-and-groove shear keys. This connection concept is as
described in (2) above with additional post-tensioning forces to avoid cracking or
opening of the joint and increase its shear capacity.

7- Welded mate grouted shear key blocks. In this concept, a steel plate or reinforcement
bar is embedded at the end of the flange and fabricated with the precast deck. A plate

24

is then welded in the field to provide a shear connection. The block-out cavity is then
grouted. This connection detail is shown in Figure 16. This concept was utilized for
the connection design of Gangarao & Taly’s pressed-formed steel box girder bridge
system (see Figure 4).

8. Reinforced grouted moment key blocks. A firll-depth block-out is reinforced with
hair-pin reinforcement protruding from both sides of the prefabricated deck
component and crossing in the region of the connection block. The region is grouted
and the joint becomes a moment resisting connection. This concept was proposed for
the Texas DOT steel tub-girder concept, see Figure 8.

9. Post-tensioned grouted female-to-fernale moment keys. This connection concept is
an extension of that in (5) with the difference that the tendon would be placed such
as to give the section moment capacity. Passive compression reinforcement would
probably be necessary to control cracking induced by post-tensioning.

10. Post-tensioned grouted towe-and—groove moment keys. This connection concept is
the same as that in (9) but applied to a tongue-and-groove geometry.

  
 

SPIRAL FOR NON—SHRINK
CONHNEMENT\ GROUT

 

 

 

 

 

 

 

 

 

\ r
(400mm LONG)

 

Figure 14. Deck Connection Detail using Reinforcement in Precast Pockets (Badie,
1999)

25

CONFINEI‘IENTI
\

ma tie BAR
@ 1000mm

PRECAST BEAM
TOP FLANGE

 
  
  
 
 
  
  
     

 

    
   
 

 

Figure 15. Deck Connection Detail using Confined Reinforcement in Full-Depth Key
(Badie, 1999)

:BOx‘SO nggfiNK GROUI

 

 

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/ /,” I PL TCXSOXIOO
I

 

 

 

 

 

PL IOxIOOxIOO. ' 2 aging;

(1100mm LONG)

 

 

Figure 16. Deck Connection Detail using Welded Steel Plate (Badie, 1999)

The advantages and disadvantages of the above listed connections will be
Considered with respect to cost, structural performance, constructability, design ease,

etc,, in order to identify three options for further study under this project (see Chapter 4).

26

3. DESIGN AND ANALYSIS CONSIDERATIONS

3.1 General

This Chapter provides the details of the standardized parameters for all of the
analyses used in this project. In general, the project followed the design and analysis
guidelines in the AASHTO LRFD Bridge Design Specifications (AASHTO, 1998).
Deviations from these specifications are noted in the respective sections. In addition to
general analysis and design specifications, this section also presents the implementation
of these guidelines in a design optimization process aimed at providing a parametric

evaluation.

3.2 Materials

The material properties for the design and analysis tasks in this study are listed in
Table 1. While the construction of the steel/concrete composite prefabricated bridges
requires diverse materials, only a few parameters of these are needed for the preliminary
design tasks and for the service-load numerical modeling. Further, some specific details
are not required such as the type of post-tensioning strands for the transverse connection

of the units since only the pressure by them is considered in the analysis.

27

Table 1. Material Properties

 

 

 

 

 

 

 

 

 

Material Properties
Concrete fc = 4,000 psi Ec = 3605 ksi y = 8.68 x lOE-S kips/cu. in.
Structural Steel Fy = 50,000 psi Es = 29,000 ksi y = 2.83 x 10E-4 kips/cu. in.
3.3 Loading

Loading for this study followed the AASHTO LRFD Bridge Design
Specifications (AASHTO, 1998). Only the considerations applying to dead load (DC),
live load (LL), and impact factor (IM) were used. When considering dead load, the self-
weight of the superstructure and a barrier were considered. These loads were calculated
by finding the volume of each component per unit length, and then multiplying that by

unit weight found in Table 1.

When considering live load, two separate entities are identified by AASHTO.
First, the vehicular live load is represented by a design lane load, which is defined to be
ten-feet wide and centered in each lane, running the length of the bridge. The magnitude
of this load is 0.064 ksf, evenly distributed across the width of the lane. This equates to
a load of 0.64 kips for each foot of each lane considered. The second part of the live
load is the design truck. The design truck has three axles, spaced at 14 feet. The front
axle carries a load of 8 kips (4 kips per tire), and the rear axles carry a load of 32 kips
(16 kips per tire). When applicable, the tire loads are applied to an area that is 20 inches
wide and 10 inches long. Otherwise, they are applied as point loads. A schematic of the
design truck is shown in Figure 17. The impact factor is applied to the design truck

only.

28

 

 

 

Front Axle: Rear Axle: Rear Axle:
l 8 kips l 32 kips l 32 kips

 

I: ,L l
' 14’ ' 14’

Figure 17. Design Truck Schematic

For this project, the HS-20 design truck was used. Although the MDOT Bridge
Design Specifications use a heavier design truck (HS-25), the HS-20 was used in this
project in order to draw appropriate parallels to AASHTO specifications. Calculations
showed that the using the HS-25 truck would increase moments by 10-12%, and

increase deflections by 17-18%.

3.4 Design Limit States

The limit states considered for the design and analysis of the prefabricated
steel/concrete bridge structures were: Strength I (to assess strength under basic load
combination to represent normal operating conditions of a bridge), Service 11 (to control
yielding of steel structures under vehicular loading) and the optional Deflection Control
(under live load only) limit state (AASHTO, 1998). The load combinations (loads and
load factors) used for these limit states were:

' Strength I: 1.25D + 1.75(L x IM)

' Service II: 1.00D + 1.30(L x IM)
I Deflection Control: 1.00(L x IM)

Where D = dead load, L = vehicular live load, and [M = impact factor = 1.33.

29

3.5 AASHTO Simplified Analysis and Design Methods

Although the prefabricated systems being studied here are not directly addressed

by the AASHTO code, the specifications for composite steel box girders were

considered applicable to the type of structure under study and thus were followed.

To demonstrate the AASHTO method, a sample bridge was analyzed. The bridge
was assumed to be a SO-fi simple span composed of five girder/deck prefabricated units

as shown in Figure 18. The load, along with corresponding bending moment and shear

demands are listed in Table 2 and Table 3, respectively.

8'-0"

 

 

9.

 

 

 

 

27"

 

 

3.75“

‘ 15.88"

W

 

 

 

‘.
'l

1d
= *1

51 .68"

 

 

Figure 18. Bridge Geometry Used in AASHTO Analysis

Distribution of moment and shear demands on the individual girder units was

estimated with the AASHTO load-distribution factors. The distribution factor for a box

section with a steel girder is given by (AASHTO, 1998):
30

 

DF 2 0.05 + (OBS—Ni] + 0425 (3-1)

B L

Table 2. Loading and Moment Demands for Beam Analysis

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AASHTO Moment at
Load Component Magnitude Midspan (kip*ft)

DC Concrete Self-Weight 0.90 kip/fl 281.3
Steel Self-Weight 0.156 kip/fl 23.3

Barrier 0.18 kip/fl 55.1
Total: 359.7

LL Vehicular Lane Load 0.64 kip/ft 200

Design Truck (Axle 1) 8 kip 34

Design Truck (Axle 2) 32 kip 360

Design Truck (Axle 3) 32 kip 216

Total: 810

IM 1 All Cases Other Than Fatigue: 1.33

 

Table 3. Loading and Shear Demands for Beam Analysis

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AASHTO Shear @ l Shear @ 2
Load Component Magnitude (kips) (lo'ps)
DC Concrete Self-Weight 0.90 kip/ft 22.5 22.5

Steel Self-Weight 0.156 kip/ft 3.9 3.9

Barrier 0.18 kip/ft 4.5 4.5
Total: 30.9 30.9

LL Vehicular Lane Load 0.64 kip/ft 16 16
Design Truck (Axle 1) 8 kip 6.6 1.4
Design Truck (Axle 2) 32 kip 17.6 14.4
Design Truck (Axle 3) 32 kip 8.6 23.4
Total: 48.8 55.2
IM I All Cases Other Than Fatigue: 1.33

 

For the bridge under consideration, Equation (3-1) becomes:

.425
DF = 0.05 + (0.85 . a + 9—2— = 0.6 (3-2)

31

The maximum bending moment (Mu) under the Strength-I load case is determined
with Equations (3-3).
[(DC)(1.25) + (VLL)(1.25) + (DT)(IM)(1.75)] x DF (3-3a)

[(359.6)(1.25) +(200)(1.25) + (610)(1.33)(1.75)]x 0.6 = 1337 kip — ft (3.31;)

Design follows from satisfying

Mu = ‘0an (34)

where Mu is the moment demand, Mn is the flexural capacity and the strength reduction

factor (pfis given to be 1.0 in AASHTO Article 6.5.4.2.

To determine the section capacity, the AASHTO bridge design specifications
outline a simplified approach for obtaining the nominal plastic moment of composite
sections in Appendix 6-A (AAHTO, 1998). A depiction of the variables to be used in

the AASHTO equations is shown in Figure 19.

Inspection of force equilibrium for the bridge model units showed that in all cases
the section neutral axis was located in the slab above the level of the bottom deck
reinforcement. This situation is defined as Case 111, IV, or V in Appendix 6-A of the
AASHTO Specifications (all three cases are identical when no deck reinforcement is
present). For such cases, with reference to Figure 19, section force equilibrium, the

plastic neutral axis depth, and the section plastic moment is given, respectively by:

32

P+P +P +P —CLbP+P
t w c rb’ t s rt (3'5)
3

 

§:tS[Prb+Pc+Pw+Pt—Prt]

 

 

 

 

PS (3'6)
VP
Mp = 21: S +[Prtdrt +Prbdrb + Pch +Pwdw + Ptdt]. (3'7)
5
1 <1
l <1 7 <1 0 1: 7 V A a A
ts A <1 0 q 0 q 7 17 A [“7 —" P
a V ‘3 s
._”_ __7 A 7 a a A V q q

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

c 1 bc
Z
D —> P,
_. ._ tw
11
tt—l : _' Pt
t ‘1
bt

Figure 19. Variables for AASHTO Nominal Plastic Moment of Composite Girders
(AASHTO, 1998)

33

For the test units under consideration, the force components at the deck
reinforcement can be neglected and thus Prb and Pr, are set equal to zero. Considering a
deck concrete compressive strength of 3.6 ksi, solution of the above equations yields a
plastic neutral axis depth (5) of 3.66 inches and a nominal plastic capacity (Mp) of

1987 kip-ft. Since the deck is nine inches deep, the plastic neutral axis is in the deck.

AASHTO Article 6.10.4.1.2-1 (AASHTO, 1998) states that the section is compact

if
2D
£33.76 % . (3-8)
tw y

Since the plastic neutral axis is in the deck, the depth of web in compression at the
plastic moment is zero. Hence, the left side of the inequality in Equation (3-8) is also
zero, and the section is compact. For compact sections, the AASHTO specifications

direct the user to Article 6.10.422. Here, a variable D’ is defined as

 

 

, d+t +t

D =13 75.5 h (3-9a)
, 27+9+0

D = 0.9 7.5 = 4.32 (3-9b)

where ,8 is given as 0.9 for Fy = 36 ksi, d is the depth of the steel, th is the haunch

thickness, and ts is the slab thickness. For the section in Figure 18 D’ is 4.32 inches.

34

Since D’ is less than the plastic neutral axis depth then Mn=Mp=1969 kip-ft (found with
Equation (3-7) above) and Mu 5 Mr making the section adequate in flexure.

The loading values used for the shear calculations are showed in Table 3. As

Table 3 shows, the highest shear value occurs at Support 2. The maximum factored

shear demand (Vu) under the Strength-I limit state is determined as shown in Equation
(3-10):
[(DC)(1.25) + (VLL)(1.2S) + (DT)(IM)(1.75)]>< DF (3-10a)

[(30.9)(1.25) + (16)(1.25)+(39.2)(1.33)(1.75)]x 0.6 = 94.7 kips - (3-101))

Equation (3-10b) gives the Vu, which is described in AASHTO Section 6.10.9.1

as shear in the web at the section under consideration due to factored loads (AASHTO,

1998). Now the shear resistance of the section must be found.

The maximum shear resistance, V”, of the section is given by (AASHTO, 1998):

Vr = ¢vVn (3-11)
where (0,, is given in AASHTO Article 6.5.4.2 as 1.0, and V” is found using Equation
(3-12) below:

3
v = 455th

n D (3-12a)

35

4.55(0.375)3 (29, 000)
V“ = 27

 

= 258 kips (3421,)

where (w is the thickness of the web, and D is the depth of the steel girder. With a

maximum shear demand ( Vu) of 94.7 kips, the section is adequate in shear.

3.6 Refined Analysis Methods

There are many other methods to analyze a bridge structure with improved
refinement. In this project, two other methods were employed. The first is the grillage
method. A grillage model is a means of representing a structure with a series of line-type
elements that have been given properties appropriate for representing the stiffness,
torsion and unit weight properties of the structure being modeled. Grillage models
reduce the number of required elements and degrees of freedom, thereby reducing the
number of equations that need to be solved to evaluate system response. Grillage models
can be two- or three-dimensional, although only two-dimensional models were used in

this project.

The second analysis method that was used is the finite element (FE) method. The
FE method is an approximate method of structural analysis that breaks the structure into
discrete pieces, or elements, connected by means of nodes. The nodes are forced to
satisfy compatibility requirements and the way in which they interact with nodes of
other elements or boundary conditions is determined by the force-deformation properties

of the elements. This method is very powerful, and it can be used to analyze very

36

 

 

'3‘ T!

complex structures to a high degree of accuracy. Care must be taken, however, to ensure
the method is used correctly. In this project, three-dimensional FE models were created

and analyzed with linear elements.

3.7 Joint Performance Criteria

As a reference point to evaluate the acceptability of the joint openings, the author
consulted the AASHTO LRFD Bridge Design Specifications (AASHTO, 1998). While
unable to locate a specific tolerance for crack opening in segmental construction, the
limit for acceptable crack width in a reinforced concrete bridge was found. This
threshold has been included in the plots of the joint opening of the models in Section
5.4.5 as a reference to the reader. However, it should be kept in mind that this is simply
a comparison that the author found to give a reasonable benchmark, not an actual

requirement by any code or governing body.

The equation used to establish the acceptability threshold was given in Article
5.7.3.4 of the AASHTO LRFD Bridge Design Specifications. The crack tolerance
varies depending on performance criteria, therefore the code lists multiple conditions.
Condition (1) applies when cracks can be tolerated due to reduced concerns of
appearance and/or corrosion. Condition (2) applies to transverse design of segmental
concrete box girders for any loads prior to full concrete strength and when there is
increased concern for appearance and/or corrosion. Because of the harsh environment to
which Michigan bridges are exposed, Condition (2) was chosen for the acceptability

threshold. The AASHTO Specifications for Condition (2) is

37

WC 2 (0.75) x (0.017 in.) = 0.0128 in. (3-13)

where we is the maximum width of a crack. Therefore, the acceptability threshold for

this project was set at 0.0128 inches.

3.8 Parametric and Optimization Analyses

To create a starting point for bridge geometries to be studied in this project, a
simple optimization program was created using Microsoft Excel. The program
incorporated the AASHTO criteria detailed in Section 3.5. This section describes the

way the spreadsheet optimization program was created and the obtained results.

3.8.1 Optimization Problem

Optimization analyses were formulated and conducted at the section level in order
to identify possible improvements to the basic design concept of a composite steel box
girder component and also to conduct parametric studies. The optimization analysis was
conducted using the nonlinear quadratic solver of Microsoft Excel. The section being
investigated is shown in Figure 20 and a View of the system using a beam-line analysis
assumption is shown in Figure 21. The problem at hand is to find the best combination

of dimensions for the girder represented in Figure 20 such that cost is minimized.

38

b

1.. V//////////////////.//

h s CONCRETE DECK
9 I s

We: 1 g I I STEEL GIRDER

be

 

 

 

 

 

 

 

 

 

 

 

 

Figure 20. Composite Steel Box Girder Cross-Sectional Geometry

q: DISTRIBUTED LOAD PER AASHTO
SPECIFICATIONS

 

Figure 21. Bridge System Profile under Beam-Line Analysis Assumption

3.8.2 Problem Formulation

Optimization algorithms are numerical methods that allow selection of structural
or material parameters for maximum efficiency through an objective function that
measures the “goodness” or “efficiency” of a structural design. The objective function is

defined by design variables, which are parameters that change during the design process.

39

 

0i

 

Design variables can be continuous or discrete depending on whether they can take
values from a continuum or are limited to a set of values. The optimization process is
then to improve the goodness of the design by automated changes in the design
variables. Optimization processes are generally performed with some limits that restrict
the choice of a design. Such limits are called constraints and usually include
performance criteria. Optimization algorithms are thus a general and versatile technique

for optimal structural design.
An optimization problem is typically defined in standard mathematical terms as:
Objective: Minimize f(x)

Subject to: gi(x) S Oi = 1 to m

hj(x)=0j=ltop

L U
where x is the design variables vector, X and X , are the lower and upper bound

vectors of the design variables, f(x) is the objective function, and gi(x) and hi(x) are the

equality and inequality constraints, respectively.

As far as the component geometry being sought, the design variables are
obviously chosen as the dimensions of the different components that govern the cross
section of the girder component. The selection of the objective function depends on the

application. For example, the objective for the current problem could be to maximize

40

CV

<11"
.00‘

v‘.

0
1*

 

 

 

stiffness, maximize strength or minimize cost. Finally, the constraints are used to
implement design limits such as maximum stresses and displacements to achieve an

optimum result.

11 Obiective Fu_nctio& The basis for determining the optimal section was that
the section was the least expensive. Consequently, the objective function was to
minimize the cross-sectional area of the steel tub-girder. The area of steel used in this
optimization was not the area per girder, but rather the area of all the girders required to
form a three lane bridge (the bridge width can easily be modified, as noted in subsequent
sections). In this way, the individual section is not being optimized, but instead the

bridge as a whole is being considered.

2) Independent Variables. The independent variables are the variables that are
changed by the solver in order to reach the optimal result. The bridge optimization
problem used six independent variables to optimize the section. These variables and
their corresponding labels in Figure 20 were:

I Deck Width, b
I Steel Plate Thickness, ts

I Compression Flange Width, w

Cf
I Tensron Flange Width, w b f
I Web Angle of Inclination, 6
I Steel Section Depth, hs

41

3LPargmeters. Parameters constitute those values in the design that do not
change during the optimization process. The parameters included in the current analyses

and their values were:

I Deck Height, h d: 9 in.

I Concrete Compressive Strength, f6: 6 ksi

I Concrete Modulus of Elasticity, EC = 4,415 ksi
I Steel Yield Strength, j; = 36 ksi

I Steel Modulus of Elasticity, ES =29,000 ksi

4) Constraints. When changing the independent variables, limits must be set in
order to ensure the optimal solution is a feasible design. The constraints to the

independent variable were as shown below:

48 in. _<_ b S 96 in.
0.179 in. S ts _<_ 0.375 in. (7 ga. — 3/8” plate)

_ . < < .
41n._wcf_61n.

I ' < < '
101n._ wa_ 24 1n.

6OOSqS76O

12 in. ShSS 54in.

Other constraints related to design values were also incorporated, namely:

I Moment Capacity > Nominal Moment
I Steel Section Width < Slab Width
I Enforce Compactness (AASHTO Eq. 6.10.4.1.2-1)

42

3.8.3 Implementation

The final step in the optimization is to create a set of dependent variables that will
change based on the changes made to the independent variables. As presented in
Section 3.5, the nominal moment was calculated per the AASHTO LRFD Bridge Design
Specifications (AASHTO, 1998). The moment demand per bridge girder component was
based on Service 11 limit state requirements. The loads considered in the analysis were
dead load, vehicular live load, and a dynamic load allowance. Distribution factors were

calculated based on the AASHTO-LRFD recommendations.

Lastly, the desired span, L, and number of lanes, N L’ was specified. These were

constant for a single run of the optimizer, but are user defined in order to find optimal

sections for varying bridge lengths and widths.

3.8.4 Results

Because of the high number of variables, there are many local minima in the
problem space and the gradient-based search algorithm in Excel easily gets “stuck” in
local minima. Therefore, the solution found is highly dependent on the starting values of
the independent variables. A table of results returned by the optimizer with the reduced
number of variables is shown in Table 4. As mentioned above, Excel has trouble with
finding local minima. Therefore, in order to achieve a solution, some of the values were

given a specific starting point in order to arrive at reasonable values.

3.4.5 Discussion

The following trends were observed in the data:

43

I The optimization algorithm seems to always choose the largest available

deck width.

I Steeper web angles improve moment capacity.

I The section geometry generally causes the plastic neutral axis to be located
in the slab, eliminating compression forces in the steel.

I Acceptable geometries were found for spans ranging between 20’-100’,
while spans greater than 100’ were not investigated.

I Spans ranging from 20’ to 40’ had identical results, implying that the lower
bounds on some of the independent variables were set too high.

Table 4. Sample Results from Cross-Section Optimization Analyses

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. Span
Parameter Symbol Units 40' . 50, 60' 70'
Deck width (spacing) b in. 96 96 96 96
Plate thickness ts in. 0.234 0.268 0.289 0.309
Compression Flange Width wcf in. 4.0 4.0 4.0 4.0
Bottom Flange Width wa in. 10.0 12.0 13.4 14.7
Angle (web-to-horizontal) q degrees 76.0 76.0 76.0 76.0
Steel depth hs in; 19.8 27.4 31.6 35.6
Total Steel Area: As sriLn. 68.8 102.5 125.1 148.2
Parameter Symbol Units Span
80' 90' 100'
Deck width (spacing) b in. 96 96 96
Plate thickness ts in. 0.327 0.344 0.361
Compression Flange Width wcf in. 4.0 4.0 4.0
Bottom Flange Width wa in. 15.9 17.1 18.5
Angle (web-to-horizontal) q degrees 76.0 76.0 76.0
Steel depth hs in. 39.3 42.8 46.1
Total Steel Area: As sq in. 171.8 195.4 219.4

 

It should also be noted that steel is not available in arbitrary thicknesses or widths.

Thus, the results found here would have to be increased to the next available standard

size, which could impact the cost of the system. As increasing the steel thickness always

 

results in an increase in moment capacity, the section will not become inadequate when

the steel thickness is increased.

45

Vr—“fi

__.——

4. CONCEPT EVALUATION

4.1 Flexural Performance of Con-Struct Bridge System

Due to MSU’s involvement with this MDOT project, the University was
approached by Nelson Engineering Services to evaluate the flexural capacity of two
scale units of their Con-Struct system, which is the concept that motivated the present
investigation. This testing project, while separate from the MDOT research, has given
the author an excellent opportunity to experimentally evaluate the prefabricated steel
box systems under consideration. With the permission of Nelson Engineering Services
(hereafter referred to as NBS), an overview of the testing conducted and the evaluation

of the results and concept follow.

Two three-point bending tests were conducted on small-scale prototypes of the
Con-Struct bridge girder system with cast-in-place and precast decks. The test units
were designed by NES and also built under their direction. The test beams were small-
scale replicas of the full-scale sections of the Con-Struct system used by NES in field
applications. A typical cross section of the low-profile steel-concrete composite box
girder section is shown in Figure 22. The steel plate used for the test unit was a
lightweight 7-gage steel sheeting unit. The test units were manufactured so that they
had an effective span of 12 ft with the beam ends encased on a concrete block for
support purposes and laminated elastomeric pads were used between the test unit and
support blocks. The overall geometry of the cast-in-place and precast deck test units are

shown in Figure 23 and Figure 24, respectively. These drawings and the specifications

46

outlined in them were provided by NES for manufacturing purposes. Overall views of

the test setup are shown in Figure 25.

 

, CONCRETE DECK

 

 

 

 

 

600"
‘\‘ \\
\ \\ ‘x
-w
wan
\\
\
\
7—41
\
I
l
\
\
\

 

 

 

 

 

I I SHEAR 511117

3.12" 6.15" \-._

\

\ STEEL GIRDER -
0.114 THICK

 

Figure 22. Typical Cross-Section of Con-Struct Test Units (Nelson, 2006)

The flexural tests showed that the overall behavior of the low profile composite
box girder system is reliable and that it can effectively exceed the nominal flexural
capacity determined according to current AASHTO specifications. As shown in Figure
26, the ultimate moment capacity of the section was found to be 106 kip-ft, while the
AASHTO capacity was 80 kip-fl. The yield point shown in Figure 26 was found using
strain gauges on the steel girder (see inset). Overall, the performance of both the cast-
in-place and precast composite girders was essentially equal, hence the precast results
are not presented here. In both cases, their ultimate capacity was limited by detailing of

the deck system to effectively carry the longitudinal shear demands.

For the cast—in-place unit the force transfer at the shear connectors introduced
longitudinal shear demands in the concrete deck that exceeded the shear strength of the

47

concrete element. In the case of the precast unit, the lack of longitudinal shear keys to
transfer shear forces across the joints of the precast panels composite the deck led to the
deterioration of the beam load carrying mechanism. In both cases, the failure modes are
clearly undesired, but they are not believed to compromise the overall efficiency of the
concept as these problems can be easily addressed. Improved performance of the cast-in-
place deck can be achieved by better assessment of the forces imposed by the shear
connectors and by providing appropriate deck reinforcement to arrest the development
of longitudinal shear cracks. Improvements in the precast system can be easily achieved
by providing well detailed transverse shear keys to the precast panels. Integration of
both of these detailing aspects will undoubtedly improve the performance of the Con-
Struct system at ultimate conditions. Clearly, this also applies to the generic

prefabricated steel box girder systems being investigated in this project.

124 3/4"

“131265 OF sTEEL sew,
TYP

 

 

._._.. _. p.

 

- ___— _ __ __ ._ __ _.. _ __ __ __ _. __ — __ __ ._.4

 

 

I 14:11

2261 1/2'

 

131$pr 5,5éIL0aIIfi. 91.-3: 959K.

-_____ 12'-0' __ _
Ia ,JQEPIBEQE HIRE MESH

 

-_.>.

, REINFORCING I
1

\D ,.
1-- _fl, 3 ,_....._..-. ..
I“ L 11 11 r r r 11 11 rj]

 

' ELEVATION OF BEAM mIrH_c_.If,pEcK_

 

Figure 23. Test Unit with Cast-in-Place Concrete Deck (Nelson, 2006)
48

1224 3/4“
EDGE OF STEEL CL SHEAR stuns,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

fBEAM, TYP / TYP
Ejé}: Te.:.-.—~_—: 79:15.3:1 —_» :._— T .13: ”3 _,_II_ Q
a ,1 N .—
l' A . v‘N A rm r“ ~ A :1- U"
_1_ ’__ :J_ _—-_-___ _:_;_ _«L _—__ +4 l (‘0'
PLAN OF BEAM WITH PRECAST PANEL DECK
1111’" 12%): _,
TOP OF DECK JOINT BETWEEN‘I CAST-IN-PLACE
r 5

 

 

// PRECAST PANEL 6 END BLOCK, TYP
1
[ 1‘11 ‘ 01:1 '1' r“ '1' 7‘1““ “‘11“ #1“ "—“11‘1/

ELEVATION 0F BEAM WITH PRECAST PANEL DECK

Figure 24. Test Unit with Precast Concrete Deck System (Nelson, 2006)

This space intentionally left blank

49

 

a) Overview

 

b) Underside View

Figure 25. General Test Setup Views — C.I.P. Test Unit

50

 

110

90
M, = so kip-ft (AASHTO)

80 —_———_———_-——————— -———————_— _—-_

70 My = 65 kip-ft

 

 

 

so 1

so \TJ

40
p
30 L,____ "ASI ___

20 “A “*1: 1 * ”A

 

Max. Applied Moment (kip-ft)

 

10

 

 

 

o IITIIIIIIIllIllIIIIIIIIIIIIWIIIIIIIIITFIIIIIIIITIFI

0 50 100 1 50 200 250 300 350 400 450 500

Curvature (rad/105m.)

Figure 26. Moment vs. Curvature Response of C.I.P. Test Unit at Mid-Span

In addition to the use of a shallow cold-bent steel profile for the composite beam,
the Con-Struct concept introduces prestressing to the steel beam during construction by
cambering it. This is done to increase the yield moment capacity and offset dead load
deformations. The efficiency gained from prestressing the steel plate during the
construction operation is a unique feature of the Con-Struct system and one that should
be considered for the general goals of this research project. It should be recognized,
however, that the prestressing effect is really beneficial only up to the onset of yield in
the critical section response for the system. Thus, benefits are to be gained while
satisfying serviceability stress limits. Gains in ultimate strength will be minor since at
full plastification of the steel section ultimate section capacity is more heavily controlled

by the effective lever arrn between tensile and compression forces and the location of the

51

plastic neutral axis. In addition, consideration should be given to the “longevity” of the
prestressing benefits since creep effects in the concrete slab and stress relaxation of the

prestressed steel plate will most likely reduce the initial stress conditions.

The experimental study also permitted evaluating the applicability of code
guidelines to assess the capacity of composite sections and showed that the shallow
composite girder system can be well predicted by conventional theory of steel-concrete

composite structures.

4.2 Concept Evaluation and Selection

Based on the literature review (see Chapter 2), one goal of this task was to
preliminarily evaluate prefabricated composite steel box systems to explore their
advantages, disadvantages, possible improvements, and the development of new similar

concepts.

Another goal of this task was to perform a preliminary study that would identify
three to five concepts with high potential that would become the focus of this research
project. All concepts are to be evaluated under a common set of structural, construction,

and durability requirements. A ranking method was used to assess their potential.

With reference to Figure l and based on what has been learned thus far from the
literature review presented in Chapter 2, a list of design alternatives based on
permutations of different features can be generated. The variable parameters were the
type of steel plate, the type of concrete deck, and the type of longtiduinal deck joint. The

different options for each of these variables are listed next.

52

A) Steel Plate. From the literature review, the author believes that the inverted
steel box solution will not be as effective as its developers envision. Thus, only the use
of a “right-side-up” steel box will be considered. Four types of steel tub-plates will be
considered based on their method of construction and implementation:

1) Pressed-formed or cold-bent — unstressed
2) Shop-welded — unstressed

3) Pressed-formed or cold-bent — prestressed

4) Shop-welded — prestressed

B) Concrete Deck. The literature review has shown advantages and
disadvantages for different types of concrete decks and different solutions have been
adopted for the prefabricated steel box systems proposed thus far. As such, the following
prefabricated deck options, based on their construction method, will be considered as

options:

1) Cast-in-place at shop/yard

2) Modular precast made continuous with passive wet longitudinal

joints at shop/yard

3) Modular precast made continuous with passive wet longitudinal
joints at shop/yard and prestressed at shop/yard before making

composite with steel girder.

4) Hybrid — precast stay-in-place form with exposed reinforcement for

a cast-in-place topping and closure pour at job site.

C 1 Longitudinal DeckfiCognectio‘lL As shown by the literature review, this detail

is the one that presents the most options. Based on the design alternatives presented in

53

Section 2.7, the following are considered viable options for the system under

consideration:

1) Grouted female-to-female shear keys

2) Grouted tongue-and-groove shear keys

3) Reinforced (confined or unconfined) shear keys blocks

4) Reinforced (confined or unconfined) female-to-female shear keys
5) Post-tensioned grouted female-to-female shear keys

6) Post-tensioned grouted tongue-and-groove shear keys

7) Welded plate grouted shear key blocks
8) Reinforced grouted moment key blocks
9) Post-tensioned grouted female-to—female moment keys

10) Post-tensioned grouted tongue-and-groove moment keys

In order to evaluate the potential design concepts that could develop from the
various permutations of the different design options, a common set of performance
criteria was used. The criteria is aimed at qualitatively ranking the performance of the
individual design options listed above, i.e., steel plate, deck, and transverse deck
connections, based on the judgment of the author. In addition, each of the criteria was
assigned a weighting factor of importance on a scale of 1 to 3 with 1 being low, 2 being

medium and 3 being high. The criteria and their weighting factors are given in Table 5.

Each of the design options was given a score for each of the criteria on a scale of
1 to 5, where 1 represented the lowest mark and 5 the highest. The tabulated results for
each of the system components are presented in Table 6. The last column in this table
shows the total “score” of the bridge component after factoring the score in each category
by the importance factors in Table 5. The highest scores for each of the design

components are shown in bold font.

54

Table 5. Design Parameter Selection Criteria and Importance Factor

 

 

 

 

 

 

 

 

 

 

Criteria Importance

ID Description Factor
A Cost Efficiency 3

B Structural Efficiency 2

C Design Versatility l

D Design/Analysis Base 1

E Construction Ease 3

F Fatigue Perlbrmance 3

Dmability &
G . . 3
Corrosron Resrstance
H Replacement/Removal 2
Ease

 

 

 

 

 

* Importance Factor: 1 = Low; 2 = Medium; 3 = High

This space intentionally left blank

55

Table 6. Scoring and Ranking of Design Options

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Design Option | Criteria* J Score
Plate A B c r) E F G H
1 5 3 2 5 5 5 58
2 3 4 4 4 2 2 37
3 5 3.5 2.5 5 4.5 5 58
4 3 4.5 4.5 4 2 2 38.5
Deck A B C D E F G H
1 5 4 4 5 4 3 3 59
2 4 4 3 4 5 3.5 3 58.5
3 3 5 4 3 4 4 2 54
4 3 4 3 2 3 3 3 46
Deck Connection A B C D E F G H
1 5 2 2 5 5 5 5 5 81
2 5 2 2 5 4.5 5 5 5 79.5
3 4 3 3 4 4 4 3 4 66
4 4 3 3 4 4 4 3 4 66
5 3 4 4 3 3 5 4 3 66
6 3 4 4 3 2.5 5 4 3 64.5
7 3.5 3 3.5 3 4 2 3 4 58
8 3 3 3.5 4 4.5 4 3 4 65
9 2.5 4.5 4.5 2 3 5 4 3 65
10 2.5 4.5 4.5 2 2.5 5 4 3 63.5

 

*Evaluation: 1 = Low to 5 = High

56

 

5. ANALYTICAL EVALUATION

5.1 General

The objective of the analytical evaluation is to develop a suite of hierarchical
finite element models to investigate issues related to structural performance, with
particular attention to connection detailing and design. The different levels of model
refinement supported each other to investigate system performance. The conducted

analyses were:

A) Stress Analysis of Bridge Component and System. 3D finite element

analyses of component and system to evaluate detailed performance of the
prefabricated element.

B) Global Parametric Analysis. 3D finite element analyses of bridge systems to
perform system parametric studies.

C) Stress Analysis and Characterization of Connection Details. 3D finite

element analyses of connection details.

5.2. Stress Analysis of Bridge Components and System

The original goal of the research was to use 3D skeletal-type (frame element)
models to perform system parametric studies to evaluate the need for any intermediate
diaphragms and the load transfer demand and performance of deck connections. The use
of full 3D finite element models was not considered appropriate for the parametric
studies due to their computational expense and effort to develop. Thus, grillage models
were initially envisioned for these studies. Despite this, both model types were created
to evaluate their performance and decide which method to use. This section presents the

development of both model types and a comparison of their performance.

57

For an initial check of compatibility between the grillage and 3-D FE models,
simple plate models were created and moment responses were compared. To begin this
comparison, two sets of models were created. One set of models were square plates,
while the other set were rectangular plates with sides at a 2:1 ratio. Two loading
conditions were considered. The first was a distributed load over the entire plate, while
the second was a point load at the center of the plate. The bending moment distribution
of each model was then compared in three different ways: at mid-span under both
distributed and concentrated loads, and its transverse distribution under the concentrated
load. The results of this comparison indicated a sufficient agreement between the two
methods to move to a more sophisticated comparison. A graphical representation of the
results can be seen in Appendix I. It should be noted that the loads and dimensions were
arbitrarily chosen and that the results were normalized for clearer presentation. After this
simple verification, the two modeling approaches were then applied to actual bridge

models under consideration and compared.

5.2.1 Model Bridge Geometry

The bridge chosen for modeling was a two-lane bridge with a 50-ft span. It
consisted of five girder/deck units, as shown in Figure 27. The geometry of the
girder/deck units was developed by making use of the Excel optimization spreadsheet
detailed in Section 3.8. However, the purpose of this exercise was not to find an
Optimum design, but rather to compare the two analysis models (i.e., grillage vs. 3D FE).

The geometry of the girder/deck units used in the comparison is shown in Figure 18.

58

 

Figure 27. Bridge being modeled for analysis approach comparison

5.2.2 Model Bridge Loading

Loading for the bridge models was chosen according to the AASHTO LRFD
Bridge Design Specifications [AASHTO, 1998]. Dead load and vehicular live load were
considered. Dead load consisted of self-weight and barrier weight. The cross section of
the barrier was that of a New Jersey Concrete Barrier as specified by the Federal
Highway Administration (FHWA) [FHWA, 2006]. The vehicular live load consisted of
the design lane load and the design truck load with an axle spacing of 14—fi (see Figure
17). Three different AASHTO limit states were evaluated, namely, live-load deflection,
Service-H, and Strength-1. A summary of the limit states and associated loads and load

factors is given in Table 7.

59

Table 7. Summary of limit states considered to evaluate bridge models

 

Loads and Load Factors

 

 

 

 

 

 

 

 

 

 

 

Load Case Dead Load Load Factor Live Load Load Factor

Deflection No n/a Yes 1 .00

Service - H Yes 1.00 Yes 1.30

Strength - I Yes 1.25 Yes 1.75
5.2.3 Grillage Model

A grillage model is a means of representing a structure with a series of beam
elements that have been given properties appropriate for representing the stiffness,
torsion and unit weight properties of the structure being modeled. Grillage models
reduce the number of required elements and degrees of freedom, thereby reducing the
number of equations that need to be solved to evaluate system response. Grillage models
can be 2D or 3D. For this project a two-dimensional grillage model was created and

analyzed, as detailed in this section.

5.2.3.1 Derivation of Grillage Member Properties

The grillage model followed the recommendations presented in Hambly (1991)
and Barker and Puckett (1997). To completely capture the behavior of the bridge,
several sections were chosen for grillage members to represent the bridge as shown in

Figure 28.

60

    

Section A Sections 8, C, D
Long. Girder/Deck El. Long. & Tran. Deck El.

Grillage Model

   

Figure 28. Schematic of grillage element cross-sections and grillage model

The longitudinal section representing the girder/deck units (see Figure 28) was
termed section A. The section moment of inertia, I, was calculated for a section in which
the concrete deck had been transformed to an equivalent width of steel using the
modular ratio of the two materials. The torsion constant, J, was also calculated for a
transformed section, but instead of changing the width, the height was modified. Then,
the torsion constant for a thin walled hollow section was determined with equation (5-1)
(Hambly, 1991)

_ 4A2

‘ 1% (5-1)
1

 

J1

where A is the area enclosed by the center line of the walls, ds is the length of each

individual wall and t is the wall thickness. This value is known as the pure torsion

constant, or J,. However, due to local deformations of the open box section, the pure

torsion constant is not valid. Thus, an equivalent torsion constant that accounts for

distortion, Jd, must also be found (Hambly, 1991). The process to obtain Jd follows.

61

The flexural rigidity of the individual sides of the box (see Figure 29) is obtained

by applying equation (5-2) [Hambly, 1991]

_ Eati
a 12(1—v,2)

 

D (5-2)

where D is the flexural rigidity, Ea is the elastic modulus, ta is the wall thickness and Va

is Poisson’s ratio; and the subscript a refers to side a (see Figure 29).

a

III/Jilllilll

 

 

b

Figure 29. Nomenclature of box sides

After calculating the flexural rigidity of each side with equation (5-2) above, the
out-of-plane shear in the bottom flange per unit torsional load, v, is given by equation

(5-3) [Hambly, 1991]

l l 3
B—c— [(2a + b)abc] + D—a[ba ]

 

v: ~
3 ' 3 (5-3)
(a+b) —a—+-Z(i(a2 +ab+b2)+Il;—

a c b

62

where Da, D], and Dc and a, b and c are the flexural rigidities and the lengths of the

walls in Figure 29, respectively.

Once v is calculated, the vertical deflection of one web per unit torsional load, 61,

is given by equation (5-4) below:

2
24(a+b) Dc a+b Da a+b '

 

 

Next, a parameter, ,6, used in the analysis of beams-on-elastic-foundations (BEF),

the theory from which the previous equations were derived, is calculated as shown in

0.25
B = 1
{Elcsl I (5-5)

where [C is the moment of inertia of the box girder cross-section.

equation (5-5) [Hambly, 1991]

 

Next a dimensionless distortion-induced deflection term, w, is obtained from a
chart presented in Hambly (1991) and reproduced in Figure 30. For this example w was

found to be equal to 1.0.

The final formula to find Jd is given in Equation (5-6) below:

_ 42 IC (1303
12 1.6w

 

d (5-6)

63

The values of J, and Jd are then combined to give the value of J used for the

grillage member, Jdt, as shown in equation (5-7) [Hambly, 1991]. For firrther

information and references on this method, the reader is referred Chapter 6.5 of Hambly

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(1991).
cd.
If 10: I 1 'lrfirr r r r 1117 1 r 1 in.+
+5) : +P ___:
if) 5.7. gt a ’ .
: _ A IlMA ..
(D -1
g " W /
a 1 /
_ E W//7 a
C 0.5 d
9 L/ m ,
U")
C >- ..
0)
g 0.1 1 11 1111 L 11 1111 l llrlll

0.01 0.05 0.1 0-5 1 .3 10
3 ’ 4
(a) w: .235le W [11:13. M
P

Figure 30. Chart for distortion deflection parameter w for simply supported beams
and box without cross-bracing or diaphragms (Hambly, 1991)

The final properties of the longitudinal girder/deck members are shown in Figure

31.

64

 

 

 

 

 

 

1 1+1
'_"=_" ‘1 64)
La la Jt
GrilfigProperties
a 50 _, A=85.91n2
I 7?
//////////// 5:29.000...
1 = 10,598 in4
.1 = 1,3491n4

Figure 31. Section A geometry and associated grillage properties

Longitudinal deck elements of different widths were also included in the model to
improve its accuracy. Sections B and C and their properties are given in Figure 32. The

moment of inertia for these elements was found with equation (5-8) [Barker, 1997]:

3
I=bh

E" (5-8)

The torsional constant was taken as twice the moment of inertia [Barker, 1997], or

J = -— (5-9)

65

44.3" A = 399 in2 113" A = 173 in2

. V m/ 1 E=3,600 ksi ‘ ' j E = 3,600 ksi

 

 

Figure 32. Section B and C geometry and associated grillage properties

Transverse grillage members represented the concrete deck. All transverse
elements had the same cross section, which was labeled section D. Their properties were
found in the same manner as for sections B and C, resulting in the values shown in
Figure 33. Because the weight of the concrete deck was already included in the weight
of the longitudinal members, the transverse deck elements were not assigned any self-

weight. A summary of the properties for the grillage members is given in Table 8.

. 2
50" A = 540 In
fu- -———-————--- ---—— -~~ —-—-—---—.
*_7"/ *T'Pr E = 3.600 ksi
/ , ' .- /,»”/',//./ 1’,/,,/ ,;

/ ' l
/ ,’ /

A L A J A ’ A ' J

 

Figure 33. Section D geometry and associated grillage properties

Table 8. Summary of grillage member properties

 

 

 

 

 

 

 

Section Area Ehstic Modulus Moment of Inertia Torsion Constant
Name Description (sq.in) (ksr) (in/‘4) ('rL"4)

A long Box Section 85.9 29,000 10,598 1,349

B long, Deck Section 399 3,600 2,693 5,385

C long. Deck Edge Section 173 3,600 1,346 2,693

D Transverse Deck Section 540 3,600 3,645 7,290

 

 

 

 

 

 

66

5.2.3.2 Application of Loads

Vehicular lane load was applied by defining a tributary width for each
longitudinal member and applying a distributed load of appropriate magnitude along the
length of the member. Applying the concentrated truck loads required the determination
of equivalent loads and moments to be applied to the existing members due to the tire
locations not corresponding with the location of the grillage members. This was
accomplished by creating a separate model of two beams intersecting at the location of
the tire load and fixed at their ends, which coincided with points on the grillage model
mesh. The truck load was applied at the intersection of the beams and the reaction forces
(fixed-end forces) at the endpoints were obtained. These forces were then applied at
their corresponding location on the master model. This approach is schematically shown
in Figure 34. The grillage model was created and computed with the general finite
element program SAP2000 (C81, 2000). A figure of the completed grillage model, as
well as its transverse moment response under the described loading, is shown in Figure
35. A discussion of the results and their comparison with those from a finite element

continuum model is provided is Section 5.2.5.

 

 

 

 

 

67

/\

Figure 34. Application of wheel loads to grillage model

 

Figure 35. Completed grillage model and system transverse moment response

68

5.2.4 Three-Dimensional Finite Element Model

The 3-D finite element model was created completely of 4-noded shell elements
(S4R, [Simulia, 2007]) — both deck and girder. The deck elements were positioned at
the neutral axis of the actual deck to match the grillage model. The modeled geometry

of the typical girder/deck unit is shown in Figure 36.

Actual Geometry: Discretized Structure:

/////////

 

 

 

 

Figure 36. Girder modification in 3-D FEA model

In this analysis the deck is modeled as one continuous slab. This assumes full
moment transfer at the joints, which may not be representative of actual behavior,
depending on the type of joints that are used. However, because the same is true of the
grillage model, this was not a problem for comparing the two modeling approaches. Yet,
it is recognized that future models will need to address this issue (See Section 5.4). Also,
the model assumes full shear interaction, meaning there is no relative slip between the
deck and the girders which again is compatible with the grillage analysis. The completed
3-D FEA model and von Mises stress contours on the underside of the bridge can be

seen in Figure 37.

69

 

Figure 37. Completed 3—D FEA model and von Mises stress contours

5.2.5 Comparison of Models

The grillage and continuum models were first compared with only the design lane
load applied. The response quantities chosen for comparison were the transverse
moment forces along a line coincident with what would potentially be a longitudinal
joint between girder units, as shown in Figure 38. The transverse moment demand for
both strength and service conditions along line A-A (see Figure 38) is shown in Figure
39. It can be seen that the finite element response is smoother than the grillage output,
which is to be expected due to the finer resolution of the nodes in comparison with
grillage intersections. However, the models are considered to compare favorably. All

other joint lines were also checked, and the results compared similarly.

70

 

Figure 38. Location of forces chosen for comparison

 

1 2 ,. _ ,7
* STRENGTH — SAP
0 9 m_ 7 , if 7,, , - SERVICE— SAP

* «- STRENGTH—ABAQUS

I
0.3 WERWCE - ABAQUS
0.7 , // - \\ _ .

 

  

 

 

 

Moment in joint (kip-in./in.)

 

 

 

 

0 1 00 200 300 400 500 600
Distance Along Span (in.)

Figure 39. Comparison of analysis tools on full scale bridge model (lane load only)

71

After the initial verification had been established, both models were updated to
incorporate the AASHTO design truck loading. The transverse moment distribution
along joint line A-A (see Figure 38) for the full live loading from both models is shown
in Figure 40. These results are again in close agreement, with the finite element model
showing a greater resolution. Upon evaluating these results, the author determined that
both the grillage model and the 3-D FEA model gave coinciding results, and that either
could provide accurate representation of the forces in the joints, as well as in the bridge
system as a whole. It follows that either model could be used for parametric studies of
the system. While the original research plan was to use the grillage model for parametric
studies due to its low computational demand, running the 3-D F EA model only took 1-2
minutes longer than running the grillage model. Yet, as noted in the comparison of
results, the FEA model provides better resolution. Additionally, the FEA models were
easier to create due to the use of the program’s (Simulia, 2007) graphical user interface.
For these reasons, the author decided to supersede the grillage model and use 3-D
continuum FEA models with shell elements not only for the detailed analyses, but for

parametric studies as well.

This space intentionally left blank

72

 

 

TVS—T30 FE Analysis
I + Grillage Analysis

 

 

\\

 

1.2 3

0.8 1

 

0.4 ~

 

Transverse Moment at Joint (klp-lnlln)

 

 

0 100 200 300 400 500 600
Distance along Span (in)

Figure 40. Comparison of analysis tools (full AASHTO loading)

5.2.6 Verification of Models Using Experimental Data

As detailed in Section 4.1, previous research performed by the author provided
experimental data that directly correlated to the system being studied (Burguer‘io and
Pavlich, 2006). Hence, this data could be used to verify that the models of the box-
girder system were producing results that match what happens in experimental
situations. General information on the Con-Struct test units and the conducted
experiments was given in Section 4.1 and complete information can be found in

(Burguefio and Pavlich, 2006).

73

In the aforementioned project, a prototype of the Con—Struct System — the concept
that motivated the present study -. was tested at Michigan State University’s Civil
Infrastructure Laboratory. The cross-section dimensions of the Con-Struct test girder are

shown in Figure 22.

The test setup for the experimental testing program is shown in Figure 41. The
test was a simple three point bending test on a girder with a span of 12 ft. Continuous
displacement and applied load measurements were recorded during the test. The
displacements were measured at the girder mid-span by linear potentiometers. The

applied load was measured with a load cell in the actuator.

The load displacement response from the girder with a cast-in-place deck is
shown in Figure 42. From the graph it can be seen that the maximum applied load
achieved during the test was approximately 35 kips. The maximum displacement of the
12 ft girder was approximately 2 inches. The response can be separated into two
portions, an assumed linear portion, and a non-linear portion. The linear of the portion
is assumed, as it is not perfectly linear. This assumed linear portion of the response is
from a load of 0 kips up to a load of 12.5 kips. The 12.5 kip point was chosen as the end
of the linear portion because after this point the slope of the load displacement response
in each of the successive load increments has a different, smaller slope. Between loads
of 0 and 12.5 kips the slope remains approximately constant. It is this pseudo-linear

portion of the response that was to be modeled using a full 3D finite element model.

74

 

Actuator Force (kips)

Figure 42. Experimental Load Displacement Response of Cast-in-Place Con-Struct

Figure 41.

Experimental Test Setup

8

 

r»u = 35.3 kips

to
UI
11I1111I111|I1111

I»
O

N
0|

Py = 21.8 klps

 

-| N
0| 0

d
O

IIIIIIIIIIIIIIIIIIIII

 

 

 

I 71* I I I I I I I I I I
1.000 1.500
Center Displacement (in.)

 

System

75

The 3D FE model of the Con-Struct system was generated by creating two parts:
one representing the deck, and one representing the steel girder. Due to its thin
dimensions, the tub was modeled with shell elements. The deck was modeled with solid
elements. Details are shown in Table 9. The dimensions of the modeled girder matched
exactly with the dimensions of the actual girder (see Figure 22 and Figure 23). The
modulus of elasticity used for the concrete was 4576 ksi, which was the tested value of
the concrete used in the experiment based on uniaxial break tests of specimens taken at

the time of casting. Properties for the concrete and steel are given in Table 10.

The 3D model also utilized a no-slip constraint at the concrete-steel interface i.e.,
full shear interaction. This assumption is considered adequate to assess service
performance of composite steel box bridge systems. Nonetheless, since failure in the
tested cast-in—place Con-Struct beam units (see Section 4.1) was controlled by the shear
interaction, incorporation of partial shear interaction between the surfaces of the
concrete deck and the top steel flanges through ABAQUS’S contact and surface
interaction modeling options might be considered for future modeling efforts. As this
type of failure was not directly applicable to the system being studied, it was ignored in
this project. The 3D model can be seen in Figure 43. A general view of the

displacement contours on the developed 3D finite element model is shown in Figure 44.

Table 9. Elements Used in Con-Struct 3D FE Model

 

 

 

Shell 'Ih'cknem Horn-glass Reduced Benin
Part Material (in) Eermnt Type Control Integration Size (in
Deck C(xicrete n/a CBD8R Active Active 4.5
Ttb Steel 0. 375 S4R Active Active 6

 

 

 

 

 

 

 

 

 

76

Table 10. Material Properties used in 3D FE model

 

 

 

 

Elastic Poisson's Unit Weight

Mater'al Modulus (ksr) Ratio (kips/in"3)
Concrete 4,576 0.2 8.68 E—5
Steel 29,000 0.3 2.83 E-4

 

 

 

 

 

 

Figure 43. Assembled 3D Model

 

Figure 44. Finite Element Model of Con-Struct System in Flexure.
(Contours Represent Vertical Displacement)

Comparative results of the load displacement response are shown in Figure 45.

This plot shows the assumed linear range of the experimental data only, to appropriately

compare with the linear elastic FE model. The nonlinear behavior of the system was not
of interest in this project and thus no effort was spent trying to calibrate an FE model

with the nonlinear experimental data.

 

 

 

 

 

Load (kips)

 

 

 

 

 

'— Experimental ‘
,— Finite Element

 

 

 

I

0 0.05 0.1 0.15 0.2 0.25 0.3
Vertical Displacement at Midspan (in.)

Figure 45. Load Displacement Results of Experimental Model vs. FE Model

The experimental data in Figure 45 has been shifted to correct for nonlinearities at
the beginning of the loading, such as settlement of the elastomer pads at supports as well
as settling of the loading element. The shift was calibrated so that the two sets of data
would be at the same value of displacement when the load was one kip. From the figure
it is possible to see that the results from the FE model were stiffer than the experiment.

The maximum displacement value of the FE model was 0.216 inches, while the

78

experimental model had a maximum displacement of 0.256 inches. This could be
attributed to further settlement and/or compression of the end supports, and slip at the
girder/deck interface. Additionally, it is well known that the finite element method
typically gives results that are stiffer than reality. However, the present study cannot

fully clarify which, if any of the listed effects are causing the slight discrepancy.

5.3 Global Parametric Analysis
To evaluate the behavior of feasible bridge systems built with the prefabricated
girder/deck units under consideration, a parametric study was performed. In the study,
the parameters under evaluation were: (1) span length, (2) girder spacing, and (3)
existence/location of intermediate diaphragms. The proposed case matrix for the
parametric studies is given in Table 11. All the bridges studied carried two design lanes
of traffic, with one design truck in each (See Section 3.3). The material properties and

limit states can be found in Sections 3.2 and 3.4, respectively.

The study was performed in order to investigate three separate responses: (1)
transverse load distribution, (2) transverse moment demands along longitudinal joints,
and (3) longitudinal moment demands along longitudinal joints. These responses of

interest are schematically shown in Figure 46.

This space intentionally left blank

79

Table 11. Case Matrix for Global Parametric Analyses

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Case Span Girder Diaphragm

# Length (ft! _Spacing (ft)

1 50 4 None

2 50 6 None

3 50 8 None

4 75 6 None

5 75 6 1/2 pt

6 75 8 1/2 pt

7 100 6 None

8 100 6 1/3 pts

9 100 8 None

10 100 8 1/3 pts

11 100 10 None

12 100 10 1/2, l/4pts

Diaphragm

 

Moment Demand
at Joints

Figure 46. Response measures of interest in parametric studies

A parameter of interest not included in the above cases is the type of longitudinal
joint used in a given bridge. While joint types will certainly influence system behavior,
they are not included in the parametric studies because modeling of their behavior is
difficult and computationally expensive. Thus, the author chose to study the effect of

80

joint type and behavior through a reduced set of selective case studies (see Section 5.4).
The parametric studies will then focus on overall behavior assuming that full moment

continuity has been achieved through the longitudinal joint.

5.3.1 Creation of 3D FE Models

To improve computational efficiency, the models generated in the matrix shown
in Table 11 were created using shell elements. More specifically, the ABAQUS
(Simulia, 2007) element S4R was used. This is defined by ABAQUS as “a 4-node
doubly curved thin or thick shell, [with] reduced integration, hourglass control, [and]
finite membrane strains”. In addition, the deck was considered to be one continuous
slab. This assumption can be considered valid if it can be shown that the longitudinal
joints can be held closed under service loads by a reasonable amount of prestressing.
This check is performed in Section 5.4. A sample bridge model can be seen in Figure

47.

 

Figure 47. Typical Bridge Model Using Shell Elements

81

As seen in Figure 47, the bridge models have end-blocks, and some models (see
Table 11), such as the model in the figure, have diaphragms. The end-blocks were
modeled with shell elements, and were assigned a thickness of 24 inches. The material
used was concrete. The diaphragms were also modeled using shell elements. They were
made of steel, and assigned a thickness of 0.5 inches. Steel was chosen for the
diaphragms to reduce weight. However, concrete diaphragms could also be used in
practice. The end-blocks were then simply supported, creating the boundary conditions
for the bridge. The sizes of the different elements vary. The original element size was 6
inches for deck and girder elements. End-block and diaphragm responses were not
being studied, and consequently they were composed of a coarser 12 inch mesh.
However, after running some analyses it was found that the deck and end-block meshes
needed to be as fine or finer than the girder mesh to prevent the girders from passing
through the deck and end-blocks. Therefore, the mesh size of the deck and end—block

elements was reduced to 4 inches. The final selection of elements is detailed in Table

 

 

 

 

 

 

 

 

 

 

 

 

12.
Table 12. Element Data for Parametric Models with Shell Deck Elements
Shell Thickness Element Hourglass Reduced Element
Part Material (in) Type Control Integration Size (in)
Deck Concrete 9 S4R Active Active 4
Tub Steel 0.375 S4R Active Active 12
iaphragm Steel 0.5 S4R Active Active 4
End Block Concrete 24 S4R Active Active 4

 

82

 

5.3.2 Selection of Model Geometries

In order to obtain realistic and usable geometries for the sample bridges used in
the parametric study, the initial dimensions were selected by making use of the Excel
spreadsheet developed for preliminary system analysis (see Section 3.8). The
combinations of span and spacing defined in Table 11 were entered into the optimization
spreadsheet, and the preliminary dimensions that were obtained have been listed in Table
13. These models were then created and analyzed using ABAQUS. The results of these
analyses were then compared against AASHTO specifications for midspan deflection and

maximum tub stress to check their feasibility. This comparison can be found in Table 14.

Table 13. Original Geometries Used for Models in Parametric Study

SectioanpIivalentTension NunirerSpacing
Girders

 

This space intentionally left blank

83

Table 14. Results of ABAQUS Analysis on Original Geometries

Results Predicted AASHTO Units
Max. Tub Midspan Max. Tub Midspan Max. Thb Midspan
Stress Deflection Stress Deflection Stress Deflection

 

As Table 14 indicates, many of the geometries obtained by using the spreadsheet
optimization were inadequate, despite incorporation of the AASHTO criteria into the
spreadsheet. This could be due to several things, but the most likely cause, as determined
by the author, is an inability of the AASHTO distribution factors to accurately model the
true load distribution. The reason for skepticism toward these distribution factors is their
inherent vagueness — the same equation is used for both shear and bending for interior
and exterior beams. In addition, the only factors considered are number of lanes and
number of beams. These observations seem to indicate that minimal time has been spent
developing distribution factors for the system being studied here, and this is reflected in

their inaccuracies, as observed in this study.

To make the parametric study more practical, the bridges were redesigned so that
they would meet the AASHTO criteria for stress and for deflection. In addition, for the
75-ft span and the 100-ft span models a “standard geometry” was chosen to be used for

several different bridge models. This was done in order to show that a single girder

84

geometry could have the versatility to be used in a variety of situations. The updated
geometries are shown in Table 15, and the corresponding system responses are shown in

Table 16.

Table 15. Modified Geometries to Meet AASHTO Specifications

SectionEqu’valartT-sn

 

Table 16. Results of ABAQUS Analysis on Modified Geometries

Results AASHTO Units
Max. Tub Midspan Max. 'Ilub Midspan
Stress Deflection Stress Deflection

 

85

5.3.3 System Response

Once it had been verified that the models for the study fit within AASHTO
parameters for stress and deflection, the response at the joints was analyzed. Specifically,
the three responses investigated were: transverse moment response along a transverse
path across the bridge, transverse moment response along a theoretical longitudinal joint,
and longitudinal moment response along a theoretical longitudinal joint (see Figure 46).
A graphical representation of these responses for individual bridges, as well as a
depiction of measurement locations, can be found in Appendices II-XIII. The vertical
lines in these plots represent the location of the tires from the design truck(s). The paths
were chosen by selecting a line passing through the areas of the deck with the highest
magnitude of the moment under consideration (located under the design truck tires). For

a visual representation of the system response, see Figure 48 and Figure 49.

 

Figure 48. Typical Deformed Shape and Moment Distribution.
(Contours Represent Longitudinal Moment)

86

 

Figure 49. Typical Deformed Shape and Moment Distribution.
(Contours Represent Transverse Moment)

To display the system responses graphically, a number of plots were generated
which show system response over a specified path. These paths were chosen to show
the most extreme forces that would be experienced by the bridge. The location of the
paths varied slightly from model to model, and thus all paths are shown in the
Appendices. In addition, Figure 50 shows where these paths were typically found.

While the plots of individual bridges have been relegated to the Appendices,
several comparisons between models will be provided here. First the data for the 50’
span bridge models are shown in Figure 51, Figure 52, and Figure 53. The data for the
75’ span bridge models are shown in Figure 54, Figure 55, and Figure 56. Finally, the
data for the 100’ span bridge models are shown in Figure 57, Figure 58, and Figure 59.

A summary of the forces represented in Figure 51-Figure 59 is shown below in

Table 17.

87

 

a) Plan View

 

b) Isometric View

Figure 50. Typical Location of Paths.
(Contours Represent Transverse Moment)

88

 

 

I— 4'SPACING
m L _______ _ 6'SPACING
8’SPACING

  

 

 

 

 

 

 

 

 

 

 

Transverse Moment (k1p-1n /1n )
|
I
* 1 g T
I / 1
I 1

 

 

 

 

 

 

 

 

o 100 200 300 400 500
Transverse Distance (in.)

Figure 51. 50' Span: Transverse Moment v. Transverse Distance Comparison

 

 

__ F 4' SPACING
6 A :- 6' SPACING

1‘; - .__— - —7\ F“: 8' SPACING
\\_ -_ :

 

 

 

Transverse Moment (kip-in./in.)

 

 

o 100 200 300 400 500 600
Longitudinal Distance (in.)

Figure 52. 50' Span: Transverse Moment v. Longitudinal Distance Comparison

89

 

1" 4’SPACING
E 6'SPACING
— 8' SPACING

l

 

 

 

 

 
  

 

 

 

 

 

 

Longitudinal Moment (kip-in./in.)

 

 

 

0 100 200 300 400 500 600
Longitudinal Distance (in.)

Figure 53. 50' Span: Longitudinal Moment v. Longitudinal Distance Comparison

 

 

 

9 m
I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

!— 4’NO DIA
8 2-2-- _. . _'— 6’1—DIA.
-—- 8.1-[NAL
f? 7 , L. -m. *___’—.___ ___.
E
\
5' 6 7 7
I
Q. __ . E
2c: 5. *
E 4«~ __2 —
°’ 1
g ,2- 2-- ___-“ - E-
2
a) 2+ A ~ * A 2 W
9
G) ___ _._fi“_ fi fig _ g a _i
> 1
E
E 0 ”L A A _ _2__._ _ _ __ __ __ ___,__ ____ “AM
P
-1 -_——» .7. AK“- , , .4 — W W L We 2%. __ —
‘2 1 ‘ 1 ___m_ 1 1 ‘ 'gf“ _*
0 100 200 300 400 500

Transverse Distance (in.)

Figure 54. 75' Span: Transverse Moment v. Transverse Distance Comparison

90

 

6 Ffi“ ' 7 ' f

l“ 4' NO DIA.
— 6’1—DlA.
2: 8'1—DIA.

siegmwega—ae #4 «a h» _e —i _e .

 

 

 

 

Transverse Moment (kip-in./in.)

 

 

 

 

0 1 00 200 300 400 500 600 700 800 900

Longitudinal Distance (in.)

Figure 55. 75' Span: Transverse Moment v. Longitudinal Distance Comparison

 

_ "4 4' N0 DIA.

 

 

 

 

 

 

 

 

 

 

. T
A J
14 “‘ W" l“ 6'1—DIA.
: 8’1—DIA.
12 +. —_ _— ”i
E I \ i
\ 10 «L-__. V_.__.V _, _ _____ -
E l
I
9 l
é.aa ++ea~~ e~ * — - — ee 1
E
(D _ xx“
E 6 « a a r” * “ \ }
o ,
E
g 4 - H ~-- — ~ ~ - e
:3 / x l
6: 2 ““/ ‘ ‘ “ ___ __ “ v ‘— ‘“ ___“ —‘
C
O ,
_l
0 I -‘“r— -—— —T— ' — +- — 1*— —* r—'— -‘—" — ’T—_—— — .
o 100 200 300 400 500 600 700 800 900

Longitudinal Distance (in.)

Figure 56. 75' Span: Longitudinal Moment v. Longitudinal Distance Comparison

91

 

 

_L
O

6' NO DIA.
8' NO DIA.
10’ NO DIA.
6' 2 - DIA.
8’ 2 - DIA.
10' 3 - DIA.

  
 
 
 
 
 
 
 
 
 
 
  

 

 

N OJ -b 01 O) V on (O
__; L l l

Transverse Moment (kip-in./in.)

 

o 100 200 300 400 500
Transverse Distance (in.)

Figure 57. 100' Span: Transverse Moment v. Transverse Distance Comparison
With and Without Diaphragms

7 fi fi
6' NO DIA.
8' NO DIA.
10’ NO DIA.
6' 2 - DIA.
8’ 2 — DIA.
10' 3 - DIA.

 

 

 

 

 

 

 

 

 

 

Transverse Moment (kip-inJin.)

O
l

 

 

 

-1

 

0 V ZDO 400 600 800
Longitudinal Distance (in.)

Figure 58. 100' Span: Transverse Moment v. Longitudinal Distance Comparison
With and Without Diaphragms

92

 

 

—" 6' NO DIA.

3 1 5 - -— 8’ NO DIA.
— 10' ND DIA.

. _ _ 6'2-DlA.
"w. __ 8'2—DIA.
103—ma

 
 
  

 

 

 

 

 

 

 

 

 

Longitudinal Moment (kip-in./in.)

 

 

0 200 400 600 800 1000 1200
Longitudinal Distance (in.)

Figure 59. 100' Span: Longitudinal Moment v. Longitudinal Distance Comparison
With and Without Diaphragms

Table 17. Summary of Maximum Forces in Bridge Models

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Max. Tran. Max. Tran. Max. Long.
Bridge Moment Moment at Joint Moment at Joint

N o. (kip—in/in) (kip-in/in) (kip-in/in)

1 7.30 6.46 11.13

2 7.01 4.43 9.42

3 6.98 5.49 10.11

4 8.08 4.44 6.84

5 6.50 3.30 6.37

6 6.81 5.86 14.17

7 8.88 5.16 7.12

8 6.00 2.99 6.02

9 9.21 5.88 7.30

10 5.81 3.15 6.36

11 8.18 5.84 8.15

12 6.52 3.66 8.19
Ag. 7.27 4.72 8.43
Max. 9.21 6.46 14.17

 

 

 

 

 

 

93

5.3.4 Discussion of Results

The results presented in Section 5.3.3 show some interesting trends. A discussion
of these trends and possible explanations will be offered here. First, the transverse
moment response along the transverse paths will be discussed. These graphs show a
trend to spike at positions where design tire loads are applied. The magnitude of the
moment increases slightly on average as the span increases, but the increase is small. As
shown in Table 17, the maximum transverse moment force that was developed in any of

the models was 9.21 kip-infin.

The transverse moment response along a longitudinal path (meant to represent the
location of a joint) provided the most intriguing results. As seen in Figure 52, Figure 55,
and Figure 58, certain models showed a decrease in the magnitude of the transverse
moment at points in line with the wheel loads. This is at odds with conventional logic.
Careful inspection of the schematics showing where the forces were extracted
(Appendix II - Appendix XIII) reveal that in the models showing the decrease in
magnitude, the wheel load falls between two girders. However, when the wheel load
falls in a location above a girder, the predicted increase in transverse moment occurs.
The author believes this phenomenon is caused by the girders absorbing much of the
force due to their increased rigidity in comparison with the deck. The maximum
transverse moment developed was 6.46 kip-in/in. This is lower than the maximum
found along the transverse path, indicating that in these simulations the maximum
transverse moment does not occur at a joint. This supports the theory that the girders

attract load with their large torsional rigidity. However, the maximum transverse

94

moment along the transverse path (9.21 kip-in/in) should be kept in mind for design

purposes, as the wheel loads’ locations will vary during live traffic.

The longitudinal moment along the longitudinal path shows a typical moment
diagram for a distributed load with spiked increases under the wheel loads. The
longitudinal moment does not appear to be affected by the placement of the wheel loads
over the girders. One notable anomaly in the data can be seen in Figure 56. Here the
increase in moment under the wheel load is extremely pronounced. Once again, this can
be explained by looking at the schematic of the bridge in Appendix VII. The figure
clearly shows the longitudinal path crossing very near to the wheel loads. This close
proximity to the wheels creates a more pronounced increase. This fact should again be
carefully considered by a designer. Trucks could certainly drift in their lane, or change
lanes and in doing so drive over a joint. Therefore, the maximum longitudinal moment

developed (14.17 kip-in/in) should be used for design.

Another trend in the data that is decisively shown in Figure 54, F igire 57, Figure
58, and Figure 59 is the effect of diaphragms on design forces. In every case the
moment magnitudes are reduced by the presence of diaphragms. However, the
reductions are most notable when considering transverse moment. Although there are
also decreases in longitudinal moment, they are not as prominent. Correspondingly, if
moment demands are of concern to the designer, the addition of diaphragms may be a

viable way to reduce forces.

95

5.4 Stress Analysis and Characterization of Connection Details

5.4.1 General

The final step in the hierarchical suite of analyses outlined at the beginning of this
chapter was to evaluate the performance of longitudinal joints between the prefabricated
girder/deck units through detailed 3D stress analyses. This step involved the largest and
most complex FE models as it required three-dimensional simulation of the connection
detail and the forces being transferred using computationally expensive solid elements.
This section describes the modeling procedure, validation, and results that are relevant to

this project.

5.4.2 Approach

The author conceptualized different options to realize the longitudinal joints of
the concrete deck flanges. While specific design options were outlined, they fall within
the following categories:

1) Cast-in-place reinforced concrete joints

2) Shear keys (keyed, grouted or reinforced with steel dowels)

3) Post-tensioned shear keys/joints

From the three main joint categories, cast-in-place reinforced concrete joints (type
1) are designed as a full moment connection joint and thus expected to behave
accordingly. Thus, no special analytical evaluation is considered to be required for this
connection type. In addition, system performance with this type of connection detail was
covered through the parametric studies (see Section 5.3).

96

Non-post-tensioned shear keys (type 2) that are not designed to transfer moments
are not permitted according to the AASHTO LRFD specifications. Rather, a minimum
post-tensioning force is specified. Thus, characterization of connection type 3, of the list
above, was considered to be of most relevance to this project. Therefore, the research
effort concentrated on studying the behavior of post-tensioned shear key joints to
evaluate their load transfer efficiency and to determine the transverse post-tensioning
level required for adequate performance. In addition, successfirl modeling of this
connection type can allow for modeling of the shear key connection (type 2) as a special
case where the transverse post-tensioning level is not enough to provide significant

moment transfer across the joint.

Finite element simulation of post-tensioned shear key/joints requires modeling
disconnected girder/deck units that are in contact only at the joints of the concrete deck.
This is achieved in finite elements through contact and interaction modeling. Successful
modeling of interaction problems is difficult. Thus, the next sections present a summary
of the efforts taken to ensure that the contact and interaction modeling options to be used

in the joints were applied properly.

5.4.3 Evaluation of Contact Interaction Modeling
5. 4. 3. 1 Evaluation Rationale

Once 3D FE modeling had been chosen as the method for analyzing the system at
the global level (see Section 5.2.5), the author opted to pursue 3D FE modeling of
longitudinal joints at the local level. The difficulty in this undertaking is accurately

modeling the contact interaction between the surfaces of the joint. To model the contact

97

interaction in ABAQUS, both normal and tangential behavior of the interacting surfaces
must be specified. In the direction normal to the surfaces, the constraint-enforcement
method chosen was the default type, and the pressure-overclosure relationship chosen
was “hard” contact. These selections were made based on recommendations in the
ABAQUS user’s manual (Simulia, 2007). It was specified in the contact property that

separation of nodes was allowed after they had come into contact.

For the tangential behavior of the interacting surfaces, a friction formulation
needs to be chosen. Originally the rough fiiction formulation was used, which does not
allow any slip once surfaces come into contact. However, a warning message generated
by ABAQUS advised that the penalty friction formulation should be used, and thus it
was adopted. Based on some findings from similar modeling efforts, a friction

coefficient of 0.5 was conservatively chosen.

Although the interaction property is well documented in ABAQUS, the author
chose to perform several checks in order to verify that the interaction property used in

the model was functioning as desired. Details of the evaluation measures follow.

5. 4. 3 .2 Qualitative Evaluation

To properly represent the behavior of the joint, the contact property needed two
characteristics. First, when nodes come into contact, the interaction property needs to
prevent them from passing through each other. Second, if the nodes lose the pressure
pressing them together, the model needs to allow them to separate. Verifying that these

two behaviors were occurring was the aim of this first evaluation.

98

The model created to perform this check consisted of two simply supported cubes
with pressure applied inward on the outer face of each block, as shown in Figure 60. The
motivation for choosing this setup was to create a situation where the blocks would
come into contact, and then separate. This first objective was achieved, as shown in
Figure 61. Loading was then applied to the top of the cubes in order to achieve a
separation at the bottom of the interface, as an actual loaded joint would behave. This is

shown in Figure 62. The separation was achieved, as shown in Figure 63.

20”

 

 

 

Contact Plane

Figure 60. Schematic of Cube Contact Model with Pressure Applied Normal to the
Contact Plane

Joint enin
/ OP 8

 

Figure 61. Cube model showing separation of nodes

99

2077

[___—l 2.00ksi
3‘?— l l l l

 

0.05ksi_. ' 20”_ h,
n l

 

 

Contact Plane

Figure 62. Schematic of Cube Contact Model with Pressure Normal to the Contact
Plane and Vertical Pressure

/ Joint Opening

 

Figure 63. Bottom view of top-loaded model showing separation of nodes under load

As Figure 61 and Figure 63 show, these models exhibited major deformations at
the element level in areas of high stress. This effect is partly due to graphical
representation of the small displacements introduced in this model. This problem could
have been remedied by increasing the number of elements or changing to a quadratic
element. However, this evaluation was qualitative; thus it was instead decided to

evaluate a model with a geometry closer to that of a bridge deck. As shown in Figure 64

100

and Figure 65, the model was modified to use flatter parts which more closely

approximate deck slabs.

The objective with this model was to learn more about creating an accurate way
of modeling the connections to be used when analyzing a joint with no moment transfer,
as well as to observe the qualitative behavior of a joint modeled with the contact

interaction. The results of this analysis can be seen in Figure 66.

 

 

 

Contact Plane

Figure 64. Schematic of Updated Model with More Accurate Geometry

This space intentionally lefi blank

101

 

Figure 65. Updated Model with More Accurate Geometry

 

Joint Opening

 

Figure 66. (a) Top view of deformed shape of model in Figure 65 and (b) Bottom
view of model in Figure 65 showing node separation

102

 

5. 4 3. 3 Quantitative Evaluation

Once it was observed that the interaction property was behaving qualitatively
correctly, a series of quantitative evaluations were performed in order to ensure that
these qualitative observations were in fact correct, and not merely a misrepresentation in
the post-processor. The first model used for this check consisted of a simply supported
rectangular beam divided in two sections at mid-span loaded transversely and “held

together” by a longitudinal post-tensioning force (see Figure 67 and Figure 68).

8.68 x lO‘ksi

 

"' 0.0938 ksi

 

l
'10”. . _ ‘ ._ ‘60”

Contact Plane

Figure 67. Schematic of Rectangular Beams Used for Quantitative Evaluation

 

Figure 68. Model of rectangular beams

To calibrate the model, hand calculations were performed to choose the
magnitude of post-tensioning required for zero longitudinal stress at the bottom fiber of
the beam at mid-span. This level of post-tensioning was chosen in order to check that the

interface would remain closed as theoretically predicted. The FE simulation showed that

103

the beam did remain closed under loading as shown in Figure 69. In Figure 69 the stress
is very close to zero at the bottom fiber (1.0037 ksi, compressive). This matches with

theoretical predictions.

A stress profile was then determined from beam theory, and compared with the
results of the ABAQUS model. This comparison is shown in Figure 70. The results
showed close agreement (<5% error) with the theoretical calculations, except at the
extreme fibers, where there was greater error. However, the author believes that the FE
model is actually correct, because beam theory assumes that plane sections remain
plane, which does not hold true for a deep beam such as the one modeled here. This

assumption was investigated further with the next model.

 

Figure 69. Deformed rectangular beam model showing no separation at midspan
(Contours Represent Longitudinal Stresses)

104

 

 

 

 

 

 

 

7" FE Model

l—o— Beam Theory;

 

 

Depth (In)

 

 

 

 

 

 

 

 

 

0 4» ———- ——~———-— 1—— .
0 0.05 0.1
Stress (ksi)

 

Figure 70. Stress profile in rectangular beam model

After verifying the accuracy of a model with a flat butt joint, a more complex
male-to-female joint geometry that more closely resembled joint types 2 or 3 (see
Section 5.4.2) in an actual bridge superstructure was investigated, as shown in Figure 71
and Figure 72. This model was subjected to a post-tensioning force and vertical loading
similar to the rectangular beam with the flat butt joint. However, in this model the post-
tensioning was proportioned so that the entire joint would remain in compression. This
kept the joint closed, as shown in Figure 73. When this model was analyzed, it matched
closely with predicted longitudinal stress values, again with the exception of the extreme
fibers. These results are shown in Figure 74. As previously mentioned, this discrepancy

was believed to be caused by shear deformations due to the relatively thick beams being

105

modeled. To check that the departure from theoretical predictions at the extreme fibers
were being caused by shear deformation and not a numerical problem caused by
modeling the joint, a beam was modeled with the same dimensions as the beam shown
in Figure 67, but without a joint. These results, shown in Figure 75, also showed the
nonlinear stress profile exhibited in Figure 70 and Figure 74. This indicates that this

nonlinearity is due to shear deformation and is not related to a modeling issue.

50” 0.01 ksi

25” 1.05 ksi
i as

Figure 71. Schematic of Male-to-Female Joint Model

 

 

iii

 

 

 

 

 

Figure 72. ABAQUS Model with Male-to-Female Joint

106

 

Depth (in)

Figure 73. FE Model of Male-to-Female Joint
(Contours Represent Longitudinal Stress)

 

 

 

1+ Left - FE
+ Left - Theory

 

 

+ Right - FE
T, Bight :Ihéon

 

Stress (ksi)

Figure 74. Comparison of longitudinal stress in FE model

107

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E‘
z + With Joint :
E + Without Joint ;
a

 

 

 

 

 

 

 

 

0 0.5 1 1.5 2 2.5 3
Stress (ksi)

Figure 75. Comparison of longitudinal stresses in models with and without joint

Afier completing these checks, the author is satisfied that the method for
modeling the interaction property is adequate. The results of these models agree with
predicted results and the physical behavior coincides with what is expected. Therefore, a
similar model can be used to assess the behavior of the longitudinal joints in the
prefabricated composite steel box girder system and determine the level of post-

tensioning required for proper system performance.

108

5.4.4 Model Characterization

Having established the functionality of the contact interaction when modeling
joints, the author began modeling a typical joint geometry that could be used in an actual
bridge. The goal is to show that joints can be kept closed with a reasonable amount of
post-tensioning. This will be done by performing a global analysis with detailed joint
modeling in order to establish the post-tensioning force required to maintain closure of
the joints under AASHTO service loading. If joint closure can be maintained, a fiill

moment connection model can be assumed to carry out parametric studies.

To verify that the deck was acting as a continuous slab, and hence could be
analyzed using a single shell-element deck, two FE models were created with solid-
element decks and shear-key type joints. Model 1 was a 50-ft bridge with double girder
units, each individual girder spaced at 4 fi. Model 2 was a 100-ft bridge with single

girder units and a girder spacing of 8 it.

The joints were modeled to represent a typical shear key joint (type 2 or 3 from
Section 5.4.2). The FE representation of such a joint can be seen in Figure 76.
Although the FE model incorporates one male and one female side of the joint, in
practice both flanges would likely be female, with a grouted key running through the.

void created by the two female flanges.

Globally, the models (particularly the IOO-fi model) were very large and
extremely cumbersome computationally. Therefore, it was advantageous to reduce the
model using symmetry. With a symmetric geometry and an anti-symmetric loading, the
model was cut in half at mid-span, and given a shear-mechanism boundary condition. A

completed model is shown in Figure 77.

109

By checking the system response under different levels of post-tensioning, the
minimum amount of post-tensioning required can be determined. Therefore, multiple
combinations of varying post-tensioning levels and loading conditions were prescribed.
A matrix of these combinations is presented in Table 18. Finally, the element types and

sizes can be found in Table 19.

 

Figure 76. FE Model of Shear Key Joint Opening Under Loading

 

Figure 77. FE Model of Bridge Model 9.
(Contours Represent Longitudinal Stress)

110

Table 18. Case Matrix of Post-Tensioning Levels and Loading Conditions

LoadCase

Pos t-Tensioning

(ksi)

Loafing Contition

(AAS HTO)

 

Table 19. Element Data for Full Models with Solid Deck Elements

 

 

 

 

 

Shell Thickness Element Hourglass Reduced Element
Part Material (in) Type Control Integgtion Size (in)
Deck Concrete n/a C3D8R Active Active 4.5
Tub Steel 0.375 S4R Active Active 6
End Block Concrete 24 S4R Active Active 4

 

 

 

 

 

 

 

 

 

5.4.5 System Response

5. 4. 5. I General

The results of these analyses were favorable for this system. Three areas of
interest were evaluated in order to determine the viability of using shear-key joints in a
prefabricated system such as the one being studied. They were:

I Longitudinal Stress in Steel Tubs

' Deflection Profile

' Joint Opening

These parameters were derived for the two models with joints, and then compared

to a model that was identical in geometry, except the segmental deck had been replaced

111

with a deck slab which was continuous over the width of the bridge. This approach
aimed to show that a prefabricated system could function similarly to a superstructure

with a traditional cast-in-place deck.

5.4.5.2 Interpretation of Results

Figure 78 shows the location of the measurements taken to evaluate the responses
listed in Section 5.4.5.1. The first parameter studied was longitudinal stress in the steel
tubs. The stress in each tub was extracted at mid-span, in the middle of the bottom
(tension) flange. The second parameter studied was the vertical deflection of the bridge
deck. The deflection at each node along the deck surface at mid-span was recorded.
The third parameter studied was the joint opening along the span of the bridge. To
obtain this data, the lateral coordinate of each node along either side of the joint was
extracted, and the difference of the two was taken to be the joint opening. Hence, the
value reported here represents the lateral distance between nodes, not the true distance
between the two. Since there is minimal vertical differential between the nodes, this
difference is negligible. To see the naming convention used to define each individual

joint, see Figure 78.

Also presented in the graphs of joint opening is an “acceptability threshold”
imposed by the author. See Section 3.7 for details on the derivation of the acceptability

threshold.

112

Transverse Deflection Profile

Joint l

 

t

Tub Stress Measurement Locations

1

Figure 78. Parameters Studied in Models with Joints

5.4.5.3 50—ft Bridge Model
The FE model used to analyze the 50-ft bridge is shown in Figure 79. The
dimensions of the girders are those of bridge model 1 of the parametric study. These

dimensions can be found in Table 15. The deformed shape is also presented in Figure

80.

 

Figure 79. FE Model with Solid Deck Elem ents and Joints Representing Model # l

113

 

Figure 80. Deformed Shape of Model in Figure 79.
(Contours Represent Vertical Displacement)

As shown in Figure 81 and Figure 82, the stress in the tubs is largely unaffected
by post-tensioning levels. The variation between the models with prefabricated decks is
very small (less than 1 ksi). However, some of the tubs in the model with a continuous
deck have stresses that differ greatly when compared with the corresponding tubs in the
segmental models. The charts show a much more uniform distribution of stress across
the width of the bridge when there is a continuous deck. However, the critical central
tubs that experience the highest stress do not see a significantly higher stress with the
segmental deck. Therefore, using prefabricated girder units does not diminish

performance when compared with a continuous-slab bridge of the same dimensions.

114

 

 

    

 

 

 

 

 

 

 

 

 

 

 

 

   

_ _ ‘0 0.250
15 l 90 0.225
H 0.200
.1: 14 _— ,- 0.175
<0 ,I 0.150
£5 13 ;- 0.125
m g CONT
3 12 ,
.2
2 11
(U
.E 10
'O
.3 9 7
g l
o a
_l .
7 ..

TUB1 TUBZ TUB3 TUB4 TUBS TUB6 TUB7 TUBB TUBQ TUB 10 TUB11TUB 12

Figure 81. Longitudinal Stress Variation by Girder (50-ft Model, Service Loading)

18 , ~ , ,

17 i.

16 """ "’ ,7 ' ‘ ’ 7 7, " " ’

14 . 7 a 7 , 7 7 7- ,7i,.
13

12 , ~ , ~ -
11 , ~ - , ,.
10

9 iii

8 . 2- n ,J ,__ . , . , _ .

TUB1 TUBZ TUB3 TUB4 TUBS TUBG TUB7 TUBB TUBQ TUB 10 TUB11TUB 12

i I‘IJIgfl ti 0':
o
_l
\l
01

Longitudinal Stress (ksi)
l

    

 

 

 

 

 

 

 

 

 

 

 

 

Figure 82. Longitudinal Stress Variation by Girder (50-ft Model, Strength Loading)

The deflection profile of the bridge deck is plotted in Figure 83 and Figure 84. As
indicated by the graphs, it is again noticeable that the load is better distributed by the
continuous slab deck. However, similarly to the longitudinal stresses, the maximum

115

values of deflection do not differ significantly in the segmental model. The increase in
maximum deflection for the model with 0.250 ksi of post-tensioning under AASHTO
Service II loading is about 0.025 inches over that of the model with a continuous slab.
The increase in deflection of the model with the lowest post-tensioning, 0.125 ksi, is

about 0.050 inches over that of the model with a continuous slab.

Another important trend in this data is the “kinking” of the deck profile at joint
locations in the segmental models. This is most prominent in Figure 84 at 282 inches
and 376 inches (the locations of Joint 3 and Joint 4). This kinking is undesirable, as it
indicates the bridge superstructure is functioning as individual pieces and not one
unified entity. This behavior occurs when the post-tensioning is 0.150 ksi or lower
under service loading, and when the post-tensioning is 0.200 ksi or lower under strength
conditions. Although this kinking may be tolerable under strength loading, it should be
prevented under service conditions.

-0.3 »- ~-

 

 

 

 

 

 

 

 

_o:4 \K ,

 

 

Vertical Disolacement (in.)

 

 

 

 

Distance Along Width (in.)

Figure 83. Transverse Profile of Vertical Displacement at Midspan Under Varying
Post-tensioning Levels (50-ft Model, Service Loading)

116

 

 

 

0.4 T-

 

 

 

 

 

 

Vertical Disolacement (in.)

 

 

 

0 100 200 300 400 500 600
Distance Along Width (in.)

Figure 84. Transverse Profile of Vertical Displacement at Midspan Under Varying
Post-tensioning Levels (50-ft Model, Strength Loading)

For the 50-fi span bridge, only Joint 3 and Joint 4 show significant opening, and
as such only the opening of those joints has been presented. Plots of the joint opening
along the span can be found in Figure 85 - Figure 88. As the plots show, the
“acceptability threshold” developed by the author was only exceeded under strength
loading conditions at Joint 4. In this circumstance, models with a post-tensioning level

of 0.200 ksi or lower do not meet the maximum opening criteria.

117

0.014 .. -mm -- - e - w ~ .. . .- .. a- ,fimh

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

__ i“— 0.250
""""""""""""""""""" ‘7‘“— 0.225
0.012 —* - “~r 4+ 0.200
- l r 0.175
777 7 n- W, h 7 .,, ,___,—-— 0.150
,- 0'01 '—+— 0.125
E‘ .__— '_ THRESH.
- 0.008 - —fi~——~ —— —— ——
o
.E
5 .
o 0.006 —-————-———--~ — — — __¢_-,_-___ — 2
O
E . , _
5 0.004 ~« —
_,
0002 m—_ W‘Mxxx “ __-- _vn
seat-,eezztttftttw:?vi H H
o l . -_--:_'::; vvvvvvvvvv . ..... - — .
0 50 100 150 200 250 300
Distance From Midspan (in.)
Figure 85. Joint 3 Opening Along Span (50-ft Model, Service Loading)
0.014 fir—m‘rrrfi” - —
‘+ 0.250
""""""""""""""""""" — 2+ 0.225
0.012 —,----— — ——~—»———— —~— 0.200
T 2 0.175
_“__A+ 0.150
f? 0.01 l ;_._ 0.125
5 . é— - THRESH.
O) 0.008 new i 5
.E .
c .
a)
o. __ __ *1
O
.‘é
0 LL __ _ LL
5 !
i
0 50 100 150 200 250 300

Distance From Midspan (in.)

Figure 86. Joint 3 Opening Along Span (50-ft Model, Strength Loading)

118

 

 

' 0.250

 

 

 

 

 

 

 

 

 

 

 

 

  
 
 
 
  

 

   

 

 

 

 

 

0.225
0.200
0.175
0.150
A 0.125
.é , THRESH.
C» H.
.E
C
03 A _,,,
Q *9; ‘
O .
.‘é
o ........ a
‘3 1
j _ _- I, iiiiiifithew 3
0 50 100 150 200 250 300
Distance From Midspan (in.)
Figure 87. Joint 4 Opening Along Span (50-ft Model, Service Loading)
0.024 1 , ~ .-~——-— .-._.if-n--__-__,___
1 —°— 0.250
; ,—-— 0.225
0.021 T -—-——~— —*1 + 0.200
0.175
0.018 . i in- ._._ 0.150
2 '. . ;—~— 0.125
5 0.015 ‘ ~ -- —~~ ., — it: THRESH.
U) .
.E ‘ l
0:) 0.012 r!
8
.. 0.009 1
.E
o
F 0.006 ~ ——
0.003 I~--—-— --
0 50 100 150 200 250 300

Distance From Midspan (in.)

Figure 88. Joint 4 Opening Along Span (50—ft Model, Strength Loading)

119

5.4.5.4 100—ft Bridge Model
The FE model used to analyze the lOO-ft bridge is shown in Figure 89. The
dimensions of the girders are those of bridge model 9 of the parametric study, found in

Table 15. The deformed shape is also presented in Figure 90.

The same parameters studied with 50-fi model were again evaluated for the 100-ft
model. The first parameter was longitudinal stress in the steel tubs. As shown in Figure
91 and Figure 92, the stress in the tubs is largely unaffected by post-tensioning levels.
As was the case in the 50-ft bridge, the variation between the models with prefabricated
decks is very small (less than 1 ksi). Consequently, the same conclusions drawn in
Section 5.4.5.3 can be drawn here: the segmental bridge does not distribute load as well,

but the maximum stresses increase only slightly.

 

Figure 89. FE Model with Solid Deck Elements and Joints Representing Model # 9

120

 

 

Figure 90. Deformed Shape of Model in Figure 89.
(Contours Represent Vertical Displacement)

The second parameter studied was vertical deflection of the deck surface, as
shown in Figure 93 and Figure 94. An important trend in this data is the “kinking” of
the deck profile at joint locations in the segmental models. This is most prominent in
Figure 94 at 282 inches and 376 inches (the locations of Joint 3 and Joint 4). This
kinking is undesirable, as it indicates the bridge superstructure is fimctioning as
individual pieces and not one continuous structure. This behavior occurs when the post-
tensioning is 0.175 ksi or lower under service loading, and in all cases under strength
conditions. This kinking is thought to be undesirable under service loading and should

be avoided.

121

 

0.250

U
11:]
C]
'l
I
I
,3.

Longitudinal Stress (ksi)

  

 

 

 

 

 

TUB 1 TUB 2 TUB 3 TUB 4 TUB 5

Figure 91. Longitudinal Stress Variation by Girder (100-ft Model, Service Loading)

Longitudinal Stress (ksi)

 

 

 

 

 

 

 

 

 

 

TUB 1 TUB 2 TUB 3 TUB 4 TUB 5 TUB 6

Figure 92. Longitudinal Stress Variation by Girder (100-ft Model, Strength
Loading)

122

 

 

 

 

 

 

 

 

 

 

 

 

  
 
  

 

 

 

 

5' — —
0:: -13 \
E
8 -1.4
L“
.3 -1.5 _______n 1’5
E _16 0.250
8 ' 0.225
'E' _1_7 in - 0.200
g i 0.175
-13 l — 0.150 g
- 0.125 ‘
_1_9 , . _ , ______,_ ,-____ _n r: THRESH.
0 100 200 300 400 500 600

Distance Along Width (in.)

Figure 93. Transverse Profile of Vertical Displacement at Midspan Under Varying
Post-tensioning Levels (100-ft Model, Service Loading)

 

 

 

 

0.250
0.225
0.200
0.175
0.150
0.125
THRESH.

 

Vertical Disolacement (in.)

 

 

 

 

0 100 200 300 400 500 600
Distance Along Width (in.)

Figure 94. Transverse Profile of Vertical Displacement at Midspan Under Varying
Post-tensioning Levels (100-ft Model, Strength Loading)

123

The third parameter studied was the joint opening along the span of the bridge.
The joint naming scheme is shown in Figure 78. In the lOO-ft model, Joints 2, 3, and 4
showed significant opening. Plots of the joint opening along the span can be found in

Figure 95 - Figure 100.

As the plots show, the threshold is exceeded under service loading conditions at
Joint 3 and Joint 4. However, models with a post-tensioning level ofO. 175 ksi or higher
always meet the maximum opening criteria under service loading. In contrast, strength
loading causes all models to exceed the criteria at Joint 4, and all but the 0.250 ksi post-
tensioning at Joint 3. Again, this criteria applies more directly to service loading than to
strength loading, so this analysis indicates that 0.175 ksi should be sufficient for post-
tensioning a lOO-fi span bridge such as the one modeled here. Joint 2 never opens far
enough to exceed the criteria. Finally, it should be kept in mind that this criteria is

simply a guideline from the author, not an official standard.

 

 

 

 

 

 

 

 

 

 

0.014 1 ~ — _2 _- ~ *5— ~ ~~+~~r—— --——
1 ,—'— 0.250
'— """"""""""""""""""""" + 0.225
0-012 q M __—" "T _ “T" — —" '— —— - — -— -———- -—e— 0.200
' 0.175
+ 0.150
"2‘ 001 h H- Vii—— “___g P“—” l—e— 0125
1C? :' THRESH.
a) 0.008 -~ ___ ___ fi_.._.._- ,_ ---.-L-_ .2. _.
.E :
c .
8.. 0.006 , _ w —__— - - _ __ _ *fi
0
E |
'5 0.004 r _’ — ‘ fl
3 ”A I
0.002 -“- __

 

 

0 100 200 300 400 500 600
Distance From Midspan (in.)

Figure 95. Joint 2 Opening Along Span (100-ft Model, Service Loading)
124

 

 

Joint Opening (in.)

Joint Opening (in.)

 

 

 

 

 

 

 

0250
0225
02m)
0175
0150
0125
THRESH.

 

 

 

 

 

 

Distance From Midspan (in.)

 

 

Figure 96. Joint 2 Opening Along Span (l00-ft Model, Strength Loading)

 

 

 

 

0.016 . — —— — — — ;_
0014 l. — — —— ——— —~———__,_
1 """""""""""""""""" "'l T
0012-,» — +~-~ ~— —~ ~ 1+
1 l_._
001 +—-4 —— ————- ~— — w —~ ~ J1:
in
i
0.000:— ———— ~—#~ ——« — ~ — ~——~ ——— —
0.006: m ~ ~ - a
0.004i — — —~—— — — m
0.002 ~ «m +—« a —~— ‘ — — m-
0 . , r .
0 100 200 300 400 500

Distance From Midspan (in.)

0250
0225
0200

’ 0175

0150
0125
THRESH.

 

600

Figure 97. Joint 3 Opening Along Span (100-ft Model, Service Loading)

125

 

Joint Opening (in.)

Joint Opening (in.)

 

 

 

0.025 ‘ ._ 7 ~ *7—

 

 

 

 

 

025)
0225
0200
0175
0150
0125

THRESH.

 

 

 

 

0 100 200 300
Distance From Midspan (in.)

 

i
600

Figure 98. Joint 3 Opening Along Span (100-ft Model, Strength Loading)

 

 

 

0250
0225
0200

‘ 0175

0150
0125

THRESH.

 

 

 

 

OIH8-———————~77—7 77777777..nn__
0016~< ~—~—— 477— 7777 77777777 _ _.___5 Ln w_.
00141—~#—- ~ ~ 47 7 7 77 7 n
0.012~‘- 777— 777777 777— ___,_
[—
..xfl. .
0.01 1,5 » ————— —7 7 77 77 7 7 77 - _ _ .‘
0m- 77 . 7-77-_.L--_2__1
* _. "'.:~— _—-— ___”; Lg H kfi¥ fi—#* Mfigik—h H '
1‘. ‘ .,____ . _ _ n v ,
0004 l A
0.002 JL-—--- - «an...I «.— - _
l 'r.~ ...............
0 l— T 1 j T
0 100 200 300 400 500

Distance From Midspan (in.)

600

Figure 99. Joint 4 Opening Along Span (100-ft Model, Service Loading)

126

 

 

 

0.03 -- -~
0.250

 

 

 

 

 

 

 

 

 

 

““ 0.225
0025 1- ——— —-z—7——7 777—7 ..7..77 0.200
7 1 ”r 0.175
' " -*- 0.150
5 0.2.7:... 7— 7 777 7 777 _- 0.125
2’ J 991% - - THRESH.
-- s
C
0.015— - .--7_..._-___
8. 4 “‘5...
o , ' —\:‘:\ - ' - """""""""""""""
,E 0.01 ‘
o .
5 1 m
0.005 '
0 .' 7 . , . .
0 100 200 300 400 500 600

Distance From Midspan (in.)

Figure 100. Joint 4 Opening Along Span (100—ft Model, Strength Loading)

5.5 Vibration Characteristics

The last task performed using the two FE models with solid deck elements was to
determine the fundamental frequencies and mode shapes of these bridge systems. This
was performed in ABAQUS using a linear perturbation step that was capable of running
an eigenvalue analysis on the system mass matrix. Since Section 5.4.5 showed that
continuity could be established with adequate post-tensioning, the dynamic analyses
were performed on the models with continuous slabs. This avoided computational

difficulties that arise out of modeling the base state of a segmental model.

The first three bending mode shapes were extracted, eliminating other mode
shapes that were not of concern (i.e., transverse/longitudinal stretching). The first three
fundamental frequencies for the 50-fl bridge model and the corresponding mode shapes

are presented in Table 20 and Figure 101—Figure 103, respectively.

127

 

 

Table 20. Fundamental Frequencies of the First Three Bending Mode Shapes, 50’
Bridge Model

 

Figure 101. Bending Mode Shape 1, 50’ Bridge Model

 

Figure 102. Bending Mode Shape 2, 50’ Bridge Model

128

 

Figure 103. Bending Mode Shape 3, 50’ Bridge Model

As the above figures show, the three bending mode shapes correspond to the first
longitudinal bending mode, followed by the first two transverse bending modes. This is
the qualitative expected result. To better visualize the bending behavior in Mode 2 and

Mode 3, bridge cross-sections are provided in Figure 104 and Figure 105.

 

Figure 104. Bending Mode 2 Cross-Section

129

 

 

Figure 105. Bending Mode 3 Cross-Section

Qualitatively, the results of the dynamic analysis on the lOO—ft model yielded the
similar results. However, the value of the frequencies decreased significantly. The first
three mode shapes, and the corresponding fundamental frequencies for the lOO-fi bridge

model are presented in Figure 106-Figure 108 and Table 21, respectively.

Table 21. Fundamental Frequencies of the First Three Bending Mode Shapes, 100’
Bridge Model

 

130

 

Figure 106. Bending Mode Shape l, 100’ Model

 

Figure 107. Bending Mode Shape 2, 100’ Model

131

 

 

Figure 108. Bending Mode Shape 3, 100’ Model

132

6. CONCLUSIONS AND RECOMMENDATIONS

6.1 Observations

The simplified analysis method presented in the AASHTO LRFD Design
Specifications (AASHTO, 1998) were found to be generally applicable for analyzing the
prefabricated composite steel box girder bridges studied in this work. However, this
method seems. to be lacking when it comes to distribution factors. Due to their
geometry, box girders distribute load differently that traditional steel I-shape girders, or
bulb-shape girders that are often used in highway bridges. Hence, their distribution
factors require additional research. However, it appears that minimal research has gone
into the development of distribution for these bridges, as evidenced by the single
“blanket” equation to describe the distribution of both moment and shear demands to
interior and exterior girders alike. Therefore, it is recommended that a refined analysis
is always performed to accompany an AASHTO analysis of a composite box girder

bridge system.

The grillage method is a well-established simplified method for analyzing bridge
structures. By idealizing a structure into a set of beam elements, the number of degrees
of freedom in a system can be greatly reduced. This subsequently reduces the number of
equations that need to be solved in order to complete a system analysis, which in turn
reduces computation time. However, with the increase in computing technology,
running more refined three-dimensional finite element analyses with continuum-type
elements no longer significantly increases computation time. In addition, when

compared with grillage models, an experienced user can create complex continuum-type

133

 

finite element models with relative ease. Therefore, it is recommended that when
performing analytical evaluations similar to the type performed in this project, the finite

element method should be used in lieu of the grillage method.

6.2 Recommendations for Design

The results of the parametric analysis in Section 5.3 indicate that at the global
level, the composite steel box girder system can easily be designed in a way that will
allow it to perform within the AASHTO specifications for stress and deflection. As seen
in the figures and tables of Section 5.3.3, adequate designs have been developed for a
range of spans and girder spacings. In addition, several of the span/spacing
combinations have been satisfied using the same girder, indicating that a single girder
could be versatile enough to be manufactured in bulk and used in a variety of situations.
The frequency analyses that were performed (see Section 5.5) also returned acceptable
results. Therefore, the design should be controlled by ensuring satisfactory behavior of

the joints.

In Section 5.4, the joint behavior was investigated. First, the prefabricated
segmental bridges were compared with another bridge model which was identical, with
the exception that the segmental deck was replaced with a continuous slab. This was
done to study the continuity that could be achieved with a transversely post-tensioned
longitudinal joint as the connection element between the prefabricated girder/deck units.
The AASHTO LRFD Bridge Design Specifications require these type of joints to be
provided with a minimum of 0.250 ksi pressure of transverse post-tensioning (after all

losses). As seen in Section 5.4, the prefabricated bridges were able to achieve continuity

134

 

 

close to that of the continuous slab bridge with post-tensioning stress values lower than
the AASHTO specified level. Stress and deflection profiles remained largely unchanged
between the segmental models and the continuous models. However, when the level of
post-tensioning drops too low (below 0.150 ksi in the SO-ft model, below 0.175 ksi in
the lOO-ft model) a kinking behavior occurs at the joints, which is undesirable. Hence, a

post-tensioning level which is equal to or greater than these values should be specified.

As described in Section 5.4.4.2, a benchmark limit to judge the adequacy of the
joint closure was proposed by the author, based on the AASHTO LRFD Bridge Design
Specifications for crack opening in a reinforced concrete structures. It was
recommended that this limit should not be exceeded under service conditions at the
longitudinal deck joints connecting the prefabricated girder/deck bride units. Using this
guideline, the transverse post-tensioning level should not fall below 0.175 ksi for the

100-ft model. All post-tensioning levels studied passed this criterion for the 50-ft bridge.

Summarizing the analysis results, the SO-ft bridge is controlled by kinking
behavior at the joints. This occurs at a post-tensioning level of 0.150 ksi, which is then
considered the minimum design value for this span length. The 100-ft bridge model is
controlled by both kinking behavior and joint opening. These both become
unacceptable at post-tensioning levels of 0.175 ksi. This level should be the minimum
design value for these bridges of this length. These results are logical in that the
transverse post-tensioning stress level required to maintain an emulative reinforced

concrete joint increases with span length.

In summary, this study has confirmed that prefabricated steel/concrete composite

girder/deck units connected together with transversely post-tensioned longitudinal deck

135

 

joints are a safe and viable option for rapid bridge construction. The parametric studies
indicated that adequate performance can be obtained for short spans ranging fi'om 50 to
100 feet. Transverse diaphragms can improve load distribution and thus lower the
moment demands on individual girder/deck units. However, cost-benefit assessment of
the added time and fabrication costs related to the addition of the diaphragms compared
to the improved efficiency gained must be evaluated. The vibration characteristics of the
system indicated that the fiindamental frequencies fall within acceptable limits. For the
short spans over which the prefabricated steel/concrete composite sections are
considered, transverse post-tensioning levels required by the AASHTO code, as well as
levels significantly lower than the required minimum, will provide firll emulative
behavior of the joint. While the results from this investigation indicate that lower post-
tensioning stress levels may be adequate, it should be mentioned that the current study
has not considered concrete volume effects on the post-tensioning force and its influence
on joint behavior. These considerations should be done before a reduced post-

tensioning level from that recommended by AASHTO can be firlly justified.

6.3 Recommendations for Future Work

To further the state-of—the-art in this field, several items for future work are
possible. The work in this project has allowed evaluation of the prefabricated bridge
concept only through numerical simulations, yet there are many aspects of the modeling
and theory behind the simulation that need to be verified. The analytical models used to
assess the global behavior of the bridge system should be trusted to a high degree of
accuracy. However, the detailed 3D stress models used to evaluate joint behavior

should be confirmed experimentally. Although great effort was taken to validate the
136

 

 

contact interaction used in the finite element models of the joints, experimental testing

could reveal issues that the numerical studies have missed. Thus, experimental

verification of the system and connection behavior that parallel the analytical evaluation

conducted in this study is recommended.

It is proposed that any experiment used to verify the work done in this project be

designed to address and confirm the following findings from the project:

1)

2)

3)

Component Stiffness: The numerical models should closely match with
experimental results. However, longitudinal shear slip, nonlinear
deformations, and other factors could affect the system response.

 

Joint Behavior: The analytical models in the project showed that adequate
joint closure could be achieved with the levels of post-tensioning that were
specified. The actual joint openings should be checked experimentally.
Further, the performance of these types of joints under fatigue loading and
volume concrete changes should be experimentally assessed.

Sgtem Response: The analytical models indicated that a kinking occurs at
low post-tensioning levels. The actual limits of post-tensioning required
for adequate behavior should be verified. Thus, system-level experiments
that permit evaluation of joint behavior under realistic loading simulation
and load distribution effects on multiple girders need to be performed.

137

 

 

APPENDICES

Appendix I. Comparison of Analysis Tools
‘ 1
14000 CorrparisonofSAPawdAB/KllS/Mflysesfiqta'e) 1

l l—o—Ust-SAP
:4—01'c-SAP
l Tiers-SAP
’—-‘;‘.—DSt-AB(2
'+CInc-ABQ
+Tra'B-ABQ

 

 

 

 

  
   
  
 

 

120.00 ~w~7~ 77 if- ~

“11(1) ~

 

 

 

 

 

 

 

 

 

 

 

 

 

CarpaisondSAPmdABKlBkrdysasQfl)

l-o—Dist-SAP I
m r- __.., _ _Wnfi— __ _ ____ _____..__. ___...___5+USl-Am
Com-SAP

30- 77 7 7- 7 7- ~—-- i-zz—Com-ABQ

'+Tras-SAP
70155' “ - r "r i r '" ** "L—o—Trans-ABQ

 

 

 

 

 

 

 

 

 

 

138

 

 

Appendix II. Bridge Case 1: FE Models Responses

Transverse Moment (kip-inJin.)

-1

-27

 

 

50’ Span, 4’ Girder Spacing: Transverse Moment v. Transverse Distance

 

 

 

 

 

 

 

 

Transverse Distance (in.)

139

 

Transverse Moment (kip-in./in.)

Longitudinal Moment (kip-in./in.)

11

-1:

50’ Span, 4’ Girder Spacing: Transverse Moment v. Longitudinal Distance

 

 

 

 

 

 

 

 

300

 

400

 

 

 

 

Longitudinal Distance (in.)

50’ Span, 4’ Girder Spacing: Longitudinal Moment v. Longitudinal Distance

 

 

 

 

 

 

Longitudinal Distance (in.)

140

 

Appendix III. Bridge Case 2: FE Models Responses

1

. I

IIIIIIIIIIIIIIIIIIIIIIIIIIIII ..IIIIIIIIIIICII-ICI.IIIUIII-IIIIIIIII
I

 

50’ Span, 6' Girder Spacing: Transverse Moment v. Transverse Distance

 

 

Transverse Moment (kip-in./in.)

 

 

 

-1.

 

 

 

 

 

 

-2 M W *. _ * H, _..A _m- _ *_._ n._. W ._

Transverse Distance (in.)

 

141

 

50’ Span, 6’ Girder Spacing: Transverse Moment v. Longitudinal Distance

 

 

 

 

 

\

 

 

 

 

 

 

 

 

 

 

 

 

Transverse Moment (kip-inJin.)
N

\

 

 

 

l
l
l
J
.
l
1
l
A

 

 

 

 

100 200

300 400 500 600

Longitudinal Distance (in.)

50’ Span, 6’ Girder Spacing: Longitudinal Moment v. Longitudinal Distance

 

 

 

Longitudinal Moment (kip-in./in.)

 

 

 

 

 

 

 

 

 

 

300

 

 

 

Longitudinal Distance (in.)

’1

142

 

Appendix IV. Bridge Case 3: FE Models Responses

 

50’ Span, 8' Girder Spacing: Transverse Moment v. Transverse Distance

Transverse Moment (kip-inJin.)
0)

400 500

   

    

Transverse Distance (in.)

143

 

Transverse Moment (kip-in./in.)

Longitudinal Moment (kip-in./in.)

101

50’ Span, 8’ Girder Spacing: Transverse Moment v. Longitudinal Distance

 

 

,__-_..H.____

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_— f —Tl

100 200 300 400 500 600
Longitudinal Distance (in.)

50’ Span, 8’ Girder Spacing: Longitudinal Moment v. Longitudinal Distance

 

 

 

 

 

 

 

 

 

 

 

 

Longitudinal Distance (in.)

144

 

Appendix V. Bridge Case 4: FE Models Responses

 

75' Span, 6’ Girder Spacing: Transverse Moment v. Transverse Distance

#MQNG‘D

Transverse Moment (kip-inJin.)
(a)

 

Transverse Distance (in.)

145

Transverse Moment (kip-in./in.)

Longitudinal Moment (kip-in./in.)

75’ Span, 6’ Girder Spacing: Transverse Moment v. Longitudinal Distance

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

"—__T t 'T Y T ‘——_‘1

1 00 200 300 400 500 600 700 800 900

Longitudinal Distance (in.)

75’ Span, 6’ Girder Spacing: Longitudinal Moment v. Longitudinal Distance

 

 

 

 

 

 

 

   

 

__ '—T _ __

300

    

Longitudinal Distance (in.)

146

 

Appendix VI. Bridge Case 5: FE Models Responses

 

75’ Span, 6’ Girder Spacing, One Diaphragm: Transverse Moment v. Transverse Distance

7
6

5

Transverse Moment (kip-in./in.)
(a)

 

 

Transverse Distance (in.)

147

75’ Span, 6’ Girder Spacing, One Diaphragm: Transverse Moment v. Longitudinal Distance

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4 f
.E' 3 -
E 'l
.911 1 - _____ _/\
5 1
2 _ _
<25 /
a f
'6
53 /
1 ___
I—

_Y_ T

 

100 200 300 400 500 600 700 800 900
Longitudinal Distance (in.)

75’ Span, 6’ Girder Spacing, One Diaphragm: Longitudinal Moment v. Longitudinal Distance

7 f;__' '

Longitudinal Moment (kip-in./in.)
(O

 

 

 

 

-‘_7“__ _7 7%“ ___

1 00 200 300 400

 

 

Longitudinal Distance (in.)

148

Appendix VII. Bridge Case 6: FE Models Responses

 

75' Span, 8' Girder Spacing, One Diaphragm: Transverse Moment v. Transverse Distance

Transverse Moment (kip-infln.)

 

Transverse Distance (in.)

149

75’ Span, 8’ Girder Spacing, One Diaphragm: Transverse Moment v. Longitudinal Distance

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6 __7-
55.——
.é
.é
a4 —* ”T—
g
"c‘
CD
83—
O
2
3
52——
>
(D
C
(O
p: .
1/ -
.1 _ 7 _- 7

 

 

100 200 300 400 500 600 700 800 900
Longitudinal Distance (in.)

75’ Span, 8’ Girder Spacing, One Diaphragm: Longitudinal Moment v. Longitudinal Distance

 

 

 

 

 

 

 

 

 

 

 

 

14
7 12
.E'
E 10
.E} !
{I l
g 8
E
O
5 6
a
.9.
‘O
2 4
'6)
C
O
‘J 2
0 . _______n_.2__nzaq 777—77

 

 

 

  

100 200 300 400 500 600

Longitudinal Distance (in.)

150

Appendix VIII. Bridge Case 7: FE Models Responses

V ~. :

 

100’ Span, 6’ Girder Spacing: Transverse Moment v. Transverse Distance

 

 

 

 

 

Transverse Moment (kip-in./in.)

 

 

 

 

 

 

Transverse Distance (in.)

151

Transverse Moment (kio-inJin.)

Longitudinal Moment (kip-in./in.)

100’ Span, 6’ Girder Spacing: Transverse Moment v. Longitudinal Distance

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

200 400 600 800
Longitudinal Distance (in.)

 

 

100’ Span, 6’ Girder Spacing: Longitudinal Moment v. Longitudinal Distance

 

 

 

 

 

 

 

 

 

 

 

 

 

200 400 600 800 1000 1200
Longitudinal Distance (in.)

152

Appendix IX. Bridge Case 8: FE Models Responses

 

100’ Span, 6’ Glrder Spacing, Two Diaphragms: Transverse Moment v. Transverse Distance

Transverse Moment (kip-infin.)

6

 

 

 

 

 

 

 

 

 

 

 

 

 

 

200 300 400 500
Transverse Distance (in.)

153

100’ Span, 6’ Girder Spacing, Two Diaphragms: Transverse Moment v. Longitudinal Distance

 

 

 

 

 

 

Transverse Moment (kio-in./in.i

 

 

 

 

 

 

 

 

 

 

 

 

 

 

200 400 600 800 1000 1200
Longitudinal Distance (in.)

100’ Span, 6’ Girder Spacing, Two Diaphragms: Longtiudinal Moment v. Longitudinal Distance

 

 

7 * —“ ‘ l

 

 

 

 

 

 

Longitudinal Moment (kip-in./in.)
O)

 

 

 

 

 

200 400 600 800 1000 1200
Longitudinal Distance (in.)

154

Appendix X. Bridge Case 9: FE Models Responses

 

100’ Span, 8’ Girder Spacing: Transverse Moment v. Transverse Distance

Transverse Moment (kip-in.fin.)

 

Transverse Distance (in.)

155

Transverse Moment (kip-in./in.)

Longitudinal Moment (kip-in./in.)

100’ Span, 8’ Girder Spacing: Transverse Moment v. Longitudinal Distance

 

MW/

/ L1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

__ fi,

400 600 800 1000 1200
Longitudinal Distance (in.)

100’ Span, 8’ Girder Spacing: Longitudinal Moment v. Longitudinal Distance

 

 

 

7A9 ’ fl __ —_ 7f

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Longitudinal Distance (in.)

156

Appendix XI. Bridge Case 10: FE Models Responses

 

100' Span, 8’ Girder Spacing, Two Dlaphragms: Transverse Moment v. Transverse Distance

 

6

 

 

 

 

 

1 E/fib —Tl _
o A. m V , L , AV
’ M00 '200 300 400 W

Transverse Distance (in.)

 

Transverse Moment (kip-inJln.)
w
l
l
l
l
l
l

 

 

 

 

 

 

 

157

100’ Span, 8’ Girder Spacing, Two Diaphragms: Transverse Moment v. Longitudinal Distance

Transverse Moment (kip-in./in.)

 

 

 

 

 

 

 

3: /\ / “
/ Sn -

 

 

 

 

 

 

 

400 600 800
Longitudinal Distance (in.)

100’ Span, 8’ Girder Spacing, Two Diaphragms: Longitudinal Moment v. Longitudinal Distance

Longitudinal Moment (kip-in./in.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Longitudinal Distance (in.)

158

Appendix XII. Bridge Case 11: FE Models Responses

 

Transverse Moment (kip-in./in.)

100’ Span, 10’ Girder Spacing: Transverse Moment v. Transverse Distance

9 1“” ———

7 1

 

 

,—/’\

 

 

 

 

 

 

 

 

Transverse Distance (in.)

159

 

Transverse Moment (kip-in./in.)

Longitudinal Moment (kip-in./in.)

100’ Span, 10’ Girder Spacing: Transverse Moment v. Longitudinal Distance

 

 

 

 

 

 

 

 

»~_____7_.. .

 

 

 

 

 

 

 

 

200

T

400

600

800 1000 1200

Longitudinal Distance (in.)

100’ Span, 10’ Girder Spacing: Longitudinal Moment v. Longitudinal Distance

 

 

 

 

 

 

 

 

 

 

 

 

 

200

.7.— —T' 7‘7

400

 

 

 

f

600

 

 

 

Longitudinal Distance (in.)

160

Appendix XIII. Bridge Case 12: FE Models Responses

 

100' Span, 10' Girder Spacing, Three Diaphragms:
Transverse Moment v. Transverse Distance

Transverse Moment (kio—infin.)

200 300

 

Transverse Distance (in.)

161

Transverse Moment (kip-in./in.)

Longitudinal Moment (kip-in./in.)

100’ Span, 10’ Girder Spacing, Three Diaphragms:
Transverse Moment v. Longitudinal Distance
4 _- _ -. .-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l
0 ’—'- .‘

200 400 600 800 1000 1200
Longitudinal Distance (in.)

100’ Span, 10’ Girder Spacing, Three Diaphragms:
Longitudinal Moment v. Longitudinal Distance

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 7. — 7777

200 400 600
Longitudinal Distance (in.)

162

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